Compressor handbook - [PDF Document] (2024)

COMPRESSORHANDBOOK

Paul C. Hanlon Editor

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Library of Congress Cataloging-in-Publication Data

Compressor handbook / Paul C. Hanlon, editor.p. cm.

Includes index.ISBN 0-07-026005-21. Compressors—Handbooks, manuals, etc. I. Hanlon, Paul C.

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vii

CONTRIBUTORS

Bark, Karl-Heinz MaxPro Technologies (CHAPTER 11 GAS BOOSTERS)

Bendinelli, Paolo Turbocompressors Chief Engineer, Nuovo Pignone (CHAPTER 3 COMPRES-SOR PERFORMANCE—DYNAMIC)

Blodgett, Larry E. Southwest Research Institute (CHAPTER 6 COMPRESSOR AND PIPING SYS-TEM SIMULATION)

Camatti, Massimo Turbocompressors Design Manager, Nuovo Pignone (CHAPTER 3 COM-PRESSOR PERFORMANCE—DYNAMIC)

Chen, H. Ming, Ph.D., P.E. Mohawk Innovative Technology, Inc. (CHAPTER 19 PRINCIPLES

OF BEARING DESIGN)

Epp, Mark Jenmar Concepts (CHAPTER 8 CNG COMPRESSORS)

Gajjar, Hasu Weatherford Compression (CHAPTER 14 THE OIL-FLOODED ROTARY SCREW COM-PRESSOR)

Giachi, Marco Turbocompressors R&D Manager, Nuovo Pignone (CHAPTER 3 COMPRESSOR

PERFORMANCE—DYNAMIC)

Giacomelli, Enzo General Manager Reciprocating Compressors, Nuovo Pignone (CHAPTER

7 VERY HIGH PRESSURE COMPRESSORS)

Gresh, Ted Elliott Company (CHAPTER 4 CENTRIFUGAL COMPRESSORS—CONSTRUCTION AND

TESTING)

Hanlon, Paul C. Lee Cook, A Dover Resources Company (CHAPTER 17 RECIPROCATING COM-PRESSOR SEALING)

Heidrich, Fred Dresser-Rand Company (CHAPTER 2 COMPRESSOR PERFORMANCE—POSITIVE

DISPLACEMENT)

Heshmat, Hooshang, Ph.D. Mohawk Innovative Technology, Inc. (CHAPTER 19 PRINCIPLES

OF BEARING DESIGN)

Kennedy, William A., Jr. Blackmer/A Dover Resource Company (CHAPTER 9 LIQUID TRANS-FER/VAPOR RECOVERY)

Lowe, Robert J. T. F. Hudgins, Inc. (CHAPTER 21 COMPRESSOR CONTROL SYSTEMS)

Machu, Erich H. Consulting Mechanical Engineer, ho*rbiger Corporation of America, Inc.(CHAPTER 20 COMPRESSOR VALVES)

Majors, Glen, P.E. C.E.S. Associates, Inc. (CHAPTER 18 COMPRESSOR LUBRICATION)

Netzel, James Chief Engineer, John Crane Inc. (CHAPTER 16 ROTARY COMPRESSOR SEALS)

Nix, Harvey Training-n-Technologies (CHAPTER 5 COMPRESSOR ANALYSIS)

viii CONTRIBUTORS

Patel, A.G., PE Roots Division, Division of Dresser Industries Inc. (CHAPTER 13 STRAIGHT

LOBE COMPRESSORS)

Reighard, G. Howden Process Compressors, Inc. (CHAPTER 15 DIAPHRAGM COMPRESSORS)

Rossi, Eugenio Turbocompressors Researcher, Nuovo Pignone (CHAPTER 3 COMPRESSOR

PERFORMANCE—DYNAMIC)

Rowan, Robert L., Jr. Robert L. Rowan & Associates, Inc. (CHAPTER 22 COMPRESSOR FOUN-DATIONS)

Shaffer, Robert W. President, Air Squared, Inc. (CHAPTER 12 SCROLL COMPRESSORS)

Tuymer, Walter J. ho*rbiger Corporation of America, Inc. (CHAPTER 20 COMPRESSOR

VALVES)

Traversari, Alessandro General Manager Rotating Machinery, Nuovo Pignone (CHAPTER

7 VERY HIGH PRESSURE COMPRESSORS)

Vera, Judith E. Project Engineer, Energy Industries, Inc. (CHAPTER 23 PACKAGING COM-PRESSORS)

Weisz-Margulescu, Adam, P. Eng. FuelMaker Corporation (CHAPTER 10 COMPRESSED NAT-URAL GAS FOR VEHICLE FUELING)

Woollatt, Derek Manager, Valve and Regulator Engineering, Dresser-Rand Company &(Screw Compressor Section) (CHAPTER 1 COMPRESSOR THEORY; CHAPTER 2 COMPRESSOR PER-FORMANCE—POSITIVE DISPLACEMENT)

PREFACE

Compressors fall into that category of machinery that is ‘‘all around us’’ but ofwhich we are little aware. We find them in our homes and workplaces, and inalmost any form of transportation we might use. Compressors serve in refrigeration,engines, chemical processes, gas transmission, manufacturing, and in just aboutevery place where there is a need to move or compress gas.

The many engineering disciplines (e.g. fluid dynamics, thermodynamics, tribol-ogy, and stress analysis) involved in designing and manufacturing compressorsmake it impossible to do much more than just ‘‘hit the high spots,’’ at least in thisfirst edition.

This is such a truly broad field, encompassing so many types and sizes of units,that it is difficult to cover it all in one small volume, representing the work ofrelatively few authors. Possibly, more than anything else, it will open the door towhat must follow—a larger second edition.

In compressors, the areas of greatest concern are those parts with a finite life,such as bearings, seals and valves, or parts that are highly stressed. Treatment ofthese components takes up a large portion of the handbook, but at the same timespace has been given to theory, applications and to some of the different types ofcompressors.

Much in this handbook is based on empirical principals, so this should serve asa practical guide for designers and manufacturers. There are also test and analysisprocedures that all readers will find helpful. There should be something here foranyone who has an interest in compressors.

Paul C. Hanlon

ABOUT THE EDITOR

Paul C. Hanlon is manager of product design with C. Lee Cook in Louisville,Kentucky. A mechanical engineering graduate of the University of Cincinnati, hehas worked for over 40 years in the design, application, and troubleshooting of sealsfor engines, compressors, and other major equipment used throughout the chemical,oil, and gas-processing industries. Mr. Hanlon is also the author of numerous articlesfor leading technical journals.

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Contents

Contributors ...................................................................................................... vii

Preface ............................................................................................................. ix

About the Editor ................................................................................................ x

1. Compressor Theory ................................................................................. 1.1 1.1 Nomenclature .................................................................................................. 1.1 1.2 Theory .............................................................................................................. 1.2 1.3 References ...................................................................................................... 1.15

2. Compressor Performance – Positive Displacement ............................. 2.1 2.1 Compressor Performance ............................................................................... 2.1 2.2 Reciprocating Compressors ............................................................................ 2.12 2.3 Screw Compressors ........................................................................................ 2.23 2.4 All Compressors .............................................................................................. 2.25

3. Compressor Performance – Dynamic .................................................... 3.1 3.1 General Description of a Centrifugal Compressor .......................................... 3.2 3.2 Centrifugal Compressors Types ...................................................................... 3.7 3.3 Basic Theoretical Aspects ............................................................................... 3.12 3.4 Performance of Compressor Stages ............................................................... 3.20 3.5 Multistage Compressors .................................................................................. 3.29 3.6 Thermodynamic and Fluid-dynamic Analysis of Stages ................................. 3.36 3.7 Thermodynamic Performances Test of Centrifugal Compressors

Stages .............................................................................................................. 3.45 3.8 Mechanical Tests ............................................................................................. 3.47 3.9 Rotor Dynamics and Design Criteria ............................................................... 3.50

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3.10 Structural and Manufacturing Characteristics of Centrifugal Compressors ................................................................................................... 3.58

3.11 Industrial Application of Centrifugal Compressors .......................................... 3.71 3.12 Antisurge Protection System ........................................................................... 3.82 3.13 Adaptation of the Antisurge Law to Multistage Compressors ......................... 3.87 3.14 Antisurge Laws for Special Applications ......................................................... 3.92

4. Centrifugal Compressors – Construction and Testing ........................ 4.1 4.1 Casing Configuration ....................................................................................... 4.1 4.2 Construction Features ..................................................................................... 4.1 4.3 Performance Characteristics ........................................................................... 4.16 4.4 Off-design Operation ....................................................................................... 4.25 4.5 Rotor Dynamics ............................................................................................... 4.27 4.6 Rotor Balancing ............................................................................................... 4.28 4.7 High Speed Balance ........................................................................................ 4.29 4.8 Rotor Stability .................................................................................................. 4.31 4.9 Avoiding Surge ................................................................................................ 4.43 4.10 Surge Identification .......................................................................................... 4.46 4.11 Liquids .............................................................................................................. 4.48 4.12 Field Analysis of Compressor Performance ................................................... 4.49 4.13 Gas Sampling .................................................................................................. 4.49 4.14 Instrumentation ................................................................................................ 4.50 4.15 Instrument Calibration ..................................................................................... 4.52 4.16 Iso-cooled Compressors ................................................................................. 4.54 4.17 Compressors with Economizer Nozzles ......................................................... 4.55 4.18 Estimating Internal Temperatures ................................................................... 4.57 4.19 Field Data Analysis .......................................................................................... 4.62 4.20 Trouble Shooting Compressor Performance .................................................. 4.63 4.21 Reference ........................................................................................................ 4.74

5. Compressor Analysis .............................................................................. 5.1 5.1 Compressor Valve Failures and Leaking Valves ............................................ 5.1 5.2 Compressor Piston Ring Failures ................................................................... 5.2 5.3 Restriction Losses ........................................................................................... 5.2

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5.4 Improper Cylinder Loading .............................................................................. 5.2 5.5 Required Information ....................................................................................... 5.2 5.6 Analysis of the Compressor Using a Pressure-volume (PV) Diagram ........... 5.3 5.7 Compressor Pressure/Time (PT) Patterns ...................................................... 5.11 5.8 Compressor Vibration Analysis ....................................................................... 5.19 5.9 Abnormal Vibration/Ultrasonic Traces ............................................................ 5.23 5.10 Systematic Compressor Analysis .................................................................... 5.28

6. Compressor and Piping System Simulation ......................................... 6.1 6.1 Introduction ...................................................................................................... 6.1 6.2 General Modeling Concepts ............................................................................ 6.2 6.3 Predicting Pulsations, Vibrations, and Stress ................................................. 6.3 6.4 Reciprocating Compressor Pressure Volume Analysis .................................. 6.9 6.5 Valve Motion Models ....................................................................................... 6.10 6.6 Thermal Flexibility Models ............................................................................... 6.12 6.7 References ...................................................................................................... 6.15

7. Very High Pressure Compressors (over 100 MPa [14500 psi]) ............ 7.1 7.1 Design Procedure ............................................................................................ 7.1 7.2 Stress Considerations ..................................................................................... 7.13 7.3 Packing and Cylinder Construction ................................................................. 7.35 7.4 Bibliography ..................................................................................................... 7.47

8. CNG Compressors ................................................................................... 8.1 8.1 Introduction ...................................................................................................... 8.1 8.2 CNG Compressor Design ................................................................................ 8.1 8.3 CNG Station Equipment .................................................................................. 8.8 8.4 CNG Station System Designs ......................................................................... 8.14 8.5 Equipment Selection and System Performance ............................................. 8.17 8.6 Codes and Standards ...................................................................................... 8.18

9. Liquid Transfer/Vapor Recovery ............................................................ 9.1 9.1 Transfer Using a Liquid Pump ......................................................................... 9.1 9.2 Air Padding ...................................................................................................... 9.2

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9.3 Transfer Using a Gas Compressor ................................................................. 9.4 9.4 Combination Compressor/Pump Systems ...................................................... 9.6 9.5 Compressors for Liquid Transfer/Vapor Recovery ......................................... 9.6

10. Compressed Natural Gas for Vehicle Fueling ....................................... 10.1 10.1 Refueling Appliance ......................................................................................... 10.1 10.2 Compressor ..................................................................................................... 10.6 10.3 Compressor Balance ....................................................................................... 10.11 10.4 Compressor Components ............................................................................... 10.13 10.5 Natural Gas as Fuel ......................................................................................... 10.14

11. Gas Boosters ........................................................................................... 11.1 11.1 Applications ..................................................................................................... 11.1 11.2 Construction and Operation ............................................................................ 11.2

12. Scroll Compressors ................................................................................. 12.1 12.1 Principal of Operation ...................................................................................... 12.2 12.2 Advantages ...................................................................................................... 12.3 12.3 Limitations ........................................................................................................ 12.4 12.4 Construction ..................................................................................................... 12.4 12.5 Applications ..................................................................................................... 12.7

13. Straight Lobe Compressors .................................................................... 13.1 13.1 Applications ..................................................................................................... 13.1 13.2 Operating Principle .......................................................................................... 13.1 13.3 Pulsation Characteristics ................................................................................. 13.2 13.4 Noise Characteristics ....................................................................................... 13.2 13.5 Torque Characteristics .................................................................................... 13.3 13.6 Construction (Fig. 13.2) ................................................................................... 13.3 13.7 Staging ............................................................................................................. 13.7 13.8 Installation ........................................................................................................ 13.8

14. The Oil-flooded Rotary Screw Compressor ........................................... 14.1 14.1 Types of Compressors (See Fig. 14.2) ........................................................... 14.1 14.2 Helical Rotors .................................................................................................. 14.3

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14.3 Advantages of the Rotary Screw Compressor ................................................ 14.5 14.4 Applications for the Rotary Screw Compressor .............................................. 14.6 14.5 Vapor Recovery ............................................................................................... 14.6 14.6 Sizing a Rotary Screw Compressor ................................................................ 14.7

15. Diaphragm Compressors ........................................................................ 15.1 15.1 Introduction ...................................................................................................... 15.1 15.2 Theory of Operation ......................................................................................... 15.1 15.3 Design .............................................................................................................. 15.4 15.4 Materials of Construction ................................................................................. 15.9 15.5 Accessories ..................................................................................................... 15.10 15.6 Cleaning and Testing ....................................................................................... 15.11 15.7 Applications ..................................................................................................... 15.11 15.8 Limitations ........................................................................................................ 15.12 15.9 Installation and Maintenance ........................................................................... 15.13 15.10 Specifying a Diaphragm Compressor ............................................................. 15.14

16. Rotary Compressor Seals ....................................................................... 16.1 16.1 Introduction ...................................................................................................... 16.1 16.2 Types of Seals ................................................................................................. 16.3 16.3 Further Reading ............................................................................................... 16.14

17. Reciprocating Compressor Sealing ....................................................... 17.1 17.1 Compressor Packing ....................................................................................... 17.1 17.2 Breaker Rings .................................................................................................. 17.4 17.3 Packing Ring Type BT ..................................................................................... 17.5 17.4 Packing Ring Type BD .................................................................................... 17.6 17.5 Common Packing Ring Characteristics .......................................................... 17.6 17.6 Packing Ring Materials .................................................................................... 17.7 17.7 Lubricated, Semilubricated and Nonlubricated Packing ................................. 17.8 17.8 Packing Ring Type TU .................................................................................... 17.10 17.9 Thermal Effects ................................................................................................ 17.10 17.10 Undersized Rods ............................................................................................. 17.11 17.11 Oversized Rods ............................................................................................... 17.11

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17.12 Tapered Rods .................................................................................................. 17.12 17.13 Packing Leakage ............................................................................................. 17.13 17.14 Ring Leakage at Low Pressure ....................................................................... 17.14 17.15 Problems Associated with Low Suction Pressure ........................................... 17.16 17.16 Problems Associated with Low Leakage Requirements ................................ 17.17 17.17 Effect of Ring Type on Leakage Control ......................................................... 17.18 17.18 Leakage Control with Distance Piece Venting ................................................ 17.18 17.19 Static Compressor Sealing .............................................................................. 17.20 17.20 Compressor Barrier Fluid Systems for Fugitive Emissions Control ............... 17.20 17.21 Wiper Packing .................................................................................................. 17.22 17.22 High Pressure (Hyper) Packings ..................................................................... 17.23 17.23 Compressor Piston Rings ................................................................................ 17.24 17.24 Compressor Rider Rings ................................................................................. 17.25 17.25 Piston Ring Leakage ....................................................................................... 17.26 17.26 Compressor Ring Materials ............................................................................. 17.28 17.27 Seal Ring Friction ............................................................................................ 17.29 17.28 Cooling Reciprocating Compressor Packing .................................................. 17.30

18. Compressor Lubrication ......................................................................... 18.1 18.1 Rotary Screw Compressors ............................................................................ 18.1 18.2 Reciprocating Compressor Crankcase ........................................................... 18.2 18.3 Compressor Cylinders ..................................................................................... 18.2 18.4 Lube Oil Selection ........................................................................................... 18.3 18.5 Oil Additives ..................................................................................................... 18.5 18.6 Optimum Lubrication ....................................................................................... 18.7 18.7 Oil Removal ..................................................................................................... 18.7 18.8 Non-lube (NL) Compressors ........................................................................... 18.9 18.9 Synthetic Lubricants ........................................................................................ 18.9 18.10 Compressor Lubrication Equipment ................................................................ 18.10

19. Principles of Bearing Design .................................................................. 19.1 19.1 Nomenclature .................................................................................................. 19.1 19.2 Compressors and Their Bearings ................................................................... 19.4 19.3 General Bearing Principles .............................................................................. 19.9

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19.4 Conventional Bearings .................................................................................... 19.24 19.5 Low-speed Bearings ........................................................................................ 19.56 19.6 High-speed and High-temperature Bearings .................................................. 19.62 19.7 Cryogenic Applications .................................................................................... 19.104 19.8 Lubricants and Materials ................................................................................. 19.121 19.9 Design Considerations .................................................................................... 19.128 19.10 References ...................................................................................................... 19.151

20. Compressor Valves ................................................................................. 20.1 20.1 Purpose ............................................................................................................ 20.1 20.2 History .............................................................................................................. 20.1 20.3 Survey of Valve Design ................................................................................... 20.2 20.4 Theory .............................................................................................................. 20.9 20.5 Valve Materials ................................................................................................ 20.19 20.6 Valve Life ......................................................................................................... 20.20 20.7 Methods to Vary the Capacity of a Compressor ............................................. 20.21 20.8 References ...................................................................................................... 20.28

21. Compressor Control Systems ................................................................ 21.1 21.1 Controls – Definitions ...................................................................................... 21.1 21.2 Reciprocating Compressor Monitoring ............................................................ 21.1 21.3 System Considerations ................................................................................... 21.2 21.4 System Selection – Define the Scope ............................................................. 21.3 21.5 Human Factors ................................................................................................ 21.3 21.6 Electrical and Electronic Controls ................................................................... 21.4 21.7 Pneumatic Controls ......................................................................................... 21.10 21.8 Manual Controls ............................................................................................... 21.11 21.9 Prelube-post Lube System .............................................................................. 21.12 21.10 Loading-unloading ........................................................................................... 21.12 21.11 Capacity Control .............................................................................................. 21.12 21.12 Loading and Unloading ................................................................................... 21.13 21.13 Sensor Classification – (Alarm Classes) ......................................................... 21.16 21.14 Sensors ............................................................................................................ 21.16 21.15 Special Compressor Controls ......................................................................... 21.18

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21.16 Temperature Control (Oil and Water) .............................................................. 21.24 21.17 Electric Motor and Pneumatically Operated Temperature Control

Valves .............................................................................................................. 21.26 21.18 Energy Management Systems ........................................................................ 21.26 21.19 Specifications, Codes, and Standards ............................................................ 21.26

22. Compressor Foundations ....................................................................... 22.1 22.1 Foundations ..................................................................................................... 22.1 22.2 References ...................................................................................................... 22.11

23. Packaging Compressors ......................................................................... 23.1 23.1 Compressor Sizing .......................................................................................... 23.1 23.2 Base Design .................................................................................................... 23.2 23.3 Scrubber Design .............................................................................................. 23.2 23.4 Line Sizing ....................................................................................................... 23.5 23.5 Pulsation Bottle Design ................................................................................... 23.7 23.6 Pressure Relief Valve Sizing ........................................................................... 23.8 23.7 Cooler Design .................................................................................................. 23.10 23.8 Compressor Lubrication .................................................................................. 23.11 23.9 Control Panel & Instrumentation ..................................................................... 23.11 23.10 Rotary Screw Gas Compressors ..................................................................... 23.15 23.11 Regulatory Compliance & Offshore Considerations ....................................... 23.17 23.12 Testing ............................................................................................................. 23.17 23.13 References ...................................................................................................... 23.17

Appendix ......................................................................................................... A.1 A.1 Definitions of Gas Compressor Engineering Terms ....................................... A.2 A.2 Conversion Factors (Multipliers) ...................................................................... A.5 A.3 Temperature Conversion Chart (Centigrade – Fahrenheit) ............................ A.6 A.4 Areas and Circumferences of Circles ............................................................. A.7 A.5 Properties of Saturated Steam ........................................................................ A.8 A.6 Partial Pressure of Water Vapor in Saturated Air 32° to 212°F ...................... A.9 A.7 Atmospheric Pressure and Barometric Readings at Different Altitudes ......... A.10 A.8 Discharge of Air Through an Orifice ................................................................ A.11

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A.9 Loss of Air Pressure Due to Pipe Friction ....................................................... A.12 A.10 Loss of Pressure Through Screw Pipe Fittings ............................................... A.14 A.11 Horsepower (Theoretical) Required to Compress Air from Atmospheric

Pressure to Various Pressures – Mean Effective Pressures .......................... A.15 A.12 n Value and Properties of Various Gases at 60°F. and 14.7 P.S.I.A. ............ A.16 A.13 Temperature Rise Factors vs. Compression Ratio ......................................... A.17 A.14 Procedure for Determining Size and Performance of Horizontal

Double-acting Single-stage Compressors for Gas or Air ................................ A.18 A.15 Procedure for Determining Size and Performance of Horizontal

Double-acting Two-stage Compressors for Gas or Air ................................... A.21 A.16 Single-stage Added Cylinder Clearance ......................................................... A.37

Index ................................................................................................................ I.1

1.1

CHAPTER 1COMPRESSOR THEORY

Derek WoollattManager, Valve and Regulator EngineeringDresser-Rand Company

1.1 NOMENCLATURE

Units(See note below)

a Speed of Sound in Gas ft /seca, b Constants in Equation of State (Pressure Form)A, B Constants in Equation of State (Compressibility

Form)B Bore InchCL Fixed Clearance as a Fraction of Swept VolumecP Specific Heat at Constant Pressure ft.lbf / lbm.RcV Specific Heat at Constant Volume ft.lbf / lbm.Re Specific Internal Energy (i.e. Internal Energy per

unit mass)ft.lbf / lbm

E Internal Energy ft.lbf

F Flow Area Inch2

h Specific Enthalpy (i.e. Enthalpy per unit mass) ft.lbf / lbm

H Enthalpy ft.lbf

HP HorsepowerJ Joule’s Equivalent ft.lbf /BTUk Ratio of Specific Heats (� cP /cV)m Mass Flow Rate lbm/secM Mass lbm

nT Isentropic Temperature ExponentnV Isentropic Volume ExponentN Compressor Speed rpmP Pressure lbf / in

2 AbsPW Power ft.lbf /min

1.2 CHAPTER ONE

q Heat Transfer Rate BTU/secQ Heat Transfer BTUR Gas Constant ft.lbf / lbm.Rs Specific Entropy ft.lbf / lbm.RS Stroke InchT Temperature Rankineu Gas Velocity ft /secUP Piston Velocity ft /minv Specific Volume (Volume per unit mass) ft3 / lbm

V Volume Inch3

W Work Done on Gas during Process ft.lbf

WD Work Done on Gas During one compressor cycle ft.lbf

Z Compressibility (sometimes calledSupercompressibility)

�P Pressure Drop lbf / in2

� Density lbm/ft3

� Crank Angle Degree� Integration Constant in expression for Average

Pressure Drop

SuffixesC Critical Pressure or TemperatureD Discharge from the Compressor Cylindereq Equivalent (Area)in At Entry to a Control Volumeo Stagnation Valueout At Exit from a Control VolumeR Reduced (Pressure or Temperature)SW Swept (Swept Volume is Maximum minus

Minimum Cylinder Volume)1, 2, 3, 4 At Corresponding Points in the Cycle (Fig. 1.2)1, 2 Before and after process

NOTE:. The basic equations given in this section can be used with any consistentsystem of units. The units given above are not consistent and the numerical factorsrequired to use the equations with the above units are given at the end of eachequation in square brackets. If the above units are used, the equations can be usedas written. If an alternate, consistent, system of units is used, the numerical factorsat the ends of the equations should be ignored.

1.2 THEORY

1.2.1 Gas Laws

By definition, compressors are intended to compress a substance in a gaseous state.In predicting compressor performance and calculating the loads on the various

COMPRESSOR THEORY 1.3

components, we need methods to predict the properties of the gas. Process com-pressors are used to compress a wide range of gases over a wide range of condi-tions. There is no single equation of state (an equation that allows the density ofa gas to be calculated if the pressure and temperature are known) that will beaccurate for all gases under all conditions. Some of the commonly used ones,starting with the most simple, are discussed below.

The simplest equation of state is the perfect gas law:

P 1Pv � � RT � �� 144

This equation applies accurately only to gases when the temperature is muchhigher than the critical temperature or the pressure much lower than the criticalpressure. Air at atmospheric conditions obeys this law well.

To predict the properties of real gases more accurately, the perfect gas law isoften modified by the addition of an empirical value ‘‘Z’’, called the compressi-bility, or sometimes the supercompressibility, of the gas. The value of Z is afunction of the gas composition and the pressure and temperature of the gas. Themodified equation is:

p 1� ZRT � �� 144

This equation is accurate if, and only if, Z is known accurately.Z can be estimatedwith reasonable accuracy in many cases using the Law of Corresponding Stateswhich states that the value of Z as a function of the reduced pressure and temper-ature is approximately the same for all gases. That is:

P TZ � ƒn (P , T ) � ƒn ,� �R R P TC c

A curve of Z as a function of reduced pressure and temperature is shown as Fig.1.1. This gives reasonable results for most gases when the gas state is not close tothe critical point or the two phase region.

It is frequently useful to have an equation to predict Z. This allows calculationof other properties such as entropy, enthalpy and isentropic exponents that areneeded to predict compressor performance. The use of an equation rather thancharts is also convenient when a computer is used to perform the calculations.Many equations are available: one of the most simple, the Redlich-Kwong Equa-tion of State is given below. Other equations are more accurate over a wider rangeof gases and conditions, but are more complex. Some of these are discussed inRefs. 2 and 3. The Redlich-Kwong equation of state is:

RT a 1P � �� 2v � b v � bv 144

1.4 CHAPTER ONE

FIGURE 1.1 Compressibility chart (based on the Redlich Kwong equation of state).

where a �2 2.5R T 1C0.42748 � �0.5P T 144C

b �RT 1C0.08664 � �P 144C

or3 2 2Z � Z � (A � B � B )Z � AB � 0

where A �PR0.42748 2.5TR

B �PR0.08664TR

Solving the above cubic equation for Z once PR and TR are known is equivalentto looking up the value of Z on Fig. 1.1.

Other equations of state commonly used in predicting compressor performanceinclude the Soave Redlich Kwong, Peng Robinson, Benedict Webb Rubin, HanStarling, Lee-Kesler, and API Method equations. Details of these methods can befound in the literature (e.g. Refs. 2 and 3) .

1.2.2 Thermodynamic Properties

To predict compressor performance ways to calculate the enthalpy, internal energyand entropy of the gas are needed. It is also often convenient to use the isentropicvolume exponent nV and the isentropic temperature exponent nT.

COMPRESSOR THEORY 1.5

The isentropic exponents are defined such as to make the following equationstrue for an isentropic change of state.

nVPV � Constant

n � 1T

nTP� Constant

For a perfect gas, the above properties are easily calculated. The following isfor a gas that obeys the ideal gas laws and has constant specific heats. Specificproperties are those per unit mass of gas.

Specific Internal Energy � e � c Tv

Specific Enthalpy � h � c Tp

n � n � c /c � kV T P V

T P2 2Change of Specific Entropy � s � s � c ln � R ln� � � �2 1 P T P1 1

For a real gas, the above properties can be obtained from a Mollier chart forthe gas or from the equation of state and a knowledge of how the specific heats atlow pressure vary with temperature. Methods for this are given in Refs. 2 and 3.

An approximation that allows isentropic processes to be calculated easily fora real gas if the Z values are known is often useful. Consider an isentropic changeof state from 1 to 2.

1 / nV� Z P T P2 1 2 1 2� � � �� Z P T P1 2 1 2 1

n �1 / nT TT P1 1� � �T P2 2

1 / n 1 / nV TP Z P2 1 2� �� P Z P1 2 1

It is found that if the gas state is not too near the critical or two phase region,and is therefore acting somewhat like an ideal gas, then nT is approximately equalto k � cp /cV. Then

1 / n 1 / kVP Z P2 1 2�� P Z P1 2 1

1.6 CHAPTER ONE

1.2.3 Thermodynamic Laws

For calculating compressor cycles, the energy equation, relationships applying toan isentropic change of state, and the law for fluid flow through a restriction areneeded.

The Energy equation for a fixed mass of gas states simply that the increase ofenergy of the gas equals the work done on the gas minus the heat transferred fromthe gas to the surroundings. For the conditions in a compressor, we can ignorechanges in potential and chemical energy. In applications where the energy equationfor a fixed mass of gas is used, we can usually also ignore changes in kineticenergy. The energy equation then reduces to:

E � E � M(e � e ) � W � Q[J]2 1 2 1

If we consider a control volume, that is a volume fixed in space that fluid canflow into or out of, we must consider the work done by the gas entering and leavingthe control volume, and in many cases where this equation is used, we must con-sider the kinetic energy of the gas entering and leaving the control volume. Theenergy equation then becomes:

E � E � M h � M h � W � Q[J]2 1 in o in out o out

where ho �1 12h � u � �2 32.18

h � e � Pv[144]

For a steady process, there is no change of conditions in the control volume andE2 � E1

Then M h � M h � H � H � W � Q[J]out o out in o in o out o in

The equations for isentropic change of state were given above. They apply toany change during which there are no losses and no heat transfer to the gas. Thechange of properties can be obtained from a Mollier chart for the gas, or if the gasbehaves approximately as a perfect gas, by the equations given above.

nVPV � Constant

n � 1T

nTP� Constant

The law for incompressible fluid flow through a restriction is:

32.18m � F�(2� �P) � �� 144

F � Effective Flow Area � Geometric Flow Area � Flow Coefficient

COMPRESSOR THEORY 1.7

For a perfect gas, if the pressure drop is low enough that the flow is subsonic,as should always be the case in reciprocating compressors, the pressure drop isgiven by:

k�1 / 2k k�1 / kp p 2 p1 2 1m � k F� � 1 [32.18]� � � �� a p k � 1 p1 1 2

if � the flow is sonic and m � k F [32.18]k / k�1 k�1 / 2(k�1)p 2 p 22 1� � � �p k � 1 a k � 11 1

1.2.4 Compression Cycles

The work supplied to a compressor goes to increasing the pressure of the gas,to increasing the temperature of the gas and to any heat transferred out of thecompressor. In most cases, the requirement is to increase the pressure of the gasusing the least possible power. If the compression process is adiabatic, that is, thereis no heat transfer between the compressor and the outside, then the least workwill be done if the process is isentropic. This implies that there are no losses inthe compressor and which is an unachievable goal, but one that can be used as abase for the compression efficiency. The isentropic efficiency of a compressor isdefined as the work required to compress the gas in an isentropic process dividedby the actual work used to compress the gas. The efficiency of a compressor ismost often given as the isentropic efficiency.

However, it is possible to construct a compressor with an isentropic efficiencygreater than 100%. The work done in a reversible isothermal process is less thanthat done in an isentropic process. In a reversible isothermal process, the temper-ature of the gas is maintained at the suction temperature by reversible heat transferas the compression proceeds. There must, of course, be no losses in this process.Many compressors have a final discharge temperature that is much lower than theisentropic discharge temperature, and the power required is reduced by this. How-ever, the power required is almost always still greater than the isentropic powerand so the isentropic efficiency is universally used to rank compressors.

1.2.5 Ideal Positive Displacement Compressor Cycle

As an example of a positive displacement compressor, consider a reciprocatingcompressor cylinder compressing gas from a suction pressure PS to a dischargepressure PD. In compressor terminology, the ratio PD /PS is known as the com-pression ratio. This can be contrasted to reciprocating engine terminology wherethe compression ratio is a ratio of volumes.

For a reciprocating compressor, the ideal compression cycle is as shown on Fig.1.2. The cycle is shown on pressure against crank angle and pressure against cyl-inder volume coordinates. The cycle can be explained starting at point 1. Thisrepresents the point when the piston is at the dead center position that gives the

1.8 CHAPTER ONE

FIGURE 1.2 Ideal compressor cycle.

maximum cylinder volume. The gas in the cylinder is at the suction pressure PS.As the piston moves to decrease the cylinder volume, the mass of gas trapped inthe cylinder is compressed and its pressure and temperature rise. In the ideal case,there is no friction and no heat transfer and so the change is isentropic and thechange of pressure and temperature can be calculated from the known change ofvolume using the above equations for isentropic change of state.

At point 2, the pressure has increased to equal the discharge pressure. In theideal compressor, the discharge valve will open at this point and there will be nopressure loss across the valve. As the piston moves to further decrease the cylinder

COMPRESSOR THEORY 1.9

volume, the gas in the cylinder is displaced into the discharge line and the pressurein the cylinder remains constant.

At point 3, the piston has reached the end of its travel, the cylinder is at itsminimum volume and the discharge valve closes. As the piston reverses and movesto increase the cylinder volume, the gas that was trapped in the clearance volume(sometimes called the fixed clearance) at point 3, expands and its pressure andtemperature decrease. Again there are no losses or heat transfer and the change ofpressure and temperature can be calculated using the expressions for isentropicchange of state.

At point 4, the pressure has decreased to again equal the suction pressure. Thesuction valve opens at this point. As the piston moves to further increase the cyl-inder volume, gas is drawn into the cylinder through the suction valve. When thepiston again reaches the dead center, point 1, the cylinder volume is at its maxi-mum, the suction valve closes, and the cycle repeats.

The work required per cycle and hence the horsepower required to drive thecompressor can easily be calculated from the pressure against volume diagram orfrom the temperature rise across the compressor.

The work done on the gas during a small time interval during which the cylindervolume changes by dV is equal to P dV and the work done during one compressorcycle is the integral of this for the cycle. That is, the work done equals the area ofthe cycle diagram on pressure against volume axes (Fig. 1.2). Note that the equiv-alence of work done per cycle and diagram area holds for real as well as idealcycles. That is, the magnitude of losses that cause a horsepower requirement in-crease can be measured off the indicator card as the pressure vs. volume plot isoften called. (If the pressure on the indicator card is in psi and the volume in cubicinches, the work done as given by the card area will be in inch lb. and must bedivided by 12 to give the work done in ft. lb.)

Once the work done per cycle is known, the horsepower can be calculated. Ifthe work done is in ft. lb., and the speed in rpm:

HP � WD N /33,000

If the heat transfer from the gas in the cylinder can be measured or estimated,the work done per unit time can be calculated from the energy equation.

Work Done per Unit Time � m(h � h ) � q[J]2 1

For a cycle with no heat transfer with a perfect gas, Q is zero and h � cp T,then

Power, PW � mc (T � T )[60]p 2 1

Now for an ideal cycle and a perfect gas, the compression is isentropic and thedischarge temperature T2 can be calculated from the pressure ratio and the suctiontemperature T1 using the isentropic relationship.

1.10 CHAPTER ONE

k�1 / kT P uP2 D S� � �T1

k�1 / kPD� Power, PW � mc T � 1 [60]�� p 1 PS

For an ideal cycle with a gas for which the compressibility at suction and theaverage isentropic volume exponent are known, the power can be derived asfollows.

For unit mass of gas compressed:

1Work Done by Gas Flowing Into Cylinder � P V � �1 1 12

2 1Work Done to Compress Gas In Cylinder � �� P dV � �

1 12

1Work Done on Gas Flowing Out Of Cylinder � P V � �2 2 12

� Work Done by Shaft per Unit Mass of Gas2

� �P v � � P dv � P v [144]� �1 1 2 21

nvNoting that Pv � Constant, and integrating

1Work Done per Unit Mass � [P v � P v ] � P v � P v [144]� �2 2 1 1 2 2 1 1n � 1v

nv� (P v � P v )[144]2 2 1 1n � 1v

n �1 / nv vn pv 2� P v � 1 [144]�� 1 1n � 1 pv 1

� Work Done per Unit Time � Power,n �1 / nv vn Pv 2PW � mP v � 1 [(144).(60)]�� 1 1n � 1 Pv 1

(Or using the modified perfect gas equation of state (Pv � Z R T))n �1 / nv vn Pv 2� Z RT m � 1 [60]�� 1 1n � 1 Pv 1

The capacity of the ideal compressor end, that is the flow rate through the end,can also be calculated from the pressure vs volume diagram. The amount of gasdrawn into the cylinder, which, in the ideal compressor, equals the amount of gasdischarged from the cylinder, is equal to m1 � m4 where points 1 and 4 are defined

COMPRESSOR THEORY 1.11

on Fig 1.2. This is often given in terms of the volumetric efficiency as definedbelow. Note that a cylinder with no losses will have a volumetric efficiency lessthan 100%. The volumetric efficiency only relates the actual capacity to the ca-pacity of a cylinder with no fixed clearance, and gives no information on theefficiency of the cylinder.

1The Capacity per Cycle � M � M � � (V � V ) � �1 4 1 1 4 1728

V � V1 4The Volumetric Efficiency is Defined as VE �V � V1 3

1� The Capacity per Cycle � � VE(V � V ) � �1 1 3 1728

The Flow Rate (Capacity per Unit Time),

1m � � VE N(V � V ) � �1 1 3 (60)(1728)

Now V � V is the Swept Volume (V )1 3 SW

If the average isentropic volume exponent is known, the volumetric efficiencycan be calculated as follows.

V � V1 4VE �V � V1 3

V V3 4� 1 � � 1� �V � V V1 3 3

Now V3 /(V1 � V3) is the fixed clearance expressed as a fraction of the sweptvolume. This is often called the clearance (CL) and is expressed as a fraction ora percent. The term V4 /V3 can be expressed in terms of the pressure ratio usingthe definition of the isentropic volume exponent nV. Then

1 / nVp3VE � 1 � CL � 1�� p4

1 / nVpDi.e. VE � 1 � CL � 1�� pS

1.2.6 Approximate Valve Losses

For a compressor with real valves, there will be a pressure drop across the valvesduring the suction and discharge processes. This will increase the power requiredto drive the compressor and decrease the capacity of the compressor. These lossescan be estimated as follows.

1.12 CHAPTER ONE

To estimate the power loss caused by the valves, it is often assumed that thegas is incompressible during the valve event. This is reasonable as the gas pres-sure remains relatively constant during the suction and discharge processes. Wewill also assume for the moment that the connecting rod is long so that the pistonmotion is sinusoidal. Then, the piston velocity is given by:

1U � �NS Sin(�) � �p 12

Now, if the gas is incompressible, the mass of gas passing through the valveequals the mass displaced by the piston.

2 2�B 1 � 12m � � U � �NSB Sin(�)� � � �p4 (60)(144) 4 (1728)(60)

Then, assuming incompressible flow through the orifice representing the valve,

22� 2�NSB Sin(�)� �2 4m 144 1

�P � �� 2 2 2 22�F 32.18 2�F (32.18)(60 )(144 )eq eq

Note that in this equation, Feq is the equivalent area of all the valves for thecorner being considered. That is the area of an ideal orifice that will give the samepressure drop as the valves for the same flow rate of the same gas. If it is assumedthat the valves are fully open for the full suction or discharge event, then Feq is aconstant that is known from the valve design. Adding the effects of the valvepressure drops modifies the cycle pressure diagrams as shown on Fig 1.3.

To calculate the work or power loss caused by the valve loss, we need to knowthe area of the valve loss on the pressure vs volume diagram (Fig. 1.3). This ismost easily obtained by calculating the average valve pressure drop and then mul-tiplying by the volume change. The average pressure drop on a cylinder volumebasis is obtained by integrating the above expression. For the suction valves withreference to Fig. 1.3.

1� �P dv4

�P �V � V1 4

Substituting for �P, integrating and simplifying gives:

22 2� � NSB 1�P � �� 2 22 4F (32.18)(60 )(144 )eq

where � � is an Integration Factor defined by this equation26VE � 4VE

COMPRESSOR THEORY 1.13

FIGURE 1.3 Cycle with approximate valve losses.

An identical expression is obtained for the discharge valves.Note that a compressor compressing a heavier (higher molecular weight) gas or

running at a higher speed will require larger valve equivalent area for a given sizecylinder to give the same efficiency.

As stated earlier, the above only applies if the connecting rod is long comparedto the stroke. For a realistic connecting rod length, the value of 8 is as given onFig. 1.4.

1.14 CHAPTER ONE

FIGURE 1.4 Integration factor used to calculate valve pressuredrop.

The power loss caused by the valves in the corner is then easily obtained.

1Power Loss, PW � N �V �P � �12

1� N VE V �P � �SW 12

1i.e. Horsepower � N VE V �P � �SW (12)(33,000)

Note that for discharge valves, the discharge volumetric efficiency must be usedin the above. The Discharge Volumetric Efficiency is defined as the actual volumeof gas discharged from the cylinder each stroke (V2 � V3 with points 2 and 3 asdefined by Fig. 1.2) divided by the swept volume (VSW).

V � V2 3That is: Discharge VE �VSW

1.2.7 Ideal Dynamic Compressor Cycle

In a dynamic compressor, the moving part increases the velocity of the gas and theresulting kinetic energy is converted into pressure energy. Typically, both processes

COMPRESSOR THEORY 1.15

occur simultaneously in the rotating element and the gas leaves the rotor at higherpressure and with a higher velocity than it entered. Some of the kinetic energy isthen converted into pressure energy in the stator by means of a diffusion process,that is, flow through a diverging channel.

If we ignore the effects of heat transfer, the steady flow energy equation statesthat the increase in stagnation enthalpy for flow in the rotor equals the work done.As there is no work done on the gas in the stator, the stagnation enthalpy remainsconstant. These relationships are true regardless of the efficiency of the process. Ina completely inefficient process, the temperature of the gas will be increased, butthe pressure will not. In an efficient process, the pressure of the gas will be in-creased as well as the temperature.

For a compressor with no losses and no heat transfer, the process will be isen-tropic. The increase in enthalpy for compression from a given initial pressure andtemperature to a given final pressure can be obtained from a Mollier chart, or froman equation of state. For an ideal gas, it can be calculated as follows.

k�1 / kP2T � T � �2 is 1 P1

h � h � c (T � T )2 is 1 P 2 is 1

The isentropic efficiency which is the work required for an isentropic compres-sion divided by the actual work can be calculated as:

h � h2 is 1Isentropic Efficiency �h � h2 1

It is sometimes considered that any excess kinetic energy in the discharge gasover that of the inlet gas is also a useful output of the compressor. It can, after all,be recovered in a diffuser. In this case, the actual stagnation enthalpies should beused and:

h � h2 is 1Isentropic Efficiency �h � ho 2 o 1

1.3 REFERENCES

1. Gas Properties and Compressor Data, Ingersoll-Rand Company Form 3519D.

2. Edmister, Wayne C., Applied Hydrocarbon Thermodynamics, Gulf Publishing, 1961, L.of C. 61-17939.

3. Reid, Robert C., John M., Prausnitz, and Bruce E. Poling, The Properties of Gases andLiquids, 4th Ed., McGraw Hill, ISBN 0-07-051799-1.

2.1

CHAPTER 2COMPRESSOR PERFORMANCE—POSITIVE DISPLACEMENT

Derek WoolattManager, Valve and Regulator EngineeringDreser-Rand Company & (Screw Compressor Section)

Fred HeidrichDresser-Rand Company

2.1 COMPRESSOR PERFORMANCE

2.1.1 Positive Displacement Compressors

Positive displacement compressors all work on the same principle and have thesame loss mechanisms. However, the relative magnitude of the different losses willbe different in each type. For example, leakage losses will be low in a lubricatedreciprocating compressor with good piston rings, but may be significant in a dryscrew unit, especially if the speed is low and the pressure increase, high. Coolingof the gas, which is beneficial, will be small in a reciprocating compressor, butmay be almost complete in a liquid flooded screw compressor.

All compressor types have a clearance volume that contains gas at the dischargepressure at the end of the discharge process. This volume may be small in somedesigns and significant in others. Some types, for example reciprocating compres-sors may have a large clearance volume, but recover the work done on this gas byexpanding it back to suction pressure in the cylinder; other types, for examplescrew compressors, let the gas in the clearance space expand back to suction pres-sure without recovering the work.

Some compressor types, specifically those that use fixed ports for the discharge,are designed to operate at a fixed volume ratio. (For a given gas, this is equivalentto a fixed pressure ratio.) As the ratio varies from this value, the compressor effi-ciency will be less than the optimum. Other compressor types use either ports thatcan be varied with slides or they use pressure actuated valves. These types areoptimized at any pressure ratio.

2.2 CHAPTER TWO

FIGURE 2.1 Frame and rod loads.

The following discussion deals specifically with the application of reciprocatingcompressors, but similar considerations apply to other types.

2.1.2 Reciprocating Compressor Rating

Each component in a compressor frame and cylinder has design limits. To ensurethat these are not exceeded in operation, each frame and each cylinder has a designrating above which it may not be used. The loads used to rate compressors arediscussed below.

Every cylinder has a maximum allowable discharge pressure. All compressorcomponents are subjected to alternating loads and the rated pressure of a cylinderwill be based on fatigue considerations.

Every cylinder has a minimum clearance it can be built with. This controlsthe volumetric efficiency of the cylinder and hence the capacity for a given pressureratio and gas composition. The clearance of a cylinder can usually be increased ifthe maximum capacity is not needed for a given application.

Every cylinder has a fixed number of valves and valve size. A cylinder witha few or small valves for its size will have high losses and will give poor efficiencyif used at its normal piston speed when compressing a high molecular weight gas,especially if the pressure ratio is small.

Each cylinder exerts a rod load on the running gear components, and a frameload on the stationary components. These can be evaluated by considering theforces acting on the various components (Fig. 2.1).

Frame Load � P A � P (A � A )HE P CE P ROD

Where

P and P � Pressure in the Head End and Crank End of the CylinderHE CE

A and A � The Area of the Piston and Piston RodP ROD

The frame load will vary through the cycle as the pressures in the head end andcrank end of the cylinder vary. The maximum tensile and the maximum compres-

COMPRESSOR PERFORMANCE—POSTIVE DISPLACEMENT 2.3

sive stresses are calculated. These are the loads the stationary components andbolting must be designed to resist.

The rod load, the force exerted on the piston rod, crosshead, crosshead pin,connecting rod and crankshaft is different for each component. It is the frame loadplus the inertia of all the parts outboard of the component that is of interest. Forexample, the rod load at the crosshead pin, the value that is usually calculated, isthe frame load plus the inertia of the piston with rings, the piston rod and thecrosshead. The inertia is the mass times the piston acceleration, and varies throughthe cycle. The rod load quoted is usually the maximum value, compression ortension, at the crosshead pin.

The crosshead pin bearings do not see full rotary motion. Rather the connectingrod oscillates through a fairly small arc. This makes lubrication of these bearingsdifficult as a hydrodynamic film is never generated. The bearing relies on a squeezefilm being formed. This requires that the load change direction from compressiveto tensile and back every revolution. Once the rod load diagram has been calculated,the degrees of reversal, that is the lesser of the number of degrees of crankshaftrotation that the rod load is compressive and the number of degrees it is tensile, isknown. The minimum acceptable number of degrees of reversal depends on thedetails of the design and will be available for each frame.

Each frame will also be limited by the power that can be transmitted throughthe crankshaft at a given speed. There will be a limit on the power of each throwand a higher limit on the total power of the compressor. Note that the totalcompressor power is all transmitted through the crankshaft web closest to the driver.

2.1.3 Reciprocating Compressor Sizing

Once the suction and discharge pressures, the suction gas temperature, the requiredflow rate and the gas composition are determined, a compressor can be selected todo the job. The selection will depend on the relative importance of efficiency,reliability and cost, but certain principles will always apply.

Compressors for a wide range of applications tend to run with about the samepiston speed. That is compressors with a long stroke tend to run slower than thosewith a short stroke. Further, short stroke compressors tend to be of lighter construc-tion with lower allowable loads. For the best efficiency and reliability at the expenseof increased cost, a piston speed at the low end of the normal range will be used.The compressor speed and the stroke will then be determined by the horsepowerrequirement. A low horse power application will require a light, low stroke, highspeed compressor. A high horse power application will require a heavy, long stroke,low speed compressor. If possible, larger compressors are directly coupled to thedriver. Thus the speed range of available drivers may influence the selection of thecompressor.

The number of stages must then be selected. One consideration here is theallowable discharge temperature; another is the pressure ratio capability of theavailable cylinders as determined by their fixed clearance; another is efficiency. Ifthe calculated discharge temperature using one stage is too high, obviously more

2.4 CHAPTER TWO

FIGURE 2.2 Effect of multi staging.

stages are needed. During preliminary sizing, the isentropic discharge temperaturecan be used, but if a certain number of stages creates a marginal situation, thedischarge temperature should be estimated more accurately. As a first estimate, itcan be assumed that equal pressure ratios are used for all stages. In practice it isoften good to take a higher pressure ratio in the low pressure ratio stages andunload the more critical higher pressure stages a little.

In almost all multi-stage applications the gas will be cooled between stages. Inthis case, increasing the number of stages, up to a limit, will increase the efficiencyof the compressor. This is because with intercooling, the compression more closelyapproximates an isothermal compression with resulting lower power requirement.An alternative way of looking at this is on a pressure volume diagram. The workrequired to compress the gas is given by the area of the pressure vs volume diagram.Fig. 2.2 shows a single- and a two-stage compression for a given application. Thediagram for single stage compression is 1-2-3-4-1. For two-stage compression, itis 1-5-6-7-3-8-4-1. As the interstage gas is cooled (5-6), its volume decreases. The

COMPRESSOR PERFORMANCE—POSTIVE DISPLACEMENT 2.5

work done as given by the areas of the diagrams is obviously less in the two-stagecase than in the single-stage case. Further, if any liquids are condensed out of thegas in the intercoolers, the liquids must be separated from the gas and the mass ofgas compressed from that interstage to the final discharge is reduced with a furtherresulting power reduction. However as stages are added, the number of compressorvalves the gas must flow through in series, and the amount of interstage piping andcoolers increase. If too many stages are used, the pressure losses in the valves andpiping will offset the gains from intercooling and the efficiency will be reduced.

The cost of a compressor to do a given task usually increases as the number ofstages is increased because of the additional compressor cylinders, coolers andpiping.

In a few applications, there will be side streams where gas either enters or leavesthe process at fixed pressures. These requirements may determine the interstagepressures used.

Once the number of stages is selected, the cylinders for each stage can beselected. Usually a selection will be made from cylinder designs available. Knowingthe inlet conditions and the required capacity, and with the speed and stroke alreadyselected, the required cylinder bore can be estimated. The available cylinders canthen be checked to see which, if any, meet the requirements. The following mustbe checked. First, the pressure rating of the cylinder must be adequate to be safeat the design and any upset conditions. The cylinder rating should be higher thanthe relief valve setting. Second, the frame load, rod load and degrees of reversalmust be within the rating for the frame components. Third, the capacity calculatedwith the minimum cylinder clearance allowing for all losses must meet the require-ments. Fourth, the power requirement of this cylinder must not exceed the powerrating per throw of the frame components. If all these requirements are met, asuitable cylinder has been chosen. Additional optimization may be needed to de-termine the best possible cylinder for this application. If no cylinder can be foundto meet the requirements, then either a new cylinder must be designed, a framerated for a higher frame load or horsepower per throw must be selected, or two ormore, smaller cylinders must be chosen to run in parallel to meet the required flow.Note that if smaller cylinders are used, the frame load and the power per throwwill be reduced. It is usual for smaller cylinders to be available in higher pressureratio versions, so all the requirements can usually be met by using multiple cyl-inders per stage.

The basic compressor sizing is then complete, but must be checked at alternatedesign or upset conditions. Additional factors such as the out-of-balance forcetransmitted from the compressor to the foundation, the potential for harmful tor-sional vibrations in the crankshaft and drive train, optimization of the compressorlayout, efficiency, and cost will be considered before the design is finalized.

2.1.4 Capacity Control

In many applications, it is necessary to be able to reduce the capacity of the com-pressor to meet changing process needs. There are several ways to accomplish this.

2.6 CHAPTER TWO

A very simple control system used mainly on air compressors is stop/startcontrol. In a compressed air system with a large receiver, the compressor can berun to fill the receiver to greater than the required pressure and the compressor canthen be stopped. When the receiver pressure falls to the lowest acceptable value,the compressor is started again. The system is very simple and requires no addi-tional equipment on the compressor, but large pressure swings must be acceptedand the frequent stops and starts can be hard on the compressor.

If a variable speed driver is available, varying the speed of the compressor isan excellent way to control capacity. It will give close, infinite step control, withoutadditional equipment on the compressor. Reduced speed operation is usually easyfor the compressor and maintenance intervals may be increased. This method isnormally used with compressors driven by an engine and is increasingly frequentwith compressors driven by an electric motor. In many cases, the speed range isnot sufficient to give the full capacity range needed and speed control is used inconjunction with other methods. Many unloading methods give step changes incapacity and speed control can be used to trim the flow rate between these steps.

The output of the compressor can also be adjusted by use of a bypass. Thisallows some of the compressed gas to be leaked back to the suction. This obviouslyis very inefficient and the bypassed gas may have to be cooled. It is the onlyunloading method discussed here that significantly decreases the efficiency of theprocess. It is, however, simple, reliable and inexpensive and is very suitable forunloading a compressor for a short period during start up or shut down. A similarlyenergy inefficient method sometimes used to adjust the flow of small compressorsis to throttle the suction. This is effective, but care must be taken not to overloadthe compressor. It may be noted here that most dynamic compressors cannot beunloaded without loss of efficiency or surge problems. Positive displacement com-pressors usually can be unloaded with either little reduction or increase of effi-ciency.

Some screw compressors have slides that change the inlet port timing and allowthe capacity to be adjusted to any value between the full capacity and some min-imum capacity.

Various schemes are available to unload an end of a reciprocating compressorcylinder. These reduce the capacity of that end to zero. With a single cylinder perstage, double acting compressor, this gives three-step control. The compressor canbe run at approximately 0, 50 or 100% capacity. If there are more than one cylinderper stage, additional steps can be arranged. For example, if a stage has two identicaldouble acting cylinders and each end of each cylinder has the same clearance, thenfive-step control can be achieved. The compressor will run at 0, 25, 50, 75 or 100%capacity. If the various ends have different clearances or swept volumes, then ad-ditional steps are available. In multi-stage units, the first stage usually controls thecapacity of the complete machine, but if only the first stage is unloaded, the inter-stage pressures will be greatly changed and the design limits of one of the higherstage cylinders will probably be exceeded. It is usually necessary to unload allstages. It is also essential that the degrees of reversal be checked on any cylinderthat is unloaded as reversal can easily be lost by unloading a cylinder end. There

COMPRESSOR PERFORMANCE—POSTIVE DISPLACEMENT 2.7

may also be limitations on how long a cylinder can be run completely unloadedwithout excessive heat build-up, or problems associated with a build-up of lubri-cating oil or process liquids in the cylinder. During normal operation, liquids thatget into the cylinder in small quantities are passed through the discharge valveswith the process gas.

Three methods are in common use to unload a cylinder end. They all work byconnecting the cylinder to the suction passage so gas flows back and forth betweenthe cylinder and suction passage rather than getting compressed. It is essential thatsufficient area for the flow is provided. If it is not, the losses will be high and aswell as consuming unnecessary power, the cylinder will overheat. If a compressoris to be run at a constant capacity less than full load for an extended time, thecompressor can be shut down and the suction valves removed. This gives verylow loss and hence very low heat build up. It requires no additional equipment,but the compressor must be shut down and worked on whenever the load must bechanged. If the load step must be changed while the compressor is running, eitherfinger unloaders (valve depressors) or plug or port unloaders can be used. Atypical finger unloader arrangement is shown as Fig. 2.3. The fingers are usuallyoperated pneumatically. To unload the cylinder, the fingers push the moving ele-ments in the valve away from their seat, thus opening the valve and holding it openthroughout the cycle. To get sufficient flow area, it is usually necessary to providean unloader for every suction valve. If it is arranged that the fingers move in andout for each compressor cycle, and if these movements are timed to delay theclosing of the valve by a varying amount, then the capacity of the cylinder end canbe varied between full and zero capacity. Typical plug or port unloaders are shownon Fig. 2.4. With these, a hole between the cylinder and the suction passage isopened when the end is to be unloaded. With a port unloader, one of the suctionvalve ports is used for an unloading plug rather than a valve. In some cases,removing a suction valve causes an unacceptable decrease in efficiency, and a plugunloader is used. In this, a special suction valve with a hole in its center is used.When the cylinder is loaded, this hole is sealed, and when it is unloaded, the holeis opened to allow flow between the cylinder and suction passage. The plug or portunloaders are usually operated pneumatically.

If it is necessary to reduce the flow in a cylinder end to some value greater thanzero, a clearance pocket can be used, Fig. 2.5. This is an additional volume thatcan be connected to the cylinder, or isolated from it, by a pneumatically controlledvalve very similar to that used for a port or plug unloader. When the cylinderclearance volume is increased by opening the clearance pocket valve, the cylinderwill compress a reduced amount of gas. In some cases, the volume of the clearancepocket is varied with a sliding piston. This allows any capacity within the rangeof the unloader to be selected. The required volume of the clearance pocket willdepend on the amount of capacity reduction required, the size of the cylinder andthe pressure ratio. If the pressure ratio is low, a very large pocket will be requiredto give a small reduction in capacity. In a larger cylinder, it is possible to fit severalfixed volume clearance pockets in one end of the cylinder. This allows a numberof different capacity steps to be used. If pockets are used on both ends of the

2.8 CHAPTER TWO

FIGURE 2.3 Finger unloader.

COMPRESSOR PERFORMANCE—POSTIVE DISPLACEMENT 2.9

FIGURE 2.4a Port unloader.

2.10 CHAPTER TWO

FIGURE 2.4b Plug unloader.

COMPRESSOR PERFORMANCE—POSTIVE DISPLACEMENT 2.11

FIGURE 2.5 Clearance pocket.

2.12 CHAPTER TWO

cylinder, and on all cylinders if there are multiple cylinders on the stage, a largenumber of different capacity steps can be provided. It is important to check thecompressor operation carefully at every possible unloaded condition to ensure thatall cylinders operate within their design limits with acceptable discharge pressures,rod loads and degrees of reversal.

2.1.5 Compressor Performance

The performance, that is the capacity (mass of gas compressed) and the powerrequired to compress the gas, is affected by many details of the compressor’sdesign. Several of these are discussed below. They are discussed first with referenceto a reciprocating compressor, and then with reference to a screw compressor. Thelosses in other types of positive displacement compressors will be similar to thosediscussed here. All types of compressors have losses caused by flow losses, by heattransfer, and by leakage from the high pressure to the low pressure zone and sometypes have losses associated with the valves.

2.2 RECIPROCATING COMPRESSORS

2.2.1 Compressor Valves

The compressor valves are the most critical component in a reciprocating com-pressor because of their effect on the efficiency (horsepower and capacity) andreliability of the compressor. Compressor valves are nothing more than checkvalves, but they are required to operate reliably for about a billion cycles, withopening and closing times measured in milliseconds, with no leakage in the reverseflow direction and with low pressure loss in the forward flow direction. To makematters worse, they are frequently expected to operate in highly corrosive, dirtygas, while covered in sticky deposits.

Compressor valves affect performance due to the pressure drop caused by flowthrough the valve; the leakage through the valve in the reverse direction; and thefact that the valves do not close exactly when an ideal valve would. Typical valvedynamics are shown in Fig. 2.6. Note that: a) due to its inertia, the valve does notopen instantaneously; b) due to the springing, the valve does not stay at full liftfor the full time it is open; and c) the valve does not close exactly at the deadcenter. All of these factors affect both the capacity and the power of the compressor.

A simple method of calculating the power loss due to the pressure drop acrossthe valve was given in the section on theory (Chapter 1). However, this assumedthat the valve was at full lift for the entire time gas was flowing through it. For amore accurate estimate of the power loss, the weighted average valve lift shouldbe used. This can be calculated from the valve lift diagram, Fig. 2.6. Obviously,the average lift is less than the full lift and so the average valve flow area is lessthan the full lift flow area. Thus the actual power loss is greater than that calculated

COMPRESSOR PERFORMANCE—POSTIVE DISPLACEMENT 2.13

FIGURE 2.6 Typical valve dynamics diagram.

by the method given under ‘‘Theory.’’ Fortuitously, that method also contains anerror that makes it overestimate the power loss and in many cases it gives a goodestimate of the true loss. One assumption of that method is that the gas is incom-pressible. That is, it is assumed that at valve opening, the pressure loss increasesinstantaneously to the value calculated from the piston velocity. In fact, due to thecompressible nature of the gas and as shown in Fig. 2.7, the pressure drop risesgradually from zero at the instant the valve opens. As the valve takes a finite timeto open because of its inertia, the pressure drop, after initially being less than thatestimated by the simple theory, then overshoots. These effects, taken with the factthat the valve starts to close well before the end of the stroke, cause offsettingerrors.

The power losses caused by the valves are well known. The effects of the valveson the capacity of the compressor are less obvious, but equally important. Thevalves affect the capacity in three ways.

1. As the valves never close exactly at the dead center, the amount of gas trappedin the cylinder is never that predicted from simple theory. The springs in acompressor valve should be designed to close the valve at about the dead center.In practice, the exact closing angle will vary as the conditions of service vary

2.14 CHAPTER TWO

FIGURE 2.7 Valve opening and closing.

and will depend on how strongly the moving parts of the valve adhere to theirstops. This will depend on the amount and nature of liquids and deposits on thevalve. For the suction process, the cylinder volume when the valves close issmaller than the maximum cylinder volume so less gas is trapped in the cylinderand compressed. Note that either too heavy a spring, which causes the valve toclose early, or too light a spring which causes the valve to close late, will reducethe capacity. For the discharge process, the cylinder volume when the valvecloses is larger than the minimum cylinder volume, and the mass of gas is largerthan the ideal. This extra gas is re-expanded to suction conditions instead ofbeing discharged at high pressure.

2. The gas is heated by the loss associated with flow through the suction valve.This causes the gas trapped in the cylinder when the valve closes to be at atemperature higher than the suction gas temperature. Thus the density is reducedand less gas is trapped in the cylinder to be compressed. The temperature risecan be discussed with reference to Fig. 2.8. Consider a particle of suction gasat condition ‘‘s’’ throttled through the suction valve to condition ‘‘5’’, the pres-

COMPRESSOR PERFORMANCE—POSTIVE DISPLACEMENT 2.15

FIGURE 2.8 Effect of valve loss on capacity.

sure in the cylinder at that time. From the steady flow energy equation, with nowork done and any heat transfer neglected, this is a process at constant enthalpy.For an ideal gas, it will be at constant temperature. As the piston slows downtowards the end of the stroke, the valve pressure drop declines and the pressurein the cylinder increases. The particle of gas we are considering is compressedisentropically from condition ‘‘5’’ to condition ‘‘1’’ with consequent temperaturerise.

3. The valve pressure drop, if it is large, can directly affect the capacity loss. Thisoccurs if the valve equivalent area is so small relative to the application that thegas cannot flow in through the suction valves fast enough to fill the cylinder.The pressure at the end of the suction stroke will then be less than the suctionpressure and the amount of gas compressed will be reduced.

2.2.2 Passage Losses

The valve losses as discussed above are always considered when predicting com-pressor performance. The additional loss caused by the pressure drop resulting fromthe flow through the remainder of the cylinder are often ignored, although they canbe comparable in magnitude to the valve losses. Over the years, the equivalent areaof the valves has been increased and the effects of the other flow losses havebecome more important. These losses typically occur in three places. First, to de-crease clearance volume, the cylinder is frequently designed so there is only asmall passage through which the gas can flow to get from the suction valves into

2.16 CHAPTER TWO

FIGURE 2.9 Typical pressure–volume diagram with pulsations.

the cylinder, and from the cylinder to the discharge valves. Second, the componentsused to hold the valves in the cylinder and any unloading devices may restrict theflow. Third, there will be losses in the cylinder passages that conduct the gasbetween the valves and the cylinder flanges.

These losses affect the compressor performance—power and capacity—in ex-actly the same way as valve losses.

2.2.3 Pulsation Losses

In the above discussion, we have assumed that the pressure in the cylinder varies,but that the pressure on the line side of the valves is constant. In practice, due tothe unsteady nature of the flow entering or leaving the compressor cylinder, thereare pulsations in the piping to and from the cylinder. The form and amplitude ofthese pulsations depends on the cylinder, the valves and the piping. Methods forcalculating the pulsations are given in Chapter 1 and a typical result is shown asFig. 2.9. The details of the pulsations depend on the complete piping system, butas a first approximation it can be assumed that the cylinder is connected by anozzle to a reservoir at constant pressure. Considering the suction process first.The pressure in the suction passage of the cylinder will usually fall as the valveopens and gas starts flowing into the cylinder. The duration of this reduced pressurewill depend on the length of the suction nozzle. If the nozzle is short, the pressurewill rapidly rise back to and will then oscillate about the suction pressure. If thenozzle is long, the pressure may stay lower than the suction pressure for the com-plete suction process. The reduced pressure has a similar effect to valve losses as

COMPRESSOR PERFORMANCE—POSTIVE DISPLACEMENT 2.17

far as the cylinder is concerned. That is more work required to draw the gas intothe cylinder. Similarly, for the discharge process, the pressure on the line side ofthe valve during the discharge process will be higher than the average dischargepressure and the power required to drive the compressor will be increased. Thepulsations also affect the capacity of the compressor by changing the pressure onthe line side of the valve at the instant the valve is closed. If the pressure in thesuction nozzle outside the valve is higher than the average suction pressure at theinstant the valve closes, the cylinder will contain more gas than expected and thecapacity will be increased. The power required will, of course, be increased pro-portionately. Conversely, if the pressure is lower the capacity will be decreased.Similar effects apply to the discharge process. In a real life system, the pulsationscan only be predicted by a detailed analysis and the compressor power and capacitymay each be either increased or decreased. However, as the energy to sustain thepulsations is provided by the compressor, it is not possible to use pulsations toincrease the efficiency. Any increase in capacity will require a corresponding in-crease in power.

2.2.4 Heat Transfer

Some compressor cylinders are cooled by liquid, usually water, some smaller cyl-inders are actively air cooled, and others are essentially uncooled with a smallamount of heat lost to the atmosphere. If the cooling liquid—water or oil—is mixedwith the compressed gas as it is in many screw compressors, the cooling can besufficient to make the compression nearly isothermal with resulting beneficial effecton the compression efficiency. While many reciprocating compressors run with adischarge temperature far below the isentropic discharge temperature, much of thecooling occurs in the discharge passages and the efficiency improvement is usuallysmall. In most cases the cooling is used to reduce part temperatures to decreasewear, especially of plastic parts; prevent distortion caused by uneven componenttemperatures; and reduce lubricating oil degradation.

Calculating the effects of heat transfer is difficult and imprecise. The magnitudeof the effects must usually be determined by testing.

The most important effect of heat transfer on performance in most compressorsis the heating of the suction gas as it flows through the suction passage, the suctionport and the valves. This is equivalent to increasing the suction temperature. Itdecreases the mass flow compressed, because the gas density is reduced, withoutchanging the required power significantly. The compression efficiency is thereforereduced.

Dynamic heat transfer in the cylinder of a positive displacement compressormust also be considered. The cylinder walls and the piston will run at a temperaturebetween the suction and discharge temperatures and this temperature will be closeto steady even though the gas temperature varies through the cycle. The temperatureof the cylinder wall will not be uniform. It will be higher close to the dischargevalves and lower close to the suction valves. Details of the temperature distributionwill depend on the cylinder design and the cooling. During the suction process,

2.18 CHAPTER TWO

FIGURE 2.10 Effect of valve and passage flow losses.

FIGURE 2.11 Effect of valve spring preload.

COMPRESSOR PERFORMANCE—POSTIVE DISPLACEMENT 2.19

FIGURE 2.12 Effect of packing leakage.

FIGURE 2.13 Effect of suction valve leakage.

2.20 CHAPTER TWO

FIGURE 2.14 Effect of discharge valve leakage.

FIGURE 2.15 Effect of piston ring leakage.

COMPRESSOR PERFORMANCE—POSTIVE DISPLACEMENT 2.21

FIGURE 2.16 Effect of internal heat transfer.

FIGURE 2.17 Effect of passage pulsations.

2.22 CHAPTER TWO

heat will be transferred from the cylinder wall to the gas, increasing the gas tem-perature. This will decrease the mass of gas trapped in the cylinder at the end ofthe stroke and hence will reduce the capacity. Note that the power will be approx-imately unchanged by this and so the efficiency will be reduced.

Heat transfer during the compression stroke also affects the compressor per-formance. During the first part of the compression, the cylinder wall is hotter thanthe gas so heat is transferred to the gas, increasing its temperature and pressure.During the second part of the compression, heat is transferred from the gas to thecylinder wall. This decreases the temperature and the pressure. The relative mag-nitude of these two effects depends on the effectiveness of the cylinder cooling.However as the gas in the cylinder spends more time at or near suction temperaturethan it does at or near discharge temperature, the average cylinder wall is usuallycloser to suction than discharge temperature, and the net effect of heat transferduring compression is to reduce the temperature and the power requirement. Thecapacity is slightly reduced by the heat transfer to the cylinder wall as the amountof gas remaining in the cylinder at the end of the discharge process is slightlyincreased by the lower temperature resulting from the cooling.

2.2.5 Leakage

All compressors have sliding seals between high and low pressure zones. Thesealways leak to some extent which always has a negative effect on compressionefficiency. In reciprocating compressors, the usual leakage paths are through thepiston rings, the rod packing of double acting compressors, and the valves, whichdo not seal perfectly against reverse flow.

The effects of leakage through the rod packing on double acting compressorsand through the piston rings of single acting compressors are easily understood.Some gas that has been at least partially compressed leaks to the atmosphere or aflare line. The power used to compress this gas is wasted and the capacity atdischarge is reduced by the amount of the leakage.

Leakage through a suction valve has a double effect. In addition to the lossdescribed for packing leakage, suction valve leakage causes hot gas to enter thesuction passage. This is equivalent to heat transfer to the suction gas and has thesame negative effect on capacity and efficiency. The change in power is usuallysmall, but may act to reduce the power due to the reduced pressure during thecompression process. In most cases, the heating effect causes greater losses thanthe direct effect.

Discharge valve leakage has the direct effect of wasting gas that has alreadybeen compressed, thus decreasing the flow without any decrease in the power. Italso increases the pressure in the cylinder during the compression process, thusincreasing the power requirement. In addition, the gas that leaks during the expan-sion and suction processes will heat the gas in the cylinder and reduce the capacityby decreasing the trapped gas density.

Piston ring leakage in a double acting cylinder is a little more complex. Gasleaks into each end of the cylinder during the low pressure part of the cycle and

COMPRESSOR PERFORMANCE—POSTIVE DISPLACEMENT 2.23

out of the end during the high pressure part of its cycle. In all cases, some of thework that has been done on the gas is wasted as it must be recompressed. Inaddition, the gas always heats the gas in the end it leaks into. A large amount ofthe leakage into an end occurs during the suction process. Thus the heating de-creases the trapped gas density and decreases the capacity.

2.2.6 Examples

The results of some calculations in which the compression is ideal except for asingle loss mechanism are given as Figs 2.10 to 2.17.* Each diagram shows theeffect of the loss mechanism on the pressure volume cards and the effect on thepower requirement and the capacity. The magnitude of the losses has been fixedat a high value so the effects can be clearly seen. The reader should be able topredict the shape of the pressure volume cards with the losses from the abovediscussion and an understanding of the processes involved.

It has been common for people to measure the volumetric efficiency of thepressure volume card. This is only adequate as a way to measure capacity in acompressor with no leakage or heating effects. As an illustration of this considerthe example with discharge valve leakage. From the pressure volume card it wouldappear that the volumetric efficiency is increased by the leakage, whereas in factthe capacity is decreased by 40%. In contrast, the power required can be calculatedaccurately from the pressure volume card.

2.3 SCREW COMPRESSORS

2.3.1 Port and Passage Losses

Screw compressors do not rely on suction and discharge valves to regulate the flowof gas through the compressor, therefore the valve loss equations typically used forreciprocating compressors do not apply. However, a series of alternate factors needto be examined. Typically, gas is moved through a screw compressor via portsmachined in the compressor housing. The design and location of these ports iscrucial to the overall efficiency of the machine. The inlet port must be sized sothat entrance flow losses are minimized. The same can be said of exit losses at thedischarge port. However, with regards to the discharge port, the most critical factoris its location. As with any positive displacement compressor, pressure is increasedby steadily decreasing the volume of the gas trapped in the compression chamber.Since there are no discharge valves, the compression process continues until thedischarge port is uncovered. Therefore, given a fixed port location, the compressoralways compresses to the same volume ratio. If the discharge port is not properly

2.24 CHAPTER TWO

located, inefficiencies can occur. The time to reach pressure is a function of thegas properties, namely the isentropic volume exponent. If the discharge port islocated early in the compression phase, the port uncovers before the gas has reachedthe proper discharge pressure. This means the pressure downstream of the com-pressor will leak back into the groove and reduce the overall volumetric efficiency.Alternately, if the discharge port is located late in the compression phase, dischargepressure is reached too soon, thus causing an overcompression of the gas whichwastes power. This loss is evident in the isentropic efficiency. Compressor manu-facturers utilize various means to locate the discharge port properly and maintainpeak compressor efficiency.

2.3.2 Heat Transfer Effects

Unlike a reciprocating compressor, screw compressors have the ability to compressup to 20 compression ratios in a single stage. This feature is achievable because asignificant amount of coolant is injected into the compression chamber during thecycle. The heat transfer effects between the gas and the coolant allow much higherpressure ratios without the penalty of extremely high discharge temperatures. Thecompression horsepower relationship is represented as:

Power Input � m h � m hgas gas coolant coolant

where

mgas � Mass Flow Rate of Gashcoolant � Specific Enthalpy Rise of Coolantmcoolant � Mass Flow Rate of Coolant

hgas � Specific Enthalpy Increase of Gas

Screw performance is balanced by a two-fold effect. If there is an increase in thevolume of coolant injected into the compression chamber, the effective volume leftfor the gas is reduced. This, in theory, reduces the capacity. However, the increasein the amount of coolant helps lower the discharge temperature, thereby producingnear isothermal compression which improves the compressor isentropic efficiency.Both factors are modeled in screw performance prediction.

2.3.3 Pulsation Effects

Screw compressors are subjected to the same effects of piping pulsation as recip-rocating compressors yet at much higher frequencies. As with reciprocating com-pressors, piping leading to and from the compressor must be sized properly, i.e.proper lengths and diameters. Typical screw machines operate at 3600 rpm. De-pending on the type of screw, compression occurs six to 12 times per revolution.Therefore, higher frequencies are important in their effect on performance.

COMPRESSOR PERFORMANCE—POSTIVE DISPLACEMENT 2.25

2.3.4 Leakage Effects

The leakage paths for a screw compressor differ from those for a reciprocatingcompressor in that instead of valves, rings and packing, a screw compressor reliessolely on tight running clearances to establish sealing. In a screw compressor, themost significant leakage occurs at

1. The interaction between the meshing rotors

2. The clearance between the rotors and the compressor housing

The impact of these leak paths must be determined to accurately predict screwcompressor performance. The leakage is reduced in an oil- or water-flooded com-pressor by the sealing effect of the liquid.

In a screw machine, compression is the result of two rotating rotors meshing,thereby reducing a volume in the groove of one rotor as part of the other rotormoves in the groove. Tight clearances must be used to maintain the increasedpressure in the groove. If the clearance between the two rotors is large, pressurizedgas will flow back to a low pressure zone. In a typical screw design, this usuallymeans back to suction. This loss will cause a decrease in volumetric efficiency orcapacity.

The potential leakage between the rotors and the housing is harder to quantifyin terms of performance loss. The main rotor lobe has two edges, the leading andtrailing edges. The leading edge faces the discharge pressure zone, while the trailingedge faces the suction pressure zone. Leakage occurs from the leading edge to thetrailing edge. This means that during the compression cycle, the gas in the groovecan leak back to the next groove in the screw since it is at lower pressure, andreceive higher pressure gas from the groove that precedes it. These two effects donot cancel each other out. They are the direct effect of the running clearancebetween the rotor and the housing. The performance effects are two fold. Sincegas is constantly being transferred from one groove to another, this becomes a fixedflow loss. Similarly, since the machine needs to recompress already worked gas,this becomes a fixed power loss. It is important to determine the effect of theseleakages to determine the overall efficiency of the unit.

2.4 ALL COMPRESSORS

2.4.1 Friction

All compressors have sliding parts in the various bearings and seals. Additionalpower is required to overcome the friction. Any friction that occurs in componentsexposed to the gas will tend to heat the gas. Depending on the point in the cycleat which the heating occurs, this may, or may not, have a significant effect on thecapacity.

3.1

CHAPTER 3COMPRESSOR PERFORMANCE—DYNAMIC

Paolo BendinelliTurbocompressors Chief EngineerNuovo Pignone

Massimo CamattiTurbocompressors Design ManagerNuovo Pignone

Marco GiachiTurbocompressors R&D ManagerNuovo Pignone

Eugenio RossiTurbocompressors ResearcherNuovo Pignone

LIST OF SYMBOLSA � Area� � Absolute flow angleb � Blade height� � Relative flow angle

�b � Blade angleB � Blockage factorC � Absolute velocity module

C� � Absolute velocity tangential componentCm � Absolute velocity meridian componentCP � Specific heat at constant pressure or pressure recovery coefficientD � Diameter or diffusion factor� � Deviation angleE � Kinetic energy� � Flow coefficienth � Enthalpy

h0 � Total enthalpy

3.2 CHAPTER THREE

H � LoadK � Loss coefficient based on total pressurei � Incidence angle

�0 � Viscosity at reference condition� � Total pressure recovery coefficientm � Mass flow rateM � Mach number

MU � Peripheral Mach numbern � Polytropic exponentN � Rotational speed (rpm)� � EfficiencyQ � Heat exchange or volumetric flow rate � Ratio between heat values of the gas � Density

0 � Total densityp � Pressure� � Load coefficientp0 � Total pressurer � radiusR � Gas constant

Re � Reynolds number� � Slip factor � Torque or working factorT � Static temperature� � Blade deflection angle

T0 � Total temperatureU � Tip speedVS � Absolute tangential velocity effect� � Rotational speed (rad/s)Z � Compressibility factor or blade number

W � Relative velocityWA � Friction losses

3.1 GENERAL DESCRIPTION OF A CENTRIFUGAL

COMPRESSOR

A centrifugal compressor is a ‘‘dynamic’’ machine. It has a continuous flow offluid which receives energy from integral shaft impellers. This energy is trans-formed into pressure—partly across the impellers and partly in the stator section,i.e., in the diffusers. This type of machine is composed (see Fig. 3.1) of an outercasing (A) which contains a stator part, called a diaphragm bundle (B), and of arotor formed by a shaft (C), one or more impellers (D), a balance drum (E), andthrust collar (F).

COMPRESSOR PERFORMANCE—DYNAMIC 3.3

FIGURE 3.1 Sectional view of centrifugal compressor schematic.

The rotor is driven by means of a hub (G) and is held in position axially by athrust bearing (I), while rotating on journal bearings (H). The rotor is fitted withlabyrinth seals (L) and, if necessary, oil film end seals (M).

Gas is drawn into the compressor through a suction nozzle and enters an annularchamber (inlet volute), flowing from it towards the center from all directions in auniform radial pattern (see Fig. 3.2). At the opposite side of the chamber from thesuction nozzle is a fin to prevent gas vortices.

The gas flows into the suction diaphragm and is then picked up by the firstimpeller (see Fig. 3.3).

The impellers consist of two discs, referred to as the disc and shroud, connectedby blades which are shrunk onto the shaft and held by either one or two keys. Theimpeller pushes the gas outwards raising its velocity and pressure; the outlet ve-locity will have a radial and a tangential component (see section 3.7 for furtherdetails). On the disc side, the impeller is exposed to discharge pressure (see Fig.3.4) and on the other side partly to the same pressure and partly to suction pressure.Thus a thrust force is created towards suction.

The gas next flows through a circular chamber (diffuser), following a spiral pathwhere it loses velocity and increases pressure (similar to fluid flow through con-duits). The gas then flows along the return channel; this is a circular chamber

3.4 CHAPTER THREE

FIGURE 3.2 Qualitative view of the flow in the volute.

FIGURE 3.3 First stage sectional view.

bounded by two rings that form the intermediate diaphragm, which is fitted withblades (see Fig. 3.5) to direct the gas toward the inlet of the next impeller. Theblades are arranged to straighten the spiral gas flow in order to obtain a radial outletand axial inlet to the following impeller. The gas path is the same for each impeller.

Labyrinth seals are installed on the diaphragms to minimize internal gas leaks(see Fig. 3.5). These seals are formed by rings made in two or more parts. Thelast impeller of a stage (the term stage refers to the area of compression betweentwo consecutive nozzles) sends the gas into a diffuser which leads to an annular

COMPRESSOR PERFORMANCE—DYNAMIC 3.5

FIGURE 3.4 Pressure distribution on the impeller.

FIGURE 3.5 Labyrinth seals and diaphragms.

chamber called a discharge volute (see Fig. 3.6). The discharge volute is a circularchamber which collects the gas from the external boundary of the diffuser andconveys it to the discharge nozzle. Near the discharge nozzle there is another finwhich prevents the gas from continuing to flow around the volute and directs it tothe discharge nozzle (see Fig. 3.7).

The balance drum (E) is mounted on the shaft after the end impeller (see Fig.3.1). It serves to balance the total thrust produced by the impellers. Having endimpeller delivery pressure on one side of the drum, compressor inlet pressure isapplied to the other by an external connection (balancing line, see Fig. 3.8). In thisway, gas pressures at both ends of the rotor are roughly balanced. To get evencloser pressure levels and, therefore, the same operating conditions for the shaft-

3.6 CHAPTER THREE

FIGURE 3.6 Last impeller of astage.

FIGURE 3.7 Discharge volute: qualitative view of the flow.

COMPRESSOR PERFORMANCE—DYNAMIC 3.7

FIGURE 3.8 External connection of the oil system.

end oil seals, another external connection is made between the balancing chambers(balancing line, see Fig. 3.8).

The gas chambers are positioned outside the shaft-end labyrinths. They are con-nected to achieve the same pressure as that used as reference for the oil seal system(see Fig. 3.8 for a block diagram). In special cases, when the seal oil and processgas have to be kept separate, inert gas is injected into the balancing chamber (buffergas system) at a pressure that allows it to leak both inwards and outwards forminga seal.

3.2 CENTRIFUGAL COMPRESSORS TYPES

Centrifugal compressors may have different configurations to suit specific servicesand pressure ratings. They may be classified as follows:

3.2.1 Compressors with Horizontally-split Casings

Horizontally-split casings consisting of half casings joined along the horizontalcenter-line are employed for operating pressures below 60 bars.

The suction and delivery nozzles as well as any side stream nozzles, lube oilpipes and all other compressor-plant connections are located in the lower casing.With this arrangement all that is necessary to raise the upper casing and gain accessto all internal components, such as the rotor, diaphragms and labyrinth seals is toremove the cover bolts along the horizontal center-line.

3.8 CHAPTER THREE

FIGURE 3.9 Horizontally-split casing.

Horizontally-split casing compressors may be further identified according to thenumber of stages.

• Multistage compressors with one compression stage only (Fig 3.9).

• Multistage compressors with two compression stages. The two compressionstages are set in series in the same machine. Between the two stages, cooling ofthe fluid is performed in order to increase the efficiency of compression.

• Multistage compressors with more than two compression stages in a single cas-ing. As a rule they are used in services where different gas flows have to becompressed to various pressure levels, i.e., by injecting and/or extracting gasduring compression.

• Sometimes compression stages are arranged in parallel in a single casing. Thefact that both stages are identical and the delivery nozzle is positioned in thecenter of the casing makes this solution the most balanced possible. Moreover, adouble flow is created by a common central impeller (see Fig. 3.12).

3.2.2 Compressors with Vertically-split Casings

Vertically-split casings are formed by a cylinder closed by two end covers: hencethe denotation ‘‘barrel,’’ used to refer to compressors with these casings. Thesemachines, which are generally multistage, are used for high pressure services (up

COMPRESSOR PERFORMANCE—DYNAMIC 3.9

FIGURE 3.10 Multistage two phase compressor.

FIGURE 3.11 Multistage three phase compressor.

3.10 CHAPTER THREE

FIGURE 3.12 Two phase compressor with a central double flow impeller.

FIGURE 3.13 Barrel type compressor with one compression phase.

to 700 kg/cm2). Inside the casing, the rotor and diaphragms are essentially thesame as those for compressors with horizontally-split casings.

• Barrel type compressors which have a single compression stage

• Barrel type compressors with two compression stages in series in a single casing

COMPRESSOR PERFORMANCE—DYNAMIC 3.11

FIGURE 3.14 Barrel type compressor with two compressionphases.

• Compressors which incorporate two compression stages in parallel in a singlecasing

3.2.3 Compressors with Bell Casings

Barrel compressors for high pressures have bell-shaped casings and are closed withshear rings instead of bolts (see Fig. 3.15).

3.2.4 Pipeline Compressors

These have bell-shaped casings with a single vertical end cover. They are generallyused for natural gas transportation (see Fig. 3.16). They normally have side suctionand delivery nozzles positioned opposite each other to facilitate installation on gaspipelines.

3.2.5 SR Compressors

These compressors are suitable for relatively low pressure services. They have thefeature of having several shafts with overhung impellers. The impellers are nor-mally open type, i.e., shroudless, to achieve high tip speeds with low stress levelsand high pressure ratios per stage. Each impeller inlet is coaxial whereas the outletis tangential. These compressors are generally employed for air or steam compres-sion, geothermal applications etc. (see Fig. 3.17.).

3.12 CHAPTER THREE

FIGURE 3.15 High pressure barrel type compressor.

FIGURE 3.16 Pipeline compressor.

3.3 BASIC THEORETICAL ASPECTS

3.3.1 Preliminary Definitions

The term turbomachinery is used to indicate systems in which energy is exchangedbetween a fluid, evolving continuously and in a clearly determined quantity, and amachine equipped with rotary blading.

COMPRESSOR PERFORMANCE—DYNAMIC 3.13

FIGURE 3.17 SR type compressor.

Turbomachines can be classified as:

• Process machines, in which the machine transfers energy to the fluid

• Drivers, in which the machine receives energy from the fluid

An initial classification of turbomachines may be made on the basis of thepredominant direction of the flow within the machine:

• Axial machines, in which the predominant direction is parallel to the axis ofrotation

• Radial machines, in which the predominant direction is orthogonal to the axis,although portions of the flow may have an axial direction

• Mixed machines, where the situation is intermediate between the described above

Turbocompressors (more briefly, compressors) constitute a special category ofprocess machines. They operate with compressible fluids and are characterized byan appreciable increase in the density of the fluid between the first and the lastcompression stages. The compression process is frequently distributed among sev-eral stages, a term used to indicate an elementary system composed of mobileblading, in which the fluid acquires energy, and fixed blading, in which the energyis converted from one form to another.

3.14 CHAPTER THREE

FIGURE 3.18 Entropy-enthalpy diagram of a compression process.

3.3.2 The Compression Process

Consider Fig. 3.18, which represents a generic compression process in the Mollierplane (enthalpy-entropy) taking place in a single compressor stage. The fluid, takenin determined conditions p00 and T00, is subsequently accelerated up to the inlet tothe stage where it reaches the conditions defined by thermodynamic state 1. Theacceleration process is accompanied by dissipation phenomena linked to the in-crease in speed of the fluid. In flowing along the rotor the fluid undergoes a trans-formation that brings it to the conditions p2 and T2. During this phase there is anincrement in potential energy per mass unit of fluid given by:

�E � h � h (3.1)P,1–2 2 1

and an increment in kinetic energy per mass unit of fluid given by:

2 2C C2 1�E � � (3.2)K,1–2 2 2

The entropy of the fluid, as it flows through the stage, increases as a consequenceof the dissipation processes involved in compression. In the stator part the kineticenergy of the fluid is converted into potential energy. The total enthalpy for state4 can thus be evaluated as:

2C4h � h � (3.3)0,4 4 2

The fluid then leaves the stage in the conditions defined by state 4, with residualvelocity C4.

COMPRESSOR PERFORMANCE—DYNAMIC 3.15

3.3.3 Basic Quantities of Compression Process

The basic quantities utilized to quantify the exchanges of energy in compressorsare given below. Note that the quantities indicated apply both to complete com-pressors and to individual stages. It is also assumed that the thermodynamic char-acteristics of the fluid are represented by the perfect gas model.

Effective Head. The effective head HR is defined as the effective work exchangedbetween blading and fluid per mass unit of fluid processed:

H � � dp / (3.4)Rp1

We also have

H � (h � h ) � Q (3.5)R 04 01 EXT

In the hypothesis of adiabatic conditions QEXT � 0 and we further obtain:

H � (h � h ) (3.6)R 04 01

Polytropic Head. The polytropic head HP is defined as the energy per mass unitaccumulated by the fluid under the form of increment in potential energy; it isexpressed by:

H � � dp / (3.7)Pp1

in which the relationship between pressure and density is expressed in the form

�np � cos tan te (3.8)

where n represents the mean exponent of polytropic transformation between thetwo states 1 and 2. Polytropic head can thus be expressed by the following formula:

(n�1 / n)n p04H � Z RT � 1 (3.9)� �P 0 00n � 1 p00� �Isentropic Head. Isentropic head is defined as the energy per mass unit accu-mulated by the fluid subsequent to a reversible (and thus isentropic) adiabatic trans-formation between states 1 and 2. This gives the following equation:

H � � dp / (3.10)Sp0

with

3.16 CHAPTER THREE

�p � cos tan te (3.11)

in which constitutes the ratio between the specific heat values of the gas.

(�1 / ) p04H � Z RT � 1 (3.12)� �S 0 00 � 1 p00� �

Polytropic Efficiency. The polytropic efficiency is defined as the ratio betweenpolytropic head HP and effective head HR necessary to effect compression betweenstates 0 and 4. Applying the preceding definition we obtain:

(n�1 / n)n p04Z RT � 1� �0 00n � 1 p� �00

HP� � � (3.13)P H (h � h )R 04 00

by developing the above equation we obtain:

n � 1� � (3.14)P (n � 1)

The polytropic head can be further rewritten in the form

( � 1)ln(p /p )04 00� � (3.15)P ln(T /T )04 00

Polytropic efficiency possesses the important property of being dependent onlyon the properties of the gas, the pressure, and temperature ratios. It is independentof the absolute pressure level from which the compression process starts.

Isentropic Efficiency. The isentropic efficiency is defined as the ratio betweenisentropic head HS and effective head HR associated with compression betweenstates 0 and 4. From this definition we obtain:

(�1 / ) p04Z RT � 1� �0 00 � 1 p00� �

HS� � � (3.16)S H (h � h )R 04 00

The isentropic efficiency can be rewritten as:

COMPRESSOR PERFORMANCE—DYNAMIC 3.17

θ1 θ2

FIGURE 3.19 The Euler turbomachinery equation.

(�1 / )p04 � 1� �p00� � (3.17)S T04 � 1� �T00

It may be stated that, for a compressor, the polytropic efficiency is always greaterthan the isentropic efficiency relevant to the same transformation.

3.3.4 Euler Equation for Turbomachines

With reference to Fig. 3.19, we may consider a rotor belonging to a generic tur-bomachine, taking into examination the conditions existing in section 1 (inlet) andsection 2 (discharge). Utilizing the equation of balance of momentum for the sta-tionary flow between two sections, it is possible to obtain:

� m(r C � r C ) (3.18)2 �2 1 �1

The work transferred through the blading per mass unit of fluid processed is thusgiven by:

W � � /m � �(r C � r C ) (3.19)x 2 �2 1 �1

The first principle of thermodynamics establishes that the work per mass unit isequal to, for an adiabatic flow, the variation in total enthalpy. We thus obtain:

�h � h � h � �(r C � r C ) � U C � U C (3.20)0,1–2 2 1 2 �2 1 �1 2 �2 1 �1

The above equation, known as the Euler equation, is one of the fundamentallyimportant equations for the study of turbomachines. Application of the Eq. 3.20shows that in a generic stage composed of a rotor and a stator, there is no transferof mechanical work outside of the rotary parts; in particular, then, the enthalpy of

3.18 CHAPTER THREE

the fluid does not change in traversing the stationary components, but only intraversing the rotary ones. Consequently it may be stated:

�h � h � h � h � h � U C � U C (3.21)0,1–4 04 00 02 00 2 �2 1 �1

and in the case of perfect gas:

�h � c (T � T ) � �h � c (T � T ) (3.22)0,1–4 P 04 02 0,1–2 P 02 01

The total temperature is thus constant throughout the stationary components.

3.3.5 Dimensionless Parameters

The behavior of a generic stage can be characterized in terms of dimensionlessquantities which specify its operating conditions as well as its performance. Thedimensionless representation makes it possible to disregard the actual dimensionsof the machine and its real operating conditions (flow rate and speed of rotation)and is thus more general as compared to the use of dimensional quantities.

The number of dimensionless parameters necessary and sufficient to describethe characteristics of a stage is specified by Buckingham’s theorem, which is alsoused to determine their general form. The dimensionless parameters used to de-scribe the performance of axial and centrifugal compressors are given below.

Flow Coefficient. The flow coefficient for an axial machine is defined as the ratiobetween the axial velocity at the rotor inlet section and the tip speed of the blade

C1A� � (3.23)1 U2

For centrifugal machines the flow coefficient is defined as follows:

4Q� � (3.24)1 2�D U2 2

Both of these definitions can be interpreted as dimensionless volume flow rate ofthe fluid processed by the machine.

Machine Mach Number. The Mach number, MU, is defined as the ratio betweenthe machine tip speed and the velocity of sound in the reference conditions:

U U2 2M � � (3.25)U a �RT00 00

The Mach number can be interpreted as a dimensionless speed of rotation of themachine.

COMPRESSOR PERFORMANCE—DYNAMIC 3.19

Reynolds Number. The Reynolds number, Re, is generally defined as the ratiobetween inertial forces and viscous forces, evaluated in relation to assigned refer-ence conditions, acting on a fluid particle for the particular fluid-dynamic problemin question.

In the axial machine field, a frequently used formulation for the Reynolds num-ber is the following:

UDRe � (3.26)

� /00 00

For centrifugal machines the following formulation is frequently used:

U D2 2Re � (3.27)� /00 00

Specific Heat Ratio. The specific heat ratio is simply defined as the ratio betweenspecific heat at constant pressure and at constant volume for the gas in question:

CP � (3.28)

The specific heat ratio is used to take account of the thermodynamic properties ofthe fluid.

Coefficients of Work and of Head. The coefficient of work for an axial machineis defined as the ratio between the work per mass unit transferred by the bladingto the fluid and the square of the tip speed.

h � h C � C02 00 �2 �1� � � (3.29)2U U2 2

In the above formula, the Euler equation and the kinematic equality U1 � U2,valid in first approximation for an axial machine, have been introduced.

For a centrifugal machine an identical parameter is defined, which is howevercalled head coefficient . It is expressed by the following equation:

h � h U C � U C02 00 2 �2 1 �1 � � (3.30)2 2U U2 2

The two quantities defined above can be interpreted as dimensionless work permass unit transferred by the blading to the fluid.

Polytropic Efficiency. The same definition given in 3.3.3 is applied.

(n�1 / n)n p04Z RT � 1� �0 00n � 1 p� �00

HP� � � (3.31)P H (h � h )R 04 00

This formula applies to both centrifugal and axial machines.

3.20 CHAPTER THREE

β1

α1

m1c1u

cθ1

θ1wu1

w2w θ2β

m2c2α

θ2c

FIGURE 3.20 Velocity (speed) triangles for an axial compressor stage.

3.4 PERFORMANCE OF COMPRESSOR STAGES

3.4.1 General Information

In any one of the compressor stages, work is transferred by the rotary blading tothe fluid in modes depending on the geometry, the fluid-dynamic conditions andthe properties of the gas processed. The study of these energy interactions, gov-erned by the Euler Eq. (3.20), calls for analysis of the speed of the fluid in suitablesections of the stage. This analysis is usually carried out utilizing speed trianglesdetermined in suitable sections of the stage.

The quantity of energy absorbed by the compressor cannot be entirely convertedinto a pressure increment in the fluid due to dissipation phenomena of variouskinds involving the machine as a whole. Among these, the pressure drops directlyattributable to effects of aerodynamic type will be examined here.

Knowledge of the energy transfer and dissipation mechanisms in a stage providesthe necessary tools for understanding the factors that determine and influence itsperformance. These aspects are examined in the following paragraphs, along withthe representations normally utilized to describe performance.

3.4.2 Speed Triangles

In studying turbomachines the concept of speed triangles is frequently used torepresent the kinematic conditions, for both fluid and blade, existing at the inletand discharge sections of a generic fixed or rotary blading.

The speed triangles for an axial compressor stage are shown in Fig. 3.20. Notethat the absolute velocity C of the fluid in a given section of the stage is obtained

COMPRESSOR PERFORMANCE—DYNAMIC 3.21

c /um

tg + tg <01 2α β

2tg + tg >0α β1

tg + tg =02α β1

FIGURE 3.21 Loading coefficient vs. flow coefficient for an axialstage.

by combining a relative velocity W with a velocity U determined by the rotationof the blade. The absolute velocity C can be further broken down into an axialvelocity CA and a tangential velocity Cq.

The speed triangle on discharge from the rotor is characterized by the fact thatthe direction of the absolute velocity vector does not exactly coincide with thedirection indicated by the trailing edge of the blade. This phenomenon, termeddeviation, determines a reduction in the value of Cq in respect to the value thatcould be theoretically obtained in the case of null deviation.

Recalling the Euler equation and the definition of work coefficient, we maywrite:

h � h C � C02 00 �2 �1� � � (3.32)2U U2 2

With reference to the speed triangle in Fig. 3.20 and also considering the simpli-fying assumption that the flow can be considered incompressible between sections1 and 2, the formula for the work coefficient can be rewritten as follows:

CX� � U 1 � (tg� � tg� ) � U[1 � � (tg� � tg� )] (3.33)� �1 2 1 1 2U

The above equation shows that, in the further hypothesis that the direction offlow does not change from blade inlet to outlet, the relation between flow coefficientand work coefficient depends in linear manner on (tg�1 � tg�2) in the mode shownin Fig. 3.21. In the hypothesis of compressible flow and non-constant angles therelation is no longer linear but the qualitative description is still valid.

The speed triangles for a centrifugal stage are shown in Fig. 3.22 The physicalinterpretation of the quantities is the same as that of the axial machine, althoughthe meridian rather than the axial components of the quantities represented shouldbe taken into consideration. In centrifugal machines too the phenomenon of devi-

3.22 CHAPTER THREE

r1ir1

r1o

1α β1

θ1wθ1c1u

1wm1c1c

m12

c c22α

θ2

β2 1w

θ2cvs

FIGURE 3.22 Velocity triangles for a centrifugalstage.

ation, conventionally termed slip, can be observed, so that the relative velocity ondischarge from the impeller is not aligned with the direction of the blade.

The head coefficient for a centrifugal compressor can be expressed as follows:

h � h U C � U C U C cos � � U C cos �02 00 2 �2 1 �1 2 2 a 1 1 1 � � � (3.34)2 2 2U U U2 2 2

The dependency between the structural angle b2 and t can be expressed in explicitform by introducing the quantity:

C Q2m 2� � � (3.35)2 U �b D U2 2 2 2

called flow coefficient at the impeller discharge section. A quantity �, termed slipfactor, which takes account of the imperfect guiding action of the impeller, is alsointroduced; it may be defined as:

VS� � 1 � (3.36)U2

where the term VS represents the tangential velocity defect associated with the slipeffect.

Utilizing these definitions and hypothesizing inlet guide vane conditions null(Cq1 � 0), Eq. (3.32) is rewritten as:

COMPRESSOR PERFORMANCE—DYNAMIC 3.23

2β >0

φ2

(forward sweep)

(sweep)β =02

(back sweep)β <02

FIGURE 3.23 Loading coefficient vs. flow coefficient for a centrif-ugal stage.

C�2 � � � � � tg� (3.37)2 b2U2

The above equation is illustrated in Fig. 3.23, which is the equivalent of the onealready given for axial machines. For centrifugal compressors, geometries withstructural angles bb2 greater than zero (i.e., blades turned in the same direction asthat of rotation) are not utilized insofar as they generate high pressure drops. Radialblades or those turned in the direction opposite that of rotation up to bb2 values ofabout �60 degrees are normally used in common applications.

3.4.3 Conventional Representation of Pressure Drop in

Compressors

Pressure drops in compressors are conventionally divided into two main categories.

1. Pressure drop due to friction

2. Pressure drop due to incidence

These two phenomena are discussed in the following paragraphs.

Pressure Drop Due to Friction. These are dissipation terms associated with fric-tion phenomena between the walls of the ports of the machine (both rotor andstationary) and fluid flowing through it. In general, the flow in compressors ischaracterized by turbulence, so it can be considered that the energy dissipated isproportional, in first approximation, to the square of the fluid velocity and thus tothe square of the volume flow in inlet conditions. This energy is not transferred tothe fluid under the form of potential energy, but only under the form of heat.

3.24 CHAPTER THREE

inci

nce

los

constant mass flow rate

FIGURE 3.24 Typical airfoil losses distribution as a functionof incidence.

Accordingly, indicating by WA the work per mass unit associated with dissipationdue to friction, we may write:

2W � k Q (3.38)A A 00

where kA represents a suitable constant that takes account of the specific fluid-dynamic characteristics of the stage in question. In dimensionless terms this canbe expressed as:

2W � k � (3.39)A A 1

Pressure Drop Due to Incidence. With reference to the classic studies on bi-dimensional wing contours, it should be recalled that the pressure drop of a genericcontour, stated in relation to the incidence, follows a trend of the type shown inFig. 3.24. This distribution can be approximated with a parabolic law that presentsa minimum point at a certain incidence i*.

Although the behavior described here applies, strictly speaking, to wing contoursalone, it may be extended with reasonable accuracy to the blading of centrifugalmachines as well. It is thus possible to define, for a generic turbomachine blading,whether stationary or rotary, an optimum incidence condition, at which the pressureloss phenomena deriving from incidence are minimum.

This optimum incidence value depends on the geometry of the blade and on thespeed triangle immediately upstream of the blade leading edge. When the speed ofrotation and the geometry have been assigned, the speed triangle and the incidencesdepend only on the volume flow of the processed fluid.

Pressure drop due to incidence may therefore be expressed in the form:

2W � k (Q � Q* ) � k (3.40)I U 00 00 0

This equation can be expressed in dimensionless form:

COMPRESSOR PERFORMANCE—DYNAMIC 3.25

I N C I D E N C E L O S S E SA '

BC '

B ' F R I C T I O N L O S S E S

FIGURE 3.25 Losses breakdown as a function of the flow coefficient.

2WyI � k (� � �*) � k (3.41)U 1 1 0

The constants k0 and k1 are once again associated to the particular problem con-sidered.

Overall Pressure Drop. In going on to consider the overall pressure drop of acompressor stage, note that in general both of the above-mentioned contributionswill be present. The overall pressure loss can thus be represented as:

2 2W � W � W � k Q � k (Q � Q* ) � k (3.42)T I A A 00 U 00 00 0

or in dimensionless form:

2 2W � k � � k (� � �*) � k (3.43)T A 1 U 1 1 0

The above equation can be given significant graphic interpretation, as shown inFig. 3.25.

Curve A represents the evaluated relationship between flow coefficient and head,evaluated taking account of the effective deviation phenomena that occur in a realblading. Curve A thus represents all of the energy per mass unit that is transferredto the fluid and that is thus theoretically available to be converted under the formof pressure. This quantity is diminished by the dissipation associated with pressuredrop due to friction (curve B) and pressure drop due to incidence (curve C), bothexpressed by parabolic equations. Point C1 thus expresses the work which is ef-fectively contained in the fluid under the form of potential energy and kineticenergy for an assigned flow coefficient ƒ1.

From this analysis, it can be stated that, due to the shapes of the various curvesconsidered, the quantity defined above tends to present a maximum in coincidencewith a clearly determined value of ƒ1.

3.26 CHAPTER THREE

Other Pressure Drop Contributions. The description given in the preceding par-agraphs of subsection 3.4.3 provides a substantially correct illustration of the maineffects linked to pressure drop in a generic compressor and their influence onoverall performance. However, real compressors present dissipation effects, whichdo not fall within the simplified scheme of pressure drops due to incidence andpressure drops due to friction. In these cases, it is often necessary to classify thepressure drop contributions through detailed reference to the physical modes inwhich dissipation takes place.

For centrifugal machines the main effects of additional pressure drop are linkedto the presence of the blade tip and casing recess (in open machines), to ventilationphenomena between the rotating and stationary surfaces in the spaces between hubsand diaphragms, and to the presence of end seals and interstage seals. Furtherpressure drops can be attributed to the presence of separation areas in the impeller.

For axial machines, the representation of pressure drop is slightly different totake account of the different aerodynamic phenomena involved. One possible dis-tinction could be the following:

• Contour pressure drop. This is pressure drop deriving from the presence ofboundary layers which develop along the blade surfaces. It can be estimatedthrough the methods used for calculating turbulent boundary layers.

• Endwall pressure drop. Pressure drop of this kind depends on the presence oflocalized limit states on the casing surface or the compressor rotor. These effectsare usually evaluated through experimental correlations.

• Pressure drop due to impact. This term indicates phenomena of the dissipationtype linked to the generation of impact waves and to consequent production ofentropy. In general these consist of leading edge impact waves and port impactwaves, depending on the place where these effects occur. These phenomena tendto involve all types of compressors, both axial and centrifugal, with the exceptionof the totally subsonic ones.

• Pressure drop due to mixing. This consists of irreversibility associated withtransition between a non-uniform fluid-dynamic state, linked for example to localseparation effects, and a uniform condition. These phenomena take place in theregions downstream of the stator or rotor blade arrays and are estimated throughexperimental correlations.

In spite of the physical diversity of the pressure drop contributions involved, thequalitative considerations on the overall pressure drop curves, presented in subsec-tion 3.4.3 in the paragraph entitled Overall Pressure Drop, remain valid in a generalsense for both axial and centrifugal compressors.

3.4.4 Operating Curve Limits: Surge and Choking

The operating curves of the stages, both centrifugal and axial, present limits to theflow ranges that can be processed by the stage itself or by the machine of which

COMPRESSOR PERFORMANCE—DYNAMIC 3.27

it is a part. These limits are established by two separate phenomena, called surgeand choking, described below.

Surge. The term ‘‘surge’’ indicates a phenomenon of instability which takes placeat low flow values and which involves an entire system including not only thecompressor, but also the group of components traversed by the fluid upstream anddownstream of it. The term ‘‘separation’’ indicates a condition in which the bound-ary layer in proximity to a solid wall presents areas of inversion of the directionof velocity and in which the streamlines tend to detach from the wall. Separationis in general a phenomenon linked to the presence of ‘‘adverse’’ pressure gradientsin respect to the main direction of motion, which means that the pressure to whicha fluid particle is subjected becomes increasingly higher as the particle proceedsalong a streamline.

The term ‘‘stall,’’ referring to a turbomachine stage, describes a situation inwhich, due to low flow values, the stage pressure ratio or the head do not vary ina stable manner with the flow rate. Stall in a stage is generally caused by importantseparation phenomena in one or more of its components.

Surge is characterized by intense and rapid flow and pressure fluctuationthroughout the system and is generally associated with stall involving one or morecompressor stages. This phenomenon is generally accompanied by strong noise andviolent vibrations which can severely damage the machines involved.

Experience has shown that surge is particularly likely to occur in compressorsoperating in conditions where the Q-H curve of the machine has a positive slope.Less severe instability can moreover take place also in proximity to areas of nullslope. This depends on the presence of rotary stall, defined as the condition inwhich multiple separation cells are generated which rotate at a fraction of theangular velocity of the compressor.

Surge prevention is effected through experimental tests in which pressure pul-sation at low flow rates is measured on the individual stages. On this basis, it ispossible to identify the flow values at which stable operation of the stage is guar-anteed. A knowledge of the operating limits of each stage can then be used toevaluate the corresponding operating limits of the machine as a whole.

Choking. Assume that a stage of assigned geometry is operating at a fixed speedof rotation and the flow rate of the processed fluid is increasing. A condition willultimately be reached at which, in coincidence with a port, the fluid reaches sonicconditions. In this situation, termed ‘‘choking,’’ no further increase in flow rate willbe possible and there will be a rapid, abrupt decrease in the performance of thestage.

The occurrence of choking depends not only on the geometry and operatingconditions of the stage, but also on the thermodynamic properties of the fluid. Inthis regard, choking can be particularly limiting for machines operating with fluidsof high molecular weight, such as coolants.

Many types of compressors, including industrial process compressors, normallyoperate in conditions quite far from those of choking. For these machines, the

3.28 CHAPTER THREE

FIGURE 3.26 Non-dimensional performance curves for a stage.

maximum flow limit is frequently defined as the flow corresponding to a prescribedreduction in efficiency in respect to the peak value.

3.4.5 Performance of Stages

The discussion contained in the previous paragraphs provides the necessary ele-ments for understanding and interpreting the global performance of a generic stageand the manner in which it is usually represented through suitable diagrams. Thissubject is further discussed in the next two paragraphs.

Dimensionless Representation of Performance. A possible dimensionless pre-sentation of stage performance can be effected as shown in Fig. 3.26. The inter-pretation of the various parameters utilized is the one given by the definitionsprovided above.

The dimensionless representation is such that once the design values for the flowcoefficients and the Mach number have been established, the behavior expressedby the curves is independent of the actual size of the stage.

Dimensional Representation of Performance. The dimensionless performance ofthe stage being known, it is possible to obtain a representation in dimensional formwith the use of equations given in (3.4) to (3.17). One possible description of thistype is given in Fig. 3.27.

The conditions of the gas on discharge from the stage can be evaluated once thegas properties and the stage inlet conditions, defined by the pressure p00 and thetemperature T00, have been specified. In cases where the behavior of the gas canbe diagrammed through the perfect gas model, we will have for instance:

COMPRESSOR PERFORMANCE—DYNAMIC 3.29

FIGURE 3.27 Dimensional performance curves for a stage.

(/�1)�P

Hp P04� � � 1 �P � �00 � Z RTP 0 0 � 1

�1/�PT � T �04 04

P04 � (3.44)04 Z RT4 04

In cases where the perfect gas model is not applicable, it becomes necessary toapply an equation of state for real gases, for example, of the type defined by theBenedict-Webb-Rubin-Starling model.

3.5 MULTISTAGE COMPRESSORS

3.5.1 General Information

The pressure ratio obtainable with a simple single-stage compressor is normallylimited by constraints of both aerodynamic and structural type.

In the field of centrifugal compressors for aeronautic applications, unitary pres-sure ratios of about 12 have been obtained. In industrial applications the values aremuch lower, usually not exceeding the limit of three. The unitary pressure ratiosof the centrifugal stages are limited mainly by the maximum tip speed allowablein relation to the structural integrity requirements of the rotor and thus of thematerial of which it is built.

For axial compressors, the maximum unitary pressure ratio obtained in advancedcompressors for aeronautic applications is about 2.5. In this case, the unitary pres-sure ratio is constrained essentially by limitations of the aerodynamic type linked

3.30 CHAPTER THREE

to the need to keep the work transferred to the fluid within acceptable limits so asto avoid stall.

In all situations where the pressure ratio exceeds the maximum unitary value forthe particular type of compressor in question it becomes necessary to recur to amultistage arrangement with two or more stages arranged in series in a repetitiveconfiguration. The methods employed are analyzed here, with determination of theoperating curves of a generic multistage compressor, taking into consideration theproblems involved in the coupling of the various stages in both design and off-design conditions.

3.5.2 Multistage Compressor Operating Curves

In selecting the stages that make up the complete machine, an obvious considerationis that each of them should be utilized in conditions of maximum efficiency. Theefficiency of a stage is maximum in the design condition identified by a given valueof the flow coefficient ƒ1, a value which decreases progressively in moving awayfrom this condition.

In designing a multistage compressor, each individual stage must be utilizedaround the design condition, accepting a performance slightly lower than that ofdesign, since it is impossible, in practice, to size the individual stage for eachspecific design condition relevant to the complete compressor. It thus becomesnecessary to establish suitable operating conditions, different from those of design,at which the efficiency of each individual stage is satisfactory while margins areprovided as regards stall and choking.

Determination of the global compressor curves requires knowledge of the per-formance curves of each of its individual stages. In the case of a multistage cen-trifugal compressor which will be examined below, the performance of the indi-vidual stage can be represented by the following parameters:

(ƒ1) �*i design flow coefficient of nth stage

�*01�� 1 )06 i

design flow coefficient of nth stage corrected for variation in densitybetween inlet and discharge

t , �*Mu head coefficient corresponding to and to Mu � M*01� *� �1 u06 i

�h* *PMu ,D2 polytropic efficiency for (ƒ1)i � (ƒ1) and for Mu � M correspond-* *i u

ing to a given reference diameter

The mode in which the performance of a stage varies around design conditionsmust also be specified. This can be done utilizing curves that describe the behaviorof the head coefficient and the efficiency in relation to independent parameters. Apossible general form of this representation is:

COMPRESSOR PERFORMANCE—DYNAMIC 3.31

� � �P 1 1� ƒ 1 � ƒ (3.45)a� � � �� 1 2�* �* � *P 1 1i i

* P 01 01� ƒ � � (3.45)b� � �� 3 1 1 * P 06 06i i i

in which the functions ƒ1, ƒ2 and ƒ3 express dependencies that can be made explicitthrough experimental tests where the performance of each individual stage is mea-sured for a particular set of operating conditions. The above-mentioned curves arealso associated to suitable constraints that represent the operating limits for thestage in question relevant to choking and surge, also determined through testing.

Calculation proceeds from the first stage, first evaluating the dimensionless par-ameters ƒ1 and Mu relevant to a generic operating condition defined by volume flowrate, Q and speed of rotation N (e.g., for the design condition). The conditions onoutlet from the first stage are then calculated utilizing equations of the type (3.44)and introducing various corrections to take account of the effects of the Reynoldsnumber. The subsequent stages are then calculated in sequence, ultimately deter-mining the compressor discharge conditions.

For off-design conditions, the volume flow rate and speed of rotation are variedin parametric manner to obtain the performance levels relevant to a prescribed setof operating conditions. Through calculation it is also possible to verify the con-ditions corresponding to the operating limits of the compressor and to identify thestages responsible for any surge or choking. If the working gases cannot be rep-resented through the perfect gas diagram it will be necessary to use a real gasmodel to calculate the thermodynamic state on inlet to and discharge from eachstage.

A typical complete compressor map, evaluated for different speeds of rotation,is shown in Fig. 3.28.

3.5.3 Effect of Variation in Flow Rate on Stage Coupling

In evaluating the behavior of a multistage compressor, changes in the operatingconditions of the individual stages consequent to variations in flow rate should beexamined.

For this purpose we may consider Fig. 3.29, which shows the Q curve for allof the stages of a multistage compressor at design speed of rotation. Assume thatthe first stage operates at its own design flow rate Q1. In this condition, the densityof the fluid on discharge from the stage is known and it is possible to evaluate thevolume flow rate Q2 for the second stage, which is hypothesized as being that ofdesign.

If the flow rate Q1 is decreased by a quantity DQ1, the first stage will thenoperate at a pressure ratio higher than in the preceding situation. In this case, itcan be seen that the density of the fluid on inlet to the second stage is increased,

3.32 CHAPTER THREE

FIGURE 3.28 Performance map for a multistage compressor.

FIGURE 3.29 Effect of mass flow rate in a multistage compressor.

COMPRESSOR PERFORMANCE—DYNAMIC 3.33

FIGURE 3.30 Effect of decrease in rotational speed in a multistage com-pressor.

so that the volume flow rate of the second stage is decreased by a quantity DQ2 �DQ1 in respect to the value Q2. All this shows that flow perturbation tends to‘‘amplify’’ in proceeding from the first to the last stage, increasingly so in propor-tion to the number of stages. From the figure it can be seen that a slight variationin flow rate on the front stage ultimately produces stall in the last stage.

When the flow rate is increased by a quantity DQ1 the pressure ratio in the frontstage decreases, so that the density of the fluid on inlet to the second stage decreasesin respect to the design value. In this case too there is a change in flow rate DQ2 �DQ1, resulting in an ‘‘amplification’’ effect capable of determining final chokingin the last stage.

These considerations show that in a multistage compressor where the stages havebeen correctly coupled, compressor stall and possible surge are always determinedby stall in the final stage due to diminution in its volume flow rate. In the sameway, compressor choking is determined by choking in the final stage, operating atincreased volume flow rate values.

3.5.4 Effect of Variation in Speed on Stage Coupling

In similar manner, the behavior of a multistage compressor is influenced by vari-ations in speed regardless of the characteristics of the individual stages.

Consider Fig. 3.30 which shows the Q curves of the individual stages for a speedof rotation lower than that of design. In this case, the reduction in speed of rotationdetermines an increment in fluid density from one stage to the next that is lowerthan at design speed. Since the stable operating range of the compressor is deter-mined by the range of the last stage, it will be the latter to determine the volumeflow rate of stall and of choking. Moreover, since the increment in density is lower

3.34 CHAPTER THREE

FIGURE 3.31 Effect of increase in rotational speed in a multistage com-pressor.

than at design speed, it follows that the front stages will move toward low flowrates and high pressure ratios as compared to the design values.

These considerations show that at very low speeds of rotation, the front stagemay operate in conditions of pronounced stall, while the final stage is working inconditions approaching those of choking. In this situation, the operating range ispractically reduced to a single point and the compressor entirely loses its flexibility.

Let us now consider an increment in the speed of rotation in respect to that ofdesign (Fig. 3.31). In this case, there is a greater increase in fluid density alongthe compressor, so that the front stages are operating in fields of high flow ratesand low pressure ratios.

3.5.5 Families of Centrifugal Stages

The concept of families of stages is frequently utilized in the multistage centrifugalcompressor field. This term indicates a group of stages having the same basicgeometry and the same design parameters ƒ and M , studied to cover a certain* *2 U

range of flow coefficients ƒ1. The individual stages belonging to a certain familyare designed for a given value of ƒ and have an assigned range of operating flow*1rates. The values of the flow coefficients and the flow ranges of the individualstages are defined in such a way as to continuously cover a range of flow coeffi-cients, thus defining the characteristic range of the family. For this purpose, thefollowing are considered:

ƒ1i* design flow coefficient of nth stageƒ1�1* design flow coefficient of nth stageƒ1, MAX* maximum design flow coefficient for the familyƒ1, MIN* maximum design flow coefficient for the familyeS � ƒ1i,S /ƒ1i* left limit of nth stage selection range

COMPRESSOR PERFORMANCE—DYNAMIC 3.35

FIGURE 3.32 Ranges of design flow coefficients for a family of stages.

eD � ƒ1i,D /ƒ1i* left limit of nth stage selection rangeƒ1i,S left limit of nth stage flow rangeƒ1i,D left limit of nth stage flow range

Assuming contiguity of the flow ranges between the nth stage and the (n � 1)thstage, we obtain:

e ƒ * � e ƒ * (3.46)S 1i S 1i�1

Assuming that the operating range of the family is covered by n stages and that eS

� cos t, eD � cos t, we will have:

�* �1,i�1 D� � C � cos t (3.47)�* �i,i S

and thus:n/n�1

�*1,MAXC � (3.48)� ��*1,MIN

so that ultimately:

�*1,MAXn � 1 � ln ln C (3.49)� ��*1,MIN

In practical applications, however, selection must take into account the variouseffects that contribute to determining impeller performance, so that it is more com-plex than the simplified diagram shown here.

3.5.6 Standardization of Centrifugal Stages

The vast and highly diversified nature of applications for industrial centrifugalcompressors calls for stages capable of working in extremely variable operatingconditions. From the engineering viewpoint, this means designing and testing stages

3.36 CHAPTER THREE

have very different geometries and highly variable values of ƒ1, ƒ2 and MU. Con-sidering the limitations of a single stage in terms of operating range, this wouldcall for the realization of an enormous number of stages, with consequent highcosts and uncertainty in predicting performance.

The ‘‘family of stages’’ concept, by extending the operating range of a genericstage, provides a tool for simplifying these problems inasmuch as it reduces vari-ation in the design parameters involved and thus reduces, in the final analysis, thenumber of stages to be designed and tested. In this case, a suitable group of familiesis defined to cover ample variations in the design parameters, particularly those ofthe quantities ƒ1 and MU. Within a single family, the individual stages are typicallydesigned to cover a much narrower range. This procedure makes it possible toreduce the number of stages to be tested, thus cutting down on time and costs ofengineering and development.

In summary, the availability of an effectively standardized group of stages, ac-companied by suitable procedures for coupling them, is an element of primaryimportance in the realization of multistage compressors.

3.6 THERMODYNAMIC AND FLUID-DYNAMIC ANALYSIS OF

STAGES

3.6.1 General Information

As mentioned in the introduction, thermodynamic and fluid-dynamic analysis ofcompressor stages is at present conducted through methodologies based on a num-ber of highly diversified physical models and assumptions. A convenient classifi-cation of these methods may be made on the basis of the type of hypothesis for-mulated to analyze the machine flow rate. On the most general level we maydistinguish between:

• Monodimensional methods. This term indicates a group of models deriving fromapplication of the hypothesis of monodimensional flow in the stage.

• Non-viscous methods. This refers to numerical techniques based on flow analysisin the individual components of the stage in the approximation of non-viscousflow.

• Viscous methods. These methods are based on flow analysis conducted throughnumerical integration of the flow viscous equations.

3.6.2 Monodimensional Methods

The monodimensional approach may be considered the most elementary level ofrepresenting the fluid-dynamic characteristics of a centrifugal stage. It is based onthe assumption that the fluid-dynamic and thermodynamic states in a given section

COMPRESSOR PERFORMANCE—DYNAMIC 3.37

of the machine can be described in terms of a single condition, which representsa mean value of the actual conditions present in the section.

The basic aspects of the single-area monodimensional approach are outlinedbelow. A specific operating condition is assumed, defined by the following para-meters, assumed to be known:

p00 � total inlet pressure

T00 � total inlet temperature

m � mass flow rate

N � impeller speed of rotation

It is also considered that the fluid thermodynamic properties , Cp, R are known.It is assumed that the flow is uniform in the inlet section, adiabatic and stationaryin respect to a datum point integral with the rotating components.

Analysis of Impeller Inlet Section. The flow between sections 0 (stage inlet sec-tion) and 1 (impeller inlet section) can usually be considered isentropic. In accord-ance with the hypotheses formulated above it can be stated that:

p � p01 00 (3.50)

T � T01 00

The conditions in section 1 can be evaluated by applying the continuity energy andmomentum equations. Determination of the quantities relevant to the streamlinepassing in proximity to the blade tip (r � r1o) is particularly important since it ishere that the highest relative Mach numbers are found.

The meridian component of the absolute velocity Cm1 can be determined throughthe continuity equation:

C � m /r A (3.51)m1 1 1

where A1 � cD (r1o2 � r1i

2)cD � blockage factor due to presence of the blades.

The tangential component of the absolute velocity Cq1 depends on whether or notinlet guide vanes are utilized. In the absence of vanes, we will have Cq1 � 0.

Consequently, it is possible to resolve the rotor inlet speed triangle, illustratedin Fig. 3.33, through the following equations:

2 2 1/2C � (C � C ) (3.52)1 m1 t1

and also:

2 2 1/2W � ((U � C ) � C )1 1o q1 m1

U � 2 p r N (3.53)1o 1o

The local absolute Mach number is given by:

3.38 CHAPTER THREE

1α β1

θ1wθ1c

1wm1c1c

FIGURE 3.33 Impeller inlet velocity triangle.

1/2M � C / (g R T ) (3.54)1o 1 2

Pressure and temperature are linked to the Mach number through the followingequations:

2 (/(�1))p /p � (1 � (g � 1) M /2)01 1 1o

2T /T � (1 � (g � 1) M /2) (3.55)01 1 1o

A further relation is provided by the perfect gas equation of state:

r � p /R T (3.56)1 1 1

Equations (3.51) through (3.56), applied, if necessary, to determination of the speedtriangle in coincidence with an arbitrary radius r, fully characterize the conditionspresent in the rotor inlet section.

Analysis of Impeller Discharge Section. As the next step the basic equations offluid mechanics can be utilized to evaluate the conditions existing in the rotordischarge section.

In this regard, consider the speed triangle relevant to section 2, shown in Fig.3.34.

The velocity U2 can be obtained through the simple kinematic equation:

U � 2 p r N (3.57)2 2

The meridian component of the absolute velocity of the fluid is calculated here toothrough the flow continuity equation:

C � m /r (3.58)m2 2 A2

with A2 � 2 p r2 b2.

The tangential component Cq2 is given by:

COMPRESSOR PERFORMANCE—DYNAMIC 3.39

c c2

2α

θ2

β2

θ2c

v s

FIGURE 3.34 Impeller exit velocity triangle.

C � U � C tan(� ) � V (3.59)q2 2 m2 b2 s

where �b2 is the structural angle of the blade at the discharge section and Vs rep-resents tangential speed defect associated with the slip factor s:

V � U (1 � s) (3.60)S 2

Numerous correlations between slip factor and rotor geometry, obtained boththeoretically and experimentally, are available for an estimation of Cq2 to be usedin design problems. A frequently used correlation is the following, proposed byWiesner:

�cos(� )b2� � 1 � (3.61)0.7Z

valid for R1i /R2 � e�8.16(cos(�b2)) /Z.Application of the Euler equation for turbomachines produces:

Dh � U C � U C (3.62)0 2 q2 1 q1

and thus the increment in total temperature, assuming that secondary energy con-tributions deriving from the effects of recirculation, friction, etc., can be ignored,is given by:

Dh � (U C � U C ) /C (3.63)0 2 q2 1 q1 P

The equations for pressure and temperature are again of the type:

2 (/(�1))p /p � (1 � (g � 1)M /2)02 2 2 (3.64)2T /T � (1 � (g � 1) M /2)02 2 2

in which:

3.40 CHAPTER THREE

2 2 1/2C � (C � C )2 m2 q2 (3.65)1/2M � C / ( R T )2 2 2

The isentropic efficiency of the impeller can be defined as follows:

(�1 / )p02 � 1� �p00

� � (3.66)S,ROT T02 � 1� �T00

The utilization of a value correlated for thermodynamic efficiency of the typedefined in (3.66), normally assumed by the design engineer on the basis of exper-imentation on real machines, makes it possible to close the system (3.58) to (3.65)and to formulate an estimate of the conditions existing in the impeller dischargesection.

In conclusion, it should be mentioned that the single-area monodimensionalmodel is dealt with comprehensively in the majority of reference texts on radialturbomachinery.

3.6.3 Monodimensional Analysis of Diffusers

Analysis methods based on monodimensional flow approximation are frequentlyutilized in the field of diffusors. The main function of these methods is that ofpredicting the performance of a given configuration, in relation to determined flowconditions existing at impeller discharge.

The most important diffusor performance parameter is the pressure recoverycoefficient Cp defined by the equation:

p � p4 2C � (3.67)p p � p02 2

This parameter is utilized to quantify the capacity for converting into pressure thekinetic energy transferred to the fluid by the impeller.

The diffusors most frequently utilized in centrifugal stages can be classifiedunder two headings: free vortex and bladed. The approach most frequently used inanalyzing free vortex diffusors hypothesizes a succession of monodimensional con-dition sections with r � constant lying between impeller discharge section anddiffusor discharge section. The fluid-dynamic balance equations relevant to thisrepresentation, inclusive of the friction terms deriving from the presence of sidewalls, can be integrated numerically starting from known conditions in the dis-charge section. This procedure can be used to evaluate the fluid-dynamic state ondischarge from the diffusor and the consequent performance of the component.

With the bladed diffusor, the substantial complexity of the conditions precludesthe use of monodimensional methods based on the application of theoretical prin-

COMPRESSOR PERFORMANCE—DYNAMIC 3.41

FIGURE 3.35 Diffuser data for compressor diffuser de-sign.

ciples alone. Consequently, the approach most commonly employed for evaluatingthe performance of this component consists of experimental correlations.

The best-known of these correlations refers to experiments conducted by Run-stadler on diffusors of bidimensional geometry with straight walls diverging on asingle plane. It shows that the recovery coefficient depends on a number of geo-metric and aerodynamic parameters, such as the length/width ratio, throat sectionL /w, and divergence angle 2q. A typical performance map, obtained from Run-stadler’s work, is shown in Fig. 3.35, where the recovery coefficient is representedin relation to the previously introduced geometric parameters.

3.6.4 Non-viscous Numerical Methods

The monodimensional methods described above present some disadvantages whichcan be summarized as follows: impossibility of obtaining an accurate representationof the fluid-dynamic field at all machine points; impossibility of diagramming thedetailed geometry of the components and its influence on the fluid-dynamic char-acteristics; and need to introduce empirical data in the form of various experimentalcorrelations.

3.42 CHAPTER THREE

The attempt to overcome at least some of these limitations has revealed the needfor analysis methods capable of resolving, through numerical calculation proce-dures, the fluid-dynamic field within the components of the stage.

In view of the complexity and expense of using viscous models, attention wasinitially focused on models based on the hypothesis of non-viscous, stationary flow.These methods frequently incorporate further hypotheses, e.g., assuming that thesurfaces along the fluid trajectories can be represented by suitable bidimensionalsurfaces, termed streamline surfaces.

Note that the hypothesis of non-viscous flow does not correspond to the con-ditions observable in experimentation, particularly as regards centrifugal machines.On the contrary, the latter show a vast range of phenomena in which viscous effectshave significant importance and extent. Accordingly, the representation obtainablethrough the non-viscous approach should be considered at most an approximationof the conditions encountered in reality.

In spite of this considerable limitation, non-viscous methods can be utilized fordiagramming that is satisfactory from the engineering viewpoint. It can in fact beassumed that the behavior of the regions subject to viscous effects, and of theboundary layers in particular, can be reconstructed from a knowledge of the ve-locity and pressure distributions obtained from the non-viscous model.

The non-viscous methods can be divided into four categories:

• Bidimensional solutions relevant to streamline surfaces lying in the hub-to-shrouddirection

• Bidimensional solutions relevant to streamline surfaces lying in the blade-to-bladedirection

• Quasi-three-dimensional solutions

• Three-dimensional solutions

In each of these categories the methods can be classified still further as stream-line curvature methods and partial derivative methods. The streamline curvaturemethods are based on the integration of ordinary differential equations of the firstorder: these describe the momentum balance along directions defined by the so-called ‘‘quasi-normals’’ to the streamlines. The partial derivative methods are basedon the integration of differential equations with the partial derivatives which de-scribe the balance of mass, that of quantity of motion and that of energy at a pointin the calculation domain.

Most of the partial derivative methods consist of developments of the formula-tion proposed by Wu in 1952. Through these it is possible, thanks to the introduc-tion of particular derivatives, to divide the original three-dimensional problem intotwo bidimensional problems relevant to hub-to-shroud surfaces and blade-to-bladesurfaces respectively.

Having briefly introduced the main categories of methods, we will go on todescribe the salient characteristics of each of them and the results obtainable.

Bidimensional Solutions Relevant to Streamline Surfaces in the Hub-to-shroudDirection. These methods are based on representation of the conditions existingon a hypothetical mean streamline surface, extending in the hub-to-shroud direction

COMPRESSOR PERFORMANCE—DYNAMIC 3.43

within the area lying between two adjacent blades. The geometry of this surface isusually established in relation to the position and orientation of the blades.

A typical calculation code for this category, utilizing the streamline curvatureapproach, is based on integration of the momentum balance equations, evaluatedin reference to a grid, defined on the hub-to-shroud surface, formed of streamlinesand quasi-normals. These equations are placed in a system with further mass bal-ance equations, and evaluated in coincidence with the quasi-normals. The positionof streamlines and quasi-normals is modified through an iterative procedure up toconvergence with the desired flow rate value. The codes based on the partial der-ivations approach frequently utilize Wu’s formulation, mentioned above.

As regards application of the results, note firstly that the assumptions madeconcerning the geometry of the hypothesized streamlines do not coincide with whathas been found in experimentation, where the movement of the streamlines is oftenhighly distorted. Furthermore, the methods described above presume conditions ofthe axial-symmetric type, which differ from the situations observed, especially inimpellers with high pressure ratios. Greater accuracy can however be obtained byassociating these procedures with methods for blade-to-blade flow analysis, dis-cussed in the following paragraph.

Bidimensional Solutions Relevant to Streamlines in the Blade-to-blade Direc-tion. These methods are based on the representation of conditions in hypotheticalstreamlines consisting of surfaces of revolution between two contiguous blades.Many of these methods employ the streamline curvature formulation. These pro-cedures are based on solving the equations along quasi-normals oriented in theblade-to-blade direction, according to a scheme similar to the one described in thepreceding paragraph. The surfaces of revolution are obtained by rotation aroundthe axes of streamlines calculated through a bidimensional method in the hub-to-shroud direction.

The most widely used approach consists however of utilizing finite differencesmethods, frequently based on the formulation proposed by Stanitz. As regardsapplication of the results, the remarks concerning the arbitrary nature of the pre-sumed streamlines, which do not usually coincide with the real streamlines, shouldapply.

The most useful aspect of the methods described here is their capacity for eval-uating the conditions existing on the blade surfaces. This makes it possible, as willbe demonstrated, to evaluate the pressure and velocity distribution, and conse-quently to predict the behavior of the boundary layers in the real machine. More-over, the methods described here can be utilized as constituent elements of quasi-three-dimensional or three-dimensional procedures, as will be shown in thefollowing paragraph.

Quasi-three-dimensional and Three-dimensional Solutions. The methods dis-cussed above refer, in all cases, to bidimensional representations of the flow. Aspreviously mentioned, these methods do not take account of the actual conditionsexisting in a centrifugal compressor, where there are important three-dimensional

3.44 CHAPTER THREE

effects. It is thus necessary to find models which go beyond the bidimensionalhypothesis.

A frequently used technique consists of producing quasi-three-dimensional rep-resentations, obtained by combining two bidimensional solutions of the types de-scribed above.

In the model developed by NREC for instance, a bidimensional solution relevantto a hub-to-shroud surface is superimposed on another bidimensional solution rel-evant to a blade-to-blade surface. The first solution is obtained through a conven-tional streamline curvature method; the second is evaluated through an approximatemethod developed by Stanitz, based on imposing a condition of absolutely nullcirculation along a closed line lying between two adjacent blades.

The study of this distribution yields a first approximation of the behavior of theboundary layers relevant to a given compressor geometry. The information obtainedin this way is of fundamental importance to design. For this reason, calculationmethods of the type described here are by now a well-consolidated procedure indesigning impellers.

The next level of approximation consists of utilizing methods which make useof an actual three-dimensional representation. Among these is the model developedby Hirsch, Lacor, and Warzee which utilizes a finite-element procedure.

3.6.5 Viscous Methods

The term ‘‘viscous methods’’ indicates a family of calculation codes based onprocedures of numerical integration of the viscous, compressible, and three-dimensional equations of motion.

Generally speaking, the system formed of the complete Navier-Stokes equationsin non-stationary form, the constitutive laws of fluid, and the equations that specifythe dependency of viscosity and thermal conductivity on other variables, providethe most general representation of a generic fluid-dynamic phenomenon.

In the case of laminar flow, a numerical simulation based on such an approachprovides a strict description of the problem in question and, moreover, does notrequire the introduction of further information based on empirical data. Most ofthe applications, however, and almost all of the cases significant for the analysisof centrifugal compressors, concern situations in which the flow is to be consideredturbulent.

In principle, it is possible to simulate a turbulent flow through integration of theNavier-Stokes equations in non-stationary form. This approach does not require theintroduction of additional information on the structure and properties of the tur-bulence. However, it implies the availability of calculation resources exceedingthose available at the moment or in the near future.

This makes it necessary to recur to formulations where the effect of turbulenceis represented by an appropriate model based on empirical data. The proceduresbased on this approach utilize Reynolds’s formulation of equations of motion, inwhich the non-stationary variables are brought to a mean value calculated in respect

COMPRESSOR PERFORMANCE—DYNAMIC 3.45

to an appropriate time interval. A turbulence model is utilized to diagram the Reyn-olds stress tensor terms appearing in the equations of motion.

A general formulation of the fluid-dynamic problem defined in this way is thefollowing:

�Q �E �F �E �FV V� � � � (3.68)� t �x �y �x �y

where

u v0 02u u � p uv

Q � E � F � E � F � (3.69)2 v xx v yxv uv v � p � � � � � xy yye u(e � p) u(e � p)

in which terms of the type xx xy represent friction effects depending on the vis-cosity � and the velocity derivations. This system of equations should be associatedwith a suitable representation of the thermodynamic properties of the fluid, gen-erally represented by the perfect gas model. Suitable equations, based in generalon Sutherland’s law, are also included to make explicit the dependency of theviscosity on temperature.

The simplest representation of turbulence is that which considers an effectiveviscosity determined by the sum total of a molecular contribution and a turbulentone (Boussinesq’s hypothesis).

� � � � � (3.70)L T

The molecular viscosity term �T can be calculated in different ways: in the classof methods termed algebraic models, an approach based on Prandtl’s hypothesis ofmixing length is used. Among these methods, the model developed by Baldwinand Lomax is especially well known.

3.7 THERMODYNAMIC PERFORMANCES TEST OF

CENTRIFUGAL COMPRESSORS STAGES

3.7.1 General

Even if computing resources are developing faster, the only solid indicator of acompressor’s performances still lies in extensive testing. Tests can be carried outon single stage scale models for basic understandings of stage behaviour and onthe whole machine for performances measurements.

Normally the gas available to the manufacturer has different properties (mainlydifferent molecular weight) with respect to the real one, hence an extensive use ofsimilitude laws is done.

3.46 CHAPTER THREE

β 1

α 1

m 1c

c θ 1

θ 1w

w 2

w θ 2

βm 2c2α

c 2

u 2

θ 2c

i 1

2δ

m 3c3α

3cc θ 3δ 3

i 2

s ta to r

ro to r

FIGURE 3.36 Velocity triangles for an axial stage.

FIGURE 3.37 Howell correlation for deviation.

Single Stage Testing. This type of test is normally performed using scale modelsand closed or open loop facilities handling air or some heavy gases available onthe market. Peripheral Mach number and Volume Flow coefficient are reproducedin the lab.

Tests are normally carried out at lower Reynolds number with respect to fullscale conditions. The higher the Reynolds number, the better the compressor effi-ciency and the higher the head. ASME standards governing thermodynamic testsstate the relevant corrections.

A facility for single stage test is shown in the Fig. 3.39.Because of the fact that the tests are carried out not on the real machine com-

ponents, many probes can be installed inside the model and temperature and pres-sure are measured at several positions for a full description of both impeller andstatoric parts performances.

COMPRESSOR PERFORMANCE—DYNAMIC 3.47

FIGURE 3.38 Correlation between diffusion factor and momentum thickness.

3.8 MECHANICAL TESTS

Mechanical tests can be of various types and complexities depending on the infor-mation that it is required to obtain. The test conditions ought to be as close aspossible to the actual contractual conditions. During the tests, the item of greatestinterest is the location of the lateral critical speed.

In general, a running test at maximum continuous speed is carried out (100%of design speed for motor driven units, 105% for steam or gas turbine units). Duringthis test, shaft vibration measurements are taken at various speeds, close to thebearings. An overspeed test is carried out up to the overspeed trip setting of theturbine to check the safety of the compressor in the event of control failure ofturbine. In this case, the speed can reach 10% over the trip after which the machineshuts down.

It is known that the coupling has a notable influence above all on the secondcritical speed; for this reason, it is advisable to carry out the tests with the jobcoupling. If a different coupling is used, care must be taken to ensure that theoverhang (consider weight and axial dimensions) is the same. In particular, thesame sleeve weight and position of center of gravity, the same distance of the teethfrom the bearing, and the same weight and flexibility as the job coupling arerequired.

The connection between compressor shaft and coupling (carried out by meansof matching teeth) is considered as a hinge: in fact the bending moment is thusnot transmitted to the compressor shaft. In particular, the weight of the spacer isconsidered divided by two identical forces acting on the end toothings.

Further, the test driver ought to be that used for the project, in fact, the driver-coupling compressor group is a whole, the interaction of the component parts of

3.48 CHAPTER THREE

FIGURE 3.39 Single stage model test facility.

which is not easy to be reproduced. In general, however, the drivers of the testfacilities are used; only with particularly critical machines are tests made using theproject driver. This is generally what concerns the elastic response of the com-pressor. One must take into account also the bearings and the seals, since the criticalspeeds are much influenced by these (type of bearings and seals, their clearances,oil viscosity etc.). It has already been seen when considering the lateral criticalspeed and instability problems, that the type of bearing and seal have a fundamentalimportance in reducing the destabilizing forces that act on the rotor-support system.It is useful to remember that the case in which asynchronous vibrations occur atspeeds which are multiples of the rotation speed, indicates misalignment, bearingfailure, or other causes of this kind. Asynchronous vibrations at speeds lower thanthat of rotation are to be attributed to instability of the oil film in the bearings orin the seals. The oil used in the test must have the same viscosity as that used atthe operating site; this can be arranged by adjusting the oil temperature to get theviscosity required at the bearing inlet.

COMPRESSOR PERFORMANCE—DYNAMIC 3.49

FIGURE 3.40 Single stage test model.

To be able to reproduce the same working conditions in the high pressure seals,the oil or gas should circulate in closed high pressure loop. This may be compli-cated and costly.

The old edition of API standards stated to carry out tests without seals installed.The new edition, on the contrary, states to carry out the test with the seals installed.This, in practice, means carrying out the test at a pressure equal to at least a quarterof that required in operation. In fact, the capacity across the low pressure ring isproportional to the pressure: at reduced pressure the cooling is less which leads toan increase in temperature.

During the tests, oil temperature and pressure are measured at inlet and thetemperature at the bearing discharge. Sometimes the bearing temperature is mea-sured by embedding a thermocouple into the white metal. Measurements on thelubricating and seal oil capacities are not frequently made. The measurement ofvibrations is carried out both on the shaft and on the case. The case measurementsare made close to the bearing positions in the vertical, horizontal and axial planes.The measuring instrument consists of an external part joined to the case and onefree, practically fixed in space, which has a very low frequency of oscillation andis not affected by the high frequency case vibration. The variation of the magneticfield in the air gap due to the relative movement between the two parts generateselectromagnetic forces which are suitably amplified and presented on a monitor,

3.50 CHAPTER THREE

and give information on the vibrations of the case. Filters are used to select thevarious harmonics for monitoring on an oscilloscope. The vibrations on the shaftare measured in different positions with probes at 90� so that on the oscilloscopeit is possible to see the orbits of the points of the shaft axis corresponding to theparticular section.

It is also interesting to see the phase variations, that is, to see how the amplitudeof the vibration moves with regard to a fixed point on the shaft at various rotationspeeds (the fixed point on the shaft can be arranged by having a reference markmonitored by a photo-electric cell). By observation of the phase, it is possible tofind between which critical speeds the operating point exists, since in passing acrossone of these there is a phase change in the vibrations. For example, before the firstcritical speed, unbalance and vibrations are in phase, beyond the first critical speedthey are in phase opposition; in reality, these phase changes are never instantaneousbut are distributed within a speed range. Naturally, it is necessary that the shaft isperfectly cylindrical and concentric with respect to the supports, otherwise consid-erable vibrations will be detected even if the shaft does not vibrate. During vibrationmeasurements, it is necessary to take into account the electric and mechanical run-outs. The electric run-out is a phenomenon due to the fact that during the forgingoperations magnetic fields are created which subsequently disturb the measure-ments. It is necessary to avoid these difficulties before the tests by de-magnetizingthe rotor with a solenoid. The mechanical run-out, due to unavoidable eccentricityand ovality of the mechanical parts, can be examined by means of other instru-ments.

At one time the trend was to limit vibration amplitude, now instead, the trendis to limit vibration speed or vibration acceleration. The vibration speed is propor-tional to the product of the amplitude by the frequency and to the dissipated energy;that’s why it is an important reference for evaluating vibrations. In general thevibration amplitudes acceptable on the case are half of those on the shaft; to givean idea of the order of these amplitudes, for a shaft running at about 5000 rpm,the vibration amplitude acceptable is up to about 40 microns. For the casing, thevibration speed limits are acceptable in the order of 10 to 20 mm/sec.

3.9 ROTOR DYNAMICS AND DESIGN CRITERIA

3.9.1 Introduction

The greatest effort in the design of centrifugal compressors mainly for high pressureapplications is at present devoted to problems connected with the lateral stabilityof the rotor. Stability problem concerns the compressor in all its components, since,all basic parts of the machine contribute to stability: rotor, bearings, oil seals,coupling and all flowdynamic parts such as impellers, diffusers, return channels.

Theoretical prediction and experimental investigation methods made available inrecent years have contributed much to the progress in this field. Referred to here

COMPRESSOR PERFORMANCE—DYNAMIC 3.51

is the availability in industry of large computers capable of carrying out very elab-orate calculation programs, and of electronic equipment for detection of vibrationsand pressure pulsations (non-contact probes, key-phasors, pressure transducers, realtime analysers etc.) which have allowed more accurate diagnosis.

The measure of mechanical behaviour of a compressor is given by the amplitudeand frequency of the rotor vibrations.

Rotor vibration amplitude must not cause: contact between rotor and small clear-ance stator parts (labyrinths), overloading of oil seals, or fatigue stress in the bear-ings. The frequency of the vibrations is a very important element in evaluatingstability of the system.

Vibration may have a frequency corresponding to the machine rotation (syn-chronous vibration) or a different frequency (asynchronous vibration). Usually inrotating machines both types of vibration can be present.

3.9.2 Synchronous Vibration

Synchronous vibrations are usually attributable to one or a combination of the twofollowing causes:

a) Accidental defects of the rotors (as for example unbalance)

b) Design defects; that is to say operating speed too close to resonance and/orinsufficient damping of the system

As regards point a), machine manufacturers now have equipment which permitsachievement of a very accurate balancing. This considerable accuracy in balancingis however sometimes upset by accidental causes so that point b) assumes greatimportance; correct design of the rotor-bearing system must assure acceptable vi-bration levels even when accidental causes destroy the original state of perfectbalance.

Two approaches are usually used to predict the synchronous dynamic behaviourof a rotor.

The first approach is the Myhlestad-Prohl numerical calculation that considersthe rotor as a dynamic system consisting of a number of concentrated massesattached to a zero mass shaft supported by bearings. The computer program solvesthe system for a variety of constant support values over the entire possible range.A diagram can be made in which the lateral critical speeds are a function of theequivalent stiffness of the supports. The actual values of lateral critical speeds canbe established on the basis of the knowledge one has of the bearing stiffness (Fig.3.41).

The original speed program also calculates the rotor mode shapes at the criticalspeeds for each specified value of the bearing stiffness (Fig. 3.42). The mode shapesare important because they indicate the relative vibration amplitude at each stationalong the rotor. If relative amplitudes at the bearings are low a high unbalanceproducing considerable deflection in some sections of the shaft will cause very

3.52 CHAPTER THREE

FIGURE 3.41 Map of lateral critical speeds.

FIGURE 3.42 Typical rotor response diagram.

COMPRESSOR PERFORMANCE—DYNAMIC 3.53

FIGURE 3.43 Damped lateral frequencies and decre-ment diagram.

small relative motion in the bearings. Without relative motion, damping of thebearings cannot be effective. Thus the bearings are not placed in the most effica-ceous position, and their position must be corrected.

The second approach is to carry out the shaft response calculation in which therotor motion throughout its operating speed range is studied as a damped systemresponse to an unbalancing excitation. The unbalances are generally placed wherethey may be expected to occur, i.e., at impellers, couplings etc. The amplitude ofrotor motion is calculated at selected stations along the rotor.

Coefficients simulating the dynamic stiffness and damping of the bearing areincluded in the calculation. The calculated whirl orbits are generally elliptical dueto the difference between the vertical and horizontal stiffness and damping. Aresponse diagram represents the variation with speed of the semi-major axis of theelliptical whirl orbit at selected stations along the rotor (Fig. 3.43).

Various tests carried out directly in actual operating conditions have shown thatthe frequencies and amplitudes measured are close to the expected values.

The design parameters available to act upon damping capacities and resonancevalues are: bearing positions, especially with respect to the shaft overhangs, bearing

3.54 CHAPTER THREE

type, type of lubricating fluid, coupling type and obviously elastic characteristicsof the rotor.

3.9.3 Asynchronous Vibration

In the asynchronous vibration field it is necessary to make a further distinctionbetween vibration frequencies that are multiples of the rotating speed and vibrationfrequencies lower or higher than rotating speed but not multiples.

To the first type belong vibrations usually caused by local factors such as: mis-alignment, rubbing between rotating and static parts, excessive stresses in the pip-ing, foundations etc.

To the second type belong vibrations that have been the cause of more seriousproblems especially in the field of high pressure compressors. They may be causedby external phenomena (forced vibrations: for example, the effect of aerodynamicforces) or by phenomena intrinsic to the movement of the rotor itself (self-excitingvibrations), which impair stability at its base.

Stability is a function of a balance of several factors. The main ones are:A—Rotor-support system with its elastic characteristicsB—Aerodynamic effectsC—Oil sealsD—Labyrinth sealsEach factor plays its part in the balance of stability and may be either positive

or negative. The system is more or less stable or unstable according to the resultof this balance.

A theoretical approach for predicting the stability of a rotating system is the logdecrement calculation.

The program calculates the natural damped frequencies of the rotor-support sys-tem at selected speeds and supplies, for each frequency, the value of the log dec-rement that is a sound indication of the stability of the system itself.

A—As far as the rotor is concerned, we have already seen how the naturalfrequencies are determined and how the bearing effectiveness can be evaluated onthe basis of the bending shapes.

To avoid or minimize internal hysteresis, shrunk assembled elements (such assleeves, spacers, impellers etc.) must be as axially limited as possible.

The keyways may cause differentiated elastic response in the various planes. Forthis reason they are reduced to the minimum size, staggered at 90 degrees betweenone impeller and the next, and in some cases they are eliminated.

As regards bearings, in order to avoid oil whip problems the tilting pad type isgenerally used. In some cases damper type bearings are also used (Fig. 3.44.).These offer the advantage of allowing independent adjustment of damping andstiffness coefficients.

B—The occurrence of rotating stall in one or more impellers may explain thepresence of pulsations indicating vibrations at the same frequency (forced vibra-tions).

COMPRESSOR PERFORMANCE—DYNAMIC 3.55

FIGURE 3.44 Damper bearing.

All centrifugal compressors, whatever the pressure, are affected by aerodynamicexcitation. Other conditions being equal, these effects increase in intensity in pro-portion to the actual density of the gas. The determinant parameter is not onlypressure, but also temperature, molecular weight and compressibility together. Thisis the reason why the problems of vibrations excited by aerodynamic effects occurmore frequently in reinjection or urea synthesis plants than in ammonia synthesisor refinery compressors, even when running at the same pressure levels.

The ‘‘unsteady flow phenomena’’ has been studied in its standard stage config-uration. The conclusions were that the aerodynamic disturbance and the consequentpressure pulsations were coming from stator blades of the return channel wellbefore coming from the impeller itself. In this case, the relevant shaft vibration hadthe following characteristics:

• Stability in amplitude

• Very low frequency (order of magnitude about 10% of the running speed)

• Amplitude function of the tip speed and the density of the gas

C—The shaft end oil seals are still one of the most critical parts in the manufactureof high pressure centrifugal compressors.

An important requirement that the oil seals must satisfy is to contribute to thestability of the system or at least not to disturb it too much. It is easy to understandthat seals, owing to their nature, would be very negative components in the stabilitybalance of the system if they were ‘‘locked’’, because they would act as lightlyloaded, perfectly circular bearings. This negative tendency is generally counteredby making the rings floating as much as possible in operating conditions.

This can be obtained by distributing the oil pressure drop on the atmosphericside amongst several rings, and reducing the surface of each ring where the pressureacts by lapping the surfaces. When these techniques are insufficient to avoid ‘‘lock-ing’’ (i.e., a high detachment limit force value), circumferential or axial grooves on

3.56 CHAPTER THREE

FIGURE 3.45 Sealing system.

floating rings may make a positive contribution to the stability influencing dampingand stiffness characteristics of the system.

D—Another important possible cause of instability and sub-synchronous vibra-tion can arise from the labyrinth seals.

In the annular surfaces the gas circumferential motions, because of the rotordisplacement, can become uneven; therefore, they can cause a non-symmetricaldistribution of the pressure, with a resultant force perpendicular to the displacementit*elf (so called cross-coupling effect). This is a typical self-exciting phenomenoncausing instability.

The importance of the phenomenon grows with gas density (therefore with thepressure) and with the location of the seal. In fact, the vibration which alwaysinitiates above the first critical speed, has a characteristic frequency just equal tothe first critical speed with the same mode shape.

Therefore particularly important from this point of view are the back-to-backcompressors in which the biggest labyrinth is in the middle (as in the highestpressure) where the shaft motions are greater.

The sealing system in Fig. 3.45b represents a first attempt to decrease or try tointerrupt the circumferential motions by means of many septums placed axially onthe labyrinth.

The honey comb seal in Fig. 3.46, is derived from the previous one by puttingthe annular surface between two consecutive teeth in communication with an innertoroidal chamber in order to equalize pressure inside as much as possible.

COMPRESSOR PERFORMANCE—DYNAMIC 3.57

FIGURE 3.46 Honey comb seal.

3.9.4 Balancing and Overspeed

The most important causes of either asynchronous or synchronous vibrations canbe very well simulated during calculation so that a good forecast of the rotordynamic behaviour is available.

Moreover, the parallel growth of instrumentation technology provides the pos-sibility of thorough verification not only of the mechanical running conditions of

3.58 CHAPTER THREE

the machine but also, and consequently, of the theoretical assumptions taken asdesign basis, therefore confirming the statements made in the first paragraph.

The rotors are balanced through the following procedure:

Impeller. The impeller is mounted on the balancing equipment.The whole unit is then mounted on the balancing machine and must be turned

by hand to check correct mounting; eccentricity is measured on external diameterof impeller seal (max. permissible value: 0.02 mm).

Next impeller is balanced at a higher speed, compatible with the machine’s limitsin accordance with its weight, by removing material on hub and shroud until finalunbalance is within permissible range given by API 617. The impeller must thenbe subjected to overspeed test.

Subsequently the impeller, mounted on the special shaft with two adaptor disksused for balancing, is fitted onto the vertical overspeed unit. Overspeed test is thencarried out maintaining the same level for about 10 minutes, in accordance withthe values given in the specification after the trip device of the unit has been setat a speed 2% greater than per specification.

Vacuum should remain at an absolute pressure of less than 1 Torr and vibrationsmeasured on the driving turbine should be less than 6 mm/sec.

Test values must be recorded; the impeller must then be rechecked by penetrantdye liquids and then assembled onto the shaft.

Rotor. Mount shaft on balancing machine resting it on its journal bearings; fitfalse half-keys and begin balancing process, temporarily adding filler on surfacesfor end locking rings, using adhesive tape for this purpose. Balancing speed isselected with reference to the characteristics of the machine, in compliance withthe degree of accuracy required by API 617 (Oct. ’73). Next, mount one impellerat a time and after each mounting, balance by removing material from hub andshroud. The end seal rings must be fitted on and the temporary weights, addedpreviously, removed. Balance by removing material, by drilling, from the ringsthemselves. Mount thrust bearing block and correct its unbalance by machining theouter diameter. Mount specified joints and check balance. For final checking, turnconnection joint on balancing machine by 180� and check balance again.

Note: The above is based on the basic criterion for a flexible rotor: to preventinternal moments arising during assembly of rotor, the rotor is balanced at differentintervals, i.e., after mounting each individual part (impeller, spacer etc.) the rotorundergoes balancing.

3.10 STRUCTURAL AND MANUFACTURING

CHARACTERISTICS OF CENTRIFUGAL COMPRESSORS

3.10.1 Casings

Horizontally-split Casings. Both half-casings are obtained from conventionalcastings. The material is chosen depending on operating pressure and temperature,size, gas handled, and regulations provided by API stds. Generally used is material

COMPRESSOR PERFORMANCE—DYNAMIC 3.59

FIGURE 3.47 Welded casing.

similar to Meehanite GD cast iron with 25-30 Kg/mm tensile strength and 70 Kg/mm compressive strength. When steel has to be used to cast these casings, ASTMA 216 WCA steel is employed; should the compressor operate at low temperaturesASTM A 352 steel is used in one of its four grades depending on the operatingtemperature; lastly, ASTM 351 Gr. CA15 steel (13% Cr) or Gr. CF8 is used incase of corrosive media.

The usual test these castings undergo is the magnetic particle inspection. Inparticular cases, when a check through the section is required, the ultrasonic testis carried out. Sometimes radiographic inspection is required; it is useful as stressesaffecting these elements are limited and the flaws existing in castings, yet accept-able and not detrimental to such castings, can be displayed in this way. The latesttendency is to use welded casings, (Fig. 3.47) this has advantages over casting inthat, it reduces rejections, repairs etc.

Vertically-split Casings. Both casings and end covers should be obtained fromforgings so that material might be as hom*ogeneous as possible, hence more resistantto failure, considering the high pressures these compressors have to contend with.

ASTM A 105 Gr. II carbon steel is generally used for the barrel, supports andend covers: the carbon content applied (0.2 to 0.25% instead of 0.35%) is enoughto get good mechanical characteristics, at the same time granting characteristics ofweldability. Alloy steel with higher mechanical characteristics is used for com-pressors running under very high pressure.

Suction and discharge nozzles are welded to the casing, generally forged in thesame material; as to pipeline compresor, owing to their complicated structure hencenot suited to be forged (see Fig. 3.47), are often made of castings.

3.60 CHAPTER THREE

FIGURE 3.48 Barrel type compressor assembly.

Diaphragms. The diaphragms form the flow path of the gas inside the compres-sor’s stator. They are divided into four types: suction, intermediate, interstage anddischarge diaphragms.

The suction diaphragm conveys the gas to the first impeller inlet. It is suppliedwith adjustable vanes when the compressor control is performed by changing theinlet angle of gas to the impeller, operating outside the compressor.

The intermediate diaphragms perform the double task of forming the diffuser,where kinetic energy is converted to pressure energy, and the return channel tolead gas to the next impeller inlet. The diffusers can be free-vortex type or vaned:these vanes while improving the conversion efficiency, reduce the flexibility of themachine.

The discharge diaphragm forms the diffuser of the last impeller, as well as thedischarge scroll.

The interstage diaphragms separate the discharge sides of the two stages in thecompressors with back-to-back impellers.

Each diaphragm has labyrinth rings to make the impeller shroud tight (to preventgas at impeller outlet from returning to suction side) and on the spacer rings to cutout interstage leaks. The seal rings, of split construction, can be easily removed.

For reasons of rotor installation, the diaphragms are halved; whether they aremounted on barrels or on horizontally split casings, the difference is not as great;they only differ in their being housed in the casing.

In barrel-type compressors, the diaphragm halves are kept together by tierodsthus making up two separate bundles; after installing the rotor they are bolted toeach other: the resulting assembly (see Fig. 3.48) is placed in the casing axially.

In the horizontally-split compressors, each diaphragm half is singly installed inthe two casing halves; the outer surface on each diaphragm has a groove to combine

COMPRESSOR PERFORMANCE—DYNAMIC 3.61

FIGURE 3.49 Diaphragm assembly with rotor assembly on lower casing.

with the corresponding relief on the casing. Each diaphragm is lowered onto thehalf-casing. (See Fig. 3.49)

Concerning the design criteria, a distinction must be made between sizing of thegas path, on the ground of thermodynamic requirements to guarantee the speed andgas angle requested, and the sizing of thickness which is based on the �p estab-lished on the two faces of each diaphragm.

In normal installations (in-line, low or medium pressure compressors) this �pvalue is that produced by each impeller: hence it does not reach very high values.In a barrel compressor, e.g., with 8 impellers and 30 ata suction and 80 ata dis-charge, we have approximately:

80 8single impeller � � 1.13�30

therefore the max. �p produced by the last impellers amounts to about 9.2 kg/cm2.For these installations, the diaphragms are nearly always cast owing to their

complicated structure. Generally Meehanite GD type or spheroidal cast iron is used,sometimes adding nickel percentages to improve its characteristic impact resistanceat low temperature (1 to 1.5% Ni). If the operating temperature is below �100�C,

3.62 CHAPTER THREE

ASTM A 352 steel is used in the four available grades or ASTM A 351, gradeCF8.

Under a certain size of gas channel, casting is somewhat difficult, thereforediaphragms are manufactured in two parts, usually one cast and the other of sheet-metal, bolted to each other.

Under severe conditions such as in high-pressure compressor diaphragms orinterstage diaphragms in compressor with back-to-back impellers (undergoing the�p of one whole stage), the design �p of a diaphragm can reach very high values.In this instance, it is necessary to use materials such as forged carbon steels (ASTMA 182 F22).

Should very high pressures be involved, it is necessary to stiffen the diaphragmbundle structure. The solution consists in manufacturing the countercasing in forgedsteel ASTM A 182 F22) made up of two half-casings where diaphragms aremounted like in horizontally split compressors. This has the advantage of smallerdiameter diaphragms in which deflection is reduced (see Fig. 3.50.)

3.10.2 Rotor

The rotor of a centrifugal compressor is made up of shaft, impellers, balancingdrum, thrust bearing collar, the coupling hub and sleeves and spacer rings.

Shaft. The shaft consists of a central section, usually with constant diameter, onwhich impellers and spacers are mounted, and two ends with diameters suitablytapered to house bearings and seals. The shaft is sized to be as stiff as possible(reducing the distance between bearing centers and increasing the diameter ac-cording to the flow-dynamic design) to reach the best flexural behaviour. The ma-terial used to manufacture shafts for many compressors is steel 40 NiCrMo7 UNI.The mechanical characteristics of this steel are better than common carbon steel,which is sometimes used in compressor shafts.

Steel 40NiCrMo7 is very suitable for hardening and tempering; the normal-sizeshafts for centrifugal compressors made up of this steel, benefit from hardeningthrough the cross section while plain carbon steel will be affected only superficially.

Since the aim is to reach good toughness and ductility, rather than very highyield point and ultimate tensile strength, tempering is carried out at temperaturewhich allows the material to reach an ultimate tensile strength over 100 Kg/mm2

and yield point over 65–75 Kg/mm2.

Impellers. Impellers are shrink-fitted on the shaft (see Fig. 3.51).Under the impellers, splines are provided to transmit torque.Impellers are interference-fitted not only because of torque transmission, but also

to avoid loosening under high speed of rotation. Stresses due to centrifugal forces,can cause impeller to loosen, become eccentric and thus create unbalance.

Impellers may be, structurally, of closed or open type. The closed impellers aremade up of one hub, a number of blades and one shroud. Blading is generally

COMPRESSOR PERFORMANCE—DYNAMIC 3.63

FIGURE 3.50 Rotor assembly on lower casing.

slanted backwards. These parts are joined in different ways, but typically by weld-ing.

Blades are generally milled (see Fig. 3.52.) on the hub (or shroud), then theshroud (or the hub) is internally welded. The blades are milled on the hub or shrouddepending on the impeller shape and, hence, on the possibility for the electrode toget into the channel.

3.64 CHAPTER THREE

FIGURE 3.51 Impeller assembly on the rotor.

If, owing to the narrower width of the impeller, it is difficult to weld internally,external welding is carried out: on the shroud (or hub) near blading and accordingto its shape, grooves are carried out superficially. Hub and shroud are connectedto each other by temporary butt-welding. By filling these grooves with weld ma-terial, the facing surfaces between blade and shroud are melted thus resulting in aweld.

The impeller manufacturing cycle is the following: welding carried out as de-scribed before; followed by stress relieving heat treatment; inspection of weldedparts; hardening and tempering; and final machining.

Open impellers are different from the closed impellers in that the open lack ashroud. Usually this kind of impeller has tridimensional blades produced by mill-ing. Blading can be radial or slanted backwards.

As to the mechanical design, it has to be taken into account that the impellersare the most stressed elements in a compressor. Reducing the number of stagesleads to higher and higher tip speeds and, hence, stresses. The stress trend in thevarious impeller parts varies, of course, according to the impeller type. Use ofFinite Element Method (F.E.M.) allows for a fine analysis of the stress distribution.

COMPRESSOR PERFORMANCE—DYNAMIC 3.65

FIGURE 3.52 Impeller automatic milling.

3.66 CHAPTER THREE

More recently, even dynamic calculations are possible in a reasonable time usingaverage level computer platforms to compute the dynamic behaviour of the impeller(natural frequencies and relevant modal shapes).

Stress values corresponding to the various speeds are proportional to the speedratio squared. The severest condition occurs during the overspeed test (at 115% ofthe continuous max. speed). In particular there are stressed areas on the leadingedge of blades. Stress concentrations must be avoided, and as a general rule, whenmanufacturing impellers much care must be taken in finishing their surfaces anddesigning them, considering particularly the thickness, the key slots and roundingoff corners. Materials and heat treatments are chosen taking account of stress dueto centrifugal force (as a function of the tip speed at which the impeller has to run)and the working conditions, such as corrosion, stress corrosion, low temperatureetc.

To get good welds in blades, they have to be made of steel with high mechanicalcharacteristics, yet low carbon content. Typical material would be a low-alloy steelcontaining 2% chromium, 1% molybdenum and 0.13 to 0.17% carbon.

When impellers are manufactured using steel with higher carbon content, thusgetting better mechanical characteristics, there would be some doubts about qualityof welding, as the weld and the area around are subject to intercrystalline corrosion.This is the reason why some manufacturers call for limits in carbon percentage.Intercrystalline corrosion leads to the relaxation of the metallographic bonds amonggrains and, hence, to degradation of strength.

A carbon content in steel higher than its austenitic matrix solubility limit deter-mines the potentiality for the steel to be subject to intercrystalline corrosion, ascarbon is the main cause for carbide precipitation and chromium impoverishmentin the area around the grain boundary. The carbides precipitated along the grainboundary can initiate fracture, while the chromium impoverishment makes the ma-terial more liable to corrosion.

If steel remains at the sensitization temperature (from 400 to 900�C) during thequenching process after heat treatment, as well as during heating for welding, thechromium carbides may precipitate to a greater extent depending on the carboncontent.

When impellers handle corrosive media, steel with higher chromium content isused, such as X15C13 (13% Cr); in particularly corrosive areas the chromiumpercentage is further increased such as with KXOA2-FNOX steels (from 15 to 19%Cr); if higher strength along with corrosion resistance is required, then MARAG-ING steels, series 17% Cr, 4% Ni are used, age-hardened at low temperature. Steelwith up to 9% nickel is used for impellers running at low temperature; this contentwas arrived at to get good impact strength down to �196�C.

Balancing Drum. During normal operation, inside the compressor a thrust isgenerated against the rotor, which has to be taken up by the thrust bearing. Sucha thrust is mainly due to the pressures acting on the impeller. The �p produced bythe impeller generates a force in suction direction expressed by the product of �pmultiplied by the area underneath the seal on the shroud.

COMPRESSOR PERFORMANCE—DYNAMIC 3.67

The sum of these thrusts is generally very high and often beyond the thrustbearing capacity. Consider a medium pressure compressor, with 5 impellers, mean�p for each impeller � 6 Kg/cm2, shaft ø � 17 cm, seal ø � 27 cm, the generatedthrust is:

� 2 2(27 � 17 ) �6 �5 10370 Kg4

Therefore a balancing drum is provided for, after the last impeller; placing itsopposite face under suction pressure and sizing its diameter adequately, a thrust isgenerated from suction to discharge side, such as to balance the thrust coming fromthe impellers. Some unbalance is provided to obtain a residual thrust capable ofbeing taken up by the bearing, to avoid any axial unstability of the rotor. Otherthrusts are generated besides those described before, such as the thrust caused bythe variation of gas flow entering the impeller axially and leaving it radially, orsuch as the thrust resulting from the irregularity of pressure acting on the impellerin high-pressure machines. Generally, these thrusts are not so high to change thestate of things.

As regards shape, it has to be noted that the width of this drum be such as tosupport the whole �p developed by the compressor. Inadequate sizing of the lab-yrinth seal results in strong gas leakage towards suction, thus impairing compressorperformance. Generally, the balancing drum is made of X12C13 steel shrink-fittedwith key like the impellers.

Coupling. The coupling transmits power from driver to the compressor. Couplingcan be direct or through a speed increasing gear. Usually, toothed couplings areused with force-feed or filling lubrication. The couplings with force-feed lubricationare designed for high speed of rotation and for the most part they only are used incompressors. Another type of couplings is sealed, generally with lubricating greaseto be filled every so often; these couplings are used only on slower speed driveshafts.

When transmitting a torque a toothed coupling can originate an axial thrust ifthe shafts to be coupled vary their relative position, during transient load state orowing to thermal expansion, getting axially closer or farther apart. A relative dis-placement of the two shafts is not allowed, until an axial force is generated overthe friction value on the coupling toothing: up to this moment this force is carriedby the thrust bearing. An example of thrust in case of a compressor with power N� 10,000, rpm n � 10,000, and radius R � 100 mm. (radius of the couplingtoothing pitch line HP, is:

716 NM � � 716 Kgm transmitted torquet n

F � M /R � 7,160 Kg tangential force transmittedt t

As the toothing friction coefficient range is: 0.15 � ƒ � 0.3, an axial force isnecessary to overcome friction on toothing

3.68 CHAPTER THREE

F � F ƒ � 1074 to 2148 Kga t

To understand the thrust behaviour, it should be taken into account that the fixedpoint of rotor is the thrust bearing and the thermal expansion of the rotor is lowerthan that of casing. The use of diaphragm couplings has recently increased. Butthis type of coupling has some disadvantages. It’s main advantage is accomodationof high misalignments, but at same time it is heavier. There’s a negative effect onthe flexural behaviour of the rotor at the second critical speed, difficulty in balanc-ing, and possibility of fatigue failure in the thin plates.

Thrust Bearing Collar. The thrust bearing collar is made of C40-carbon steeland is generally force-fitted hydraulically.

Spacer Rings. The spacers are sleeves placed between impellers having doublefunction: to protect the shaft from corrosive media (generally they are made ofX15C13, a stainless steel with 0.15% carbon and 13% chromium), and to fix therelative position of one impeller versus another.

The spacers are shrink-fitted on the shaft with 0.5 to 1% interference. The stressresulting from such a shrinkage is:

�1 1 1 2� � �E; � � � � � 21,000 � 21 Kg/mm1 1000 1000

The tangential stresses �t caused by the centrifugal force could eliminate thisinterference, should they overcome those due to shrinking. If it’s considered that aspacer is stressed at most by �t � 8 Kg/mm2 at a tip speed � 100 m/sec (rarelythis speed is exceeded in usual cases because of the small radii), then the spacershould not detach from the shaft.

Sleeves Under Oil Seals. Sleeves under oil seals are of carbon steel, coated withvery hard material (600 Brinell hardness). Colmonoy is typical of coatings usedfor this purpose. These sleeves are applied to protect shaft from corrosion and anyscoring; in addition they can be easily replaced. In case of high pressure, Colmonoycoated sleeves are not used because they are limited in the amount of shrink thatcan be applied; in this case sleeves of 40 NiCrMo7 hardened and tempered steelare used (300/350 Brinell hardness).

3.10.3 Seals

Seals at the two shaft ends, at the points where shaft comes out of the casing, areused to avoid or minimize leakage of compressed gas or air getting into the com-pressor casing. This seal can be of three types: labyrinth, oil or mechanical seal.

Labyrinth Seals. These seals are made of blades of light-alloy or material resis-tant to corrosion, with hardness lower than the shaft, to avoid damaging it in caseof accidental contacts. They can be easily removed. The blade number and clear-

COMPRESSOR PERFORMANCE—DYNAMIC 3.69

FIGURE 3.53 Mechnical type seal.

ance value depend on the operating conditions. If no slight gas leakage is allowed(poisonous, explosive gases etc.), the labyrinth seals are combined with extractionor injection systems. Labyrinth seals are sometimes made of annealed aluminumalloy (70–80 Brinell hardness); if aluminum is not compatible with gas corrosivity,stainless steels are used with 18% Cr and 8% Ni content. There is no limitation touse other materials such as bronze, babbitt etc.

Oil Seals. Oil seals consist of two floating rings (H.P. ring on high pressure side,L.P. ring on low pressure side) babbitt-lined (see Fig. 3.45–3.46 showing a pictureof a typical compressor equipped with several L.P. seal rings).

Seal oil is introduced, at a pressure slightly over the gas, into the annular spacebetween the two rings and flows through the gap left between rings and shaft. Oilcoming from the low pressure side goes back to the reservoir and is recirculated;oil from h.p. side is drained by automatic traps.

Oil is prevented from flowing into the gas by a large labyrinth seal placedbetween the oil seals and compressors inside, equipped with an intermediate pres-sure balancing chamber.

The oil seals are made up of a carbon steel support ring, coated with a thinwhite metal layer or copperless white metal, if not compatible with the gas handled.

Mechanical Seals. The mechanical seal consists chiefly of a carbon ring, gen-erally stationary, kept in contact with a steel collar rotating with the compressorshaft. This contact is maintained by the combined action of elastic elements

3.70 CHAPTER THREE

(springs or bellows) and the distribution of pressure acting on the ring. Heat isgenerated by the contact between collar and ring and must be removed by coolingthe oil seal. The differential pressure between oil and gas must be high (3 to 5ata), to lubricate the gap between collar and ring. To keep this �p constant, apressure chamber has to be built up, making it necessary to have a low pressureseal between pressurized oil and atmosphere. In most instances the seal is a carbonfloating ring.

Mechanical seals are applied where oil contaminating the gas must be kept tominimum; in fact, oil leaking from the H.P. ring is about 10% that from usual oilseals. In case of compressor shutdown for lack of oil, the seal can continue sealinggas with the machine at a standstill (even if not perfectly, depending on conditionof the mating surfaces between collar and ring).

3.10.4 Bearings

Journal and thrust bearings are usually plain type with pressure lubrication. Theyare placed outside the compressor casing and can be inspected without releasingpressure from casing inside. Generally, the thrust bearing is mounted outside thejournal bearings and on the side opposite to the coupling. This solution aims atreducing the center distance, thus improving the flexural behavior of the compres-sor.

For machines constituting a compressor train, having two couplings, the abovesolution would result in having one shaft end loaded by the coupling and the thrustbearing weights—thus possibly leading to flexural problems, because masses con-centrated outside the journal bearings produce the second critical frequency. Toovercome this, the thrust bearing is mounted inboard as compared with the journalbearings.

Journal Bearings. At present, many compressors are equipped with tilting padbearings. They seem to be the most suitable for resisting any unbalancing actionof the oil film.

Their use is based on computers studies of the effect on shaft vibration fre-quencies. Carbon steel is the backing material chosen for most bearings. Workingfaces of the pads are usually coated with babbitt metal (a tin alloy); the metalapplication applied by centrifugal casting techniques.

Thrust Bearings. The thrust bearings used on many compressors are also of thetilting pad type, provided with supports to distribute load equally (see Fig. 3.54).The pads act on the collar hydraulically fitted onto the shaft. Although compressorsare designed to run generally with a positive thrust, i.e., towards the thrust bearingoutside, their bearings are double-acting type. They have, pads also inside to sup-port negative thrusts caused by extraordinary conditions (transient states, start-upsetc.).

Outside the bearing a ring with a gauged hole is provided to control oil flow forlubrication. Typically speed of the collar should not exceed 190 m/s, and load on

COMPRESSOR PERFORMANCE—DYNAMIC 3.71

FIGURE 3.54 Thrust bearings.

bearing not over 50% of maximum limit stated by manufacturer. These are typicalparameters adopted to choose the bearing to be mounted.

3.11 INDUSTRIAL APPLICATION OF CENTRIFUGAL

COMPRESSORS

Centrifugal compressors have a large number of applications in numerous sectorsof industry and particularly in many processes that call for very wide performanceranges. The last 30 years in particular have seen continuous expansion in the fieldof application which has grown to encompass some services traditionally coveredby other types of compressors. This is also due to a big rise in individual plantcapacities as well as to introduction of new processes. In fact, centrifugal com-pressors were initially used mainly as atmospheric air blowers for blast furnaces,mines, etc. They had flow rates that varied greatly from case to case, but alwayslow pressure ratios. Later, as they began to become more common in chemical

3.72 CHAPTER THREE

FIGURE 3.55 Schematic diagram of a refinery.

plants these machines had to change considerably. The gases compressed changedfrom atmospheric air to different gases and then to gas and/or vapor mixtures, allwith different characteristics from air. Also the compression flows and pressureratios increased remarkably to meet process requirements. Some of the main pro-cesses requiring centrifugal compressors are outlined below along with the principalfeatures of the machines used for them.

3.11.1 Refineries

Fig. 3.55 shows a schematic diagram of a refinery with the main process lines.The heart of a refinery is a fractionating column which separates the various

crude components that may be used as they are, or further treated

Reforming. In reforming plants hydrocarbon molecular structures are changedfrom an open-chain to a cyclic structure which translates into an improved octanerating for reformed substances. This reaction which involves evolution of hydrogentakes place in a reactor with a catalyst which is almost always platinum, hence theterm platforming generally used to indicate this process.

The compressor’s task is to recycle the gas mixture in the reactor with a highpercentage of hydrogen which minimizes side reactions that tend to form carbondeposits on the catalyst eliminating its porosity and consequently deactivating it.

COMPRESSOR PERFORMANCE—DYNAMIC 3.73

The extra pressure the compressor gives the gas is therefore used essentially tomake up for the pressure losses in the system ensuring a constant gas flow.

As a rule, pressure ratios are not very high and operating pressures vary from20 to 40 bars. It is interesting to note that the molecular weight of compressed gasmay vary in time in relation to the condition of the reactor. This is because thecatalyst tends to become more and more heavily coated with carbon deposits andtherefore the compressor has to recycle gas which has more and more hydrogen init. Beyond a certain limit it is necessary for the economy of operation to regeneratethe catalyst.

Cracking. The heavy distillates produced by the fractionating column can betreated by a cracking process in order to break the heavy molecules into lighterones to get premium grade fuel.

There are several types of cracking processes, one of which is Fluid CatalyticCracking (FCC) which requires centrifugal compressors. This process gets its namefrom the fact that the reactor has a fluid catalytic bed. This feature offers severaladvantages such as an even distribution of temperature, a very large area of contactand good heat transmission. Air compressors are required with delivery pressureswhich may vary from 2 to 4 bars depending on the process. Also cracking gascompressors with a relatively high molecular weight (30 to 40) and delivery pres-sures around 15 to 17 bars are necessary. Axial compressors are sometimes usedto compress the air as low pressure ratios and relatively high flows are required.

Lubricant Production. In plants which utilize the heavy distillates produced bythe fractionating column, centrifugal compressors are chiefly used in the oil de-waxing process. Since paraffin wax crystallization takes place at low temperaturesand separation at low pressures, it follows that two different types of compressorsare necessary:

• Refrigerating compressors, which generally handle propane with design temper-atures around �20�C

• Compressors that maintain a high vacuum level (suction pressure is usually 0.2bars) inside the large rotary filters where the crystallized paraffin wax is depos-ited. Both machines have low operating pressures and therefore they normallyhave horizontally split casings.

Bitumen and Asphalt Production. Bitumen is obtained by oxidating the heavydistillate produced by the fractionating column in a tower with air flowing throughit. A low-pressure air compressor is therefore required, generally on-line withoutintercooling.

3.11.2 Ammonia Synthesis Plants

NH3 synthesis plants have been extensively applied in industry particularly overthe last 20 years. It has been noted that the trend is for bigger and bigger plants

3.74 CHAPTER THREE

FIGURE 3.56 NH3 synthesis plant outline.

while processes have been developed with lower and lower synthesis pressures. Atpresent, the most common size of plant ranges between 800 and 1800 metric tonsper day and synthesis pressures vary between 180 and 260 bars depending on theprocess. An NH3 synthesis plant is outlined very schematically in Fig. 3.56. Theprocessed materials are natural gas (most common), water or air.

Natural gas compressed to approximately 40 bars by compressor C1 is injectedinto the desulphurization plant to protect the catalysts used in the process from thesulphur. The gas is then sent to the first reformer where steam is injected; with acatalyst it slowly combusts producing H2, CO, CO2 and considerable quantities ofmethane.

The mixture of hot gases then passes to the second reformer where it is mixedwith heated air at 30 to 40 bars from compressor C2. Due to the presence of aircombustion in the second reformer is rapid. It may be expressed as follows:

→2H � CO � N (exothermic reaction)CH � O � N ← 2 2 24 2 2

The heat developed by this reaction which raises the temperature of the reagentsto around 1000�C is used to produce the steam required for the process that is

COMPRESSOR PERFORMANCE—DYNAMIC 3.75

generated in exchanger S1 downstream from the second reformer. The gas mixturethen flows into a separator where the carbon monoxide is removed. It is cooled toeliminate excess water vapor and finally put into a separator to eliminate the carbondioxide CO2. To purify the mixture of any remaining CO or CO2 methanizationfollows whereby carbon residues are hydrogenated to produce methane and water.At this point of the process, a mixture of H2 and N2 is obtained containing a smallpercentage of methane which forms the synthesis gas mixture. This mixture is thenbrought to a pressure, which may vary according to the type of process used, inorder to make the synthesis reaction shift more easily:

→ 2NH (exothermic reaction)N � 3H ← 32 2

Since the reaction is exothermic here too the heat is recovered downstream fromthe reactor to generate steam. The ammonia is condensed next by cooling with achiller plant; a refrigerating compressor CF is used for this using ammonia as therefrigerating fluid for obvious reasons. Finally, in separator S the ammonia that hasformed is separated and the gas that has not transformed into ammonia is remixedwith the fresh gas and recycled through compressor CR. It has been seen howseveral types of centrifugal compressor are used in an ammonia synthesis plantprocessing gas differing in nature, pressure and temperature; the characteristics ofthese machines are briefly outlined below.

Natural Gas Compressors. Compression takes place in one or two casings reach-ing a final pressure of approximately 40 bars. In units with two casings, there is alow pressure compressor with a horizontally split casing, MCL type, and a highpressure compressor with a barrel type casing open vertically at both ends.

Air Compressors. A final pressure of 30 to 35 bars is normally reached with twohorizontally split compressor casings.

Each compressor casing houses two back-to-back compression stages with ex-ternal cooling. This arrangement is preferred for the lesser number of compressorcasings and lower absorbed power.

Synthesis Compressors. A train of synthesis compressors is composed of a min-imum of two casings and maximum of four depending on plant dimensions andthe processes used, i.e., the pressure ratios to be achieved.

Barrel type compressors are employed incorporating either a single stage (BCLcompressor) or two stages (2BCL compressor) in a back-to-back arrangement. Therecycled gas is normally compressed by a single impeller positioned in the endcompressor casing back-to-back with the impellers that compress the fresh gas.These compressors were the first centrifugals widely applied in industry in the 60’sfor high pressures.

Refrigerating Compressors. This service, which uses NH3 as refrigerant fluid, isnormally performed with one or two low pressure compressor casings.

3.76 CHAPTER THREE

FIGURE 3.57 Axial compressor for process applications.

3.11.3 Methanol Synthesis Plants

Methanol or methyl alcohol CH3OH is obtained today by synthesis processes. It ismainly used for the following:

• As solvent in the chemical industry for preparing paints, etc.

• As the starting product for preparing formic aldehyde (formalin)

• Preparing antifreeze aqueous solutions (a solution made up of 40% methyl al-cohol in water freezes around �40�C)

• As fuel, especially blended with petrol (10 to 20%) in order to considerablyincrease the fuel grade (the octane rating of methyl alcohol is 120)

As regards the process in recent years there has been a tendency to use lowpressure processes while plant capacities have grown considerably. Nowadays 2000to 2500 MTPD plants are normally required and there are projections for 5000MTPD plants. A typical low pressure process (ICI) makes it possible to obtain 99.5to 99.99% methanol starting with natural gas, steam and carbon dioxide.

After the natural gas is desulphurized it is reformed with steam to obtain syn-thesis gas consisting of CO, CO2, H2 and CH4. The reforming pressures and tem-peratures depend on the quality of the initial material but range between 10 and20 bars, 800 and 900�C. The heat developed by the synthesis gas reactions is mainlyused to produce steam. The gas is then cooled and sent to the compressors whichcompress it to 80 to 90 bars and send it to the reactor for conversion into methanol.On leaving the reactor, the gas is cooled and the methanol separated from the gasthat has not reacted. As usual there is a recycle impeller to recompress the gas andsend it back into the reactor. Machines in methanol synthesis service are normally

COMPRESSOR PERFORMANCE—DYNAMIC 3.77

FIGURE 3.58 Gas turbine axial compressor.

made up of 2 or 3 compression stages in 2 barrel type compressor casings. Com-pressors that handle the synthesis gas are normally directly coupled to a steamturbine, frequently the type with a double exhaust. The recycle compressor is some-times driven separate from another steam turbine.

3.11.4 Urea Synthesis Plants

Like the NH3 synthesis plants, urea synthesis plants have developed in recent yearsreaching ever greater capacities while the trend has been towards relatively lowpressure synthesis processes. Now plants utilizing centrifugal compressors onlyvary in size from a minimum of 600 to a maximum of 1800 MTPD; up to theearly 70’s, CO2 was compressed by a combination of centrifugal and reciprocatingcompressors. The processes that have become most common can be divided intotwo categories requiring pressures of 150 to 160 bars and 230 to 250 bars respec-tively.

Urea is obtained by synthesis of liquid NH3 and gaseous CO2 through the knownchemical reactions

→2NH � CO NH CO NH (exothermic reaction)←3 2 4 2 2→NH CXO NH ← NH CONH � H O (exothermic reaction)4 2 2 2 2 2

In practice, with the first reaction carbamate is formed and then dehydrated to formurea. Centrifugal compressors were used that compress almost completely pure CO2

from atmospheric pressure to the synthesis pressure. Compression normally takesplace in two casings (150 to 160 bar synthesis) or in three casings (230 to 250 barsynthesis).

3.78 CHAPTER THREE

A train is made up of a low pressure compressor with two compression stages(2MCL compressors) and of one or two high pressure compressors (2BCL andBCL compressors). These machines have to achieve very high pressure ratios con-sequently with great differences in flow rates between the beginning and end ofcompression (the pressure ratios are 150 to 160 or 230 to 250 respectively). Highgas density even at not particularly high pressures calls for special attention in themechanical sizing of the rotors. This is peculiar to urea synthesis as compared toas in ammonia synthesis, for instance, the problem does not exist on account ofthe lower molecular weight of the gas.

Another difference is that CO2 is corrosive, particularly if wet; its corrosivenessis related to pressure and temperature and therefore also the type of material em-ployed has to vary along the compression path. Although carbon steel is normallyused in the first compressor casing all parts in contact with the gas in followingcasings have to be stainless steel.

3.11.5 Natural Gas Service

Demand for machines to compress natural gas to medium and high pressures hasgrown considerably in recent years as a result of development of some specialservices such as reinjection, transportation and gas liquefaction followed by regas-ification. The first two services basically originate from the fact that in the last tenyears or so, it has become more and more economical to recover gas that used tobe flared at wellheads or that at any rate failed to be put to profitable use. Theseservices are outlined here below and the machines most commonly used described.

Gas Reinjection. Natural gas reinjection has become widespread over the last tenyears. It has several purposes chiefly depending on the nature of a field. In short,one can say that natural gas is reinjected for any of the following reasons:

• To maintain wellhead pressure with the gas that is obtained during extraction ofcrude oil, thus allowing the production of crude to be kept practically constant.Gas injection has a ‘‘piston’’ effect.

• Gas storage: consisting in storing the gas which is usually obtained along withcrude oil in wells until it can be used as a source of energy.

• Gas lift system: consisting in injecting gas into the crude production well in orderto lighten the well column. This system is normally adopted in fields where waterinjection is used for extraction. By injecting water and extracting crude in timethe specific gravity of the mixture tends to increase and the percentage of crudedrops. The gas lift technique is used to improve well productivity.

• Peak shaving: a system used in highly developed industrial areas.

This is particularly advantageous from a saving point of view when there is adepleted natural reservoir in a highly industrialized area. The natural gas pipeline,in this case, can be sized for the average consumption in the area and during hot

COMPRESSOR PERFORMANCE—DYNAMIC 3.79

periods, excess gas is stored in the reservoir. In cold weather, the stored gas canbe used for peak demand.

• Gas is injected in noncondensed gas fields: or into gas fields contain widelyvarying quantities of condensate. For example, at Groning (Holland) the conden-sate content is 6 g/m3 whereas at Hassi R’Mel (Algeria) it is over 220 g/m3.

The condensates are separated in de-gasolining units and the dry gas can bereinjected into the field. The aim of this injection is to maintain pressure in thefield and with the injected dry gas to facilitate absorption of condensates in thegas. The end purpose is therefore that of producing gasoline with the gas actingas vector fluid. Main features of the compressors may be summarized as follows:

• Delivery pressures vary from 100 to 150 bars for gas lift service and some peakshavings, to 250 to 500 bars for the other systems with the exception of somereinjections which requires pressures of 600 to 700 bars (the maximum requiredtoday for centrifugal compressors). The problem of designing machines capableof reaching such high pressures has been solved only since the 70’s.

• The compressors are therefore barrel type, but train compositions vary greatlyfrom application to application.

• These compressors handle high density gas, therefore as was mentioned for ureasynthesis, particular attention has to be given to the mechanical and aerodynamiccalculations and tests.

• Finally, since these units are often situated in desert areas or at any rate far fromindustrialized areas, a characteristic in particular demand for these units is thatthey are packaged. That is, the machines have to be self-contained, easy to trans-port and to install (package units), should require minimal maintenance and haveremote control.

Gas Transportation. The numerous compressor stations distributed along gaspipelines normally utilize PCL centrifugal compressors. These are machines withmodest pressure ratios (r � 1.2 to 1.8) which are required to provide relativelyhigh efficiency as they are usually driven by gas turbines which burn a high qualityfuel such as the very gas that is in the gas pipeline.

Particular attention is therefore dedicated to the design and engineering toachieve high efficiencies. Three-dimensional impellers are normally used and theconfiguration of the machine allows the impellers to be spaced out along the axiswith gently curved return channels for good impeller inlet conditions.

Liquefaction and Regasification. The growing demand for natural gas for use inindustry and domestic heating makes it necessary to use the huge quantities of gaswhich are available also from fields such as those in Algeria or Libya from whichgas is transported in liquid form.

Among the equipment required for this technology, centrifugal compressors inparticular and rotary machines in general have proven to be very versatile by being

3.80 CHAPTER THREE

FIGURE 3.59 Diagram of oxygen compression from1 to 40 bars in four stages.

able to be used for gathering as well as in the later stages of transportation, liq-uefaction and regasification. The gas that comes out of the wells is compressed bymeans of centrifugal compressors and put into a gas pipeline which takes it througha series of compression stations, previously described, to the liquefaction stationlocated near the gas loading buoys. The gas is liquified in plants using centrifugalcompressors whereas the ships are often driven by gas turbines fueled on part ofthe substance that changes from liquid to gaseous state during transport. The naturalgas is stored at the port of arrival in liquid form in special tanks; it is then takenfrom these to be heated, vaporized and put into the gas pipeline again by centrifugalcompressors.

The mechanical energy required to compress the gas is provided by a gas turbinesystem and the thermal energy necessary for vaporizing the gas is recovered fromthe exhaust gases from the same system.

A typical regasification station in Italy is the one at Panigaglia in the gulf of LaSpezia.

3.11.6 Oxygen Service in Metallurgical Plants

One of the initial premises for the development made in steel production is thepossibility of utilizing great quantities of very cheap oxygen (Fig. 3.59).

Construction of the most advanced low pressure air separation plants alongsidethe steelworks has been expanding now for years. The average capacity of theseplants has risen from approximately. 300-t/d (ton per day) in 1965 to the present1000 to 1500 t/d for every unit installed and units are being designed for over5000 t/d.

COMPRESSOR PERFORMANCE—DYNAMIC 3.81

FIGURE 3.60 Gas turbine centrifugal compressor.

Another determining element in connection with these new production levels isuse of the oxygen centrifugal compressors which are now constructed for largeflows and high pressures and are therefore capable of satisfying the most exactingrequirements of modern metallurgical plants as well as influencing the choice ofrequirements. The advantages ensuing from introducing centrifugal compressorsalso in the metallurgical sector soon became apparent as a consequence of theeconomy due to the simple operation, modest maintenance requirements and rel-atively low total cost of installation.

Around 1965, centrifugal compressors were installed with capacities rangingfrom 16,000 to 28,000 Nm3/hr and final pressures of 25 to 30 bars; in recent yearscentrifugal compressors have come into operation compressing 40,000 Nm3/hr at40 bars and machines are now being designed for chemical service to reach over60 bars. These achievements have been made possible by overcoming the problemsthat principally concern the danger of fire as a result of 99% pure oxygen in contact

3.82 CHAPTER THREE

FIGURE 3.61 Typical performance map for a compressorstage.

with flammable materials including the metal used to construct the compressors.The risks of fire grow considerably when gas pressures, temperatures and flow ratesrise and the causes can only be partially controlled.

Compressors for service in steel works are presently employed at an operatingpressure of approximately 40 bars, which is the highest pressure standard of thoseadopted in metallurgical plants for the oxygen distribution network. The gas isgenerally compressed in four successive stages in two casings: The cast iron andsteel casings are for low and high pressure respectively, they are horizontally-splitand each has balanced opposed stages with sidestream suction nozzles and inter-stage discharges.

The gas is cooled after each discharge in water coolers installed outside themachines.

3.12 ANTISURGE PROTECTION SYSTEM

3.12.1 General

Surge control represent a regulation system to maintain compressors inside theirstable working range, assuring a volume flow rate at impeller inlet section, higherthan the surging rate. An efficient control method prevents compressors and otherturbo-machines from crossing the surge line and avoids rotating stall conditions forcompression ratios as wide as possible. These aerodynamic instabilities are intrinsicto almost all kinds of turbo-machines, and often represent a strong limitation tothe range of efficient performance. Anti-surge control systems can thus representa useful instrument to improve the global performance of a compressor.

Fig. 3.61 represents a typical performance map, obtained from compressor testresults. In the figure the compression ratio � (p2 /p1), across the whole machineis plotted against volume flow rate Q1. One of the most striking features of a typical

COMPRESSOR PERFORMANCE—DYNAMIC 3.83

performance characteristic is the strong dependence shown by the compressor onthe rotational speed (N1 and N2 in figure). As previously stated for a centrifugalcompressor efficient operation at constant N lies to the right side of a pseudo-parabolic line called ‘‘surge’’ line, approximately falling near maximum point forpressure. Both for a axial or centrifugal compressor the surge line delimits therange of stable working conditions, unstable operation being characterized by se-vere oscillation of the mass flow rate.

The extreme regulation line (dotted line in the picture), should be parallel andslightly to the right with respect to the actual surge line.

The measure of the volumetric flow rate processed by the turbo-machine isnecessarily the key point for any kind of regulation system. In general the surgecontrol system can be chosen according to different specific requirements and relieson other physical variables different from volume flow rate, but some basic featuresshould be guaranteed:

a. The regulation line should be as close as possible to the surge limit line movedparallel to the capacity axis by an established amount.

b. When conditions of the suction fluid vary, the regulation line should not get anycloser to the surge line, relating to the design conditions, than may be necessaryfor proper operation of the antisurge system.

c. The regulation system should protect the machinery in an automatic way duringstart up, standstill, and all possible off design conditions.

3.12.2 Basic Regulation Theory

The application of general formulation of similarity laws in a turbo-machine states:the working condition for two different rotational speeds are dynamically similarif all fluid particles, in corresponding points within the machine, have the samedirection and velocities proportional to blade speed.

If points, belonging to different dimensional characteristic curves, represent dy-namically similar states, then the nondimensional groups of variables involved inthe physical problem (ignoring Reynolds number effects), are expected to have thesame numerical value.

The dotted line in Fig. 3.61 shows that the set of dynamically similar states lieson a parabola, since the nondimensional groups Q / (ND3) and gH / (ND)2 are insimilarity.

If similarity theory is applied to the same turbo-machine, D is constant, sodynamic head becomes proportional to N2 and volume flow rate to N. In particular,for surge points the following laws can be applied:

Q � K�N (3.71)1

2H � KN (3.72)p

Eliminating N, from (3.71) and (3.72), the equation for the surge curve can beobtained:

3.84 CHAPTER THREE

2H � K�Q (3.73)p

Surge points, in a single stage compressor, for the various speeds lay on a parabolawith vertex in the origin and axis coinciding with the axis of ordinates on thepolytropic head—volumetric flow rate plane.

The polytropic head can be obtained from (3.8), while volume flow rate can beexperimentally derived from measures with a calibrated orifice, through the follow-ing relation:

Q � C � � �2gh (3.74)1 Q 2 c

in which h is the measured pressure loss in the orifice, expressed in mmH2OCQ is a flow coefficient depending both on the geometrical characteristics of theorifice (�2 /�1) and, the real flow conditions though Cr (related to viscosity lossesand flow contraction):

CrC � (3.75)Q 2�21 � � �� 1

Fluid compressibility is accounted in equation (3.74) �c depending on pressuredrops in the orifice.

Once the geometry of the orifice and his fluid-dynamics characteristics areknown the following expression for volume flow rate can be used:

h1Q � � (3.76)1 �1

where 1 is the specific weight, expressed in the following way for a perfect gas:

41 P 101 3 � � � (Kg/m ) (3.77)1 R 3Z T1 1

Substituting in equation (3.76) the 1 value obtained from equation (3.77), thefollowing final expression for the volume flow rate can be obtained:

h � R � Z T1 1 1Q � � (3.78)1 � P1

with h1 expressed in Kg/cm2

Substituting equations (3.74) and (3.78) in (3.73) the following relation can beobtained between stage compression ratio in incipient stall condition and volumetricflow rate measured in the calibrated orifice:

n h � RZ T1 1p�1 / n 2Z RT ( � 1) � K� � (3.79)1 1 n � 1 P1

Simplifying:

COMPRESSOR PERFORMANCE—DYNAMIC 3.85

n h1n�1 / n 2( � 1) � K�� (3.80)n � 1 P1

or equivalently:

1 n n�1 / n� P � 1 � h (3.81)� �1 12K� � n � 1

For different inlet conditions and speeds surging can be avoided, from formula(3.81) if:

1 n n / n�1h � � P ( � 1)1 12K�� n � 1

or equivalently if:

h 11 � (3.83)2n K��n�1 / n( � 1)P1n � 1

Formula (3.83) is a very useful relation to avoid surge and stall condition for thefollowing reasons:

1) The rotational speed of the compressor is not explicitly involved.

2) The calibrated orifice pressure loss (h), is the only required measurement, re-gardless pressure, temperature, gas composition.

3) Gas composition can be explicitly accounted through polytropic exponent n,changes of n having however very poor effect on the following value:

n n / n�1( � 1)n � 1

so they be neglected in first attempt.From a more physical point of view, in formula (3.83) the compression ratio,

depending both from speed and inlet conditions is employed to balance the volumeflow rate.

Although extremely simplified, formula (3.83) can be too complex to be realizedwith simple instrumentation. However, if the compression ratio is small enough,for example in single or two-stage compressors, the quantity n /n � 1 ( �n / n�1

1) can be substituted by ( � 1) in first approximation. The error is always in thesafe direction being:

nnn�1 � 1 � ( � 1).

n � 1

With this approximation formula (3.83) becomes:

3.86 CHAPTER THREE

h 11 � 2P ( � 1) K��1

or better:

h1 � K�� (3.84)P ( � 1)1

where

1K�� .2K��

A first estimate of percentage error can be obtained from the expression:

� 1� � 100 � � 1 (3.85)

n n�1 / n� �( � 1)n � 1

Leading to the following expression for the percentage error in the volume flowrate:

�� 100 � 1 � � 1 (3.86)� �Q1 � 100

In general, error in flow rate is about one half of that due to the substitution of( � 1) with n /n � 1/( � 1) so that:n / n�1

�� Q � (3.87)1 2

Rewriting formula (3.84) in the following way:

h� K�� (3.88)

P � P1 1

or:

h� K�� (3.89)

�p

(3.89) is the equation of a parabola (in the plane ,Q1) with origin in the point � 1; Q1 � 0 (see Fig. 3.62).

This type of anti-surge system is extremely simple. All the necessary informationto protect the machine can be collected with only two differential pressure trans-ducers, the first instrument measuring pressure drops through the calibrated orificeand the second the real pressure rise inside the centrifugal compressor stage. The

COMPRESSOR PERFORMANCE—DYNAMIC 3.87

FIGURE 3.62 Surge line in � Q1 plane.

values, previously converted in electric signals are sent to a divider unity, whichcomputes the result of the ratio in (3.89). This value is then transmitted sent to aregulation unit, on which the value of the anti-surge regulation set-point K’’ issettled. The regulator acts on the by-pass valve, preventing the ratio from goingbelow the established set-point avoiding unsafe working range to be reached.

3.13 ADAPTATION OF THE ANTISURGE LAW TO MULTI-

STAGE COMPRESSORS

When the compression ratios are high as for multistage compressors, surge curves,are no longer parabolic. Surge conditions can be due to different impellers at dis-parate speeds and thus the previously obtained equation it is no longer safe toprotect the machine unless cutting wide operating range areas, otherwise useable(see Fig. 3.64 as a reference).

This kind of situation can be avoided through the transformation of the basicequation with the introduction of a multiplicative factor in the expression of�p (P1) leading to the following formula:

h1 � K (3.90)P � aP2 1

The introduction of a coefficient allows the shifting of the origin of the parabolaalong the vertical axis, from � 1 up to � 0 (see Figs. 3.65., 3.66., 3.67.), whilemaintaining the basic characteristics of the original equation.

If vertex of the parabola is in the origin of the reference system, where � 0,equation (3.90) can be simplified in:

3.88 CHAPTER THREE

FIGURE 3.63 h1 /�p � K regulationscheme.

FIGURE 3.64 Regulation curve for multistage compressor.

h1 � K (3.91)P2

To make the h1 /P2 � aP1 � K equation, one makes use of the diagram in Fig.3.68.

If a � 0 then the simplified schematic diagram in Fig. 3.69 can be used.If the operating ranges of a multistage compressors are wide, the maximum

employment exploitation of the stable compressor field becomes necessary. Now-adays, always more often the preceding equation may not suffice for the purposeand further processing can be required. As a consequence a function generator canbe introduced on either the left and right signals of the basic equation (3.90). Thus

COMPRESSOR PERFORMANCE—DYNAMIC 3.89

FIGURE 3.65 Regulation curve for multi-stage compressor (Es. a).

FIGURE 3.66 Flexible regulation curve formultistage compressor (Es. b).

the antisurge curve can be modified in order to fit the surge curve as accurately aspossible. A typical form of the basic equation is reported in eq. (3.92) and repre-sented schematically in Fig 3.70:

h1 � K (3.92)ƒ(�p)

in which function ƒ can have the most general expression (based on the require-ments of the function generation unit) as shown in Fig. (3.70).

The use of a general function for the generation of one the two signals can havesome drawbacks. In fact, in all the previously stated antisurge laws, h and �p signals

3.90 CHAPTER THREE

FIGURE 3.67 Flexible regulation curve formultistage compressor (Es. c).

FIGURE 3.68 Regulation scheme type h1 / (p2

� aP1) � K.

were both linearly dependent with the inlet pressure (h1 � Q12P1; �p � P1( �

1)) and, as a consequence, the resulting antisurge curves were insensitive to theinlet pressure changes. In this case the generic signal ƒ(�p) can depend upon inletpressure in a more complicated way.

For a generic function y � ƒ(x), the ratio between the relative variation of thedependent variable y is related to the relative variation of the independent variablex in the following way:

�y �x y�� y � � � � �x (3.93)

y y y

where y � is the first derivative of y in the point (x;y).

COMPRESSOR PERFORMANCE—DYNAMIC 3.91

FIGURE 3.69 Regulation scheme type h1 /p2 �K.

FIGURE 3.70 Regulation curve.

Eq. (3.93) can be applied in the surge problem. The change for ƒ(�p) expressedas a function of the relative ratio �p, of the inlet pressure P1, is given by thefollowing expression:

�ƒ(�p) ƒ�(�p)� ��p (3.94)

ƒ(�p) ƒ(�p)

where:

3.92 CHAPTER THREE

��p � (P � P )( � 1) (3.95)1 1

and ƒ �(�p) is the derivative of function ƒ(�p) in the considered point.The h1 relative change is related relative change of P1 around point 1 by theP

relation:

�h P � P1 1 1� (3.96)h P1 1

The percentage error on the inlet volume flow rate, expressed as a function of thegeneric anti-surge curve at the design pressure 1 is:P

ƒ �(�p) � (P � P ) ( � 1)1 11 �ƒ(�p)

�Q (%) � 100 � 1 (3.97)1 P � P1 11 �� P1

In a series of machines, where the change in the inlet pressure could be remarkable,the shift in position of the antisurge curve is large enough and only partially bal-anced by the corresponding movement of the surge curve. In fact, (supposing theinlet pressure is the only modified variable), the latter feels a change in P1 both inZ1 factor and n value,

In these cases, the balancing of the two signals (h and �p) with the inlet pressureis an efficient tool to obtain antisurge curves almost insensitive to changes in theinlet pressure.

The general formulation can be therefore written in the following form:

P1h �1 P1 � K (3.98)P1ƒ �p �� P1

The practical realization of this equation can be performed through the schemeshown in Fig. 3.71:

3.14 ANTISURGE LAWS FOR SPECIAL APPLICATIONS

The antisurge law (3.97) previously developed is completely general, no assump-tions having been made about the particular behavior of the machine. As a con-sequence, its validity is not compromised even when applied in complex systems.However, sometimes some simplifications can be introduced in plain cases, ac-

COMPRESSOR PERFORMANCE—DYNAMIC 3.93

FIGURE 3.71 Regulation scheme.

cording to the special features of the particular systems. Two cases will be brieflyexamined: Electric Driven Compressors and Variable Speed Compressors with Con-stant Inlet Conditions.

3.14.1 Electric Driven Compressors (Fixed RPM)

If the inlet pressure conditions remain constant, the following law can be used:

h � K (3.99)1

since:

1�Q � C h � (3.100)1 1 �

This law can be represented by straight line parallel to the vertical axis crossinghorizontal axis at the point Q1 � 1.Q

The error in the volume flow rate, expressed as a function of inlet flow char-acteristics is:

� � P � T � Z1 1 1 1� % � 100 � 1 (3.101)� �Q1 �� P � T � Z1 1 1 1

A schematic practical realization of the equation h1 � K can be fulfilled with theprocedure shown in Fig. (3.74):

3.94 CHAPTER THREE

FIGURE 3.72 � K regulation line.h1

FIGURE 3.73 � K regulation line.h2

3.14.2 Variable Speed Compressors with Near Constant Inlet

Conditions

When inlet pressure and delivery temperature (cooler) are kept constant, or when,for design or economical choices, the continuous measurement of the inlet flowrate is not possible, the following law can be considered in substitution of (3.97)Considering that,

Z �T1 1 3Q � C � �h � � (m /h) (3.102)1 2�Z � T �� P2 1 2 1

can be represented graphically with a parabola having the origin in the origin of

COMPRESSOR PERFORMANCE—DYNAMIC 3.95

FIGURE 3.74 h1 � K regulation scheme.

FIGURE 3.75 h2 � K regulation scheme.

the reference system as shown in Fig. 3.73. The percentage error in the flow rateexpressed as a function of suction and delivery conditions is:

Z T Z �T � � � P1 1 2 2 2 1� % � 100 � 1 (3.103)� �Q1 �Z � T � � � PZ T 2 2 2 21 1

The scheme shown in Fig. 3.75 can be used for the practical realization of (3.99).

4.1

CHAPTER 4CENTRIFUGAL COMPRESSORS—CONSTRUCTION AND TESTING

Ted GreshElliott Company

A centrifugal compressor is a dynamic compressor and thus depends on motion totransfer energy from the compressor rotor to the process gas. Compression of thegas is implemented by means of blades on a rotating impeller. The resulting rotarymotion of the gas results in an outward velocity due to centrifugal forces. Thetangential component of this outward velocity is then transformed to pressure bymeans of the diffuser.

4.1 CASING CONFIGURATION

The centrifugal compressor is a very versatile machine that can be readily adaptedto a wide range of mechanical and process demands.

For example, depending on the head and flow requirements, the number of im-pellers used may be varied from one to as many as 10 or more in one casing. Inletand exhaust nozzles may be located up, down or at some offset angle. Additionalnozzles for economizers or other side streams or for cooling between stages, areeasily accommodated. This flexibility of configuration is especially augmented byfabricated casing design (Fig. 4.1).

A few of the more common casing configurations are shown in Figs. 4.2 to 4.8.

4.2 CONSTRUCTION FEATURES

The major elements of the centrifugal compressor (Fig. 4.9) consist of: (a) the inletnozzle; (b) inlet guide vanes; (c) impeller; (d) radial diffuser; (e) return channel;(f) collector volute; and (g) discharge nozzle.1

4.2 CHAPTER FOUR

FIGURE 4.1 The Fabricated Compressor Casing is a flexible design for ac-commodating the specific requirements of the application including specialnozzle arrangements. 1) The center section, a cylindrical shell of rolled andwelded steel plate is joined by welding to two dished heads formed by hotspinning. Photo shows automatic girth welding of heads to shell. 2) Assemblyis cut longitudinally into two equal halves and sturdy flanges are welded toeach half of the shell. 3) Holes are burned in the shell and fabricated sectionsare welded together to form inlet, discharge, and sidestream nozzles.

The inlet nozzle accelerates the gas stream and directs it into the inlet guidevanes, which may be fixed or adjustable.

On a multi-stage compressor, the inlet nozzle is generally radial. In this case,the inlet guide vanes are necessary to properly distribute the flow evenly to thefirst-stage impeller (Fig. 4.10). Single-stage compressors frequently incorporate anaxial inlet. In this case, inlet vanes may not be used.

CENTRIFUGAL COMPRESSORS—CONSTRUCTION AND TESTING 4.3

FIGURE 4.2 Basic single-stage com-pressor. Typical construction is impelleroverhung from the bearing housing(courtesy Elliott Co.).

Because of the rotational effects of the impeller, the gas travels through thediffuser in a spiral manner. Therefore before entering the next impeller, the flowmust be straightened out by the return channel vanes (Fig. 4.11).

4.2.1 Diaphragms

A diaphragm consists of a stationary element which forms half of the diffuser wallof the former stage, part of the return bend, the return channel, and half of thediffuser wall of the later stage. Due to the pressure rise generated, the diaphragm(Fig. 4.12) is a structural as well as an aerodynamic device.

For the last stage or for a single-stage compressor, the flow leaving the diffuserenters the discharge volute. It is common to design these volutes for constant

4.4 CHAPTER FOUR

FIGURE 4.3 For high speed single-stage compressors, maximum efficiency can be realizedwith intercooling between each stage. Also, cooling is required to keep operating temperaturesbelow material limitations (courtesy Elliott Co.).

angular momentum (RiVi � constant). This generally results in limited velocitychange through the volute (V2 to V5). Once the gas leaves the volute, it passesthrough the discharge nozzle which reduces the velocity somewhat before enteringthe process piping. Figure 4.13 represents such a constant angular momentum vo-lute.

CENTRIFUGAL COMPRESSORS—CONSTRUCTION AND TESTING 4.5

FIGURE 4.4 Basic straight through multistage compressor with a balancing piston.This arrangement may employ 10 or more stages of compression. This arrangement ismost often used for low-pressure rise process gas compression. Casing design shown isa barrel construction used for high pressure or low mol weight gases which provideslimited leakage areas and thus better contains the process gas (courtesy Elliott Co.).

Since velocities are relatively high through the diffuser section (several hundredfeet per second), surface finish/friction factor is crucial to overall efficiency of theunit.

In many processes, dirt or polymer buildup on the impeller and diaphragm sur-faces will give the aerodynamic surfaces a rough finish (Fig. 4.14). In some casespolymer buildup has been known to severely restrict the diffuser passage. Bothconditions cause increased pressure losses and result in reduced overall efficiencyof the compressor.2

The chemical mechanism that takes place to generate polymerization is not wellunderstood, but experience has shown that under the right conditions polymers doform and bond tenaciously to the component base metal. Factors that have beenfound to be critical to the fouling process include: 1) temperature—polymerizationoccurs above 194�F; 2) pressure—the extent of fouling is proportional to pressurelevel; 3) surface finish—the smoother the surface the less apt the component is tofoul; 4) gas composition—fouling is proportional to concentration of reactablehydrocarbons in the process gas.

4.6 CHAPTER FOUR

FIGURE 4.5 Double flow compressor. This arrangement is used to double the maximumflow capability for a compressor frame. Since the number of impellers handling each inlet flowis only half of that of an equivalent straight through machine, the maximum head capability isreduced accordingly (courtesy Elliott Co.).

Operating temperature can be reduced by water injection at each stage startingafter the first wheel. The water should be injected via atomizing spray nozzles, andthe amount should bring the gas to just below the saturation level.

Surface finish in these critical areas can be enhanced and preserved by applyinga non-stick coating, such as fluorocarbon-based (Teflon) material, or a corrosion-resistant coating, such as electroless nickel. Multi component coating ‘‘systems’’that provide a barrier coating, an inhibitive coating and a sacrificial coating haveprovided the best long term service. Compressor performance is best preserved byincluding a wash system that includes water with detergents or hydrocarbon sol-vents to wet aerodynamic surfaces preventing attachment of the polymers and tohelp wash compressor surfaces once bonding of the polymers occurs. Wash liquidsintroduced should be limited to 3% of the gas mass flow rate to prevent erosionand be injected stage by stage with increasing amounts at the discharge.

The long-term effects that include on-line liquid washing that might utilize hy-drocarbon solvents or detergent enhanced water are shown in Fig. 4.15.2

4.2.2 Interstage Seals

Due to the pressure rise across successive compression stages, seals are requiredat the impeller eye and rotor shaft to prevent gas backflow from the discharge to

CENTRIFUGAL COMPRESSORS—CONSTRUCTION AND TESTING 4.7

FIGURE 4.6 As in Fig. 4.3, cooling is required to keep operating temperatures belowmaterial or process limits as well as to improve operating efficiency. Iso-cooling nozzlespermit the hot gas to be extracted from the compressor and to an external heat exchanger,then returned to the following stage at reduced temperature for further compression (cour-tesy Elliott Co.).

inlet end of the casing. The condition of these seals directly affects the compressorperformance.

The simplest and most economical of all shaft seals is the straight labyrinthshown in Fig. 4.16. This seal is commonly utilized between compression stagesand consists of a series of thin strips or fins, which are normally part of a stationaryassembly mounted in the diaphragms. A close clearance is maintained between therotor and the tip of the fins.

The labyrinth seal is equivalent to a series of orifices. Minimizing the size ofthe openings is the most effective way of reducing the gas flow. Labyrinths cloggedwith dirt (Fig. 4.17) and worn or wiped labyrinths with increased clearances (Fig.4.18) allow larger gas leakage. This can affect compressor operation, and thereforethe seals should be replaced.

Labyrinth material has typically been aluminum, because aluminum is compat-ible with most gases and is ductile enough to prevent rotor damage in the event ofrubbing. Where corrosive elements are a concern, plastics such as Arlon CP (PEEK)and Torlon have been successfully used without the need to increase the seal clear-ances since the material has similar mechanical properties as aluminum. Thesematerials (Arlon and Torlon) have been touted as rub tolerant when a raked toothdesign of 15� is used, allowing a 50% reduction is seal clearance relative to alu-minum labyrinth seals.

4.8 CHAPTER FOUR

FIGURE 4.7 Side stream nozzles permit introducing or extracting gas atselected pressure levels. These flows may be process gas streams or flowsfrom economizers in refrigeration service. Sideloads may be introducedthrough the diaphragm between two stages (sideload 3), or if the flow ishigh as in sideloads 1 and 2, the flow may be introduced into the areaprovided by omitting one or two impellers (courtesy Elliott Co.).

A hard labyrinth material such as stainless steel or cast iron could result in drywhirl and catastrophic failure of the compressor. One such case occurred whenaluminum seals were replaced with cast iron seals. Since the clearances were notincreased, the rotor touched the cast iron labyrinths while passing through thecritical speed and dry whirl occurred. Vibration was so severe that the bearingretainer bolts backed out and the bearing housings fell off the compressor case.Needless to say, the damage was extensive.

Calculations and field performance data indicate that wiped interstage seals candecrease unit efficiency by 7% or more. Operating modes that contribute to laby-rinth damage include surging, running in the critical speed, and liquid ingestion.A common problem is a trip on a compressor that has a rotor with buildup (un-balance) and a small, slow opening anti-surge valve. This condition will cause ahigh response through the first critical and open the seal clearances.

In order to reduce or negate the performance effects common with damagedinterstage seals, several improvements have been adopted by compressor manufac-turers. Most noteworthy is the use of abradable seals in the impeller eye and shaftseal areas. Advantages include tighter design operating clearances and minimalefficiency effects after a seal rub, as shown in Figs. 4.19 and 4.20.

CENTRIFUGAL COMPRESSORS—CONSTRUCTION AND TESTING 4.9

FIGURE 4.8 The back to back design minimizes thrustwhen a high pressure rise is to be achieved within a singlecasing. Note that the thrust forces acting across the twosections act in opposing directions, thus neutralizing oneanother (courtesy Elliott Co.).

The efficiency gain of abradable seals is achieved through the reduction of sealclearances, thereby reducing recirculating flow through the impellers. Impeller eyeseals, interstage shaft seals, and balance piston seals are effective in improvingcompressor efficiency when changed to the abradable design. Abradable seals alsocontrol impeller thrust, which varies with seal clearance (Fig. 4.21).

Having the fins as the rotating element permits centrifugal force prevents thebuild up of process deposits. Where conventional static labyrinths are used on afouling duty, build up of deposits adversely affects the flow characteristic acrossthe labyrinth, with detrimental effect on compressor efficiency. Rotating fins min-imize this problem (see Fig. 4.17.)

A rub on an aluminum labyrinth causes the tips of the aluminum fins to mush-room out (Fig. 4.18). This creates undesirable flow characteristics across the lab-yrinth and increases the radial clearance. These factors are detrimental to com-pressor efficiency due to the resulting increased leakage and will have an effect onthe thrust loading of the machine. With the abradable design, the rotating fins rubinto the static element without damage to the fins and without effect on the normalrunning clearances. No performance deterioration or change in thrust load occurs(Figs. 4.19 and 4.20).

4.10 CHAPTER FOUR

FIGURE 4.9 Major elements of a multi-stage centrifugal compressor: a) inlet nozzle,b) inlet guide vanes, c) impeller, d) radial diffuser, e) return channel, f) collector volute,and g) discharge nozzle.1

FIGURE 4.10 Multi-stage compressor inlet showingsplitter vanes and guide vanes.1

The overall efficiency improvement attainable by using abradable seals in acompressor varies with several factors, most notably the size of the compressor.Flow capacity increases as the square of the impeller diameter, while seal clearanceincreases more linearly with impeller size and is also dependent on other factorssuch as bearing clearances and manufacturing tolerances. Therefore as the com-pressor size increases, the leakages involved become a smaller portion of the total

CENTRIFUGAL COMPRESSORS—CONSTRUCTION AND TESTING 4.11

FIGURE 4.11 Flow path of gas from tip to return channel.1

FIGURE 4.12 Multi-stage centrifugal compressor dia-phragm.1

flow. As this happens, the improvements gained by reducing these leakages havea diminishing impact on the machine’s overall efficiency. Therefore it is the smaller,higher pressure compressors that benefit most from abradable seal.

4.2.3 Balance Piston Seal

A balance piston (or a center seal) is utilized to compensate for aerodynamic thrustforces imposed on the rotor due to the pressure rise through a compressor. Thepurpose of the balance piston is to utilize the readily available pressure differentials

4.12 CHAPTER FOUR

FIGURE 4.13 Discharge volute.1

FIGURE 4.14 Photo of polymer build up in impeller and diffuser passages on anethylene feed gas compressor.

to oppose and balance most of these thrust forces. This enables the selection of asmaller thrust bearing, which results in lower horsepower losses.

A certain amount of leakage occurs across the balance piston since a labyrinthseal is utilized. This parasitic flow is normally routed back to the compressorsuction, thus creating a known differential pressure across the balance piston (Fig.4.22). Occasionally, leakoff may be routed to other sections to gain an efficiencyadvantage. Air compressors generally route the balance piston leakage to atmo-sphere.

CENTRIFUGAL COMPRESSORS—CONSTRUCTION AND TESTING 4.13

FIGURE 4.15 Effect of coated and non-coated surfaces on an ethylene feed gas com-pressor.2

Since the balance piston seal must seal the full compressor pressure rise, integ-rity of this seal is crucial to good performance. A damaged seal results in higherleakage rates, higher horsepower consumptions, and greater thrust loads.

One user of a compressor noted the following data before and after a balancepiston seal replacement. This machine was in refrigeration service and was requiredto maintain a constant discharge pressure.

Before After

Discharge pressure (PSIG) 410 410Discharge temperature (�F) 142 116Axial position (Mils) 24 19Balance line DP (PSID) 4.7 1.5Speed (RPM) 11440 10770Thrust metal temperature (�F) 240� 165

The balance piston damage was a result of surging and vibration excursions.The interstage seals were also extensively damaged, which contributed to the poorcompressor efficiency. Note the differences in the various data before and after theseal replacement. The discharge temperature was high, since more work input was

4.14 CHAPTER FOUR

FIGURE 4.16 Aluminum labyrinth in newcondition. Tight clearance and flow turbulencecreates resistance to leakage flow.1

FIGURE 4.17 Fouled labyrinth. Tur-bulence is reduced and leakage flow isincreased.1

required to achieve the desired discharge pressure. In order to get the higher levelof work input, the speed was increased. The wiped seals not only caused increasedinefficiencies, but also higher thrust loads. This showed up in the axial positionand thrust bearing temperature.

4.2.4 Impeller Thrust

Impeller thrust is generated by the differential force on the cover and hub of thewheel. These forces are the summation of the product of the pressures acting onthe cover, hub, and the differential area from the shaft to the tip of the wheel.3

The impeller generates thrust between the eye and tip of the wheel, as well asbelow the eye. These forces (thrust) are caused by several different effects:

1. Rotational inertia field

2. Leakage

3. Friction

4. Diffusion

CENTRIFUGAL COMPRESSORS—CONSTRUCTION AND TESTING 4.15

FIGURE 4.18 Rubbed labyrinth.Clearance is increased and turbulencereduced resulting in increased leak-age.1

FIGURE 4.19 Abradable seal. Tight clear-ance and turbulence creates resistance toleakage flow.1

The effects of friction and diffusion are insignificant.As indicated by the flow paths (Fig. 4.21), gas will flow toward the tip of the

wheel along the hub and toward the eye of the wheel along the cover. Due to thepressure rise in the diffuser, the return channel pressure is greater than the pressurebehind the impeller hub. Leakage therefore occurs from the return channel towardthe impeller hub and outward toward the impeller tip. The effect of the pressureestablished by this leakage, superimposed upon the rotating inertia field, is shownin Fig. 4.21a.

From Fig. 4.21, it can be seen that there is an obvious net pressure differentialtoward the suction of the machine in addition to the area caused by the eye of theimpeller. This is indicated in Fig. 4.21b. Integrating the products of the pressureand area from eye to tip results in the net thrust on a wheel.

For a ‘‘perfect’’ (zero leakage) seal at the impeller eye and shaft areas, the thrustis simply a function of the area inside the eye seal. For ‘‘real’’ seals with largeclearance and corresponding high leakage in these areas, the net thrust can be asmuch as 50% greater.3 Thus, maintenance of tight seal clearances is crucial formechanical as well as aerodynamic concerns.

4.16 CHAPTER FOUR

FIGURE 4.20 Rubbed abradableseal. Tight effective running clearanceis unaltered and turbulence continuesto create resistance to leakage flow.1

4.3 PERFORMANCE CHARACTERISTICS

The characteristics of a centrifugal compressor (Fig. 4.23) are determined by theimpeller and diffuser geometry. Simply stated, kinetic energy is imparted to thegas via the impeller by centrifugal forces. The diffuser then reduces the velocityand converts the kinetic energy to pressure energy.

There are three important aspects of the compressor curve that will be discussed(Fig. 4.24):

1. Slope of the curve

2. Stonewall (or choke)

3. Surge

4.3.1 Slope

To understand about the slope of the centrifugal compressor head curve, it is nec-essary to first understand what is going on at the impeller discharge in terms ofvelocity vector diagrams.

Vrel (Fig. 4.25) represents the gas velocity relative to the blade. U2 represents theabsolute tip speed of the blade. The resultant of these two velocity vectors isrepresented by V, which is the absolute velocity of the gas

U � V � V (4.1)2 rel

Knowing the magnitude and direction of this absolute velocity, we can break thisvector into its radial (VR) and tangential (VT) components (Fig. 4.26).

For a radial inlet impeller (Fig. 4.23), the head output is proportional to theproduct of U2 and VT.

For a typical backward-leaning bladed impeller, as the flow decreases at constantspeed, Vrel decreases. This causes VT to increase, which increases head output. This

4.1

FIGURE 4.21 (a) Diagram showing the pressure pattern on the impeller. (b) Net Pressure. (c)Net thrust.3

4.18 CHAPTER FOUR

FIGURE 4.22 Schematic of compressor thrust. Pressure drop in the balance line is normally1 to 3 psi.3

FIGURE 4.23 Velocity /pressure development for a typi-cal radial inlet impeller.4

CENTRIFUGAL COMPRESSORS—CONSTRUCTION AND TESTING 4.19

FIGURE 4.24 Head curve for a compressor stage.5

FIGURE 4.25 Vector diagram of the gasvelocity relative to the impeller blade. Theslope of the characteristic curve is stronglyinfluenced by this relationship.5

head increase with decreasing flow is what causes the basic slope to the centrifugalcompressor performance curve (Fig. 4.27).

Figure 4.28 shows characteristic curves for three basic configurations: forward-leaning, radial, and backward-leaning blade profiles. Note that the forward-leaningblades provide a positive sloping head curve and the maximum head output. Thisis because VT is increasing with increasing flow.6

A radial bladed impeller has a theoretical constant (flat) head curve, since VT

does not change with flow.Overall stage efficiency is highest for backward-leaning impellers, while effi-

ciency is lowest for forward-leaning blades. For best efficiency, most modern cen-trifugal compressors use backward-leaning bladed impellers. Directionally speak-

4.20 CHAPTER FOUR

FIGURE 4.26 Vector diagram of the gas velocityshown in Fig. 4.25 in radial and tangential com-ponents.5

FIGURE 4.27 The effect of a change in flow rateon the vector diagram at the impeller O. D. is shown.Note that VT decreases as flow increases (Vrel in-creases) for a backward-leaning impeller blade. Thisgives the backward-leaning impeller the characteristicnegative-sloping head curve shown in Fig. 4.24.5

CENTRIFUGAL COMPRESSORS—CONSTRUCTION AND TESTING 4.21

FIGURE 4.28 Three basic head curve shapes for centrifugal compressors.6

ing, the greater the backward lean, the better the efficiency. However, as the angleincreases, the head is reduced (see Figs. 4.28c and 4.29). A designer can select ablade angle and tip width to best fit the desired head and efficiency characteristicsof the particular application.

4.3.2 Stonewall

Stonewall, or choke, is a condition at which increased capacity (flow) results in arapid decrease in head as flow is increased (see Fig. 4.30). This occurs because theMach number is approaching 1.0.

Operating at a very high flow rate has very negative effects on the performanceof a centrifugal compressor, and can sometimes be damaging. The stonewall effectof the centrifugal compressor stage with vaneless diffuser is controlled by impellerinlet geometry.

U1 in Fig. 4.31 represents the tangential velocity of the leading edge of theblade. V represents the absolute velocity of the inlet gas, which, having made a90� turn, is now moving essentially radially (in the absence of prewhirl vanes)—hence the name radial inlet. By vector analysis Vrel, which is gas velocity relativeto the blade, is of the magnitude and direction shown.

V � U � V (4.2)1 rel

At design flow, Vrel lines up with the blade angles. As flow increases beyond

4.22 CHAPTER FOUR

FIGURE 4.29 The effect of impeller blade an-gle on head.

FIGURE 4.30 Stonewall. Flow is limited in impeller throat due toflow separation and developing shock wave.

design, V increases. As V increases, so does Vrel. Vrel now impinges at a negativeangle to the blade, a condition known as negative angle of attack. High negativeangles of attack contribute to the stonewall phenomenon because of boundary-layerseparation and a reduction of effective area in the blade pack. This area reduction,in addition to the already high Vrel, brings on Mach 1 and a corresponding shockwave, as shown in Fig. 4.30.

4.3.3 Surge

Surge flow has been defined as peak head. Below the surge point, head decreaseswith a decrease in flow (Figs. 4.24 and 4.30).

Surge is especially damaging to a compressor and must be avoided. Duringsurge, flow reversal occurs resulting in reverse bending on nearly all compressor

CENTRIFUGAL COMPRESSORS—CONSTRUCTION AND TESTING 4.23

FIGURE 4.31 Flow vectors for impeller design condition.5

FIGURE 4.32 Flow through a dif-fuser.5

components. The higher the pressure or energy level, the more damaging the surgeforces will be.

As flow is reduced at constant speed, the magnitude of Vrel decreases propor-tionally, causing the flow angle to decrease (see Figs. 4.27 and 4.32). Additionally,the incidence angle i is increased (Fig. 4.33).

The smaller the flow angle �, the longer the flow path of a given gas particlefrom the impeller tip to the diffuser outside diameter (Fig. 4.32). When anglebecomes small enough and the diffuser flow path long enough, the flow momentumof the gas is dissipated by the diffuser walls by friction to the point where thefrictional forces are increasing (versus flow reduction) faster than the head is in-creasing (versus decreasing flow).

The high losses associated with low flow (see Fig. 4.33) are partly caused by apoor incidence angle i, which can result in flow separation at the low pressure sideof the blade leading edge. This flow separation frequently starts at one or moreblades and continuously shifts around the impeller blades. This occurs at relativelylow speeds just before full surge occurs. At higher speeds, the compressor generally

4.24 CHAPTER FOUR

FIGURE 4.33 Rotating stall.

FIGURE 4.34 Diffuser vanes.4,5

goes directly from stable operation to flow separation on all blades and full reverseflow. Rotating stall can also originate in the diffuser.

The flow separation plus the higher frictional losses result in a positively slopedcurve. Since system resistance curves are also positively sloped, the system isunstable.

The point at which a compressor surges can be controlled somewhat by thedesigner adjusting the diffuser area to increase Vr and flow angle a. Of coursehigher velocities result in higher frictional losses, so a designer must balance be-tween desired surge point and stage efficiency during the design process.

The surge point is reduced by the addition of vanes in the diffuser (Fig. 4.34).The vanes shorten the flow path through the diffuser, reducing frictional losses andcontrolling the radial velocity component of the gas. Due to lower friction, headand efficiency are enhanced, but the operating range is reduced. Off-design oper-ation rapidly changes the incidence angle to the vanes and flow separation occurs,resulting in the reduced operating range.

CENTRIFUGAL COMPRESSORS—CONSTRUCTION AND TESTING 4.25

FIGURE 4.35 Surge. Once the pressure in the tank exceeds the ca-pability of the compressor to produce head, reverse flow occurs.

To better understand what is occurring during surge, visualize the simple systemshown in Fig. 4.35. The system consists of a small motor-driven compressor deliv-ering air to a relatively large tank. While in an idle state, the entire system is atambient conditions. The instant the unit reaches design speed, the pressure in thetank is still zero (Point 1). As time passes, the pressure builds in the tank and flowis reduced due to increased resistance. Eventually Point 2 is reached, where thepressure of the tank causes such a high backpressure on the compressor that flowthrough the impeller is significantly reduced. Much of the energy input is going tofriction instead of building head. This is due to both the mismatch of inlet angleand the longer diffuser passage described earlier. Since this effect continues to buildas flow is reduced, the slope of the head curve is reversed. As flow is reduced toPoint 3, the head output of the compressor is also reduced. Since the pressure inthe tank is still at Point 2, flow occurs from the tank to the compressor. Once thepressure in the tank is reduced (by reverse flow) to a level less than the headcapability of the compressor, the process will then recover and the gas will flowfrom the compressor to the tank. This process will continue to repeat itself indef-initely.

4.4 OFF-DESIGN OPERATION

Off-design operation of a compressor can dramatically affect the performance char-acteristic curve shape. Any change in inlet conditions can change the dischargepressure and gas horsepower as shown in Fig. 4.36.5

In addition to changing the characteristic pressure and horsepower curves, thecharacteristic head curve also changes. This is due to volume ratio effects andequivalent speed effects.

If a constant discharge pressure is desired and gas conditions are changed (inletpressure or temperature, mole weight change), a speed change is required. Sincethe curve shape changes with speed (higher losses at higher speeds), the head curveshape then changes (Fig. 4.37). This effect is further compounded by volume ratioeffects (Fig. 4.38).

4.26 CHAPTER FOUR

FIGURE 4.36 The effect of varying inlet conditions at constant speed for a single-stage compressor. For a multi-stage compressor, the curve shape and operating range isfurther compounded by volume ratio effects. See Fig. 4.38.3,5

FIGURE 4.37 The effect of speed change on compressor per-formance curve.

CENTRIFUGAL COMPRESSORS—CONSTRUCTION AND TESTING 4.27

FIGURE 4.38 Volume ratio effects.3

The head characteristics are a function of the acoustic velocity of the gas. Know-ing this, it is most convenient to refer to some ‘‘constant’’ gas and obtain an‘‘equivalent tip speed.’’ This reference constant is typically air at 80�F, since thisis what most ‘‘developmental’’ testing uses as a test medium.

As an example, we know the sonic velocity of air at 80�F is 1140 fps and thatof propylene at �40�F is 740 fps. If a compressor stage is operating at a mechanicaltip speed of 780 fps on propylene at �40�F, the equivalent tip speed is:

U � 780 � 1140/740 � 1200 fps (4.3)eq

The stage characteristic head curve shape at 780 fps on propylene is therefore thesame as 80�F air at 1200 fps. (Note: This is not exact. There is also an impellertip volume ratio effect based on gas density that causes head and work input tochange somewhat. An air and propylene test will not result in exactly the samehead curve at constant equivalent speed, but for all practical purposes the resultsare close enough to be considered the same.)

In a multi-stage compressor the ‘‘equivalent speed’’ effect is compounded byvolume ratio effect (Fig. 4.38). If the gas density varies, the pressure rise andvolume ratio will also vary. This will feed a different flow rate to the second stage.The effect on following stages will be compounded. The end result is a prematurechoke and surge.

4.5 ROTOR DYNAMICS

The primary factor to assure long-term reliability of any rotating machinery is agood understanding of the rotor dynamics of that equipment. While there are manyfacets to rotor dynamics, the first and primary concern is good balance.

4.28 CHAPTER FOUR

FIGURE 4.39 Rotor lateral critical speed mode shapes: left) 1st critical mode shape,right) 2nd critical mode shape.

4.6 ROTOR BALANCING

The purpose of balancing rotors is to improve the mass distribution of the rotorand its components (caused by machining tolerances and non-uniform structure) sothe mass centerline of the rotating parts will be in line with the centerline of thejournals. To accomplish this, it is necessary to reduce the unbalanced forces in therotor by altering the mass distribution. The process of adding or subtracting weightto obtain proper distribution is called balancing.

Correction of unbalance in axial planes along a rotor, other than those in whichthe unbalance occurs, may induce vibration at speeds other than the speed at whichthe rotor was originally balanced. For this reason, balancing at the design operatingspeed is most desirable in high speed turbomachinery.

To help understand the effects of altering the mass distribution of a compressorrotor, it is important to categorize rotors into three basic groups:

1. Stiff shaft rotors—Rotors that operate at speeds well below the first lateralcritical speed. These rotors can be balanced at low speeds in two (2) correctionplanes and will retain the quality of balance when operating at service speeds.

2. Quasi-flexible rotors—Rotors that operate at speeds above the first lateral criticalspeed, but below the higher lateral critical speeds. In these cases, modal shapesor modal components of unbalance must be taken into consideration, as well asthe static and couple unbalance (Fig. 4.39). Low speed balancing is still possibledue to balancing techniques which correct the static and couple unbalance andsufficiently reduce the residual modal unbalance to retain the quality of balancewhen run at service speeds. Most multi-stage compressor rotors fit in this cat-egory.

3. Very flexible rotors—Rotors that operate at speeds above two or more majorlateral critical speeds. Due to their flexibility, several changes in modal shapeoccur as speed is increased to the operating range. These rotors require highspeed balancing techniques utilizing numerous balance planes to make the nec-essary weight distribution correction.

4.6.1 Two-Plane Balancing

The completed rotor is placed in a balancing machine on bearing pedestals. Theamount of unbalance is determined and corrections made by adding or removing

CENTRIFUGAL COMPRESSORS—CONSTRUCTION AND TESTING 4.29

weight from two predesignated balancing planes. These two planes are usually nearthe 1/4 span of the rotor.

Following the final corrections, a residual unbalance check is performed to verifythat the residual unbalance is within the allowable tolerance.

Maximum allowable residual unbalance guidelines:

4 � (rotor weight)oz. � in. � (4.4)

rotor speed

or56,347 � (journal static loading)

oz. � in. � (4.5)2N (max. continuous rpm)

4.6.2 Three-Plane Balancing

For low speed balancing of quasi-flexible rotors, major components (shafts, wheels,etc.) are individually balanced using two-plane balancing. For clarity, static (orforce) and dynamic (or moment) balancing will be referred to as single-plane andtwo-plane balancing, respectively.

The rotor is completely assembled using pre-balanced components. Using thetwo-plane technique, the amount of unbalance in the two outer planes (wheels) isdetermined. This is resolved into a force component and a moment. The single-plane (force) correction is made as near the center of gravity of the rotor as pos-sible. The residual unbalance moment is then corrected in two planes through theend wheels, which are usually situated near the one-quarter point of the rotor spanbetween bearings. Following the final unbalance corrections, a residual unbalancecheck is performed to verify that the remaining unbalance is within tolerance.

The following items will help to ensure a satisfactory balance:

1. All components (wheels, impellers, balance piston) are individually balancedprior to assembly on the balanced shafts.

2. Mechanical runout is checked and recorded prior to balancing.

3. Combined electrical and mechanical runout checks are performed and recorded.

4.7 HIGH SPEED BALANCE

Axial unbalance distribution along any rotor is likely to be random in nature. Localunbalances can result from shrink fitting discs, impellers, sleeves, etc., along withresidual unbalances present in all component parts. The vector sum of the unbal-ance distribution is compensated for in completely assembled rotors by balancingthe assembly in a low speed balancing machine. The low speed machine measureseither bearing displacement or bearing forces and provides information for correc-tion in two or three transverse radial planes. The low speed machine can measure

4.30 CHAPTER FOUR

FIGURE 4.40 Compressor rotor in at-speed balancing machine. Therotor is balanced at operating speed in a vacuum chamber.

only the sum of the unbalances; therefore, the individual unbalances can excite thevarious flexural modes when the rotor is accelerated to operating speed. Addition-ally, when a rotor is operated at its maximum continuous speed or trip speed, forcesacting on the various component parts, along with temperature changes, will alterthe distributed unbalances. Rotors are processed through the high speed facility tomeasure vibration amplitudes and display mode shapes with the intention of min-imizing these deflections.

4.7.1 Setup and Operation

Prior to operation, the rotor is placed in isotropic supports which are contained ina vacuum chamber (Fig. 4.40). The vacuum chamber is sealed and evacuated to 5to 7 Torr. The rotor is accelerated slowly to maximum continuous speed whilemonitoring vibration levels and critical speeds.

Vibration tolerances are formulated to limit alternating forces at the bearings to10% of static load (0.1g).

During the first run, if vibration levels do not exceed limits, the rotor is accel-erated to trip speed or rated overspeed and held there for a minimum of 15 minutes.This process ‘‘seasons’’ the rotor by stabilizing the rotor temperature and at thesame time seats component parts. After overspeed, the rotor is brought to rest and

CENTRIFUGAL COMPRESSORS—CONSTRUCTION AND TESTING 4.31

again accelerated to operating speed while vibration levels are recorded. The pro-cedure is repeated until repetitive vibration levels are observed, and the balancingprocess is started. (If the rotor is within tolerance at this point, a plot of vibrationlevels through the entire test range is made and the test is terminated.)

When repetitive indications are available from the measuring instrumentation,they are stored in the computer memory and considered to be the reference con-dition or initial unbalance. Test weights are now fabricated and one test weight isadded in one correction plane. The rotor is accelerated to maximum continuousspeed and unbalance response at various speeds is recorded. These test runs arerepeated with one test weight in each correction plane.

When the test runs are completed, a correction weight set is determined. Cal-culations are conducted by the computer via the influence coefficient method. Thecalculated weight set is then applied to the rotor and additional measuring runs aremade to check the results of the correction process. The sequence is repeated untilthe tolerance level is reached.

4.8 ROTOR STABILITY

One of the most important problems affecting the operation of high speed turbo-machinery is stability of rotor motion. The susceptibility of a rotor to self excitecan mean the difference between a smooth running piece of equipment and virtualself destruction.

4.8.1. Stability

The stability of a vibratory system is determined by observing the motion of thesystem after giving it a small perturbation about an equilibrium position. If thismotion dies out with time and the system returns to its original position, the systemis said to be stable; on the other hand if this motion grows with time, it is said tobe unstable (see Fig. 4.41).

4.8.2 Idealized Damped System

In order to understand rotor instability, it is first necessary to understand a simpleidealized damped system. This is normally represented by a mass (M) supportedby a spring (K), with a dash pot (b) to damp the system motion (see Fig. 4.42).

In this example, the system is stable. Both the spring force and the dampingforce tend to return the system to the original position once the system is disturbedby an external force. The slope of the damping curve is positive. Increasing velocitygenerates an increasing force which opposes motion. Likewise, the spring forceincreases and opposes increased displacement from the equilibrium point.7

4.32 CHAPTER FOUR

FIGURE 4.41 The natural response of stable and unstable systems.

FIGURE 4.42 An idealized damped system. With any perturbation, the motion will die outand return to zero.7

CENTRIFUGAL COMPRESSORS—CONSTRUCTION AND TESTING 4.33

FIGURE 4.43 An inverted pendulum. The ‘‘negative spring’’force increases with increased angle �. Time behavior is di-vergent and unstable.7

FIGURE 4.44 A valve in a near closed position is a second-order mechanical systemthat is unstable.7

In an unstable system, just the opposite occurs. Negative spring forces and/ornegative damping tend to increase velocity and displacement with time.

4.8.3 Negative Spring

A good example of a ‘‘negative spring’’ is an inverted pendulum or a valve in thenear closed position (Figs. 4.43 and 4.44). It is easy to visualize what happens to

4.34 CHAPTER FOUR

the balanced inverted pendulum once disturbed. A small initial disturbance will‘‘push it over the hill.’’ Due to the configuration of the system, the force of gravitywill overcome any damping forces in the system and the pendulum will go to andremain at a fully extended position.

Similar to this are the problems of valve chatter. The example in Fig. 4.44 showsa model of a fuel valve. When near the fully open position, the net spring constantis positive, and the system is stable. However, when near closed, the pressure forcesexceed the spring forces and the net spring force is negative, causing the valve tobecome unstable.

4.8.4 Negative Damping

Negative damping is much more common in familiar physical systems than manymay realize. A good way to understand what negative damping is, is to simplylook at it as the opposite of positive damping. Damping, as usually thought of ina positive value, is represented as a dash pot or shock absorber in an automotivesuspension system. The dash pot or shock absorber generate a force that is a func-tion of velocity (see Fig. 4.42c).

F � bV (4.6)

Since the force generated is increasing with velocity and opposes the velocity,the dash pot tends to reduce oscillation of the system. This is ‘‘positive damping.’’

Now consider a system where the damping force generated decreases with anincrease in velocity.

F � �bV (4.7)

In this situation, the force will tend to increase the oscillation of the system.This is called ‘‘Negative Damping.’’

Examples of instability due to negative damping include the dry-friction vibra-tion produced while playing a violin or the tool chatter produced in a machiningoperation (Fig. 4.45b). In rotating machinery, a labyrinth seal rub, or friction be-tween elements on a rotor, can produce similar results.

These dry-friction systems are inherently unstable because the effective systemdamping constant is negative. An increase in velocity leads to a decrease in thefriction force opposing that velocity.

The ‘‘galloping transmission line’’ problem is also a good representation of neg-ative damping (Fig. 4.45a). Aerodynamic lift forces in the direction of velocitylead to unstable oscillations.

Vibrations which are sustained by the energy from a steady or non-oscillatingforce are known as ‘‘self-excited oscillations.’’ The unstable, growing motion ofeach system described above can occur only because energy is being supplied tothe system from an external source. The energy to sustain vibration of the violinstring is supplied through the bow by the musician’s arm.

CENTRIFUGAL COMPRESSORS—CONSTRUCTION AND TESTING 4.35

FIGURE 4.45 Two second-order mechanical systems that exhibit oscillatory in-stability. a) The ‘‘galloping transmission line’’ problem is a result of aerodynamiclift forces in the direction of velocity that lead to unstable conditions. b) Dry-frictionvibration produced while playing a violin is an example of negative damping.7

4.36 CHAPTER FOUR

4.8.5 Rotor Stability

During stable motion, a rotor assumes a deflected shape dependent upon the rotorelastic properties and the forces exerted upon it by the bearings, seals, aerodynam-ics, and unbalance. The deflection is primarily induced by a mass unbalance dis-tribution along the rotor. The deflected rotor then whirls about the axis of zerodeflection at a speed equal in direction and magnitude to the rotational or operatingspeed of the machine, and the whirl motion is therefore termed synchronous. Al-though the actual path described by each point in the rotor need not be circular,the size of the orbit remains constant in time (assuming the speed and unbalancedistribution remain constant). When the motion is unstable, however, the size ofthe orbits described by each rotor point increases with time and the whirl motionof the rotor, while generally in the direction of the operating rotation, is at a lowerfrequency. Such whirl motion is generally termed subsynchronous. With very fewexceptions, the whirl frequency is half of the operating speed when the rotor speedis less than two times the first critical speed. At and above two times the firstcritical, the whirl frequency locks onto the first critical frequency.

The operating speed at which the motion becomes unstable is dependent on thetype of instability mechanism and its magnitude, but is generally above the firstcritical speed of the rotor. This speed is generally termed the instability onset orthreshold speed. Although the rotor whirl orbits generally increase only to a certainsize because of non-linearities in the system, they can become quite large; and inmany instances it is not possible to operate the rotor much faster than the instabilitythreshold speed, and in some instances actual rotor failure may occur.

4.8.6 Instability Mechanisms

The significant mechanisms which cause rotor instability can generally be foundin one or more of the following categories:

1. Hydrodynamic bearings

2. Seals

3. Aerodynamic effects

4. Rotor internal friction

The first three categories are usually those encountered in practice, althoughinternal friction damping is generally present in all machines to some degree andreduces the overall stability of the machine. In certain instances, such as withunrelieved shrink fits or unlubricated splines, internal rotor friction may become asignificant source of rotor instability.

Although the mechanisms causing instability are varied, they all have certaincharacteristics in common, the most important of which is a cross coupling effectof the forces (see Fig. 4.46). The cross coupling can exist in both velocity (damp-ing) and displacement (stiffness), but displacement cross coupling is the more im-

CENTRIFUGAL COMPRESSORS—CONSTRUCTION AND TESTING 4.37

FIGURE 4.46 Bearing stiffness and damping. If the amountof cross coupling is large enough so that the cross coupledforces exceed the damping forces, the rotor will be unstable.8

portant of the two, and is characterized by a force due to a displacement of therotor acting at a right angle to the displacement vector. The cross coupled forcesact in a direction such that they oppose the damping forces; and if the amount ofcross coupling is large enough so that the cross coupled forces exceed the dampingforces, the rotor will become unstable. In effect, the cross coupling forces createnegative spring and damping forces.8

4.8.7 Susceptible Designs

As discussed in the previous section, mechanisms for instability are: bearings, seals,aerodynamics, and rotor internal friction. Designs most susceptible to instabilitywill have several or all of the above mechanisms at work.

The cross coupling forces in hydrodynamic liner bearings are relatively low onlow speed, heavily loaded bearings. On high speed, lightly loaded bearings, thecross coupling forces are relatively high. Similar statements can be made concern-

4.38 CHAPTER FOUR

ing bushing type seals. However, the difference with bushing seals is that they aremounted so as to ‘‘float’’ with the shaft. Actual forces transmitted via the floatingbushing seal if properly balanced should be negligible.

Cross coupling forces occur, not only in bearings and seals, but also anywherealong the rotor where there is relatively close proximity between rotating and sta-tionary parts. Cross coupling forces occur in these areas similar to those in ahydrodynamic liner bearing: between impellers and diaphragms, shaft and labyrinthseals—balance piston seal, shaft seal, and impeller eye seal.

Aerodynamic cross coupling forces are most significant for high pressure, highspeed (tip speed), close clearances, non concentric, mid span areas. The most pro-nounced example of these features is the center seal (balance drum) on a back-to-back design compressor, since this design has all of the above features. The centerseal has a very close clearance to minimize leakage from one section to the next.The seal is of significant length (large L/D) to further minimize leakage, andconcentricity is generally poor due to rotor sag. A regular balance piston seal hasthe same effect, but to a lesser degree due to it’s location at one end of the rotoraway from maximum deflection point for the first critical speed (see Fig. 4.39).

Most high speed turbomachinery rotors are made up of several parts that aresomehow fitted together. These fits can be slip fits, bolted or riveted arrangements,shrink fitted, or even welded joints. Any of these joints that have any relativemovement during operation can generate destabilizing forces or ‘‘negative damp-ing.’’

4.8.8 Analytical Analysis

The analysis of rotor bearing systems for stability reveals a large amount of usefulinformation on the behavior of the system. It answers the question as to whetheror not the system is stable at the operating speed for which the analysis wasperformed.

The rate of decay of a damped vibrating system takes the form of the naturallog of the ratio of successive peak amplitudes (Fig. 4.47) and is therefore calledthe logarithmic decrement (�) and is used as a measure of the rotor damping. Ifthe log dec value for the first forward even mode at the first critical frequency ofthe rotor is positive, the rotor is stable. If the log dec value is negative, the rotoris unstable and whirling of the rotor at that frequency will occur.9

As with any analytical method, some assumptions are necessary; and the modeldoes not quite represent the actual situation. For this reason, a safety factor isapplied.

It is very important to realize that there is a significant difference in rotor dy-namics programs used.

Some stability programs use damping and stiffness parameters which are fre-quency depending. That is, the stiffness and damping parameters used are basedupon individual pad data and varies with the particular frequency being evaluatedand the synchronous speed. Other stability programs use stiffness and dampingparameters at synchronous speed or are synchronous dependent.

CENTRIFUGAL COMPRESSORS—CONSTRUCTION AND TESTING 4.39

FIGURE 4.47 Logarithmic decrement (log dec.). The time decay of aviscous damped system is a natural log function.9

Because of the differences in the various rotor dynamics programs, one must bevery careful in comparing the results of one program to another. Log decrementsare widely being used as a measure of rotor damping. A particular log decrementvalue is dependent upon the stability program in use. For example, a log decrementof �.05 may be considered as having adequate stability margin utilizing one pro-gram, while another may require a log decrement of �.4.

It is also most important when discussing log decrement values as to whetherthe value being referenced is a basic log decrement without aero excitation or isan adjusted log decrement value, which includes aero cross coupling effects.

4.8.9 Identifying Instability

As noted previously, rotor instability shows up as just under half running speedfrequency when operating below 2x the first critical speed. When operating above2x the first critical speed, the instability locks onto the first critical speed (see Fig.4.48). Operating vibration levels during unstable operation can be relatively low orso high that the unit is inoperable. Energy levels can be so high during instabilitythat the unit can self destruct in a few seconds of operation. The energy levels canbe so low that the only problem is that bearing life is reduced.

The equipment needed to analyze the rotor is a vibration pickup and a frequencyanalyzer. Start-up and shutdown response can be recorded to obtain actual NC1and the point at which instability first begins.

A non-contacting probe is preferred, since it records actual rotor movement.Casing velocity or acceleration measurements can introduce questionable data dueto foundations or piping vibration.

4.40 CHAPTER FOUR

FIGURE 4.48 Waterfall spectra of compressor shutdown showing aero-dynamic instability. a) High response at running speed indicated rotor firstcritical speed. b) Synchronous amplitude at normal operating speed. c) Sub-synchronous amplitude at normal operating speed. Note how the subsyn-chronous frequency (c) aligns with the first critical speed frequency (a).

API limits on subsynchronous vibration is 1/4 of running speed amplitude inthe operating speed range. Accordingly, if levels are less than this, operation issatisfactory and corrective procedures are not necessary. If the subsynchronous levelis greater than 1/4 of RSV amplitude, then corrective measures should be taken.

4.8.10 Corrective Measures

Whether instability of a rotor system is discovered by operation or by analysis, thebest tool for correcting the situation is a rotor stability analysis program. Possiblecorrective measures can then be analyzed and the best possible solution can beselected. Some methods of improving stability are listed below. Please note theseare general comments and are not always true for every case. One change mayhelp one case while of little benefit to another. Each situation must be separatelystudied.

A. Labyrinth seals

1. BufferSupplying buffer to a labyrinth seal introduces to the seal a gas flow that isabsent of any tangential velocity. This reduces the average tangential velocityof the gas through the seal, thereby reducing the cross coupling forces(which are function of the tangential velocity). See Figs. 4.49 and 4.50.10

CENTRIFUGAL COMPRESSORS—CONSTRUCTION AND TESTING 4.41

FIGURE 4.49 Conventional balance piston flow. The flow entering thebalance piston seal has a circumferential component due to the rotationof the impeller.10

FIGURE 4.50 Balance piston flow with buffer. The buffer introducesthe gas without a tangential velocity, thus reducing the average circum-ferential velocity in the seal and therefore reducing the crosscouplingforces.10

2. Dewhirl vanesDewhirl vanes (Fig. 4.51) or straightening vanes upstream of a labyrinth sealprovide similar effects to buffer by reducing or eliminating tangential veloc-ity before the gas enters the seal.

3. Honeycomb sealsSeals that have a honeycomb pattern (Fig. 4.52) on the stationary portionand smooth rotating drum tend to have a reduced average tangential velocityover standard labyrinth seals. This reduced tangential velocity reduces cross

4.42 CHAPTER FOUR

FIGURE 4.51 Swirl brakes eliminate tangential velocity ofgas prior to entering labyrinth seals (courtesy Sultzer).

FIGURE 4.52 Honeycomb seals can add stability to the rotorsystem.

coupling forces and therefore delays the onset of instability. Additionally,the cavities of the honeycomb act as dampers contributing to the systemstability.

4. TAM sealThe TAM seal is a labyrinth seal with teeth on the stationary member anda smooth rotating drum. Specially designed barriers in the circumferentialcavities between the labyrinth teeth break up the tangential swirl of the gasand generate pressure dams with damping properties.

5. ConcentricityCross coupling forces are related to the non-concentricity of the labyrinthseal. Since cross coupling forces are only fully developed in a non-concentricseal, centering of the shaft in the seal will reduce these forces significantly.This is one reason why a compressor which has a balance piston near onejournal bearing may be stable, while a similar compressor with a balancepiston in the center of the rotor is unstable (eccentricity due to rotor sag).

6. Gas densityCross coupling forces are a function of gas density. Higher gas density willgive higher cross coupling forces and vice versa. Although it is usually nota practical solution, reducing gas density will improve stability.

B. Journal bearings

CENTRIFUGAL COMPRESSORS—CONSTRUCTION AND TESTING 4.43

1. Liner bearingsLiner bearings have inherently high cross coupling forces due to the highdensity of the oil lubricant, the close clearances, and the usual high offsetof the bearing to journal. Several means of altering the liner bearing to reduceor counteract the cross coupling forces are available. These include: damtype bearings, lemon shape, offset bearings, and lobed bearings. Generallythe most reliable correction is to change to tilt pad bearings.

2. Tilt pad bearingsTilt pad bearings by nature have little or no cross coupling forces. Thus,changing from liner to tilt pads can eliminate the instability if the primarycause is the bearing. If, however, the primary source is elsewhere and tiltpads are already in use, the tilt pad bearing can be enhanced. This can bedone by several methods: reduced positive preload, increased L/D, offsetpivots, load on pad orientation (for 5 pad bearing), increased clearance. Adamped bearing support system can further stabilize the system.

3. Magnetic bearingsStability or dampening characteristics of this type of rotor bearing system isdependent on the control system. The interaction of the power and feedbackcircuits will determine stability of the overall system.

4. Sleeve sealsSleeve type seals or bushing seals have the same characteristics as linerbearings, except that the seals, if properly designed, are ‘‘free floating.’’ Thismeans that the seals are concentric and negligible forces are transmitted tothe shaft. Wear on the seal face can restrict the seal radial movement andlead to subsynchronous vibration.

C. Rotor design

1. StiffnessIncreasing rotor stiffness improves rotor stability. Anything, therefore, thatincreases the critical speed will improve stability. This includes reduction ofbearing span, increased shaft diameter, reduced overhang, or reduced rotorweight. A common parameter to consider is the ratio of the running speedto the first critical speed. Lower values are preferred.

2. Rotor fitsAny parts that can rub during rotor flexing can cause negative dampeningor destabilizing forces. It is therefore prudent to eliminate any source ofrubbing between parts such as is caused by loose or slip fit sleeves, marginalshrink fits, or sleeves that touch end to end. Bolted, riveted, or shrunk fitsmust remain tight at speed so as to eliminate relative motion.

4.9 AVOIDING SURGE

The anti-surge control system should maintain a minimum volume of flow throughthe machine so that the surge condition is never encountered. This is achieved by

4.44 CHAPTER FOUR

FIGURE 4.53 Damage from surging.

bleeding flow from the discharge of the machine to maintain a minimum inlet flow.This flow can either be dumped to atmosphere or recirculated back into the inletof the compressor. In the latter case, it must be cooled to the normal inlet temper-ature. For most applications, a simple control based on a flow differential is ade-quate for this function. However, on machines where the speed or the gas conditionsare variable, the control may have to be more sophisticated to insure proper op-eration under all conditions. This is frequently achieved by modulating the controlwith a signal for pressure, temperature, speed, or a combination of parameters.11

Provisions must be made for start-up and trip-out of the machine with sufficientthrough flow to prevent surging and excessive heating of the inlet gas.

On any control scheme, a trip-out of the driver should be interlocked to openthe anti-surge valve within three seconds and allow the machine to coast to a stopwith this line open. Otherwise, the machine could be surging constantly whiledropping down in speed, causing mechanical damage to the equipment (Fig. 4.53).This is particularly important for axial compressors and also for high-pressure,high-horsepower centrifugal applications. Basic components of a typical anti-surgecontrol system are shown in Fig. 4.54.

A description of the function of each component is as follows:

FE—The flow element is usually an orifice located in the compressor suction,although it can be a venturi or calibrated inlet such as those used in axial com-pressors. Its purpose is to cause a temporary pressure drop in the flowing me-dium in order to determine the flow rate by measuring the difference of staticpressures before and after the flow-measuring element.

CENTRIFUGAL COMPRESSORS—CONSTRUCTION AND TESTING 4.45

FIGURE 4.54 Typical anti-surge system.11

FT—The flow transmitter is a differential pressure transmitter which measuresthe pressure drop across the flow element and transmits a signal that is propor-tional to flow squared.

DPT—The differential pressure transmitter measures the differential pressureacross the compressor and transmits an output signal that is proportional to themeasured pressure differential.

FX—The ratio station receives the signal from the flow transmitter and multi-plies the signal by a constant. This constant is the slope of the control line.

FZ—The bias station receives the signal from FX, the ratio station, and biasesthe surge control line.

The ratio station must have both ratio and bias adjustment to enable the controlline to be placed as parallel to the compressor surge line as possible (see Fig. 4.55).

�P � Ch � b (4.8)

where �P � Calculated compressor differential signalC � Control line slope (ratio signal)h � Inlet orifice differential signal measured by FTb � Control line bias (could be zero)

FIC—The surge controller is a flow control device which compares the calcu-lated output of FZ to the measured �P output of the DPT with �P as definedabove.

When the calculated �P is greater than the measured �P, the compressor isoperating to the right of the control line. When the calculated �P is equal to or

4.46 CHAPTER FOUR

FIGURE 4.55 Surge control line.11

less than the measured �P, the compressor is on or to the left of the control line,and the surge controller functions as a flow controller and opens the anti-surgevalve as necessary to maintain operation of the compressor on this surge controlline.

For rapid flow changes, the response of the control system must be rapid toprevent surge.

LAG—This device functions to enable the surge controller to open the recyclevalve quickly, while providing a slow closure rate. This feature provides stabilitybetween the anti-surge control system and the process by minimizing the huntingeffect between control system and recycle valve.

LX—The low signal selector is set up for two inputs and one output. The inputsare a 100% signal valve and the surge controller output signal. The output ofthe low selector is sent to the recycle valve as well as back to the surge controllerin the form of a feedback signal. This prevents the surge controller from windingup. Windup of the controller penalizes the reaction time of the anti-surge controlsystem.

FCV—The anti-surge recycle valve functions to prevent surge by recycling flowfrom the compressor discharge back to the compressor inlet. Sizing of the anti-surge valve should be at 1.05% of design flow at design pressure rise.

4.10 SURGE IDENTIFICATION

The following is the preferred procedure for establishing the location of the surgepoint.

1. Slowly close the recycle or blow off valve, while monitoring the followingparameters:

CENTRIFUGAL COMPRESSORS—CONSTRUCTION AND TESTING 4.47

a. Blow off or recycle valve position, % open.b. Audible sound level at the inlet of the compressor. Listen for a pulsing sound.c. Audible sound level at the compressor discharge. Listen for a pulsing sound,

a low frequency 0 to 25 Hz.d. Compressor suction pressure immediately upstream of the compressor inlet

flange. Monitor both the local pressure gage (for low pressure, a water ma-nometer works well) and the pressure transmitter. Watch for a bouncing inthe pressure level. Note that the pressure transmitter may not show this unlessit is rated as a dynamic device, with a rise time below 0.1 sec. When thedynamic amplitude exceeds 20% of the gage static pressure or the compres-sor pressure rise, consider the unit to be in surge.

e. Compressor discharge pressure near compressor discharge flange. As theblow off valve is slowly closed, the pressure will rise. Monitor both thepressure gage and the pressure transmitter. Watch for the pressure to bounce(see ‘‘d’’ above). Also watch for any drop in pressure. At the first indicationof a drop in pressure (with decreasing flow), consider this to be surge, andrecord data.

f. Compressor flow rate. Watch for fluctuations in the flow meter differentialpressure. Note that an electronic output on the flowmeter will not indicatesurge unless the device is rated for dynamic conditions, with a rise time below0.1 sec. It is best to locally attach a manometer (for low pressure) or differ-ential pressure gage and monitor this. Any dynamic differential pressure inexcess of 20% of the nominal (steady state) differential at the given flow rateis to be considered surge, if no other indications (c, d, e, or f) are observed.

g. Compressor vibration level. Pay particular attention to subsynchronous am-plitudes. Very small increases or bouncing of amplitudes indicate possibleonset of surge. An increase of 20% at the given speed of the overall vibrationlevel, or 0.20 mils increase of the subsynchronous, while alone not a sign ofsurge, indicates the proximity of an instability. Use extra caution when ex-ceeding these values.

2. When any of the above items (except the peak head condition, e above) indicatessurge, the position of the blow off or recycle valve should be immediately noted,and then opened to the full open position.

3. Close the valve back to within a few percent of the point where the instabilityoccurred. Example: The suction pressure began to bounce at blow off valveopening of 79%. The valve is immediately opened to 100% open. The blow offvalve is then closed back to 81% open.

4. Wait a few minutes to assume data is stable and then record the data.

5. Repeat steps 1 through 4 for the other speed lines, or inlet guide vane positions.

6. Record all data for future reference.

Note that the ideal method of detecting the point of aerodynamic instability, isto monitor dynamic pressure probes near the inlet to the impeller and in the diffuser.Flow instability can develop in either location. In some units it appears in the inlet

4.48 CHAPTER FOUR

due to flow separation on the inlet of the impeller blades. The position of this pointon the compressor head curve generally lines up with the point of peak head. Onother units, stall will occur in the diffuser section. This is caused by the inabilityof the diffuser to overcome the compressor discharge pressure. This event may notfall in line with peak head.

Sophisticated instrumentation is not required to detect surge. The instability usu-ally can clearly be heard and even felt when standing near the compressor. Some-times the instability is subtle and you must listen very closely.

If you are standing in the compressor discharge area, you may not hear an inletstall condition. Likewise, if you are in the control room observing the flow andpressure on the slow responding process monitor equipment, you may only see adeep hard surge condition, when it occurs.

Keep in mind that too much surging will eventually cause equipment failure.Surge the equipment hard enough and long enough and something will eventuallybreak. When setting the surge line, the equipment should experience only one ortwo surge pulses. Allowing the unit to surge any more is only asking for trouble.In order to accomplish this, the recycle or blow off valve must have a quick opening(1 to 2 sec.) response and a slow (10 to 20 sec.) closing time to keep the systemstable.

Be safe and assume that the unit is very sensitive to surge and that the machinecould easily wreck if surged very much.

4.11 LIQUIDS

One of the most potentially damaging occurrences for a compressor is the ingestionof liquid with the process gas stream.3

Liquids condensing in the recycle line can minimize the effectiveness of anyanti-surge system by creating a blockage in the line.

Liquid quench used on refrigeration systems during startup must be minimizedto avoid carryover into the compressor suction. This liquid which is in a mist formcan easily pass through the compressor inlet knockout drum and its demisters.When large amounts of liquid are ingested, the liquid is vaporized creating anexcessive volume of gas in the back of the compressor causing an extreme mis-matching (see Fig. 4.38) of the last stages and turbinizing of the last impeller(s).The high velocities associated with this condition have been known to cause me-chanical damage to the compressor, particularly to the last stage impeller.

The full range of operation should be studied to avoid having liquids enter thecompressor during normal operation and upsets.

1. Trim cooling water or other process conditions to keep the compressor inletconditions above the liquefaction points for any gas constituent.

2. Heat trace, bleed off, or purge normally stagnant lines when liquids form as thestagnant gas cools down to ambient temperatures.

CENTRIFUGAL COMPRESSORS—CONSTRUCTION AND TESTING 4.49

3. Recycle lines should re-enter the main gas stream either upstream of or at theinlet knockout drum.

4. If any potential for liquid formation exists upstream or downstream of the com-pressor, drains and level indicators should be provided at all low spots of pipingand vessels. This will allow routine checking for liquids and draining as re-quired.

5. After shutdown, be sure all liquids formed by cool down of the stagnant processgas are drained away before the compressor is restarted.

6. Limit liquid quench on startup of refrigeration compressors assuming that theliquid will not vaporize instantly and that the knock out drum will not removeall the remaining liquids.

4.12 FIELD ANALYSIS OF COMPRESSOR PERFORMANCE

Field testing process compressors is not a simple task, but the proper proceduresand tools simplify the project. Accurate data and proper analysis is necessary tocompare operating data to the manufacturer’s guarantee. Proper analysis is requiredto justify a project whether it be new equipment, a rerate, or an overhaul. Frequentand regular testing is essential to monitor operating expenses and to aid in deter-mining overhaul frequency.12

The field test check list:

• A method of obtaining accurate pressure and temperature at each compressorflange. ‘‘Snapshot’’ data is preferable to minimize the effects of transients.

• A means of calculating the mass flow rate to the compressor. This is generallydone with an orifice plate or nozzle.

• Vane setting for variable inlet vane units

• Gas analysis via gas chromatograph

• A compressor performance program that utilizes BWR equations of state

• Driver power

• Compressor and driver mechanical losses

• Manufacturers performance curves

• Speed

4.13 GAS SAMPLING

Follow proper precautions when taking a gas sample. Condensate can form on thegas sample container walls and give erroneous results unless proper procedures arefollowed. Confirm values by comparing the discharge gas analysis to the inlet gas

4.50 CHAPTER FOUR

analysis for the same section. The accuracy of test results are no better than theagreement between gas analysis results.

A stainless steel sampling cylinder should be used. It should be at least 300 mlin size and have straight cylinder valves on both ends. The pressure rating of thecylinder should be high enough so that it can withstand full system pressure. Toprevent gas condensation (the walls of the cylinder and tubing are relatively cool)during the sampling process, the cylinder and lines leading from the process pipeshould be insulated and heat traced. The sampling container should be purgedbefore closing the valves and trapping the gas at process pressure.

The containers are then transported to the laboratory. During the transportation,the samples cool and therefore drop in pressure. The cooling of the sample mayresult in condensation of some of the gas. This condensation must be gasified beforefeeding into the gas chromatograph. The only sure way to do this is to heat thesample to or above the sample temperature. It may be wise to then bleed off somepressure before feeding the gas chromatograph. Plot this out on a Mollier diagramof the gas. This brings gas conditions further away from the dew point and providesfurther assurance of avoiding condensation.

A cross-check on accuracy can be made by checking the weight of a separatesample. This sample container should be at a vacuum and heated before fillingwith the process gas. Weigh the sample container evacuated and with the sample.Knowing the weight and volume will give the specific volume. Check this againstthe calculated specific volume for temperature and pressure of the sample pointusing the composition given by the gas chromatograph.

Of course this procedure is not necessary in all cases, such as low mole weightmixtures. For heavy hydrocarbons, however, it is essential that the above procedurebe followed. Errors in gas analysis can give significant errors in performance.

4.14 INSTRUMENTATION

General instrumentation requirements are shown in Fig. 4.56. All temperature andpressure indicators should be dual, i.e., a minimum of two independent instrumentsper location.13 If existing single point instrument tapping points must be used, caremust be taken that those used are well located. There must be no valves, strainers,silencers, or other sources of significant pressure drop between the pressure tappoints and the compressor flanges. Pressure taps near an elbow should be normalto the bend and not in the bend plane.

Ideally, such as under development testing conditions, the static pressure taphole should be very small (approximately 1/5) compared to the boundary layerthickness.15 But on a more practical note, the static pressure connection shouldhave a pressure tap hole .25 inch in diameter, but no greater than 0.5 inch, deburredand smooth on its inside edge with a sharp corner. A smaller hole will collect dirtor condensate. Note that the hole must be deburred but have a sharp corner on themeasurement side. Take care that the deburring procedure does not round the edges,as this will give erroneous readings (Fig. 4.57).

4.5

FIGURE 4.56 Typical performance test setup.13,14

4.52 CHAPTER FOUR

FIGURE 4.57 Static pressure tap. The hole should be 1/4 to1/2 inch in diameter. It should be deburred but have a sharpedge.13,15

All pressures should be measured using quality pressure transducers or pressuregauges, 6-inch or larger diameter, having a 0.25% sensitivity and a maximum errorof 0.5% full scale

Pressure readings during testing should be at mid-scale or greater. Mountingshould be on a vibration-free local panel, connected with pressure lines of at least1/2 inch I.D. tubing; lines will continually slope down toward the unit to auto-matically drain any condensate. Block vent valves should be mounted at the gaugesto facilitate their in-place calibration.

Temperatures should be measured using a thermocouple or RTD system havinga sensitivity and readability of 0.5�F and an accuracy within 1�F. Care should betaken to avoid intermediate T-C junctions at terminals and switch boxes with athermocouple system. Glass-stem thermometers are generally unacceptable forsafety reasons. The temperature sensing portion of the probe must be immersedinto the flow to a depth of 1/3 to 1/2 the pipe diameter. The temperature sensingelements should be in intimate thermal contact if using wells, utilizing a suitableheat transfer filling media, such as graphite paste. Stem conduction errors can befurther minimized by wrapping the stem and well with fiberglass or wool insulation.

To minimize effects of system transients, the data should be collected via adigital monitoring system so all data is collected at the same instant in time.

Speed should be determined utilizing two independent systems, one being thecompressor key-phasor with calibrated digital readout with 0.25% or better systemaccuracy.

Pressure taps should be spaced 90� apart. On horizontal runs of pipe, pressuretaps must be in the upper half of the pipe only.

Flow rates derived from the process flow indicator should be checked by directcomputation of mass flow rates through the metering device. For this reason me-tering device upstream temperature, upstream pressure, and differential pressuremust also be recorded.

4.15 INSTRUMENT CALIBRATION

In general, all instruments used for the measurement of temperature, pressure, flow,and speed should be calibrated by comparison with appropriate standards beforethe test. General recommendations for calibration procedures are outlined below.

CENTRIFUGAL COMPRESSORS—CONSTRUCTION AND TESTING 4.53

FIGURE 4.58 Typical instrument line with gages mounted above the pressure tap.13

A comprehensive log book should be maintained for all calibrations. Calibrationusing a certified dead weight tester is preferred. Suggested arrangements are shownin Figs. 4.58 and 4.59. Pressure transducer calibration should state actual dead-weight standards throughout the range. Calibration using both increasing and de-creasing pressure signals should be done to check for hysteresis. Transducers notwithin 0.5% error of full scale should not be used. Needles should not be changedor adjusted. The pressure transducers or gauges must have a readable sensitivity to0.25%.13

There should also be a check on the accuracy of the thermocouple system (leadwires, reference junctions, readout devices) for each thermocouple. One method ofaccomplishing this is to read voltage output of the thermocouple locally, and thencompare this to the remote reading of thermocouple output.

It is also recommended that the accuracy of the thermocouple itself be checkedby subjecting it to varying temperatures and comparing its output to a referencestandard. The thermocouple should be checked throughout its operating temperaturerange. The thermocouple system should have a readable sensitivity to 0.5�F and anaccuracy within 1�F.

Calibration of the flowmeter differential pressure transmitter can be verified byimpressing a known differential pressure across it and measuring its output. Finally,

4.54 CHAPTER FOUR

FIGURE 4.59 Typical instrument line where pressure line cannot be sloped continuously upwardfrom the pressure tap to the gage.13

an overall system check can be made by impressing a differential pressure acrossthe transmitter and reading the final control room output. The flowmetering deviceshould be removed, and its dimensions should be checked, recorded, and comparedto design criteria. Orifice plates should have a sharp edge.

The tolerance for the measurement of compressor speed should not exceed0.25%. Use of two independent instruments, one to provide a check on the other,is recommended.

4.16 ISO-COOLED COMPRESSORS

Field testing Iso-cooled compressors (Figs. 4.3 and 4.6) can be straight forward,but a few precautions are in order. Each section of the machine should be treatedlike a separate single section compressor, but with the following items in mind.

Process gas flowing to the second section of the compressor may, due to the gascomposition, be different than the first. Liquids may form in the cooler and bedrained out prior to continuing on to the next section. Flow to the second sectionthus will have a lower mass flow rate and the gas will have a lower mole weight.This is especially true for installations like wet (rich) gas compressors.

Measuring the flow of liquid flowing from the cooler and the process gas flowat the compressor main inlet (or discharge) will provide the mass flow rate for theother section by subtracting (or adding).

CENTRIFUGAL COMPRESSORS—CONSTRUCTION AND TESTING 4.55

4.16.1 Heat Transfer

Heat conduction from the discharge of the first section to the next section inlet(Fig. 4.6) can make results confusing. For example, assume that a compressor hasa discharge temperature for the first section of 356�F and an inlet to the secondsection of 90�F. It is easy to understand that there is considerable heat flowingacross the wall separating the two sections because of this high temperature dif-ferential. This heat is of course flowing from the discharge of the first section tothe inlet of the second. The measured temperature at the discharge flange of thefirst section thus does not accurately represent the true temperature at the dischargeof the last wheel of that section. Likewise, the temperature at the inlet flange tothe second section does not represent the true temperature at the first impeller inthe second section due to the heat transfer effect.

The first stage discharge temperature is artificially low thus a higher than actualefficiency and corresponding low power is calculated. Just the opposite is true forthe second section. While this effect should be reflected in the manufacturers pre-dicted performance values, the actual sectional performance can be difficult toaccurately predict.

4.16.2 Seal Leakage

To fully understand the performance of Iso-cooled compressors, seal leakage mustalso be considered. The two areas of importance are the balance piston seal andthe seal between the iso-cooled sections.

Normal seal leakage is represented in the compressor design performance. Sealdegradation will affect the observed power and efficiency values.

Higher than design flow across the balance piston seal will affect the dischargetemperature of the first section since the hot balance piston leakage will heat upthe compressor first stage inlet gas (assuming the balance line is returned to themain inlet). Calculations with a defective balance piston will thus show a higherthan normal power consumption (low efficiency) for the first section. The secondsection will be affected slightly due to the increased discharge temperature of thefirst section and resulting increase in heat transfer to the second stage inlet, butusually this effect is insignificant.

If the internal seal between the two sections is damaged, increased flow acrossthis seal will affect test results. Higher leakage from the wiped seal will increasethe temperature of the second section inlet since the 356�F gas (discharge of thefirst section) is flowing to and mixing with the 90�F second stage inlet gas.

4.17 COMPRESSORS WITH ECONOMIZER NOZZLES

Proper analysis of a sideload compressor (Fig. 4.7) requires internal temperatureand pressure probes in order to properly calculate the performance of the individual

4.56 CHAPTER FOUR

FIGURE 4.60 The internal detail of a sideload compressor where the economizer (sideload)stream meets and mixes with the main refrigeration fluid.

sections of the compressor. This is the normal procedure in any proof test followingthe purchase of a new refrigeration compressor with economizer nozzles since thisis the only way that the compressor performance can be properly analyzed andcompared to predicted values.

Preferred instrument locations are as shown in Fig. 4.60. Sideload and extractionlines, if applicable, are to be treated as inlet and discharge lines, respectively.

Pressure and temperature taps can be added to a horizontally split compressor(Fig. 4.60), by drilling and tapping the casing in the return channel crossover area.A minimum of two each pressure and temperature taps should be used.

Once pressures and temperatures are known at the discharge of Section I, amixing calculation is required to establish suction conditions for the next section.

P � P � P (4.9)8 10 9

where 8 � Discharge of Section I9 � Mixed Suction to Section II

10 � Sideload Condition

CENTRIFUGAL COMPRESSORS—CONSTRUCTION AND TESTING 4.57

M h � M h � M h (4.10)8 8 10 10 9 9

where M8 � M10 � M9.

T9 is then found by working back through the gas properties or Mollier diagramknowing h9 and P9.

T9 may be approximated by

T � (M T � M T ) /(M � M ) (4.11)9 8 8 10 10 8 10

A summary of calculation results are shown in Fig. 4.61.

4.18 ESTIMATING INTERNAL TEMPERATURES

Unfortunately, the above type of test may be a little impractical to do for a fieldlocation, since the internal instrumentation can be a long-term liability regardingemissions (additional connections that may leak) and maintenance concerns (in-struments might break and go through the compressor) as well as additional upfront costs. It is generally out of the question to shut down following a field testto remove the internal instrumentation.

Special data reduction techniques can be used on sideload and extraction com-pressors where internal pressures and temperatures are not available. Internal pres-sures can be estimated from flange pressures, gas velocity through the compressornozzle, and standard pressure drop loss coefficients for a given sideload or extrac-tion nozzle design.

Internal gas temperature at the discharge of each section is also required todetermine sectional performance. This can be accomplished through an iterativeprocess which makes use of predicted work for each section. The procedure beginsfor a given test point by establishing the inlet volume flow for Section I. From thepredicted work curves, the estimated work input is obtained. These data, along withthe internal pressure determined above, are used to establish the estimated dischargetemperature for Section I.

A BWR gas properties program or data with the enthalpy as a function ofpressure and temperature is used. The sideload flow, as measured on site, will thenbe mixed with the calculated discharge flow from Section I to establish the inletflow to Section II. This procedure is then repeated for each following compressorsection using its respective work input. The test on the validity of the work inputis made by comparing the calculated final discharge temperature with the measuredfinal discharge temperature. If these two temperatures agree, the assumption ismade that the correct work input has been used. If, however, the two temperaturesdo not agree, the work input for each section are varied by the same percentage,and the process is repeated.

Once the sectional inlet and discharge conditions are determined, the sectionalheads and efficiencies can be calculated. Note that it is not possible to tell where

4.58 CHAPTER FOUR

FIGURE 4.61 Calculation summary for a sideload compressor.

the deficiencies if any might be. All sections are treated equally. The efficiency ofeach section is modified equally up or down until a match is made with the dis-charge temperature.

4.18.1 Procedure for Calculating Overall Power and Efficiency

Following is an approach that determines overall power and efficiency rather thansectional performance. A typical refrigeration cycle with economizers is depicted

CENTRIFUGAL COMPRESSORS—CONSTRUCTION AND TESTING 4.59

FIGURE 4.62 Typical refrigeration heat cyclewith economizers.

in Fig. 4.62, while a ‘‘modified’’ cycle is demonstrated in Figs. 4.63 and 4.64. The‘‘modified’’ cycle uses an approach that eliminates the requirement of hard to obtaindata points 8, 11 and 21. Internal mixing is assumed not to occur for the ‘‘modified’’cycle in order to obtain a manageable solution. Instead, the system is treated asthree separate and parallel flow paths with measurable end points.

4.18.2 Overall Power

The gas horsepower for a single stage compressor is:

778.16GHP � (h � h )M (4.12)2 133000

where 1 � Inlet conditions2 � Discharge

For a sideload machine:

778.16GHP � (M�h) (4.13)�l,i i33000

where i � the number of sections of the compressor

For a compressor with two sideloads (three sections):

GHP � 0.0236[M (h � h ) � M (h � h ) � M (h � h )] (4.14)a 14a 7 b 14b 10 c 14c 13

4.60 CHAPTER FOUR

FIGURE 4.63 Figure 4.61 in a simplified ‘‘blackbox’’ form. The typical economizer cycle is de-picted with only external data points.12

FIGURE 4.64 Equation (4.17) assumes that the sideloadsdo not mix with the main fluid.12

4.18.3 Overall Efficiency

Efficiency for a single stage compressor is defined as head divided by the workinput:

H� � (4.15)

For a multi-section compressor, an overall compressor efficiency can be calcu-

CENTRIFUGAL COMPRESSORS—CONSTRUCTION AND TESTING 4.61

lated by dividing the total of the sum of the head from each section by the sum ofthe work from each section:

H � H � H7�8 9�11 12�14� � (4.16)W � W � W7�8 9�11 12�14

For the case of the field sideload compressor where points 8 and 11 are notavailable (Figs. 4.62, 4.63 and 4.64):

H� �

HM� �

H M � H M � H M7�14a a 10�14b b 13�14c c�W M � W M � W M7�14a a 10�14b b 13�14c c

and

W � (�h)778.16

H M � H M � H M7�14a a 10�14b b 13�14c c� � (4.17)778.16[(h � h ) M � (h � h ) M � (h � h )M ]14a 7 a 14b 10 b 14c 13 c

While this procedure may not correctly model the true polytropic process as shownin Fig. 4.62, it does give a very close approximation of the overall compressorperformance.

Any error realized from using Eq. (4.17) in place of Eq. (4.16) is reduced asthe main inlet flow is increased and the side stream flows are decreased.

Example:

Use Eq. (4.17) only when external data is available:

H M � H M � H M7�14a a 10�14b b 13�14c c� �778.16 [(h � h ) M � (h � h ) M � (h � h ) M ]14a 7 a 14b 10 b 14c 13 c

Ma � 3258.5 #/min @ �29.4�F, 18.72 PSIAMb � 310.3 #/min @ �6.3�F, 35.03 PSIAMc � 1152.7 #/min @ 19.9�F, 58.55 PSIAMt � 4721.5 #/min @ 133.8�F, 162.1 PSIA

H7�14 � 35,188H10�14 � 25,518H13�14 � 17,126

h14a�h7 � 155.4 � 102.8 � 52.6h14b�h10 � 156.5 � 109.5 � 47

4.62 CHAPTER FOUR

h14c�h13 � 156.7 � 116.5 � 40.2

Note that for this example, each section has a different gas analysis. This is whyh14a does not equal h14b or h14c.

35188 * 3258.5 � 25518 * 310.3 � 17126 * 1152.7� �

778.16 [52.6 * 3258.5 � 47 * 310.3 � 40.2 * 1152.7]

142330030�

180781929

� 0.7873

Use Eq. (4.16) with internal data and sectional head and work can be accuratelycalculated:

� � 0.796

Error � �1.2%

4.19 FIELD DATA ANALYSIS

Trend the performance data looking for any changes. To confirm accuracy of data,compare the total compressor power to the driver power and monitor the compres-sor work input, which is a good indication of the collected data accuracy. Workinput values remain constant for varying inefficiencies in the compressor. If workinput is off design, then there may be instrumentation problems or something af-fecting the compressors ability to do work, such as flow swirl.

Set up a spread sheet and plot the manufacturers data for the compressor headand efficiency vs. flow as well as work vs. flow (see Eq. (4.15)). Data plotted onthese curves should be fan law corrected for speed differences (Figs. 4.65 and 4.66).

Nomenclature:

a � Main inlet

b � 1st sidestream

c � 2nd sidestream

t � Total, discharge flow

7 � Main inlet

8 � Disch first section

9 � Inlet second section

10 � 1st sideload

11 � Disch second section

CENTRIFUGAL COMPRESSORS—CONSTRUCTION AND TESTING 4.63

FIGURE 4.65 Plot both head and compressor work input. Work input can be a good indicatorthat the data used is valid. Fan law correct the data to compensate for speed variations fromthe reference curve.

12 � Inlet third section

13 � 2nd sideload

14 � Final discharge

h � total enthalpy

M � Mass flow

H � Head

W � Work

� � Efficiency, polytropic

GHP � Gas horsepower

4.20 TROUBLE SHOOTING COMPRESSOR PERFORMANCE

Large dynamic compressors are commonly the heart of various petrochemical andindustrial processes. The plant output as well as the power consumption is con-trolled by the compressor performance. Reduced compressor efficiency will not

4.64 CHAPTER FOUR

FIGURE 4.66 The efficiency cannot be fan law corrected, but the flow for the data pointshould be corrected.

only cause increased utility bills, but may also limit plant production rates. Maxi-mization of compressor efficiency is therefore most crucial in assuring maximiza-tion of plant profits.

Correction of compressor performance deficiencies can be very complex, and avery methodical procedure is necessary in pinpointing the root cause of the situa-tion. The following outline is a starting point.

1. Define the problem.

a. What exactly is the problem?b. What should the performance be?c. What is the performance now?

2. Outline the history of the compressor.

a. How long has it been operating?b. When was the last overhaul?c. What changes were made at that time?d. When did the problem start?e. Was it a quick or gradual change?f. Note the trend of various parameters.g. What else changed, what other problems occurred at this time

i. on the compressor?

CENTRIFUGAL COMPRESSORS—CONSTRUCTION AND TESTING 4.65

TABLE 4.1 Troubleshooting Checklist1

• Define problem—what, where, when.• Outline history of operation—trend data.• Verify data.Test data

Complete power balance.Check pressure taps: location, size, and condition.Is there liquid in pressure lines?Note the temperature probe insertion depth, and heat transfer.Calibrate instruments.Inspect flow meter: wear and sludge build up.Are there condensates in gas analysis?Is there a vortex or undeveloped velocity profile upstream of flow meter?Conduct a mass flow balance.

Equipment problemsVortex or undeveloped velocity profile upstream of compressor suctionInternal leakage across diaphragm splitlineRecirculation from rubbed interstage seals or balance piston seals, casing drains, otherareasForeign object damage or blockageLiquids in processDirt accumulation or polymer buildupErosion of impeller blades and diffuser passagesProper direction of rotationBalance line sleeve

EconomicsPer diem cost to operate as isAssociated risksCost for repairsCost for down time to complete repairsSafety concerns

ii. in the process?iii. in operation and control?

3. Verify all data.

a. Have instruments been calibrated?b. Do cross checks agree?

A thorough performance test should be the first step. Follow as closely as pos-sible ASME PTC10 test procedure. If possible get several operating points at onespeed so a full curve can be plotted. This can be a big help in determining correctivemeasures.

Refer to guide in Table 4.1 for help in trouble shooting aerodynamic problems.

4.66 CHAPTER FOUR

4.20.1 Common Sources of Test Error

In order to trouble shoot any problem, it is important to have correct informationon the subject. Aerodynamic performance is very involved and data errors canrapidly mushroom, thereby misleading the problem solver. It is therefore essentialthat accurate data be obtained.

Before trouble shooting the compressor, trouble shoot the testing procedure. Thebest way to do this is a power balance. If it is not feasible to do a power balance,or if there is a significant error (7%) between the compressor power and the driverpower, a thorough analysis of the test procedure is necessary.

4.20.2 Gas Analysis

To have good test results, it is critical to have an accurate gas analysis. This canbe a bit complex on high pressure, high mole weight gas. If the sample is taken athigh temperatures, some of the heavy gas may condense on the walls of the samplecontainer when it cools. If the sample is taken at the inlet, there may be someliquids in the gas stream that will remain in the sample container. When testingthe gas, this condensed liquid will remain in the bottle unless heated.

For best results, take samples at both the inlet and discharge points. Check forcondensibles and compensate by heating the sample before testing.

4.20.3 Liquids in the System

If there is liquid anywhere in the system, it is possible that some may carry overinto the compressor. Knockout drums and demister pads do not always work theway they should. This liquid carryover will give erroneous results on the perform-ance test.

Another liquid problem is liquid in pressure tap lines. Be sure all lines areproperly sloped and drained. If lines are too small (less than 1/2 inch), capillaryaction will hold liquid in the lines.

Be sure to open drain valves at low spots in process piping and instrument linesbefore, during, and after test.

4.20.4 Pressure and Temperature Measurement

Be sure that a proper pressure tap is installed (see Fig. 4.57). Inspect the insideedge of the hole to see that it was deburred and that it has not been eroded,corroded, or plugged with dirt.

Check thermocouple installations. Thermocouples should be inserted into thepipe one-third to one-half the pipe diameter. Use graphite paste in the thermowellto assure good heat transfer between the thermowell and thermocouple.

Be sure to only use instruments that have recently been calibrated.

CENTRIFUGAL COMPRESSORS—CONSTRUCTION AND TESTING 4.67

FIGURE 4.67 The vortex or flow swirl shown is caused bytwo elbows in different planes. The vortex can be correctedby installation of a simple vane flow straightener. Length ofvanes should be two times the pipe diameter. A flow straight-ener may be more effective without a flow equalizer due tothe high pressure drop associated with the flow equalizer.

4.20.5 Cleaning Centrifugal Compressors

Sometimes dirt, polymer build up, or other substances can clog the compressorinternally and seriously degrade performance. Very small amounts of dirt on axialblades alter the blade profile and degrade performance. Cleaning a compressor maybe all that is required to regain ‘‘like new’’ performance.

A centrifugal compressor can be easily cleaned during normal operation (designspeed) by using mild abrasives such as cooked rice or walnut shells. More commonis the use of liquid cleaning agents sprayed into the process and into the returnchannel areas of the compressor.

4.20.6 Velocity Profile

A major source of compressor performance problems can be attributed to an in-complete velocity profile or a vortex upstream of the compressor or process flowmeter. Either situation will seriously alter the compressor and/or flow meter per-formance. A flow straightener device is required when flow swirl or a vortex ispresent. This can occur when there are two or more adjacent elbows in differentplanes. A flow straightener can be a tube bundle or an ‘‘egg crate’’ as shown inFigs. 4.67 and 4.68.

A flow equalizer is required when the velocity profile is not uniform. This canbe caused by flow hugging one side of a pipe due to flow around an elbow or flowthrough a partly closed butterfly valve. This situation is best corrected by an equal-ization plate which is essentially a perforated plate. Think of it as parallel orificesin a flow path. At high velocities, the resistance (pressure drop) is greater. The

4.68 CHAPTER FOUR

FIGURE 4.68 Mitered, vaned elbow. A flow equalizer canbe used, but at the price of a significant pressure drop.17

higher velocity side of the velocity profile is restricted more than the lower velocityside, causing a shifting and equalization of the velocity profile (see Fig. 4.67).

When designing a flow equalizer, it is important to realize that pressure dropcan be significant, especially if the plate becomes plugged with debris. The bestmethod for calculating pressure drop is to add the area of all the holes in the plateand determine an equivalent single hole orifice while calculating pressure dropaccordingly. Be sure to note the effect of the recovery factor.

Make a schematic diagram of the compressor and adjacent piping. Note thelength of straight runs of pipe, elbows, flow meters, valves, suction strainers, knock-out drums, silencers, flow straighteners, instrumentation, etc. This will help in re-solving system-related problems.

If possible, a flow meter should be installed in each inlet and discharge pipe soa mass flow balance in the system can be carried out. This is done by simplycomparing the total mass inflow to the total mass outflow. The difference is theaccuracy of the flow meters.

ASME ‘‘Fluid Meters’’ provide comprehensive guidelines on the straight runrequired upstream of an orifice or flow nozzle.16

4.20.7 Inlet Piping

Compressor performance is very dependent on obtaining a uniform flow distributionto the impellers. Great pains are taken by the compressor designer to assure proper

CENTRIFUGAL COMPRESSORS—CONSTRUCTION AND TESTING 4.69

FIGURE 4.69 Maximum velocity allowed at the suctionflange based on Eq. (4.18).17

flow distribution to intermediate impellers. Although inlet guide vanes may existon a compressor, this alone does not assure proper flow distribution to the firststage impeller. Compressors are designed assuming a relatively uniform velocityprofile at the compressor inlet flange.

Although ASME goes to some detail in describing upstream straight-run re-quirements for orifice meters, the requirement for compressors is very simplystated. The straight-run requirement for axial inlet compressors is 10 pipe diametersand for non-axial inlets, 3 diameters. Additionally, if the velocity pressure exceeds1% of the static pressure, a flow equalizer must be used at the exit of the elbowupstream of the compressor inlet flange.

PV � 0.01 (4.18)P1

where

2P V1 1P � (4.19)V 2gZRT1

Values for Pv /P1 � .01 are shown in Fig. 4.69. Note that for 100�F air (MW �29), the maximum inlet velocity for a three-diameter straight run without an equal-izer is 140 fps. For propane (MW � 44) at 0�F, the maximum velocity would be100 fps.

According to Hackel and King17 the ASME guideline is adequate but could bemodified to call for a reduced straight run for lower Pv /P1 values, and greaterstraight run for larger Pv /P1 values. Also, additional length of straight run shouldbe required for compound piping arrangements.

4.70 CHAPTER FOUR

FIGURE 4.70 Straight pipe run requirements for the basecase (Fig. 4.71, A and Table 4.2).17

For a base case of one elbow in a plane parallel to the compressor axis and fora radial inlet with 50�F gas, Fig. 4.70 gives the minimum straight run required.

To correct for other suction temperatures, use the following equation to find theequivalent velocity for 50�F. First calculate the actual velocity V1.

22.6V1V � (4.20)50�F �T1

where

T � �F1

For axial inlets and/or other inlet piping arrangements, use Fig. 4.70 along withthe multipliers provided in Table 4.2.

Example

Consider a gas with a MW of 25, inlet temperature of 85�F and suction velocityof 100 fps. The piping configuration is a radial inlet multi-stage compressor with

CENTRIFUGAL COMPRESSORS—CONSTRUCTION AND TESTING 4.71

TABLE 4.2 Multipliers for Various Inlet Piping Arrangements*

Piping Configuration (Radial Inlet) Multiplier

One long radius elbow in a plane parallel to compressor shaft (Fig. 4.71) 1.0One long radius elbow in a plane 90� to compressor shaft 1.5Two long radius elbows at 90� to each other 2.0Two elbows in the same plane parallel to compressor shaft 1.15Two elbows in same plane 90� to rotor 1.75Butterfly valve 2.0Gate valve wide open 1.0Swing Check valve balanced 1.25Vortex Separator 4.0Reducer /Expander /Dutchman 1.25Tee 1.0Axial inlet 1.25

*Use with Eq. (4.20) and Fig. 4.70 to determine required straight run of piping for a given arrange-ment.

FIGURE 4.71 Base case. Long radius elbow in a planeparallel to the compressor shaft. A minimum of 10 pipe di-ameters straight run upstream of the elbow is required. Find‘‘A’’ from Fig. 4.70 and Eq (4.20).17

4.72 CHAPTER FOUR

two elbows in different planes upstream of the compressor. The elbow nearest thecompressor is in a plane parallel to the rotor. Upstream of the two elbows is abutterfly valve.

Figure 4.70 gives a straight run requirement of 1.45 diameters. The multiplierfor the two elbows is 2.0 and butterfly valve factor is 2.0.

Multiplying

1.45 � 2.0 � 2.0 � 5.8

Six pipe diameters of straight run are required for this application.

4.20.8 Double Flow Compressors

A common method of increasing capacity of a system is using two or more com-pressors in parallel. However it is feasible, since the ‘‘identical’’ units are alwayssomewhat different and system resistance varies, that both units will not be oper-ating at the same point on the performance curve. It is therefore always recom-mended that each unit have a separate anti-surge system. For a double flow com-pressor this is not very simple due to the common discharge nozzle. The design ofthe inlet piping must be such to achieve a well-balanced, distortion-free flow intoeach inlet of the compressor. Otherwise, as with the parallel compressors, the flowrates to each side may not be balanced and premature surging will occur.

The most reliable inlet piping design for a double flow compressor utilizing adrum to split the flow is shown in Fig. 4.72. While a Y with a proper upstreamstraight run of pipe may seem like a good design, it should be noted that even thesmallest disturbance in the piping upstream of the Y will cause the flow to shift toone leg of the Y or the other.

More often than not, some type of trimming device (orifice plate, butterfly valve,or others) is used in one or both legs of double flow compressors to equalize theflow. For this reason, the most economical method may be to simply install abutterfly valve upstream of a Y connection (Fig. 4.72).

Field Problems. The following are some actual case histories where inlet pipingalone was the source of some serious performance problems.

Case 1. During commissioning, a double flow compressor was found to be lowin head. Also, the unit surged prematurely.

The inlet piping caused unequal flow distribution to the compressor inlet. Thisresulted in one section running near surge while the other section was operatingnear the overload region. The inlet piping to the compressor was modified utilizinga mitered elbow at the tee, a flow equalizer, and a trim valve to improve flowdistribution.

Case 2. Two duplicate single-stage air compressors were found to have a sig-nificant capacity difference during commissioning.

Both compressors had been performance tested at the factory and were within1.0% of each other. The suction piping for each unit was identical to the other

CENTRIFUGAL COMPRESSORS—CONSTRUCTION AND TESTING 4.73

FIGURE 4.72 Suggested piping for double flow compres-sor (left). D3 and D1 sized according to Fig. 4.69. Size D2

to achieve a velocity 1 /4 of that in Fig. 4.69. Note that anti-surge line should be fitted to the knockout drum further up-stream and not to this distribution drum. Piping legs from thedrum to each inlet must be identical mirror image of eachother. For a Y type splitter (right) note the large radius at thedividing point. A mitered type joint with a sharp, pointeddividing geometry could cause flow separation and unevendistribution. A minimum of 10 pipe diameters is requiredupstream of the Y joint. Low velocity (relative to Fig. 4.69)will help assure equal flow distribution.

except that they were mirror images. The axial inlet compressors had two elbowsat different planes and a suction throttle valve. This piping arrangement causedflow swirl which caused prewhirl at the impeller and effected the head output. Theinlet piping was modified to include mitered elbows which minimized the problem.

Case 3. During commissioning, a high pressure multistage compressor was foundto be low in head and efficiency. Near surge, control became unstable. The com-pressor would rumble and continue to surge even with the recycle valve open.Eventually, it would trip on high vibration.

It was found that a vortex separator was being used upstream of the compressorto assure liquids did not enter the compressor. The residue vortex affected both theorifice and compressor performance.

Flow straightening vanes (egg crates) were utilized downstream of the separatorto reduce the vortex.

4.74 CHAPTER FOUR

FIGURE 4.73 Double flow compressor suction piping.Flow distortion caused by piping caused the compressor tosurge prematurely.1

TABLE 4.3 Maintenance Checklist1

Check for the following items:• Preshutdown performance• Interstage labyrinth seal clearance• Balance piston seal clearance• Blade tip clearance on open centrifugal impellers• Internal splitline leakage• Impeller to diffuser alignment• Cleanliness of internal parts• Surface finish of internal parts (pitting, corrosion, buildup of foreign material, etc.)• Proper installation of stationary guide vanes, splitter vanes, etc.• Performance at start-up

4.21 REFERENCE

1. Gresh, M. T., Compressor Performance: Selection, Operation, and Testing of Axial andCentrifugal Compressors (Stoneham Mass.: Butterworth-Heinemann, 1991).

2. Chow, R. C. (Novacor Chemicals), R. McMordie (Sermatech International) and R. Wie-gand (Elliott Co.), Performance Maintenance of Centrifugal Compressors Through theUse of Coatings to Reduce Hydrocarbon Fouling, 1994.

CENTRIFUGAL COMPRESSORS—CONSTRUCTION AND TESTING 4.75

3. Compressor Refresher (Jeannette, PA.: Elliott Co., 1975).

4. Paluselli, D. A., Basic Aerodynamics of Centrifugal Compressors (Jeannette, PA.: EliottCo.).

5. Hallock, D. C., Centrifugal Compressors...The Cause of the Curve (Jeannette, PA.: El-liott Co., 1968).

6. Sheperd, D. G., (Cornell University), Principles of Turbomachinery (New York, NY.:Macmillan, 1967).

7. Cannon, R. H. (Stanford University) Dynamics of Physical Systems (New York, NY.:McGraw-Hill, 1967).

8. Nicholas, J., Fundamental Bearing Design Concepts for Fixed Lobe and Tilting PadBearings (Dresser IN.: 1986).

9. DeChoudhury, P., Fundamentals of Rotor Stability (Jeannette, PA.: Elliott Co.).

10. Fox, Aziz A., (Solar Turbines Inc.) An Examination of Gas Compressor Stability andRotating Stall, San Diego, CA.

11. Salisbury, R., Compressor Performance (Jeannette, PA.: Eliott Co., 1985).

12. Gresh, K. K. (Flexware Inc.) Field Analysis of Mulit-Section Compressors (Jeannette,PA.: Hydrocarbon Processing, Jan. 1998).

13. Bensema, D., Field Performance Testing Elliott Co. (Jeannette, PA.: Elliott Co., 1986).

14. ASME PTC 10, Compressors and Exhausters, New York, 1965.

15. Leipman, H. W., A. Roshko (California Institute of Technology), Elements of Gas Dy-namics, (New York, NY.: John Wiley & Sons, 1957).

16. ASME PTC 19.5, Fluid Meters, American Society of Mechanical Engineers, NY., 1971.

17. Hackel, R., and R. King, Centrifugal Compressor Inlet Piping—A Practical Guide (Jean-nette, PA.: Elliott Co.).

5.1

CHAPTER 5COMPRESSOR ANALYSIS

Harvey NixTraining-n-Technologies

The practice of utilizing compressor analysis has areas of extreme diversity. Thishas historically been dependent on the industries or facilities reliance on compres-sors in the production of product. While production remains a viable rationale foranalyzing compressors, maintenance and energy costs are also a concern. Whetherthe compressor is engine-driven or electric-driven, the costs of energy consumptionalone can be very high.

By reducing the losses created by inefficient compressor operation, load can bereduced on the driver (engine or motor). This makes horsepower (hp) available forincreased production or reduction in energy costs. Improvements in compressorcomponent life and decreased maintenance costs are within the realm of a com-pressor machinery analysis program. It has been estimated that up to 50% of horse-power load to the driver from a compressor is not required when compressor com-ponents go unchecked. The reasons for increased load are relatively few, butoverlooked.

5.1 COMPRESSOR VALVE FAILURES AND

LEAKING VALVES

In multiple valve cylinders, one valve may fail and not much difference will beseen in the temperature of the cylinder. However, throughput and efficiency willbe down. Unless there is a means of measurement, determination of hp losses areimpossible to achieve. Once a cylinder is identified with a valve problem, identi-fication of the particular valve(s) can save maintenance time. Another benefit ofanalysis is the determination of the severity of capacity loss. This information canhelp determine when it is economically justified to shut down a unit to performmaintenance.

5.2 CHAPTER FIVE

5.2 COMPRESSOR PISTON RING FAILURES

An analyzer can trend ring degradation over time, thus scheduled maintenance canbe performed. Many rely on increased cylinder temperatures to determine ringfailure and usually a significant cylinder temperature increase warning is correct,but there is no guarantee that it is the rings and not the valves causing the tem-perature increase. Another way to identify ring wear is to perform periodic main-tenance by pulling the piston out after a certain time period. If this is done, thepiston may be pulled out too early or too late shutting the unit down, and possiblycreating an unnecessary loss of production. Lastly, because the unit is now apart,it may be that life of other components is jeopardized.

5.3 RESTRICTION LOSSES

Valve inefficiencies and gas flow restrictions can be created by a number of faults,typically: design, plugged screens, pulsation of gasses, build up of solids, re-machining of valves, incorrect lift of plates, and improper springing of valves. Thisis an area where savings in dollars, for both maintenance and production, is real-ized.

5.4 IMPROPER CYLINDER LOADING

Cylinder loading is an area of compressor analysis that sometimes has been left toflow charts and curves using ideal and theoretical assumptions. There are programson the market today that create operating curves based upon actual operating con-ditions that can save hundreds of thousands of dollars for corporations; lost dollarsof which the corporations are not even aware. The measurement of volumetricefficiencies and the determination of true rod loads can be greatly enhanced to savemachines, production and money.

Increased emphasis will be placed upon reciprocating machines in the future. Itseems to be the general consensus that many are inefficient and need to be replaced.Replacement of compressors with rotary compressors is expensive. There are meansto improve existing units so they deliver what they should, cost less, and are moredependable than what existed in the past.

5.5 REQUIRED INFORMATION

Here are some components needed to perform compressor analysis:

COMPRESSOR ANALYSIS 5.3

• Rated speed

• Rated load

• Bore

• Stroke

• l / r ratio (some analyzers)

• Connecting rod length

• Rod size/loads

• Suction/discharge pressure

• Cylinder clearance information

• Unloader information

• Crank angle positions between cylinders

• Valve design information

• Gas composition

The manufacturer will provide this information when requested. The design clear-ance volume of the cylinder is required to perform calculated theoretical through-put. The Crank angles for piston to piston and crankshaft relationships are neces-sary.

Valve design information may be left out, but has great value when determiningwhy components are failing. Pertinent information is required on the design lift,throughput, temperature, gas composition, and required valve springs. Many times,incorrect spring sizes lead to early valve failure.

5.6 ANALYSIS OF THE COMPRESSOR USING A PRESSURE-

VOLUME (PV) DIAGRAM

5.6.1 PV Sequence of Events

The primary tool for the determination of reciprocating compressor performance isthe pressure-volume (PV) diagram. The PV diagram describes the relationship ofinternal pressure relative to the volume (% of stroke) of a particular end of acompressor cylinder.

Figure 5.1 represents a PV diagram and its significant features with a discussionfollowing. This discussion will consider the head-end (HE) of a compressor only,while all also applies to the crank-end (CE) of a cylinder.

Line 4-1: The suction valve opens at point 4. As the piston travels toward BDC,the volume in the cylinder increases and gas flows into the cylinder. The pressureinside the cylinder is slightly less than suction line pressure. This small differentialallows the valve to open and holds it open during the suction stroke.

Line 1-2: The suction valve closes as pressure across the valve equalizes as thepiston has reached BDC and changes direction at point 1. The cylinder volume

5.4 CHAPTER FIVE

DISCHARGE VOLUME ACTUAL CYLINDERDISCHARGE PRESSURE

DISCHARGE DIFFERENTIAL(INDICATED POWER(DIPd))

3 2

TOP DEAD CENTER

RE-EXPANSION

SUCTION INTAKE VOLUME

COMPRESSION

SUCTION DIFFERENTIALINDICATED POWER

(DIPs)

BOTTOM DEADCENTER

ACTUALCYLINDERSUCTIONPRESSURE

SWEPT VOLUME ORPISTON DISPLACEMENT (Pd)TOTAL CYLINDER VOLUME (INCLUDING POCKETS)

VOLUMEEVs = (SUCT. INTAKE VOL.)/PdEVd = (DISCH. VOL.)/Pd

CLE

LUM

E(I

LUD

ING

FIGURE 5.1 Near ideal PV diagram.

decreases as the piston moves towards TDC, raising the pressure inside the cylinder.The shape of the compression line (Line 1-2) is determined by the molecular weightof the gas or compression exponent. For an ideal gas (adiabatic-process—no flowof heat to or from the gas being compressed), the compression exponent is theisentropic (constant entropy) exponent that is equal to the ratio of specific heat ofthe gas being compressed.

Line 2-3: At point 2, the pressure inside the cylinder has become slightly greaterthan discharge line pressure. The resulting differential pressure across the dischargevalve causes the valve to open, allowing gas to flow out of the cylinder. The volumecontinues to decrease toward point 3, maintaining a sufficient pressure differentialacross the discharge valve to hold it open.

Line 3-4: At point 3, the piston reaches TDC and reverses direction. At TDC,as the piston comes to a complete stop prior to reversing direction, the differentialpressure across the valve becomes equal. This allows the discharge valve to close.The volume increases, resulting in a corresponding drop in pressure in the cylinder.The gas trapped in the cylinder expands as the volume increases toward point 4.At point 4, the gas pressure inside the cylinder becomes less than suction linepressure, creating a differential pressure that opens the suction valves. The cyclethen starts over again. The shape of the re-expansion line (Line 3-4) is dependenton the same compression exponent that determines the shape of the compressionline.

5.6.2 Suction Valve Leak

Figure 5.2 illustrates the PV diagram of a typical compressor cylinder with suctionvalve leakage. The difference between the theoretical PV diagram and the actual

COMPRESSOR ANALYSIS 5.5

THEORETICAL DIAGRAM

22A3B3

ACTUAL P-V DIAGRAM

4A 4 1

FIGURE 5.2 PV diagram illustrating the effects ofsuction valve leakage.

PV diagram will depend on the severity of leakage through the suction valves. Thefollowing is a step-by-step analysis of the PV diagram in Figure 5.2.

Line 1-2A: During compression, gas leaks out through the suction valve(s). Sincegas is being pushed out of the cylinder during the compression stroke, the pistonmust travel further to reach the discharge valve opening pressure. If the leak issevere enough, the pressure within the cylinder will not reach discharge pressure.The cylinder volume at point 2A is less than point 2, resulting in a shorter effectivedischarge stroke or a loss in discharge volumetric efficiency (DVE).

Line 2A-3B: During the discharge stroke, gas is exiting through both suction anddischarge valves. Should the leak be severe enough, the discharge valve will closeprematurely at 3B instead of point 3.

Line 3B-3A: With the discharge valve prematurely closed, the piston is stillmoving towards TDC as gas continues to leak out of the cylinder through thesuction valve. The internal cylinder pressure at point 3A is less than discharge linepressure at point 3. This effect may not be noticeable unless severe leakage ispresent.

Line 3A-4A: The cylinder’s re-expansion slope occurs more quickly than normaldue to the continuing gas leakage through the suction valve(s), thus causing thesuction valve to open at point 4A.

Line 4A-l: The early opening of the suction valves causes the actual suctionvolumetric efficiency (SVE) to be greater than the theoretical SVE.

Symptoms:

1. Inlet temperature rises because of the re-circulation of the gas.

2. Leaking suction valve cap temperature will increase. Other valve cap tempera-tures may increase, but not as significantly.

3. Actual discharge temperature will increase (actual discharge temperature com-pared to theoretical discharge temperature).

4. Indicated horsepower may be lower than normal.

5. Compression ratio may decrease.

5.6 CHAPTER FIVE

2 2A

ACTUAL P-V DIAGRAM

11B4A4

THEORETICAL P-V DIAGRAM

FIGURE 5.3 PV diagram illustrating the effects of dis-charge valve leakage.

6. The calculated capacity based on the SVE will be higher than the calculatedcapacity based on the DVE, resulting in a capacity ratio greater than 1.0.

7. The compression and re-expansion lines will not match the theoretical PV curve.

5.6.3 Discharge Valve Leak

Figure 5.3 illustrates the PV diagram of a typical compressor cylinder which isexperiencing discharge valve leakage. The difference between the actual PV dia-gram and the theoretical PV diagram will depend on the severity of leakage throughthe discharge valves. The following is a step-by-step analysis.

Line 3-4A: During re-expansion, the trapped gas in the cylinder is expanded asgas leaks through the discharge valve(s) into the cylinder increasing internal cyl-inder pressure. This increase in pressure causes the piston to move further downthe stroke, re-expanding gas as it enters the cylinder through the discharge valveuntil it reaches a point where pressure is reduced, allowing the suction valves toopen at point 4A. The result is a smaller effective suction stroke, thus reducingsuction volumetric efficiency. If the discharge leak is severe enough, the internalcylinder pressure will not reach suction pressure.

Line 4A-1B: During the suction portion of the cycle, gas is entering the cylinderthrough the open suction valve and leaking discharge valves. The cylinder pressurecan rise to a point causing premature closure of the suction valves at point IB.

Line 1B-1A: The suction valve has closed, cylinder volume is increasing, andthe internal cylinder pressure is rising, which results in a higher pressure at point1A than suction line pressure at point 1.

Line 1A-2A: The actual compression line will not match the theoretical com-pression line since the pressure at 1A is not the same as the pressure at 1, and gascontinues leaking into the cylinder through the discharge valves during the com-pression stroke. The discharge valve opens when cylinder pressure rises abovedischarge line pressure.

COMPRESSOR ANALYSIS 5.7

3 3B 2A 2

THEORETICAL P-V DIAGRAM

11B44A

ACTUAL P-V DIAGRAM

FIGURE 5.4 PV diagram illustrating the effects ofring leakage.

Symptoms:

1. The actual discharge temperature will be higher than the discharge temperatureobserved in normal operation, or as compared to the theoretical discharge tem-perature.

2. The measured cylinder capacity will be less than the design cylinder capacity.

3. Capacity calculations based on DVE will be greater than capacity calculationsbased on SVE, resulting in a capacity ratio of less than 1.0.

4. Indicated horsepower may be lower than normal.

5. The actual compression and re-expansion lines will differ from a theoretical PVcurve.

5.6.4 Piston Ring Leakage

Figure 5.4 illustrates the PV diagram of a typical HE compressor cylinder whichis experiencing piston ling leakage. The shape of the actual PV diagram will dependon the severity of the leakage.

Line lA-2A: As the piston travels from point 1A to 2A, gas is initially leakingfrom the HE side of the piston into the CE, as would happen with a leakingdischarge valve.

Line 2A-3B: Gas is exiting through the discharge valve and continues to leakpast the rings. Should the leakage be severe enough, premature closing of thedischarge valve could occur at point 3B.

Line 3B-3A: As the piston slows, and continues toward TDC, gas continues toleak past the ring, resulting in internal cylinder pressure drop to point 3A. Thispressure at point 3A is lower than application pressure (point 3).

Line 3A-4A: During the re-expansion stroke, gas continues to leak past the rings,resulting in a much quicker drop to suction pressure until pressure equalizes onboth sides, just like a leaking suction valve. After pressure equalizes fairly far downthe stroke, pressure is now higher on the crank-end side of the cylinder, and gas

5.8 CHAPTER FIVE

FIGURE 5.5 Operational and design problems.

starts leaking into the head-end side, again looking like a leaking discharge valve.Usually this happens so far down the stroke that it is not noticeable.

Line 4A-1B: Gas is entering the cylinder through the suction valves and is leak-ing past the piston rings. This leakage results in premature closing of the suctionvalves at point 1B.

Line 1B-1A: The suction valves have closed and the cylinder volume is increas-ing. Pressure in the cylinder increases due to continued piston ring leakage intothe cylinder. The pressure at point 1A is higher than design pressure (point 1).

Symptoms:

1. Measured capacity might be lower than the application capacity.

2. Discharge temperature will increase due to re-circ1uation of the gas. Compareactual discharge temperature to a normal value or theoretical discharge temper-ature. With severely leaking rings, discharge temperature may rise 80�F or more(double acting cylinder).

3. Leaking rings usually show up as a capacity ratio of greater than 1. However,leaking rings can also show up as a capacity of less than 1.

4. The measured compression and re-expansion lines will not match theoreticalcompression and re-expansion lines.

5.6.5 General Operation Limits

Generally, three common operational problems grouped together are: pulsation ef-fects, valve losses, and cylinder gas passage losses. Their effect on compressorperformance should be minimized as much as possible in the cylinder design andtaken into consideration in the stated compressor horsepower and capacity figures.Even though they are taken into account in the compressor design, they are some-times either underestimated or undefinable to the accuracy required and are re-sponsible for performance problems. Figure 5.5 illustrates the cylinder losses for atypical PV diagram.

COMPRESSOR ANALYSIS 5.9

DISCHARGE RESTRICTION

NORMAL TRACE

FIGURE 5.6 Discharge passage too small PV.

Another area of fault is that of restricted passages. Passageways may be blockedfor a number of reasons. Some of these include: incorrect cylinder design or sizingbottle restrictions such as plugged screens or broken diffuser tubes, valve restric-tions such as plate lift decreased through improper machining processes or debrisstuck in the valves. In the case of discharge, it may be plugged with melted pistonring debris. When passages are restricted, there may be excessive valve losses withthe hump of the discharge line more pronounced towards the end of the stroke.

If a sharp rise should occur just before the end of the stroke, valves may bepartially covered by the piston. DVE will be smaller than before, but due to theadded valve losses, hp may not necessarily be less. In fact, total hp may be higherthan normal.

These restrictions can also occur on the suction side for the same reasons, forthe same type of action, but during the suction cycle. Suction terminal pressuremay be less than the line pressure. Because enough gas cannot get into the cylinder,the slope of the compression line will be longer. This will mean less capacity anda lower than normal DVE. Horsepower may decrease somewhat and suction valvehp losses will be high.

5.6.6 Pulsation Effects

While the suction and discharge valves are open, the acoustic pulsation present inthe system is passed into the compressor cylinder. Should the pulsation levels beof sufficient amplitude, the valve opening and closing times can be affected. Also,the average inlet and/or discharge pressures of the cylinder may be different thanthe design pressures with the net result being horsepower and capacity values whichare different than the design values. These values may be greater or smaller, de-pending on the pulsation characteristics. The change in horsepower and flow maybe proportional, resulting in actual BHP/MMSCF figures that are the same asdesign. However, the predicted loading curves will no longer be accurate.

5.10 CHAPTER FIVE

NORMAL TRACE

SUCTIONRESTRICTION

FIGURE 5.7 Suction passage too small PV.

5.6.7 Valve and Cylinder Gas Passage Losses

Valve horsepower loss is due to the pressure drop across the compressor valve.Cylinder gas passage loss is the pressure drop between the cylinder flange and thecompressor valve. Should these losses exceed the cylinder design allowances, actualflow will be less than the design flow. (Note that these losses are also affected bygas pulsations.) A general rule of thumb is that valve and cylinder gas passagelosses should not exceed 5% of the indicated horsepower for that cylinder end.

5.6.8 Excessively Strong Discharge Valve Springs

Strong discharge valve springs will be evident when evaluating a PV curve, usuallyidentified by a normal trace until the start of the discharge stroke. Pressure willhave to rise higher than normal to open the valve. A single hump may appear andthen taper off until the cylinder reaches the end of the discharge stroke. Withextremely stiff springs, there may be oscillations above and below the dischargeline throughout the discharge stroke. Pressure pulsations can also show a similarpattern. In this case, it is necessary to look at the bottle pressure trace for indicationsof pulsations. Horsepower may not increase much, but excessive valve hp losseswill be evident.

5.6.9 Excessively Strong Suction Valve Springs

The suction valve may have stiff valve springs as well. The same effects occurwith suction springs as with discharge. For stiff springs, a single dip would appearat the beginning of the suction stroke. SVE will probably stay the same or a littleless, but computed valve losses would be much higher.

An easy way to determine the difference between excessive spring forces andvalve chatter created by weak or broken springs, with either suction or discharge,is:

COMPRESSOR ANALYSIS 5.11

EXCESSIVELY STIFFSPRINGS

NORMAL TRACE

FIGURE 5.8 Stiff discharge spring PV.

EXCESSIVELY STIFF SPRINGS

NORMAL TRACE

FIGURE 5.9 Stiff suction spring PV.

• If valve hp losses are high, then the most probable cause is excessively stiffsprings.

• If valve hp losses are low, then the most probable cause is weak or brokensprings.

5.7 COMPRESSOR PRESSURE/TIME (PT) PATTERNS

5.7.1 Double Acting Compressor Cylinders

A double acting cylinder moves gas on both sides of the piston simultaneously.The furthest end from the crankshaft is referred to as the head-end (HE), and thecylinder end closest to the crankshaft is the crank-end (CE). A double acting cyl-inder requires suction and discharge valves on both ends of the cylinder.

5.12 CHAPTER FIVE

SUCTION

DISCHARGE

RODCRANK SHAFT

PACKINGCEHECYLINDER HEAD

FIGURE 5.10 Double acting compressor cylinder.

There are three possible pressure measurement points:

• Suction nozzle/bottle

• Discharge nozzle/bottle

• Head and crank end cylinder measurements

While HE and CE cylinder pressure measurements are the most common, nozzlepressures also have value in determining causes of excessive valve and passagelosses, or pulsation. The analyst must decide what is to be done with informationobtained when determining the necessity to collect the above pressure readings.

TDC BDC TDC

HEAD END TRACE

CRANK END TRACE

FIGURE 5.11 Double acting compressor cylinder PT.

The above diagram represent typical HE & CE cylinder pressure traces with thesuction and discharge pressure traces overlaid.

5.7.2 Suction Pressure Time Trace

At line #1 (Fig. 5.12), suction line pressure, we see a line moving across the screen.Ideally, the line would be very steady. This represents the pressure, preferably atthe suction inlet nozzle of the cylinder. The function of this line is to allow theanalyst to evaluate the flow of gas entering into the compressor cylinder and its

COMPRESSOR ANALYSIS 5.13

TDC O

BDC 180

TDC 0

DISCHARGEPRESSURE

SUCTIONPRESSURE

1CB

TBC BDC TBC

DISCHARGEPRESSURE

SUCTIONPRESSURE

AED

FIGURE 5.12 HE & CE with suction and discharge PT’s dis-played.

effect on the internal cylinder pressures. The area below the suction pressure linewithin the PV curve is considered valve and passage horsepower loss.

5.7.3 Discharge Pressure Time Trace

In a similar manner, the trace at the #2 position is that of the discharge line pressurecollected from the discharge nozz1e leading into the discharge bottle. Ideally, thisline should be very steady. As with the suction pressure trace, this aids in thedetermination of internal cylinder pressure characteristics. The area above the dis-charge pressure line within the PV curve is considered valve and passage horse-power loss.

5.7.4 Head-End Pressure Time Trace (Internal Cylinder Pressure)

Trace #3 is a representation of the head-end pressure within the cylinder. Top deadcenter (TDC) starts at the far left of the pressure screen. At TDC, both the cylinderpressure and discharge line pressure should meet as the discharge valves close.

Line A-B: The cylinder pressure quickly drops to just below suction line pres-sure, allowing the suction valve to open.

5.14 CHAPTER FIVE

TDC BDC TDC

DISCH.PRESS.

SUCT.PRESS.

LEAKING TRACE

NORMAL TRACE

LEAKING TRACE

180° 360°0°

FIGURE 5.13 Discharge valve leaking.

TDC BDC TDC

DISCH.PRESS.

SUCT.PRESS.

NORMAL TRACE

LEAKING TRACE

LEAKINGTRACE

0° 180° 360°

FIGURE 5.14 Extreme discharge valve leak.

Line B-C: The cylinder draws gas as the piston moves toward bottom dead center(BDC). As the piston slows and comes to a stop at BDC, pressure equalizes acrossthe valve and the suction valve closes.

Line C-D: The piston moves from BDC toward TDC, compressing the gas withinthe cylinder until the pressure gets above discharge line pressure, allowing thedischarge valve to open.

Line D-E: The cylinder discharges gas and continues moving towards TDC. Thepiston slows and comes to a stop at TDC. At TDC, pressure across the valveequalizes, allowing the discharge valve to close.

5.7.5 Abnormal Pressure Time (PT) Patterns

The PT trace is usually used to provide pressure reference points with overlaidvibration traces. Internal cylinder pressures are at given degrees of crank angle.From this it can be determined where normal vibration events will happen, andpossible causes for other vibration events. While suction valve, discharge valve,and ring leaks affect the pressure time curve, and can be evaluated using the PTcurve, they are more easily diagnosed using the PV curve.

5.7.6 Passage Restrictions

The next problem seen is that of restricted gas flow through the valves and piping.Gas flow restrictions could be caused by: the passageway being too small for thevolume of gas; restricted suction screens; orifice plates that have been incorrectlydesigned; or other obstructions. Recognition of a restriction is easily made by thePT or PV curve. Figure 5.17 illustrates how a cylinder trace would appear with arestriction on the discharge side of the cylinder.

COMPRESSOR ANALYSIS 5.15

TDC BDC TDC

DISCH.PRESS.

LEAKINGTRACE

SUCT.DISCH.

NORMAL TRACE

NORMALTRACE

LEAKING TRACE

0° 180° 360°

FIGURE 5.15 Suction valve leaking.

TDC BDC TDC

NORMAL TRACE

DISCH.PRESS.

LEAKING TRACE

SUCT.PRESS.LEAKING

TRACE

0° 180° 360°

FIGURE 5.16 Extreme suction valve leak.

SUCTION

DISCHARGE

FIGURE 5.17 Restricted passages.

5.7.7 Rod Load Reversal

There are two types of reversals. The first, piston or crank angle reversal is thephysical reversing in direction of the piston, which happens at both TDC and BDCpositions. The second type of reversal is pressure reversal. Pressure reversal occursas the internal cylinder pressure goes from more pressure on the head-end side tomore pressure on the crank-end side of the piston. Without pressure reversal, lu-brication of both sides of the crosshead pin may not take place. This lubrication isnecessary and lack of lubrication will cause early failure.

5.16 CHAPTER FIVE

TDC BDC TDC

CRANK END TRACE

HEAD END TRACE

FIGURE 5.18 HE & CE PT trace.

The head-end trace begins with the re-expansion stroke. The pressure is higherthan the crank-end side of the cylinder during the re-expansion until it meets theincreasing pressure of the crank-end at point #1 (Fig. 5.18). When pressure ishighest on the head-end side of the cylinder, the rod is said to be in compression,and the cross head pin is being pushed to the back of the bushing. At point #1,the pressure on both sides of the piston is equal.

Continuing to follow the head-end trace during the re-expansion cycle, the pres-sure becomes less than that of the crank-end which places the rod in tension. Theclearance is changed in the bushing and the pin is forced to the other side of thebushing. In a similar manner, the pressure will reverse just after the head-end beginsits compression stroke and the crank-end is on its re-expansion stroke. The pressureagain equalizes (at point #2) with a change from rod tension to compression. Thismoving back and forth of the pin allows the clearance on both sides to open andaccept oil and thus provide a lubricating oil film.

With improper cylinder unloading, it is possible to create a situation in whichrod load reversal does not take place. Valve failures can also produce a non-reversalsituation if the compressor is already running close to a non-reversal condition. Itis necessary for the rod load to go from compression to tension for a short periodof time. (API standard 618 provides additional information on the duration requiredto provide adequate lubrication.)

5.7.8 Partially Covered Valves

Partially covered valves are sometimes seen in cylinders with large piston/headclearance after an overhaul as a result of incorrect setting of the piston position.

COMPRESSOR ANALYSIS 5.17

PARTIALLY COVERED VALVES

NORMALTRACE

FIGURE 5.19 Partially covered valves using PT trace.

Generally, the clearances are set at one-third of total on the crank side and two-thirds on the head side. This allows for thermal growth in the rod and piston andthe operating clearances should then be equal on each side. If improperly set, itcan affect cylinder performance. Figure 5.19 indicates that a problem exists witheither the way the piston was set, or the machining in the process of a cylinderrefit, or in the dimensions of a new piston. The PT shows the possibility of partiallycovered valves. Note how the pressure rises suddenly at the end of the stroke. Oneway for this to occur is by covering valves so that the gas is restricted as it leavesthe cylinder.

5.7.9 Compressor Rod Loading

Calculation of rod loads may be done with external suction and discharge linepressures. More accurate values will be obtained using actual internal cylinderpressures, taking into account the rise in pressure caused by valve restrictions orother factors that might be present within the cylinder.

5.7.10 Rod Load Calculations

Compression Rod Load (CRL) Internal � (HEA � HEPmax) � (CEA � CEPmin)

HEA � Area of HE of the cylinderHEPmax � HE discharge pressure that yields maximum total differential pressure

with CE pressure throughout cycleCEA � Area of CE of the cylinder minus rod area

CEPmin � Suction pressure at point of maximum differential pressure with HEpressure

5.18 CHAPTER FIVE

Tension Rod Load (TRL) Internal � (HEA � HEPmin) � (CEA � CEPmax)

HEPmin � HE suction pressure at point of maximum differential pressure withCE pressure

CEPmax � CE discharge pressure that yields maximum total differential pressurewith HE pressure throughout cycle

Compression Rod Load (CRL) Using Line Pressures � (HEA � HEPd) � (CEA � CEPs)

HEPd � HE discharge measured line pressureCEPs � CE suction measured line pressure

Tension Rod Load (TRL) Using Line Pressures � (HEA � HEPs) � (CEA � CEPd)

HEPs � HE suction measured line pressureCEPd � CE discharge measured line pressure

Manufacturers will provide actual rod load limits for both compression and tension,as found in most compressor manuals.

Below is an example from real data gathered in the field on an actual unit.Calculated rod loads using line pressures and then rod loading using internalpressures.

Line pressures of the cylinder were found to be:

• Suction � 700 psi

• Discharge � 1733 psi

• Piston diameter � 4.625�

• Rod diameter � 2.500�

Compression � (3.14 � 2.31ˆ2 � 1733) � ((3.14 � 2.31ˆ2) � (3.14 � 1.25ˆ2))� 700 � 20793 lbs

Tension � (3.14 � 2.31ˆ2 � 700) � ((3.14 � 2.31ˆ2) � (3.14 � 1.25ˆ2)) �1733 � 8848 lbs

The compression and tension loads differ. Limits from the manufacturer may bedifferent between each as well. The limits for this rod might be something like25000 lbs. compression and 15000 lbs. tension.

The actual measured internal pressures of this cylinder as read from the PTcurve are different from the measured line pressures. Both cylinders go over themeasured discharge line pressures. The suction pressure also is different from thehead to the crank-end.

The maximum pressure on the head-end is 2040 psi. At the same time, the crank-end pressure is 660 psi. These are the two pressures to be used for discharge andsuction for internal calculations. The maximum pressure during the CE cycle issomewhat less at 1940 psi and the suction pressure is 600 psi. This represents themaximum differential experienced during the tension rod load cycle. This is whatis used for the calculation of rod load tension.

COMPRESSOR ANALYSIS 5.19

HE 2040

CE 1940

DISCH 1733

SUC 700

CE 660

HE 600

2000

1500

1000

500

-180 -120 -60 0 60 120 180

ANGLE (DEGREE)

FIGURE 5.20 PT diagram for rod load.

Compression � (3.14 � 2.31ˆ2 � 2040) � ((3.14 � 2.31ˆ2) � (3.14 � 1.25ˆ2))� 660 � 26427 lbs.

Tension � (3.14 x2.31ˆ2 � 600) � ((3.14 x2.31ˆ2) � (3.14 � 1.25ˆ2) � 1940� 12990 lbs.

The results indicate that rod loads as predicted from line pressures would be lessthan those measured from actual operating data.

5.8 COMPRESSOR VIBRATION ANALYSIS

The basic types of vibration associated with compressors are the same as for en-gines. Recognition of these types is of concern for the analyst. Vibration causedfrom transients is the first group. When a valve slams open with a sharp mechanicalimpact, a high, straight line peak is created that exists only briefly. The secondgroup is a flowing pattern. A vacuum or leak, where the velocity of the gas changesenough to produce a wedge-type formation, will be seen with the trace. The last

5.20 CHAPTER FIVE

MECHANICAL IMPACTS GAS PASSAGE NOISE

ROUGH LINER

FIGURE 5.21 Types of vibration.

group is scuffing or roughness. This is seen as a broadening of the trace throughoutthe area. The width of the base line determines when a cylinder has become scored.

With compressors, there are basically three events within the cycle that shouldcause normal vibration for a single cylinder end.

• One is suction valve opening. This event should represent a sharp mechanicalimpact. A gas passage noise may be present for a short period of time.

• Another is discharge valve opening. Here we see a sharp mechanical impact anda short period of flowing gas at the opening of the valve.

• Last is discharge valve closing. Because of the pressure present in the dischargeline, the valve will quickly close. Therefore, there should be a small closing peakwith a slight blow as the gas is being shut off.

Suction valve closing is a definite event, but the pressure drop during closingchanges relatively slowly. Because the pressure slowly changes from suction tocompression, the valve should gently close with low flow.

When analyzing compressors, the repeatability of patterns compared to basemeasurement is critical. Pattern repeatability and data collection consistency areimportant. While trending or during a first-time analysis, the analysis may be dif-ficult.

COMPRESSOR ANALYSIS 5.21

HEAD END VIBRATION WITH P/T TRACE

VIBRATIONTRACE

DISCHARGE CLOSING Ps

DISCHARGE OPENING

SUCTION OPENING

DISCHARGE OPENING

FIGURE 5.22 Normal head-end vibration with PT trace.

SUCTIONOPENING

DISCHARGE CLOSING

DISCHARGE OPENING

CRANK END VIBRATION WITH P/T TRACE

FIGURE 5.23 Normal crank-end vibration with PTtrace.

5.8.1 Use of An Analyzer

When using vibration instruments in the time domain, the acceleration should beset to 1.0 to 2.0 volts/division for most units. For others using computerized anal-ysis equipment, the default scale should be set to 2.0 g’s. What is most importantis a standard baseline scale that is set for each type of equipment.

5.8.2 Normal Vibration Patterns

All the events previously discussed may be seen in Figs. 5.22 and 5.23. The openingevents may change relative to crankshaft position due to operational changes. The

5.22 CHAPTER FIVE

H.E.TDC 0°

H.E.BDC180°

H.E.TDC 0°

e a

E DISCHARGEPRESSURE

VIBRATIONULTRASONICTRACE

SUCTIONPRESSURE

FIGURE 5.24 Normal PT and VT illustration.

actual position of the opening/closing events should be referenced to the pressuretraces. The diagrams show normal events of the head-end and crank-end of thecylinder. These relationships are the same: vibration versus time, and pressure ver-sus time.

An overlay of both head and crank-end will show complete cycle of both endsof the cylinder. Just as with engines, compressors exhibit cross talk and echoingas described below.

5.8.3 Compressor Cross Talk

Cross talk is the effect of one valve, on one end of the cylinder, presenting itselfin the vibration/ultrasonic waveform of other vibration traces collected around theentire cylinder body. This is the reason that overlaying one pattern on top of anotherprovides valuable information.

Figure 5.24 indicates normal valve action of both the head and crank-end asreferenced to pressure.

Key:

HE denoted by capsCE denoted in lower caseA,a Discharge Closed A,a to B,b Re-expansion StrokeB,b Suction Opening B,b to C,c Suction StrokeC,c Suction Closed C,c to D,d Compression StrokeD,d Discharge Opening D,d to E,e Discharge StrokeE,e Discharge Closing 1 & 2 Cylinder Pressure Equalization

COMPRESSOR ANALYSIS 5.23

FIGURE 5.25 Head-end PT with vibration overlaid.

5.8.4 Pressure Reversal

An event that should not be seen as vibration, except in very low amplitude or inmagnified resolution, is pressure reversal. The pressure reversal does not changewhen the piston changes direction. The load on the wrist pin and rod componentswill be compression or tension depending on the pressure difference that existsbetween the HE and CE. The change in direction of this difference will cause thecross head pin clearance to shift from one side to the other.

The change in clearance from one side to the other allows penetration of oilinto the clearance to lubricate the crosshead pin. The pressure reversal occursjust after the two pressures equalize. This can be seen in the Fig. 5.24 at points 1and 2.

5.8.5 Normal Vibration Pattern Wrap-up

When looking at a single trace of either end, one must remember what other eventsare occuring and when the vibration/ultrasonic trace is being viewed. When ex-amining ends of the cylinder individually, the size of the vibration events shouldbe compared. Crank-end events will, or should, become smaller when measuringthe head end valves. The converse is also true when measuring the crank-endvalves. Figures 5.25 and 5.26 indicate what should be seen.

5.9 ABNORMAL VIBRATION/ULTRASONIC TRACES

5.9.1 Leaking Suction Valves

Beginning at BDC, which is where the suction valve closes, as the piston movestowards TDC, and as soon as compression pressure starts to build, the suction valve

5.24 CHAPTER FIVE

FIGURE 5.26 Crank-end PT with vibration overlaid.

LEAKING SUCTION LEAKING SUCTION

LEAKING SUCTION PRESSURE TRACE

FIGURE 5.27 Head-end suction valve leak.

may start leaking. This is not to say that all suction valves leak immediately afterthey close. There are many cases in which valves will close immediately after BDCand remain closed until there is enough pressure to force gas back out of the suctionvalve. If a suction valve is going to leak at all, it must leak during the dischargestroke, which is the area of highest differential pressure across the suction valve.With the capability of using a filter for both the vibration and/or ultrasonic trans-ducers, this vibration will usually show up as high frequency in nature since thisinvolves a leak rather that a mechanical event. There are three rules for identifyingleaking valves:

1. Valves will not leak when they are open. This is because there is a free flow ofgas through the valve.

2. A valve can leak from the time it closes until it opens again.

3. The greatest area of leakage will occur when the greatest pressure differentialacross the valve is present. Leakage of a suction valve will be greatest duringthe discharge stroke.

COMPRESSOR ANALYSIS 5.25

LEAKING DISCHARGE PRESSURE TRACE

LEAKING DISCHARGE

FIGURE 5.28 Head-end discharge valve leak.

5.9.2 Leaking Discharge Valves

With discharge leakage, the trace remains similar in that the leak is again indicativeof a high frequency rather than that of a mechanical low frequency. In this case,the use of a filter is highly recommended. The vibration pattern of a leaking dis-charge valve will:

1. Not indicate a leak when valve is open

2. Only show a leak from time valve closes until it opens again

3. Indicate most likely time of leakage will occur when greatest pressure differ-ential across the valve is present. This would mean that leakage of a dischargevalve will be greatest during the suction stroke.

5.9.3 Leaking Rings

Leakage across rings will occur when there is sufficient pressure differential acrossthem. The key to identifying leaking rings is to determine when rings would notleak. This would occur when pressure is equal on both sides of the piston. Referto points #1 and #2 of Fig. 5.29. Rings will leak the most when the greatest pressuredifferential is present. To help identify ring leakage, consider that:

1. Rings will not leak when the pressure is equal on both sides of the piston.

2. Rings are going to leak when the greatest pressure differential is present.

5.9.4 Cylinder Roughness

With cylinder roughness, the baseline of the trace will broaden in the roughest area.This is typically seen when abrasives enter the cylinder, when the cylinder surface

5.26 CHAPTER FIVE

H.E.TDC 0°

H.E.BDC180°

H.E.TDC 0°

DISCHARGEPRESSURE

SUCTIONPRESSURE

e a

B C

D c

FIGURE 5.29 Leaking rings.

FIGURE 5.30 Head-end cylinder roughness.

fails (scuffing or scoring), or when large wear particles come from the rings orpiston. Although the rubbing, or scraping, is a mechanical action, the frequency ishigh in most cases. If analysis is not performed at least once every six weeks, thecylinder may become smooth, and even though the injury or wear may still exist,the vibration pattern may not show up. This does not mean the fault is gone, butthat the components have worn each other to the point where lower friction iscreated. This may be difficult to see if the pressure trace is not monitored with thevibration. A look at the pressure trace will show the resultant leak. Figure 5.30below indicates roughness in the cylinder. Note the difference in baseline traceduring the rub.

COMPRESSOR ANALYSIS 5.27

FIGURE 5.31 Head-end over lubrication.

FIGURE 5.32 Head-end cylinder liquids.

5.9.5 Over Lubrication/Leaking Glycol System

If the glycol leak is relatively small, the symptoms will be similar to over lubri-cation. If the leak is large, there will be extreme changes during compression andre-expansion as the slope will be very steep. Over lubrication of a cylinder willcreate impact spikes seen in the trace. They will usually appear to be evenly spacedand show up as impact moments. Since this is mechanical in nature, the frequencywill be low. Figures 5.31 and 5.32 shows a representation of over lubrication orpresence of liquids.

5.28 CHAPTER FIVE

FIGURE 5.33 Head-end piston / rod looseness.

5.10 SYSTEMATIC COMPRESSOR ANALYSIS

The primary focus of a systematic analysis approach is to ensure a thorough com-pressor evaluation that consumes the least amount of time. Utilizing a form suchas in Fig. 5.34, to record all the pertinent information makes it less likely to wastetime or overlook important analysis infomation.

Follow the analysis format by completing items 1-17 as shown in Fig. 5.34. Usea check mark to indicate good condition; a check mark with a line through it toindicated marginal condition; an X to indicate poor condition; and a — to indicatenot applicable or no data was taken or available.

This should only be considered a guideline, adjusted to meet specific needs andabilities. It is assumed that the analyst has a thorough grasp of the analysis conceptsdiscussed here.

5.10.1 Data Validity (Basic PV/PT)

Check the basic PV/PT for accuracy.Look to see that the head end PT curve pressure drops off immediately after

TDC to ensure that phase angles are correct. Look to see that the crank end PTpressure curve drops off immediately after BDC.

Channel resonance can be identified by a jagged line during the compressionand re-expansion strokes. If channel resonance is present, it should be corrected ifpossible, then this process started over again.

5.10.2 Corrections (VEs, VEd, CRC, Ps, Pd, MCA)

If any of the following corrections are made, note them with the below abbrevia-tions:

COMPRESSOR ANALYSIS 5.29

FIGURE 5.34 Systematic analysis work sheet.

VEs or VEd—Volumetric Efficiency(Suction or Discharge)

CRC—Channel Resonance Correction

Ps—Pressure Suction(Suction Terminal Pressure)

Pd—Pressure Discharge (Discharge Terminal Pressure)

MCA—Marker Correction Angle

It is important that any changes in the data be easily recognized by anyone thatmay review analysis.

5.10.3 Theoretical PT/PV

Many analyzers are now able to overlay collected PV’s over theoretical curvesbased upon operating conditions. This display can prove helpful in identifying bothsubtle and obvious distortions in the PV curve. While this is a helpful tool, itshould not be relied upon as the only indicator on which to make analysis calls.

It is important to make sure the information necessary to create theoretical curvesis correct (gas analysis, clearances, geometry information).

5.30 CHAPTER FIVE

Analysis of theoretical PT/PV—With the ability to overlay and display theoret-ical pressure volume and pressure time curves to actual curves, the analyst shouldevaluate curves looking for differences.

5.10.4 Trend (All Collected Data)

At start use alarm limits that are set per design operating conditions. Values forcertain operating parameters change with operating conditions. Temperatureschange with load and overall vibration changes with load. Because operating con-dition changes with load, it is not the individual readings themselves that are thehelpful indicators of condition, but deviations from a baseline curve over an op-erating envelope. If the system is not capable of such calculations, uti1izing statis-tical process control features may be a way of developing an alarm limit that takesinto consideration changes in operating conditions. The most basic form of trendsis a raw trend line of parameters. These can be helpful when looking at correlatedparameters. Valve cap temperatures can be compared to each other on a singlecylinder or like stages. Temperatures can be compared as well as ratio of capacities.Compare values across the unit in a single step or come up with a single efficiencynumber that can be used to determine compressor degradation (flow balance, actualcapacity vs theoretical capacity, etc.).

Analysis of trends—Use whatever form of trending capabilities are availablethrough the system. Note any anomalies.

5.10.5 Compression Ratios

This is the ratio of absolute discharge pressure (PSIA) to absolute suction pressure(Pd/Ps). Atmospheric pressure is added to both suction and discharge pressuresread from the PV curve to convert Pd and Ps to absolute. In most cases, if ameasured value is not put in for atmospheric pressure, the system will assume 14.7psi (pressure at sea level) for calculations.

Analysis of compression ratios—Generally, compression ratio should not causerod loads to exceed manufacturer limits. When compression ratio approaches 3.0,VE is very low, especially DVE. When VE is less than 25%, the analyst shouldquestion the calculations that rely heavily on accurate VE.

5.10.6 System (Valve) Losses

From pressures at inlet and discharge nozzle, cylinder system losses can be cal-culated. System losses refer to horsepower lost due to piping and valve pressuredrop. If nozzle pressures are not taken, the area above Pd and below Ps are con-sidered system losses. In most cases, pressure is taken at the neck of the bottle,just prior to gas entering the cylinder, or just after gas is leaving the cylinder.Valves are designed with losses in mind. (Generally, the more efficient the valve

COMPRESSOR ANALYSIS 5.31

is, the less durable it is. Also a valve can be durable at the expense of high losses.)To measure actual compressor valve horsepower losses, collect a pressure tracefrom a tapped compressor valve cap and overlay on the PV curve.

Analysis of valve (system) losses—As a general rule, total system losses above5% should be investigated further to determine root cause of the losses. By takingnozzle pressure, it may be possible to further identify the reason for losses—todetermine if losses are piping or valve related. If valves are suspected to be theproblem, it may be worth tapping a single valve to obtain a pressure trace tocompare with the PV curve.

5.10.7 Capacity

Using calculated capacities for analysis purposes requires some foreknowledge ofthe compressor application and design specifications, or previous data collectionwith which to compare. Capacities are calculated from the SVE and DVE eachindependently. The results are suction capacity and discharge capacity. In theory,they should be equal or very close to equal. Usually when they are not, it is anindication of a problem occuring within the cylinder.

Analysis of capacity—Measured capacity should be compared to theoretical ca-pacity. Also compare capacities to horsepower curves generated for the unit. Ca-pacities can only be trended when operating conditions are constant.

5.10.8 Ratio of Capacities (ROC)

ROC is a single measure of cylinder condition. In simplest terms, ROC is suctioncapacity divided by discharge capacity or gas-in divided by gas-out. The ratioshould be 1 or as near to 1 as possible. A range for determining acceptability isgenerally .95 to 1.10. The ROC should be considered when compared to historicalreadings for the cylinder and unit. ROC greater than 1.1 indicates leaking suctionvalves or rings. ROC less than .95 indicates leaking discharge valves or rings.

TDC reference must be accurate. VE must not be affected by pulsation or chan-nel resonance. The smaller the VE, the more likely there exists an error within theresulted calculated values.

5.10.9 SVE and DVE

Suction volumetric efficiency and discharge volumetric efficiency are obtained fromthe pressure volume curve. They are also known as the effective suction and dis-charge stroke. They are read from the terminal pressure curve, crossing either thecompression or re-expansion line.

Analysis of SVE and DVE—Note VE less than 30%: there may be calculationerrors if VE is less than this.

5.32 CHAPTER FIVE

5.10.10 Discharge Temperature Delta

This reading is the actual discharge temperature minus the theoretical dischargetemperature. In most cases, theoretical discharge temperature does not take intoconsideration frictional heat, so the actual discharge temperature should be higher.

Analysis of DTD—High DTD generally indicates re-circulation of gas causedby leaking valves or rings. A general rule of thumb is that the DTD should rangefrom 10 to 40�F higher than theoretical. This value should be trended. With ringleakage, DTD can go to 100�F or more. Valve leakage results, typically, in DTDof 40 to 50�F.

Negative numbers for the temperature difference identify a need to evaluate whatgoes into the theoretical calculation and the method of discharge temperature col-lection. Taking temperatures using skin temperature values typically give readings10 to 20�F cooler than internal temperatures. Ambient temperature, sunlight, andwhether the unit is inside or out, affect the readings.

5.10.11 Rod Load

The maximum rod load reached in compression and tension during the strokeshould not exceed equipment manufacturer (EM) limits, and should go from com-pression to tension for a short period of time. Rod reversal allows lubrication toboth sides of the cross head pin. Rod load can be based upon internal cylinder orline pressures and should consider effects of inertia. It is important to identify themethod used by the EM to set the limits and make any comparisons on same basis.

5.10.12 Valve Cap Temperatures

Temperatures are the least reliable single indicator of valve leakage. Temperaturesdo help confirm leaking valves when applied with other information throughout theanalysis process.

Analysis of valve cap temperatures—In addition to actual valve temperatures,discrepancies in temperatures between valves on the same cylinder can give a goodindication of possible problems.

5.10.13 Cross Head Knock

Looseness associated with cross head knock comes at pressure reversal points. Thisreversal is also called the cross over point. This refers to the change from com-pression on the rod to tension. Valve vibration events should not be confused withknocks at the reversal points.

Analysis of cross head knocks—Match the rod load display with the vibrationtraces taken. Look for events that occur at the reversal points. Make sure the eventsare not valve related. Knocks identifed in this area should be of immediate concern.

COMPRESSOR ANALYSIS 5.33

5.10.14 Gas passage noise as expected

Analysis of gas passage noise as expected—Identify any pattern that exhibits un-expected gas passage noise. Concentrate on noise associated with leakage.

5.10.15 Impacts as Expected

Impacts as expected—Identify any abnormal impacts throughout the vibrationtraces.

5.10.16 Cylinder Stretch/Flap Analysis

Cylinder stretch is simply the movement in the horizontal direction from the frameto the end of the cylinder. Horizontal is perpendicular to the crankshaft. Movementshould be very small and typically less than 3 mils. If this exceeds 3 mils, a readingshould be taken on the distance piece to determine where the source of movementstarts. A general rule is when the movement is greater than 3 mils in the horizontaldirection, cylinder supports should be checked.

Flap analysis refers to the end of the cylinder flapping or having movement inall directions (horizontal, vertical, and axial). If this movement appears to be ex-cessive, it can be assumed that bolts connecting the cylinder to the distance pieceor frame are loose or broken.

5.10.17 Condensed Liquids Entrapped In The System

Similar results are obtained when condensation of liquids occurs in the system.These liquids are formed when pressure differential and temperatures are just rightto cause the gas to condense. This typically occurs on the suction side due to lowertemperatures. If condensation is heavy enough, vibration will become audible asfluid is slammed through the valves by the piston. If allowed to increase, the resultscan be almost as bad as detonation within an engine cylinder. If fluids in thecylinder are from a cooling system leak that has reached large enough proportions,the trace may be similar. The use of a filter may indicate both high and lowfrequency vibration.

5.10.18 Steps in the Cylinder, Ring Land, and Wear Band

Looseness

Vibrations may occur at strange frequencies in line with steps in the cylinder. Theywill typically be present near the end or beginning of the cylinder stroke. Band orring looseness will again appear at points of either the pressure or mechanicalreversals.

5.34 CHAPTER FIVE

5.10.19 Other Types of Looseness

These are types that exist in the mechanical train. Crosshead bushings/shoes, rods,bearings, pins, pistons and clearance plugs will all create vibrations that are similarto vibrations due to looseness of rings and wear bands. The amount of loosenesswill determine what amplitudes are seen. As discussed in the pressure section, themost likely places for this to occur are at the points of pressure and mechanicalreversals. The vibration event will be seen from 10 to 25 degrees after the event.Exactly where it is seen is dependent on the acceleration of the rod, which is afunction of speed of the unit. When viewed with a filter, the vibration typically islow frequency.

Figure 5.33 illustrates a cylinder with a piston that is loose on the rod. There isa difference in the valve and rod events in reference to crank angle position. Withdouble acting cylinders, the event should be seen on both reversals. Some analystshave monitored this event in a logarithmic scale in order to track the loosenessearlier.

5.10.20 Unloader Faults and Problems

Unloaders sometimes create more problems than is realized. The problem is that,if the unloader is not permitting the valve plate to return to its original position, itwill usually look like a leaking suction valve. The typical causes of this problemincludes the fingers not being dimensioned correctly or use of a compressed gasket.Unloader chairs or valve chairs may be loose in the cylinder, which can causevibration.

6.1

CHAPTER 6COMPRESSOR AND PIPINGSYSTEM SIMULATION

Larry E. BlodgettSouthwest Research Institute

2.1 INTRODUCTION

Simulation of compressors and piping systems covers a broad range of disciplinesAny discussion of simulation would be incomplete without an understanding of thenature of the process simulated and the simulation objective. The simulation ofpulsations requires plane wave acoustics and occasionally three dimensional acous-tics. The simulation of mechanical vibrations (excited by acoustic shaking forces)requires mechanical dynamics and finite element understanding. The simulation ofstress requires mechanics of materials and fatigue theory. Reciprocating compressorpressure volume simulation requires fluid dynamics and thermodynamics. Recip-rocating compressor valve simulation requires acoustics, mechanical dynamics andfluid dynamics. The central concept that relates these disciplines is the dynamicconcept. Of course an understanding of statics is also required, although it is usuallynot at the heart of most efficient designs. A basic understanding of both statics anddynamics is required to recognize what is necessary in developing and using aparticular simulation or model.

The term simulation or model will be used interchangeably to mean a tool whichexhibits similar properties of an actual machine. The simulation is usually basedon mathematically analogous processes. Therefore most simulations are mathe-matical ideas that respond in a similar enough fashion to predict the desired prop-erties of the system to be designed or analyzed.

Another central issue in compressor and piping simulation is the realization thata system is an assemblage of compressor and piping that forms a unified system.Proper simulation must address itself to the system as a whole and not isolateprocesses which are interactive in the system. Statics and dynamics both influencea machine’s performance, therefore they must both be included in an optimizedmachine design. Specialization that minimizes the overall character of the system,usually detracts from the success of a design effort.

6.2 CHAPTER SIX

6.1.1 Defining The Overall Task

The task of designing or analyzing a compressor and piping system includes:

• Piping acoustics (from compressor valve to acoustic termination)

• Piping mechanical dynamics (compressor manifold and external)

• Pressure drop analysis (efficiency considerations)

• Compressor valve dynamics (both performance and reliability)

• Compressor performance (cost efficiency)

• Piping mechanical statics (thermal expansion, etc.)

The major point to be made by addressing the overall design task is that the sub-projects are all influenced by each other. Mechanical piping changes can influencethe acoustics and acoustics can influence both mechanics and performance. Thecost-effective and technically sound acoustical design cannot be performed in avacuum. The use of concurrent analysis1 is without doubt the best approach.

6.2 GENERAL MODELING CONCEPTS

Normally, model processes are separated into areas which efficiently exhibit thedesired properties. Many models are limited intentionally so that the designer willnot make an effort to misuse the model. Therefore, it is not uncommon to seeseveral seemingly isolated simulations being performed which are then appliedsimultaneously. The use of a simultaneous design philosophy is very beneficial. Tothis end, we will be illustrating simulations in a focused effort to indicate the natureand use of simulations realizing that they will all be combined in a unified effortto optimize machine reliability and efficiency.

6.2.1 Static Systems

Static analysis in piping systems is usually divided into two areas:

• Static fluid loss associated with pressure drop and fluid dynamic efficiency (fluidrelated)

• Temperature, weight and pressure forces which determine static integrity (me-chanical related)

Pressure drop simulations vary considerably in use and complexity. They arebased initially on the fundamental loss mechanism. For pipeline efficiency, this lossfactor might be empirical such as Spitzglass, Babco*ck, Weymouth or Panhandle.The rational method of Darcy is more common in simulations in the last 20 years.The Darcy method is rationally developed from the physical properties of fluidsand Bernoulli’s general energy theorem. Bernoulli’s theorem can be stated as fol-lows:

COMPRESSOR AND PIPING SYSTEM SIMULATION 6.3

2 2P � P �1 1 2 2Z � � � Z � �1 2� 2g � 2g1 2

Z1 and Z2 � potential head at condition 1 and 2P1 and P2 � static pressure at condition 1 and 2�1 and �2 � density at condition 1 and 2V1 and V2 � velocity at condition 1 and 2

g � acceleration due to gravity

All practical formulas for fluid flow are derived from this theorem, with modifi-cations to account for frictional losses.

Mechanically related models dealing with temperature, weight and static pres-sure forces are usually included in a thermal flexibility analysis. The major staticissues are pipe stress, displacement, machinery forces and moments, and coolernozzle forces and moments. These will be discussed in detail in the section reservedspecifically for them.

6.2.2 Dynamic Fluid Transient Systems

The modeling of dynamic flow which is not acoustically related is generallyachieved through solutions of the basic equations of energy, motion or continuity,plus equations of state and other physical property relationships. The most popularsolution is the characteristics method (method of characteristics). This methodconverts the two partial differential equations of motion and continuity into fourtotal differential equations. These equations are then converted to finite differenceexpressions using a method of specific time intervals. The resultant computationalprocess is performed in the time domain and can yield very rigorous results. Whenlarge intermittent fluid flow problems are solved, this type of approach is necessary.It can also be applied to acoustic problems but is computationally intensive. Emer-gency shutdown and sudden machinery loading must be analyzed in the time do-main using such techniques.

6.3 PREDICTING PULSATIONS, VIBRATIONS, AND STRESS

Pulsation, vibration and dynamic stress can best be understood in terms of a dy-namic energy source and systems which can be resonant. Initially, the energy isgenerated by the machinery (reciprocating compressor). If the piping natural fre-quencies are frequency coincident, the energy is magnified through acoustic reso-nance. The unbalanced pressure forces in piping systems couples into the mechan-ical piping system causing vibration. If the mechanical natural frequency of thepiping is frequency coincident with the pulsation energy, secondary magnificationresults. When large vibrational displacements occur in stiff systems, excessivestress results at the points of stress concentration. If the cyclic stresses exceed theendurance limit of the piping material, fatigue failure results.

6.4 CHAPTER SIX

FIGURE 6.1 Typical compressor flow patterns.

6.3.1 Pulsations and Piping Acoustics

Dynamic energy is generated by the compressor in normal operation. The recip-rocating process produces intermittent flow and pressure. These flow and pressurevariations are conveyed into the gas in the piping. The dynamic energy (both pul-sative flow and pressure) first transfers into the gas or piping acoustics. Figure 6.1illustrates the mass flow versus time waves that commonly occur at compressorvalves. Figure 6.2 illustrates the frequency content of the head end discharge flowpulse. It is readily apparent that the frequency content of the pulsative flow islimited to compressor rpm and multiples of compressor RPM. A single compressorend produces decreasing amplitudes moving from the first compressor order (rpm� 1) to the higher multiples. When the front (head end) and back (crank end) endsof the piston are used simultaneously, cancellation and reinforcement of compressororder occurs. Most notably, the odd orders (1�, 3�, 5� ...) tend to be reduced dueto cancellation of the two ends. Reinforcement occurs on the even order (2�, 4�,6� ...). Therefore, double acting compressors cylinders produce strong pulsativeflow at even orders. This reinforcement and cancellation occur with significantacoustic involvement (on a single cylinders) due to the relatively close proximityof the head end and crank end valve in the cylinder passage. A much more complexcase occurs when multiple cylinders (operating in parallel or series) are connectedby piping elements. In such cases, the reinforcement or cancellation of energy

COMPRESSOR AND PIPING SYSTEM SIMULATION 6.5

FIGURE 6.2 Spectrum of head end discharge flow pulse showing compressor orders.

occurs due to the crank shaft phase and the piping acoustics between the cylinders.The models to analyze simple systems are almost trivial compared to the level ofsophistication required to analyze multiple cylinders with complex piping systems.It is always good to keep in mind the transfer of energy through a system is:cylinder excitation; acoustic transfer and amplification; mechanical transfer andamplification; acoustical to mechanical coupling; resultant shaking force; mechan-ical vibration; and eventual pipe material strain and stress.

The piping system can be viewed as a complex organ pipe network. The normalpiping system will have several acoustic natural frequencies which, if excited, de-velop standing wave patterns (acoustic mode shapes). As the flow and pressurewave travel out from the compressor, they are transmitted and reflected in the pipingsystem. Whether a wave is reflected or transmitted is determined by the change inimpedance from element to element. The simple acoustic impedance (Z) is deter-mined by the gas velocity of sound (c � ft /sec), the gas density (� lb/cu ft) andcross sectional flow area (A � sq ft) of the acoustic element.

�cZ �

This type of simplistic thinking is actually the basis for more complex models thatare used in everyday acoustic analysis.

6.6 CHAPTER SIX

The design of piping systems related to compressors from an acoustic viewpointwas first developed in 1952. Forty-four years of advances in analytical dynamics,instrumentation, and computer systems have continuously improved the engineer’sability to develop low maintenance, cost-effective and efficient designs. For manyyears, the only available techniques were based on electro acoustical (analog) orsimple mathematical models. With the advent of the desktop computer came digitalacoustic techniques. The use of the computer to solve basic acoustic piping cal-culations was not new. It actually existed on mainframe computers for many years,but the man-to-machine interface was inefficient and cumbersome.

There are many different types of acoustic piping models in use today. Themajority of digital models use the transfer matrix method. A fairly complete listof methods would include the following:

• Electro acoustical model (the analog)

• Transfer matrix

• Method of characteristics

• Simultaneous differential equations

• Acoustic finite wave

• Finite difference methods

• Spectral method

• Boundary-integral method

• Impedance methods (linear analysis)

An accurately modeled compressor and piping system requires both time domainand frequency domain calculations. The use of frequency-to-time domain trans-forms has led to a semi-rigorous approach in the frequency domain appearing tohave true time domain interaction when in reality it does not exist. True timedomain models include electro acoustic (analog), method of characteristics, or si-multaneous differential equation solutions.

6.3.2 Time Domain Models In Reciprocating Compressors

The process of developing a reciprocating compressor and piping design involvesthe representation of the compressor cylinder, pressure operated valves and a validacoustic piping model. The piston motion and the valve action produce a periodicintermittent mass flow from the suction piping and into the discharge piping. It isimportant to note the discontinuous nature of the flow pattern. If a single flow pulseis converted to the frequency domain, the flow can be viewed in terms of frequencymultiples of the compressor speed (rpm/60). The nature of these discontinuouspressure functions results in pressure pulses being produced at the machine speedand multiples of one times machine speed.

The acoustic natural frequencies of the piping system can be excited by thepiston pulse causing pressure and velocity magnification. The volumetric properties

COMPRESSOR AND PIPING SYSTEM SIMULATION 6.7

of the piping tend to introduce a smoothing process to the more severe interruptionscharacteristic of the opening and closing compressor valves.

The performance of reciprocating compressors can be generally inferred fromthe internal cylinder pressure and the manner in which it interacts with the pressuresoutside the suction and discharge compressor valves. The cylinder external pres-sures can be helpful or harmful to the overall cylinder compression and flow pro-cess. It is important to note that the piston motion, mechanical valve model, andoutside pressures should be represented in the time domain to allow for properinteraction.

When acoustic standing waves are present in the piping system, they can couplethrough elbows and capped ends, resulting in significant shaking forces. The majorcontributor of acoustic shaking force is due to the standing wave which is a by-product of acoustic resonance. Therefore, acoustic resonance has two disadvan-tages: the amplitude of the pulsative is magnified; and the energy is concentratedin a form that efficiently couples to shaking forces. By limiting or controlling thepulsation amplitude, the coupled shaking force can also be limited. The control ofshaking forces reduces vibration that can cause maintenance problems or fatiguefailures.

Through design analysis, non resonant acoustical and mechanical systems canbe designed which limit vibration, ensure efficiency and increase reliability of themachine and its piping system.

In simple systems, the design analysis approach can be closed form equationsin combination with past successful experience. However, in most cases, the com-plexity associated with multiple cylinders and extensive piping configurations re-quires the use of Analog or digital techniques.

6.3.3 Frequency Domain Acoustic Models

The most popular model used in piping acoustics is based on the transfer matrixapproach. The development of the equations used in constructing the model followsthe following path:

• Plane waves in an inviscid stationary medium

• Plane waves in a viscous stationary medium

• Plane waves in an inviscid moving medium

• Plane waves in a viscous moving medium

Implicit in the development of the impedance in acoustical systems is the rec-ognition of a direct analogy to frequency domain analysis of electrical transmissionnetworks. This is the fact that inspired the first acoustic piping design tool whichdominated piping design for many years, and continues to hold considerable ad-vantage compared to existing digital computer applications. The use of inductors(coils), capacitors and resistance forms the basic analogous components which re-late directly to fluid mass property, fluid resiliency and fluid resistance. The mass

6.8 CHAPTER SIX

flow and fluid pressure are directly analogous to electrical current and electricalvoltage. Even today the pro and cons of ‘‘analog’’ versus digital continues to be amatter of much debate.2 The real test of any model is its ability to produce faithfulresults that allow a knowledgeable piping designer to produce safe efficient com-pression systems.

6.3.4 Piping Mechanical Models

The single most important factor in dynamic mechanical models is determinationof accurate natural frequency calculations. Accurate natural frequency calculationsallow for the proper separation of pulsative energy (both incident and resonant)and mechanical natural frequencies. Should coincidence occur, mechanical reso-nance results and almost certain problems will ensue. High vibration due to reso-nance can result in one or more of the following problems.

• Loosing nuts and bolts associated with valves, piping restraints or other boltedelements. This results in general high maintenance cost.

• Vibration induced fatigue of smaller lines such as instrument lines

• Vibration induced fatigue of major piping elements

Where piping is the primary moving element, the vibrational mode shapes aredependent on the model possessing the distributed stiffness and mass properties ofthe pipe. When valves or concentrated masses are present, it is also important thatthese elements have specified rotational inertia properties. It is very important thatrestraints are modeled with proper stiffness values. As a general statement, themass and stiffness distribution and magnitude must be properly modeled to ensureaccurate natural frequency calculations. A knowledge of vibrational mode shapecan help in determining when a piping geometrical configuration is susceptible topulsation energy. The transfer of pulsation energy to the mechanical system gen-erally occurs due to area coupling at pipe closed ends and piping elbows. In pipingsystems with pulsation energy, the more elbows the greater probability of a vibra-tion problem.

6.3.5 Compressor Immediate Mechanical Analysis

Reciprocating manifold systems are composed of crosshead guides, distance piecescylinders, cylinder supports, suction nozzles, discharge nozzles, suction manifoldbottles, discharge manifold bottles, discharge bottle restraints and attached pipingon suction and discharge. The vibration patterns associated with such elements aremost accurately viewed as lumped masses connected with generally masslesssprings. Therefore, the approach required to model a compressor manifold is quitedifferent than that required to model the distributed properties of pure piping sys-tems. Calculating proper natural frequencies and mode shapes for compressor man-ifolds requires a very specialized understanding of such elements as:

COMPRESSOR AND PIPING SYSTEM SIMULATION 6.9

• Crosshead guide flexibility

• Distance piece flexibility

• Cylinder rotary inertia

• Nozzle branch connection flexibility

• Manifold bottle rotary inertia

• Discharge bottle restraint added stiffness

• Attached piping dynamic effects

6.3.6 Dynamic Stress Models

Dynamic stresses can be calculated in both piping systems and manifold systemswith proper attention to the element properties and the forces and moments at eachend of the element. In most cases, a finite element type of approach can be usedto calculate the dynamic stresses. Experience has shown that a distortion energytheory algorithm correlates well with practical field failure experience. The im-provements of the distortion energy theory over the total strain energy theory ac-count for the experimental observation that hydrostatic states of stress must beproperly assessed. The later contributions of Von Mises and Hencky have led tothe best overall techniques. The effort associated with a complete FEA analysis isnot necessary and would be prohibitive (if performed correctly) from a time andcost viewpoint. Practically, the most conservative and reliable dynamic stress cri-teria is to simply ensure the maximum dynamic peak-to-peak stress is less than6,000 psi. This accounts for worse case mean stress, stress concentration, surfaceeffect and size effects.3

6.4 RECIPROCATING COMPRESSOR PRESSURE

VOLUME ANALYSIS

Compressor system models are composed of both the compressor and the pipingsystem. Therefore, when a compressor simulation analysis is performed, a PV(pressure vs. volume) and PA (pressure vs. crank angle) display of the cylinderinternal pressure is available. Figure 6.3 illustrates the PA display along with actualpressure levels at the suction and discharge valves. Figure 6.4 illustrates a typicalPV card. The advantage of this PV card is the inclusion of the pulsation effects.Ideal PV calculations yield four basic components.

• Suction volumetric efficiency

• Discharge volumetric efficiency

• Compression line

• Re-expansion line

6.10 CHAPTER SIX

FIGURE 6.3 Cylinder pressure and valve pressure vs. crank angle.

During the period of time the suction or discharge valve is open, the internalcylinder pressure is influenced by the pressure beyond the valve in the piping. Thechanges in acoustic impedance cause pulsative energy to reflect back upon thecompressor valve and to actually enter the valve port. This influence is very sig-nificant. The nature of the pressure profile on the PV card during these time periodsis very similar to the pressure immediately outside the valves. A primary influenceis on the area of the card which is proportional to the work performed for eachrotation of the shaft. The work combined with the rpm yields the horsepower ofthe compressor. High frequency pulsative energy tends to produce numerous wavesduring the inlet or outlet flow time. Low frequency pulsative energy tends to causethe PV card to balloon or swell. A ballooning card usually suggests the horsepoweris increased with a corresponding increase in flow. Therefore, the efficiency of thecompressor is deteriorated. The compression and re-expansion lines can also bedisplaced, causing very significant increases in required horsepower with a smallincrease in flow. Displaced compression and re-expansion lines in many cases aresymptoms of increased valve impact velocities and limited valve life.

6.5 VALVE MOTION MODELS

The suction and discharge valve motion is determined by the dynamic properties(mass, stiffness and damping) of the valve elements and the differential pressure

COMPRESSOR AND PIPING SYSTEM SIMULATION 6.11

FIGURE 6.4 PV card display.

across the valve. The differential pressure and the effective pressure area determinesthe force that operates the valve. The differential pressure is composed of bothstatic and dynamic components. The valve motion cannot be properly predictedwithout including the pulsative energy present in the system. Figure 6.5 illustratesthe pulsative pressure at the exit of the discharge valve and also in the commonnozzle. This data shows the complex nature of pulsative energy and why this wouldsurely influence the valve motion. The energy content is quite different as youmove from the valve exit to the common nozzle. Figure 6.6 illustrates the spectralcontent of the energy in the nozzle. This spectral energy content shows the domi-nance of the basic double acting cylinder (dominate rpm � 2 energy) and acousticresponse associated with the cylinder internal passage at approximately 64 to 69Hertz. This is typical and illustrates the requirement of the modeling process.

An adequate compressor model will include a mechanical valve model coupledinto the driving pulsative energy and the open and closed limits of valve elementtravel. It is important that this model be evaluated in the time domain. The resultsof the model should yield valve spring and weight parametric analysis capabilities.The valve displacement, velocity and acceleration are directly available, allowingfor direct evaluation of impact velocities and forces. At present, several valve man-ufacturers have impact velocity criteria which are used to screen valve reliability.These criteria have not proven totally reliable up until now, and are used as asimple criteria which should not be over emphasized.

6.12 CHAPTER SIX

FIGURE 6.5 Pulsation at valve and nozzle.

Ultimately, the dynamic valve simulation should perform accurately enough toallow for optimization of the valve motion so that the valve operates ideally.

6.6 THERMAL FLEXIBILITY MODELS

The modeling of thermal expansion and piping flexibility has grown considerablysince its introduction with the Mare Island Project. Several commercial programshave been developed over the years to calculate pipe stresses, displacements, forcesand moments on piping systems as well as external loads on machinery compo-nents. The most important aspect of thermal, pressure and weight modeling is toproperly define the end conditions or limitations of such elements as stops, sup-ports, hangers, clamps and anchors. The common but false assumption that usinglarge values will ensure a conservative design is simply not true. Where pipingsystems are large and interactive, the restraining effects actually determine if amodel is valid or simply an educational exercise. Here again the real value of staticanalysis is dependent more on engineering expertise than on the model per se. Thisis true since most of the commercial models are adequate from a technical view-point.

COMPRESSOR AND PIPING SYSTEM SIMULATION 6.13

FIGURE 6.6 Pulsation spectrum at nozzle.

6.6.1 Piping Thermal Effects—Forces, Moments, Stresses

Depending on the program used, several force drivers can be included. A list mightinclude the following:

• Thermal expansion

• Pressure

• Thermal bowing

• Weight

• Wind

• Earthquake

• Support and restraint displacement

• Restraint friction

• External loads

Such forces are combined to determine total forces which, through the geometryof the system, result in moments. These forces and moments induce stress in thepiping which is compared with various piping codes in the generation of a code

6.14 CHAPTER SIX

compliance report. The codes also specify the calculation of stress intensificationto be used in the compliance report.

In thermal flexibility analysis, it is important to point out one very commonmodeling procedure which yields incorrect results. It is common to model ex-tremely high stiffnesses (anchors) as boundaries of the system and also to simulatethe effect of piping restraints. Stiffness characteristics of piping restraints such asbase elbows, piping clamps and directional guides should be properly evaluatedand applied to the flexibility model. This is important to achieve proper results andalso to allow for economically viable designs. The use of large or infinitely rigidvalues is defended on the basis that it is always conservative. This may be trueregarding calculated stresses, but in terms of economics, mechanical stability (sus-ceptibility to vibration) and overall design quality, it is often not conservative. Suchmodeling techniques often result in unnecessary design changes (i.e. additionalelbows, expansion loops, deletion of dynamic restraint) which give the systemexcessive flexibility. Without the use of proper restraint flexibilities, most analysesare of questionable value.

As with most models, it is important to understand that the results are based onthe ideal behavior of a perfectly constructed computer model. In addition, numerousassumptions are made during the modeling process, all of which affect the calcu-lated loads. Therefore, computer models used in this type of analysis should serveas design tools to provide general characteristics of a piping system and to avoidsignificant thermal-related problems. The application of codes for pipe stress andcompressor loading are meant to serve as guidelines, and strict adherence to orviolation of these codes neither guarantees success or failure of a piping system.

6.6.2 Forces and Moments on Machinery

The forces and moments due to the static piping effects are combined accordingto codes or manufacturer’s guidelines to determine the forces and moments on themachinery component (centrifugal compressor case or reciprocating cylinder). Thecalculated values are then compared with allowable values to determine if thepiping system is exerting an excessive load on the machinery. Large forces andmoments on high speed rotating equipment tend to produce case distortion andmisalignment. Such distortion produces excessive wear and bearing failures as wellas excessive vibration at rpm and rpm � 2. Where such analyses are performed,all legitimate flexibility should be included to ensure the forces and moments arereasonable and consistent with actual conditions. It is advantageous to understandthat the most commonly overlooked property is hidden flexibility. The actual sys-tems tend to be more flexible than expected. In most cases this tends to producelower forces and moments, but there are some exceptions.

6.6.3 Forces and Moments on Coolers

The application of thermal modeling to predict forces and moments on coolernozzles has become a common practice. There are several factors which must be

COMPRESSOR AND PIPING SYSTEM SIMULATION 6.15

considered to ensure proper modeling yields relevant results. In cases where over-simplified assumptions are made, the risers to coolers are made extremely flexibleand become candidates for severe vibration when significant pulsative energy ispresent. The proper balance of static and dynamic considerations is the only realassurance of true reliability.

6.6.4 Buried Piping Models

Buried piping models have been developed based on soil properties and mechanics.The soil stiffness is simulated through the use of discrete restraints distributed alongthe buried pipe. In some cases the restraint distribution is evenly spaced, and inother cases the distribution is variable. The ability to analyze buried pipe is a verydesirable capability and is much needed due to the fact that a great deal of pipingis buried. Although, these models are a valiant effort to simulate soil, they havenot been totally proven in terms of accuracy. Perhaps the most obvious questionarising in the mind of the analyst is the assumption that soil is hom*ogenous innature. Common knowledge suggests that soil components vary greatly over a givenarea and depth. Therefore, the results derived from such models should be closelymonitored and evaluated to ensure the results do not violate common engineeringunderstanding.

6.7 REFERENCES

1. Drummond, Rick, ‘‘Concurrent Analysis of Compressor Piping Systems,’’ Southwest Re-search Institute, San Antonio, Texas, 1994.

2. Blodgett, Larry E., ‘‘Using Analog and Digital Analysis For Effective Pulsation Control,’’American Gas Association, Operations Conference, Operating Section Proceedings, 1996.

3. Young, Warren C., Roark’s Formulas for Stress and Strain New York, N.Y.: McGraw-Hill, 1989).

7.1

CHAPTER 7VERY HIGH PRESSURECOMPRESSORS(over 100 MPa [14500 psi])

Enzo GiacomelliGeneral Manager Reciprocating CompressorsNuovo Pignone

Alessandro TraversariGeneral Manager Rotating MachineryNuovo Pignone

7.1 DESIGN PROCEDURE

7.1.1 General Information on High Pressure Services

The mechanical difficulties connected with high pressures were encountered bycompressor manufacturers during the development of ammonia synthesis processesafter 1920, as pressures of about 100 MPa (14500 psi) were reached.

Subsequently, the ammonia synthesis process was developed by reducing thefinal pressure and today’s values are around 32 MPa (4640 psi). Other applicationssuch as Urea production required pressure up to 35 MPa (5075 psi), but today, dueto improvement in the process, reaction can be obtained at pressures of 15 to 20MPa (2175-2900 psi). The storage and reinjection of natural gas also use highpressures ranging between 15 and 60 MPa (2175 to 8700 psi). Each applicationhas particular difficulties connected to gas compression, liquid carry over, lubri-cation and corrosion.

The use of high pressure processes increased after World War II with industrialdemand for low density polyethylene (LDPE),1 whose polymerization is achievedby bringing the gas up to 350 MPa (50750 psi) by using special types of recipro-cating compressors (Fig. 7.1). Compressors in this service have been given thename hypercompressor.

7.2 CHAPTER SEVEN

FIGURE 7.1 12 cylinder compressor for very high pressures (courtesy of Nuovo Pignone).

Plant capacities have considerably increased. In the early 1960s, the normalproduction per single line was on the order of 7,000 t /yr,* while lines producing200,000 t /yr LDPE are now in operation.

These plants are dangerous in case of erroneous or unsafe operation, because ofthe high flammability of the gas and the very high pressures involved in the pro-duction process.

One of the sources of risk is to be found in the secondary hypercompressor,where two main areas called for special care in the design and manufacturingstages: parts subjected to pressure and the crankgear.

The cylinders are subject to pressure fluctuations, which can cause fatigue failureif design, manufacture and material selection are not adequate.

The crank mechanism, driving the plungers, must perform its task with greataccuracy, because any misalignment might cause failure2 with possible risk of fire.Plungers are in fact brittle items owing to the very hard metal used, generally solidtungsten carbide.

As a consequence, the design of these machines must be based on sound fun-damental choices3 and supported by the most up to date analysis methods andexperimental techniques.4

*The abbreviation t denotes the metric ton of 1,000 kg.; yr � year.

VERY HIGH PRESSURE COMPRESSORS 7.3

Polyethylene types, differing in molecular weight, density, and degree of crys-tallization, can be divided into two categories depending on the process used topolymerize the ethylene:

• High Density Polyethylene (HDPE) is obtained with a low-pressure process,working at pressures below 5 MPa (725 psi) and giving a product with densityranging from 0.945 to 0.970 g/cm3 (.034–.035 lb/in3).

• Low Density Polyethylene (LDPE), produced by high-pressure processes, oper-ating between 100 and 350 Mpa (14500–50750 psi), gives a product with a littlelower density (0.91 to 0.93 g/cm3) (.033–.034 lb/in3).

The introduction of low pressure processes producing Linear Low Density Pol-yethylene (LLDPE) with operating pressures below 2 MPa (290 psi) began to erodethe sectors served by LDPE, reaching today plant capacities up to 500,000 t /yr ofpolyethylene.

The possibility of obtaining linear polyethylene with high pressure (HPLLDPE)was then investigated and practical applications were found in some existing plantswith final pressures from 80 to 170 MPa (11600 to 24650 psi), in order to providesome operating flexibility. Since the polymerization of these products requires themachine to operate in very difficult conditions, the process is now applied only inexisting plants.

Although extremely good results were obtained with plastic sealing elements onthe packings, the difficulty of controlling the process, in general, the severe lubri-cating conditions and the presence of aluminalkyle were resulting in unreliableperformance.

About 50% of the new plants for Low Density Polyethylene today are built touse compressors to bring ethylene to high pressure and then subject the gas in areactor to temperature and a catalyst. The polymer formed has good mechanicaland optical properties. Furthermore, these processes have no environmental impact,as they contain no metals and involve only ethylene and energy.

This technology is simple to use, competitive and offers possibilities for devel-opment of catalysts such as the ‘‘metallocenic’’ ones, well fitting with hom*ogeneoussystems (like the high pressure LDPE).

At present, high pressure polyethylene production covers the following sectors:

ProductDensity

g /cm3 (lb / in3) GasPressure

MPa (psi)

LDPE 0.920 (.033) ethylene 120–350 (17400–50750)Copolymers 1 0.927–0.935 (.033–.034) ethylene � vinylacetate (5 to 40%) 120–350 (17400–50750)Copolymers 2 0.927–0.935 (.033–.034) ethylene � acrylates 120–350 (17400–50750)HPLLDPE 0.880–0.920 (.032–.033) ethylene � butylene (10 to 40%) 80–150 (11600–21750)

7.4 CHAPTER SEVEN

FIGURE 7.2 Special crank mechanismwith self-aligned high pressure cylindersdirectly connected to the frame.

Although low pressure processes are continuously improving, with the help ofspecial catalysts, the high pressure process will still be needed in future.

7.1.2 Features of the Machines for LDPE Services

These pressures are reached by reciprocating compressors, having special designand using advanced materials such as NiCr-Mo steels vacuum melted and sinteredtungsten carbide.

For safety and reliability of operation, the following aspects need to be faced:

• The fatigue of the components subject to fluctuating pressure between suctionand discharge

• The sliding seal, between piston and cylinder

• The definition of a crankmechanism capable of giving perfect linear movementof the pistons

• The risks connected with the gas in the polymerization of ethylene

The proper design of very high pressure machines requires investigation of ther-modynamic, mechanical, process, operational and safety aspects.5 As an example,the motion work (Fig. 7.2), should drive the plungers with absolute precision.

The crosshead movement should be perfectly straight and coincide with thecylinder axis under both cold and warm conditions. The thermal expansion of thecrosshead should not affect alignment. Both planes of the vertical and horizontalguides should pass through the centerline of the plunger, which is centered to thecrosshead without clamping and is supported by the packing bush in the cylinder.The cylinders (Fig. 7.8), which are directly connected to the frame, require partic-ular care in the design of parts subject to gas pressure and of the seal arrangement.

Poppet type valves should be sized to minimize fluttering phenomena that woulddamage both the seat and the poppet.

Solid tungsten carbide or plated plungers are used with bronze or very specialplastic packing, depending on the process and pressure.

VERY HIGH PRESSURE COMPRESSORS 7.5

FIGURE 7.3 Crankgear using conven-tional and auxiliary crossheads.

For reasons of safety, a distance piece is inserted in the cylinder arrangement.A first recovery vent connected to flare or safe area, an oil barrier used to cool theplunger, and an emergency vent allow for proper gas leakage control without en-tering into the crankcase. Should gas enter the frame in emergency conditions,relief valves are provided. Nitrogen purging of the crankcase to eliminate oil vapormixtures ensures safe operation.

7.1.3 Crankgear Arrangements

For structural reasons, it is preferred the cylinders be of the single acting type. Thethrust mechanism of each plunger is subjected to a unidirectional load with diffi-culty of lubricating the load bearing connections, where surfaces always remain incontact, without the possibility of establishing an oil film (for example, betweenthe small end of the connecting rod and the crosshead pin.) In the design of thecrank-mechanism for polyethylene compressors, various compressor manufacturershave used different solutions to resolve the problem of the linear transmission ofmovement and the unidirectional load.

• The conventional type of crosshead drives through a spherical coupling an aux-iliary crosshead (Fig. 7.3), in order to reduce the oscillation transmitted to theplunger, but does not provide reversal of load on the small-end bearing. Thisbearing must be sized with low specific loading to allow for conditions of pre-carious lubrication and the transient state between liquid film lubrication and dryfriction.

• An external auxiliary crosshead (Fig. 7.4) is driven by the main crosshead throughtie bolts. Opposed plungers are attached to this auxiliary crosshead (yoke). Withthis construction, the thrust reversal is met and oscillation due to the low frictionforce acting on it is reduced by the auxiliary crosshead. The problem of thermalexpansion might still exist, but the solution for this is to locate the main andauxiliary crossheads in different frames, at some distance apart. Accessibility ofthe inside cylinder may still be somewhat restricted in this type machine.

7.6 CHAPTER SEVEN

FIGURE 7.4 Crankgear with main crossheads connected toauxiliary crossheads in separate frame.

FIGURE 7.5 Crankgear using two spe-cial crossheads with tie bolts and auxiliarycrossheads.

• Another solution is to utilize a hydraulic device for the transmission of force tothe piston. This is able to provide capacity variations, give perfect linear move-ment to the pistons, and also may have a complete oil control circuit.

• Two special crossheads (Fig. 7.5), one directly attached to the connecting rod,the other positioned on the opposite side of the crankshaft, connected by tie bolts,satisfy the thrust reversal requirement. Auxiliary crossheads are required to avoidtransmitting to the pistons oscillations and to absorb the thermal expansion ofthe main crosshead. This expansion is a function of the distance between thecrosshead pin and sliding surfaces and causes a displacement between the axisof the crosshead with respect to the axis of the cylinder.

• Another special arrangement (Fig. 7.6) has a crosshead, with sliding surfaces andguides in the lower part of the frame. Two connecting rods are used on each side.Thrust reversal is ensured by having two plungers on opposite sides of the maincrosshead. In order to obtain adequate linear movement during operation, anauxiliary crosshead is necessary to eliminate the thermal expansion resulting fromthe distance between plunger and main crosshead guides.

VERY HIGH PRESSURE COMPRESSORS 7.7

FIGURE 7.6 Special crosshead with twoconrods and with auxiliary crossheads.

FIGURE 7.7 Special crosshead self-aligned as-sembly, adopted for secondary compressors inLDPE Plants.

• A special and precise solution (Fig. 7.7), with two opposed plungers, is driventhrough a special crosshead, within which rotate crankshaft and connecting rod.The crosshead guides are plain and their axis is placed on the centre-line. Thedistance between crosshead slides is long, with a small clearance, and thus mis-alignment due to thermal expansion is avoided as the plunger axis and the slidesare on the same plane. This patented solution5 meets the above requirementsmost satisfactorily.

As a result, the movement of this crosshead is perfectly straight-line and coincidingwith cylinder axis under both cold and warm conditions. In fact:

• Pitching is mechanically prevented by the very small clearance ratio betweenguide and wing and distance between the guides and also because the frictionforce on the slides practically coincides with the gudgeon pin axis;

• Thermal expansion of the crosshead does not affect alignment, as the two planesof the vertical and horizontal guides pass through the plunger center-line.

7.8 CHAPTER SEVEN

FIGURE 7.8 Cylinder with radial valves.

This solution avoids the use of auxiliary crossheads which are necessary when aconventional main crosshead is used, to correct its rocking movement. Auxiliarycrossheads make the machine longer, more complicated, more difficult to align and,above all, they do not allow the cylinders to be directly connected to the frame, toeliminate the need for external support. This condition is in fact fundamental tobuilding a machine which is really ‘‘factory aligned’’ and needs no realignment inthe field.

The last two solutions are the only ones still applied in new plants.

7.1.4 Characteristics of Cylinders

As they work at very high pressures, hypercompressors should incorporate featuresto make them safe, reliable, and efficient.5

The cylinders, connected by long hydraulically-tightened tie rods, consist ofthree major parts: a flange connecting the cylinder to the motionwork frame, themain packing housed in a cartridge assembly, and the cylinder head containingsuction and discharge valves.

The cylinder with radial valve arrangement (Fig. 7.8) is a typical structure witha compression chamber, and a plunger with packing for gas sealing. Packing cupgeometries are complex, as housings are provided for guide bushes and seal rings,and also because of the presence of lube oil holes.

Similar cylinder arrangements are used with high pressures over 230–250 MPa(33350 to 36250 psi), where the cylinder head will have axial valves (Figs. 7.9 and7.10).36

VERY HIGH PRESSURE COMPRESSORS 7.9

FIGURE 7.9 Axial valve cylinder head.

FIGURE 7.10 Multipoppet axial valve cylinder head.

Construction with vertical or radial pipes-inlet and outlet (Fig. 7.9)-allows betterfastening to the foundation in order to obtain a very low vibration level. An ar-rangement with axial and radial pipe arrangement (Fig. 7.10) is also used in relationto plant layout requirement.

Valves of radial type (Fig. 7.11) are used up to 250 MPa (33350 psi). Axialcombined suction-delivery valves cover the entire operating pressure range with

7.10 CHAPTER SEVEN

FIGURE 7.11 Radial valve assem-bly.

FIGURE 7.12 Axial combined valve assembly.

monopoppet (Fig. 7.12) or multipoppet (Fig. 7.13) solutions. All valves are of thepoppet type with gas velocity usually between 30 and 60 m/s (98 to 197 ft/sec).Experience indicates outstanding performance of radial valves with over 30,000hours of operation, due to the following advantages:

VERY HIGH PRESSURE COMPRESSORS 7.11

FIGURE 7.13 Axial multipoppet valve as-sembly.

Greater reliability

• A very simple valve structure• Less possibility of polymer formation since the gas velocity is a little higher• Very low sticking effect on the poppet during operation because of higher

clearance and higher drag force on the poppet• Larger diameter of springs gives greater endurance

Better sealing

• The machining of the seats is more difficult on multipoppet valves• The higher clearance on a monopoppet valve allows for a better contact be-

tween seat and poppet with less possibility of damage

Monopoppet valves have greater allowance for reconditioning after long oper-ation and are easy to assemble.

On the axial valves, special seals separate the two sections from each other andfrom the outside. This solution serves a dual purpose by:

Allowing precompression of the valve bodies with pressure outside them, so thattheir tensile stresses are minimized.

Eliminating high stress fluctuations in the cylinder head at the suction and dis-charge crossbores.

The areas of heads subjected to high stress work in a precompression state,when ‘‘autofrettage’’ is applied.

7.12 CHAPTER SEVEN

Two-piece construction for compression chamber and packing cups is obtainedby shrink-fitting to precompress the most highly-stressed areas.

The cylinder heads have large holes intersected by lateral ducts for gas suctionand discharge. Cylinder design is important in order to attain the goal of safety-reliability-performance.6 It is necessary to solve problems connected with highfatigue stresses due to high fluctuating pressures and the variations in geometriescausing stress raisers.

Variations in geometry are minimized to reduce the effects of stress concentra-tion. Surface roughness is very important from the fatigue point of view and specialmachining procedures are needed to obtain very high levels of finish. In case of acylinder head with radial valves, where the whole crossbored cylinder is subject topressures varying between suction and delivery, stress fluctuations must be evalu-ated at the critical points and adequate prestressing applied.

The highest pressures require a solution with a combined suction-dischargevalve, enabling reduction of stress concentration effects on the head by setting theintersection points at places where pressure fluctuation is low.

In a cylinder for very high pressures, the material must also be efficiently ex-ploited by the use of prestress methods such as shrink-fitting and autofrettage,which ensure more uniform stress distribution across the cylinder wall. These twomethods may also be applied together when a high compressive prestress level isnecessary in order to operate safely.

7.1.5 Safety Aspects

Safety is of great importance in LDPE plants on account of the flammability of thegas and the high pressures involved. The discharge temperature of the gas is limitedtoday to 100 to 110�C* to reduce the risk of dissociation of ethylene in the cylinder,while in the past 120�C was reached in single stage compressors. In this case, toensure low final temperature, the gas was cooled before entering the cylinder.

As a further precaution, the plant is usually installed in the open air, sometimesunder roofing, or in well-ventilated enclosures to prevent any accumulation of gasdue to accidental leakage.

For the safety of personnel, it is the practice of engineering and manufacturingcompanies to position the instrumentation and control equipment at some distancefrom the most hazardous parts of the plant, and to ensure appropriate managementand use of modern monitoring and automation systems.8 Centralized control andoperation of the plant also allows optimization of process parameters and shorterperiods of transient operation, with even more outstanding performance of thewhole plant.

Additional benefits derive from the application of monitoring systems with main-tenance based on predictive rather than preventive criteria.

* In 1st stage 130�C shutdown, 115�C alarm. In 2nd stage 120�C shutdown, 100�C alarm.

VERY HIGH PRESSURE COMPRESSORS 7.13

FIGURE 7.14 Plunger—crosshead specialconnection.

With modern materials and design techniques, reciprocating compressors in-cluding very high pressure units now reach very high safety levels with reliabilityand availability factors over 99.5%.

Special safety concepts are applied to compressors, as the plungers are verybrittle and misalignment may produce failures. An intrinsically safe crank mecha-nism is of prime importance.7 The plungers must always be kept free to rotate andto move axially and a special connection to crosshead (Fig. 7.14) is required.

Furthermore, the cylinder bolts must be long enough to permit elastic elongationin case of decomposition or overpressure in the cylinder. The head is lifted by theelastic stretching of the tie rods and the gas is released through special reliefchannels in the head itself. A separation chamber between cylinder and frame isdesigned to vent any excess ethylene leakage from packings to the atmosphere,thus preventing gas from entering the frame. Nitrogen purging is applied to theframe as in internal combustion engines. The material used for high pressures zonesis selected ductile enough to ‘‘leak before breaking.’’

7.2 STRESS CONSIDERATIONS

7.2.1 Heavy-walled Cylinders Under Pressure

Typical arrangements of high-pressure cylinders of the plunger and packing types(Figs. 7.8, 7.9, and 7.10) consist of cylindrical bodies, nearly symmetrical, such as

7.14 CHAPTER SEVEN

FIGURE 7.15 Shear stress versus K � OD/ID ratio onheavy-wall cylinders.

the cylinder head, where suction and delivery valves are housed, formed by theintersection of the central duct and the lateral ducts feeding the valves, the com-pression chamber and the packing cups.

As all these areas are under pressures ranging from the value of suction to thatof delivery, they are susceptible to fatigue. For the highest pressures, a solutionutilizing a combined suction and discharge valve is employed. Stress concentrationin the head is reduced by arranging these points of intersection at a position oflow pressure fluctuation (Figs. 7.9 and 7.10).

At the design stage, the target is to simplify the shape by reducing it as nearlyas possible to a cylindrical form or, to the intersection of cylinders. This facilitatescalculation and tends towards a safer design.

Thick cylinders under internal pressure have distribution of stresses in the wallsuch that the radial stress (always in compression) has a value equal to the internalpressure and decreases to zero at the outside diameter, while the circumferentialstress (always tensile) has a maximum value at the inside diameter and decreasesto a value which remains above zero. Circumferential and shear stress cannot bereduced below the value of the internal pressure at the inner bore.

This distribution is a disadvantage, as a small part of the cylinder wall is underhigh stress, the outer fibres being less loaded as evidenced by the trend of the shearstress per unit pressure (�c � p) /p versus the OD/ID (outside diameter/ insidediameter) ratio K (Fig. 7.15). For values of K in excess of 2.5 there is little advan-tage in increasing the wall thickness, and over 5 the inside ideal stress is practicallythat of a cylinder with infinite wall thickness.

VERY HIGH PRESSURE COMPRESSORS 7.15

FIGURE 7.16 High pressure cylinder with WCliner and piston rings.

To design cylindrical bodies for very high pressures, it is necessary to utilizethe material more efficiently by using prestressing methods such as shrinkage orautofrettage, which result in a more uniform stress distribution across the wall.

The simplest method of prestressing is compound shrinkage. It makes it possibleto have the critical parts working at points that are more favourable on the endur-ance limit diagram, while the stress range will remain unchanged, depending onthe total radial thickness only.

Tungsten carbide liners (with a normal modulus of elasticity about three timesthat of steel) have been used inside the cylinder. These offer resistance to fatiguewhen the tungsten carbide is prestressed so that it is always in compression evenunder the most severe operating conditions.

This construction was applied with piston rings as sliding seals, between pistonand cylinder (Fig. 7.16). Tungsten carbide has a low friction coefficient, greatresistance to wear, and good resistance to corrosion. It is a suitable material forsliding seal elements under heavy contact pressure.

The application of brittle wear resistant materials is important, although they areundesirable if highly stressed in high-pressure equipment because of the risk offragmentation if they should fail.9 The failure criterion for brittle materials is themaximum tensile stress, i.e., when the liners are subjected to internal pressuregreater than external pressure, the circumferential stress at the inner diameter hasto be considered.

7.16 CHAPTER SEVEN

The state of stress in any cylindrical body is worsened by the presence of radialholes, necessary in the cylinder for the suction and delivery of gas (in the heads),as well as for bringing lubricating oil to the sealing elements in the packing cups.

In the intersection of the radial holes with the bore, the stress system10 is com-posed of:

�c � circumferential stress at intersection of radial hole, with the bore due to theinternal pressure in the bore and within the radial hole

�a � axial stress due to preload on the cylinder and effects of internal pressurewithin the radial hole

�r � radial stress caused by the internal pressures acting on the points of inter-section of the radial hole and the bore

The presence of cross-bores and the consequent stress concentration has a strongeffect on the fatigue strength of cylinders. To reduce the risk of failure, the materialhas to be prestressed, inducing compressive stresses by shrinkage or autofrettage.

The latter process consists of stressing one part of ring beyond the yield pointof the material. A greater plastic deformation occurs on the inside of the cylinder.When the autofrettage pressure is released, a compressive stress results in the innerzone and a residual tensile stress in the outer part. This method is preferred toshrink-compounding in the presence of crossbored cylinders such as those used forhigh-pressure cylinder head and packing cup.

Some tests11 made on a cylinder with a ratio of 2.25 between OD and ID di-ameter, with the cylinder wall overstrained up to the geometric mean radius, showedit to be as strong after autofrettage as non-autofrettaged cylinders without stressconcentration. These results were obtained after applying pressure at least onemillion times. It is possible to use shrinking and autofrettage, thus obtaining theadvantage of a more uniform stress distribution across the total cylinder wall thick-ness, ensuring a safer component under working conditions.

7.2.2 General Design Criteria

Most of the analytical design considerations on the components of the cylindersare based on the traditional equations of stresses and strain related to a cylinderunder pressure. Therefore, the formulas needed to obtain the stress level and thedetermination of the point of failure can be found in the contributions of manyauthors.

• Materials used in high pressure services are normally steel alloys with mechanicalproperties ranging from 1000 to 1500 MPa (145000–217500 psi) UTS (UltimateTensile Strength).

• Selection of materials is generally related to the stress level, as the corrosioneffects are negligible, apart from very special applications, where stress corrosionmay occur.

VERY HIGH PRESSURE COMPRESSORS 7.17

FIGURE 7.17a Traction-compression Smith diagramfor NiCrMo steel.

• When high stress levels are involved, Vacuum Remelted (Electroslag or VacuumArc Remelted) or superclean steels have to be used.

• These features are very important because the inclusion level is very low and therisk of fatigue failures is strongly reduced. The characteristics of such materialswith relevant endurance limits are reported on Fig. 7.17a and 7.17b.

The design of cylinder components has to make reference to thick walled cyl-inders under pressure, with the use of shrink-fitting construction,11 autofrettagetechnique,12,13,14,15 often applied to cross-bored cylinders16,17,18 generally under fa-tigue.19,20,21

The initial contact pressures, between the various components of the cylinders,arising after preloading of the main bolts, should have a safety factor of 1.2 againstyield stress of the material. The preload is usually established by assuming contactpressure on two adjacent parts will come to a level 10 to 20% above the internalpressure.

Stress risers have to be accounted for when holes or changes in geometry areinvolved. The stress concentration factors are generally applied to the range partat the stress, without considering the mean stress level.

Various methods could be applied to determine factor or safety. The basic ap-proach is to compare in a consistent way the stress level in operation with anallowable value, usually endurance or yield strength, for the material being used.

7.18 CHAPTER SEVEN

FIGURE 7.17b Fatigue diagram of cross-bored cylinder(K � 3) with and without autofrettage, tested with internalpressure.

A combined stress calculated for a cylinder component is usually based on theVon Mises criterion since almost always a triaxial stress state is generated by thecomplex loading of the cylinder components.

Considering the fact that cyclic stress is made up of mean (m) and range (R)stresses, the conditions related to suction and discharge are reduced to a meanstress and a range stress and then combined in accordance to the criterion of VonMises

2 2� � (1/�2) [(� � � )] � (� � � )mises m c (mean) r (mean) r (mean) a (mean)

2 1 / 2� (� � � ) ] (7.1)a (mean) c (mean)

2 2� � (1/�2) [(� � � )] � (� � � )mises R c (range) r (range) r (range) a (range)

2 1 / 2� (� � � ) ] (7.2)a (range) c (range)

Safety factors are thus defined in respect to the Mises (mean) and the Mises (range)stresses as:

VERY HIGH PRESSURE COMPRESSORS 7.19

V � yield strength/� (7.3)m mises m

V � endurance strength/� (7.4)R mises R

A combined safety factor, under fatigue conditions, is defined in order to make acomparison of the stress level during operation relative to the allowable limits.

1 � V � Vm RV � (7.5)ƒ V � Vm R

As the stress level is generally very high, the prestress level is determined insuch a way as to put the most critical parts, i.e., those subject to high variablepressures, always under compression. As fatigue failures occur when tensile stressesare present, the possibility of operating under precompression stresses practicallyeliminates this phenomenon.

The thickness of various components is very high because they are sized forfatigue and not for steady state conditions. Considering the geometry of such com-ponents, they are usually oversized against failure under steady pressure conditions.

The Results of the Repeated Pressure Fatigue Tests. Fatigue strength of cross-bored cylinders made from forged materials have been investigated for the com-ponents used on packing cups. Thick-walled cylinders with OD /ID � K � 3,internal bore diameter 12 mm (.47 inch) and radial holes 2.5 mm (.10 inch) weresubjected to cyclic internal pressure.

Different NiCrMo steels with different heat treatment and autofrettage conditionswere tested.

The non-autofrettaged fatigue strength of all cross-bored specimens was around175 to 189 MPa (25375–27405 psi), which is a typical value. With material havinga UTS 50% higher the endurance limit was 10% lower because of a higher notchsensitivity.

Autofrettage at 750 MPa (108750 psi) increases the endurance limit of all ma-terials tested up to about 350 MPa (50750 psi) and 6% fatigue strength increasecan be obtained raising the autofrettage pressure 11%. When autofrettaging at thesame pressure, increasing the ultimate tensile strength of the material does notimprove the fatigue limits of cross-bored cylinders. Only radiusing corners andimproving surface finish, increases fatigue limits.

7.2.3 Formulas for LDPE Cylinder Components

Calculation of Packing Cups with Axial Holes. On a generic cup idealized inFig. 7.18, the effects of preload and operating pressures will influence the stresslevel. This can be determined by the following formulas.

The cylinder bolts provide preload, on area A � B.This preload is reduced by internal pressure acting over the area within D1.

7.20 CHAPTER SEVEN

FIGURE 7.18 Sketch of packingcup with axial holes.

2 2 2 2A � (� /4)(D � D ) and B � (� /4)(D � D )2 1 4 3

It is desirable, for sealing purposes, to maintain contact pressure higher than thedischarge pressure pd by a coefficient x, so

2F � [(� /4)D � x(A � B)] p (7.6)1 d

Bolt load F will increase over the initial preload and has to be determined byanalysis of all the cylinder components in (Fig. 7.21). From this the initial preloadP required from the bolting and thus the initial face contact pressure pSAB can bedetermined.

The contact pressure due to preload on the mating surface of two adjacent cupswithout internal pressure is

p � �P / (A � B) (7.7)SAB

The value of axial stress during operation, on the internal part of the cup is

k �c 2P � D p� � 1k � k 4c b� � � (7.8)a � 2 2� ((D � � h) � D )4 g4

VERY HIGH PRESSURE COMPRESSORS 7.21

where p � generic value of the pressure that will assume the value of suction ordischarge for fatigue analysis considerations

kc � spring constant for cupskb � spring constant for bolting� � tang �� allows to calculate the conical volume where the axial stresses

are acting (generally �� 20�)

The contact pressure on the mating surface s of two adjacent cups, taking intoaccount of the service pressure (suction/discharge) effect, is

k �c 2p� � P � D p / (A � B) (7.9)� � � �SAB 1k � k 4c b

The load value P may be estimated or calculated with accuracy using the modelshown in Fig. 7.21.

The equation that correlates the interference fit pressure at diameter Do with theYoung’s Modulus (Ee, Ei) of the external and internal materials involved and thedimension of outer and inner rings, is

p � E I /Z (7.10)s i

where I � interference fit (per diam. Do) where the ratios between diameters, andouter ring and inner ring modulus of elasticity are

K � (D /D ) K � (D /D�) � � (E /E ) (7.11)o e o i o i i e

where average ID of the cup, considering the groove size is

D� � D � [(D � D ) � g /h] (7.12)i i g i

and the geometrical characteristics of the shrink-fit cylinder are given by the co-efficient

2 2 2 2Z � � (K � 1)/K � 1) � (K � 1)/(K � 1) � .3 (� � 1) (7.13)o o i i

The radial stress (i.e., the contact pressure between external and internal part ofthe cup) at interference fit diameter due to internal pressure is

2p � � (2p) /[Z(K � 1)] (7.14)s i

The total radial stress at diameter Do due to shrink fitting and pressure is

p � p � p� (7.15)o s s

The circumferential stress on the bore of the external part is

2 2� � [(K � 1)/(K � 1)] � p (7.16)ce o o o

As the service pressure is variable, it is necessary to obtain the mean (m) and therange (R) values of axial, circumferential and radial stresses, between suction (s)and discharge (d).

7.22 CHAPTER SEVEN

� � � �� ce ce ce ced s d s� � , � � (7.17)ce ce(m) (R)2 2

�p � p ��p � (�p )�o o o os d s d� � , � � (7.18)re re(m) (R)2 2

� � � �� ae ae ae aed s d s� � , � � (7.19)ae ae(m) (R)2 2

On the most heavily loaded point (the bore) of the external part of the cup, themean Mises stress and the amplitude of the range of the Mises stress are calculatedwith formulas (7.1) and (7.2). The compound safety factor under fatigue conditioncalculated with formulas (7.3), (7.4) and (7.5).

Inner ring circumferential stress level at the hole is

2 2p � K p (p � p )D 1i o o o� � � � p (7.20)� �ri 2 2 2K � 1 K � 1 Di i ƒ

where Df is the diameter where the hole is located.The circumferential stresses at the hole in the inner ring are

� � [(� � � ) /2] � [k (� � � ) /2] (7.21)cin cis cid t cid cis

where kt is the stress concentration factor due to notch or hole.The radial stress at the hole is

2 2p � K p (p � p )D 1i o o o� � � � p (7.22)� �ri 2 2 2K � 1 K � 1 Di i ƒ

The total concentrated circumferential stress, due to the hole, is

� � � � � � p (7.23)ci cin ri

The mean and range values of circumferential, radial and axial stresses at thenotch at discharge are

� � � �� ci ci ci cid s d s� � , � � (7.24)ci ci(m) (R)2 2

�p � p ��p � (�p )�s d s d� � , � � (7.25)ri ri(m) (R)2 2

p � p p � p �SAB SAB SAB SABs d s d� � , � � (7.26)ai ai(m) (R)2 2

where pSAB has been calculated with (7.9).

VERY HIGH PRESSURE COMPRESSORS 7.23

FIGURE 7.19 Thick-walled cylinder withplastic deformation.

The mean and the amplitude of the range of Mises stress are given by formulas(7.1) and (7.2).

The compound safety factor for the inner ring Vƒi, can be calculated as before,using formulas (7.3), (7.4) and (7.5).

Typical Pressures for a Thick-Walled Cylinder Subject to Autofret-tage. Considering the idealization of a cylinder (Fig. 7.19) and that K � De /Di

and Kc � Dc /Di and Kx � Dx /Di the following formulas apply:Autofrettage pressure, i.e., the pressure necessary to reach the yielding condi-

tions at the diameter Dc of the cylinder, having a yield point �y is

2 2P � (� /�3) [1 � (K /K ) � 2 ln K ] (7.27)A y c c

The pressure producing yielding at inner diameter, obtained by putting Kc � 1,is

2p � (� /�3) [1 � (1/K )] (7.28)y y

The full autofrettage pressure, i.e., the value of internal pressure capable toplastically strain the whole thickness of the cylinder is

p � (2/�3) � ln K (7.29)ƒA y

The bursting pressure, according to Faupel,35 considering the ultimate tensilestrength �U, is

p � (2 � /�3) ln K [2 � (� /� )] (7.30)b y y U

The stresses in the plastic zone, i.e., when 1 � Kx � Kc, are calculated with thefollowing formulas (characterized by index p � plastic)

• Stresses during autofrettage (index A)

7.24 CHAPTER SEVEN

Circumferential stress

2 2 2� � 1,155 � {1 � ln (K /K ) � [K � K ) /2K ]} (7.31)cpA y c x c

Radial stress

2 2 2� � �1,155 � {ln (K /K ) � [K � K ) /2K ]} (7.32)rpA y c x c

Axial stress

2 2 2� � 1,155 � {0,5 � [(K � K ) /2K ] � ln (K /K )} (7.33)apA y c c x

• Stresses after autofrettage (Residual stresses) (index Res)

Circumferential stress

2 2 2 2� � � � {[1/(K � 1)][(K � K ) /K ] p } (7.34)cpRes cpA x x A

Radial stress

2 2 2 2� � � � {[1/(K � 1)][(K � K ) /K ]] p } (7.35)rpRes rpA x x A

Axial stress

2� � � � [1/(K � 1)] p (7.36)apRes ap A A

where PA has been calculated with (7.21).

• Stresses during operation (index OP)

Circumferential stress

2 2 2 2� � � � {[1/(K � 1)][(K � K ) /K ] pcpOP cpRes x x i

2 2 2� [K / (K � 1)][1 � (1/K )] p } (7.37)x e

Radial stress

2 2 2 2� � � � {[1/(K � 1)][(K � K ) /K ] pr pOP r pRes x x i

2 2 2� [K / (K � 1)][1 � (1/K )] p } (7.38)x e

Axial stress

2� � � � [1/(K � 1)] p (7.39)apOP apRes i

where pi are the suction or the discharge pressure and pe is the external pressureduring operation.

The Mises stresses in the plastic zone during operation is

2 2 2� � (1/�2) �(� � � ) � (� � � ) � (� � � )misesOP cpOp rpOP rpOP apOP cpOP apOP

(7.40)

Stresses acting into the elastic zone (Kc � Kx � K) are calculated with thefollowing formulas: (characterized by index e � elastic)

VERY HIGH PRESSURE COMPRESSORS 7.25

Stresses during autofrettage

2 2 2 2 2� � 0,577 � (K � K )K / (K K )] (7.41)ceA y x c x

2 2 2 2 2� � �0,577 � [(K � K )K / (K K )] (7.42)reA y x c x

2 2� � 0,577 � (K /K )aeA y c

Stresses after autofrettage (residual stresses)

2 2 2 2� � � � {[1/(K � 1)][(K � K ) /K ] p } (7.43)ceaRes ce A x x A

2 2 2 2� � � � {[1/(K � 1)][(K � K ) /K ] p } (7.44)reaRes re A x x A

2� � � � [1/(K � 1)] p (7.45)aeaRes ae A A

Stresses during operation

2 2 2 2 2� � � � {[1/(K � 1)][K � K ) /K ) /K ]pceOP ceaRes x x x i

2 2 2� [K / (K � 1)][1 � (1/K )] p } (7.46)x e

2 2 2 2� � � � {[1/(K � 1)][K � K ) /K ] preOP reaRes x x i

2 2 2� [K / (K � 1)][1 � (1/K )] p } (7.47)x e

2� � � � [1/(K � 1)] p (7.48)aeOP aeaRes i

The Mises stresses in the elastic zone during operation

2 2 2� � 1/�2 �(� � � ) � (� � � ) � (� � � )miseseOp aeOP reOP reOP aeOP aeOP ceOP

(7.49)

7.2.4 Advanced Analysis of Stresses on Compressor Cylinder

Components

Compressor Cylinder Idealization by FEM. Computer programs can be used toevaluate stress and strain in compressor cylinders (Figs. 7.8, 7.9, and 7.10) bymeans of the finite element method (FEM). Especially subjected to the effects ofcyclic pressure are the compression chamber and the first packing cups, bolts andvalve elements and radial valve cylinder heads. Due to the pressure drop generatedby the seal rings, the packing cups downstream of the first seal element undergolower fluctuation.23 The axial valve cylinder head, owing to the layout of the suctionand delivery ducts, is subject to practically static suction pressure along the out-board section of the valve housing bore and practically static delivery pressurealong the inboard one.

Proper selection of the tie rod axial preload is also very important, to avoidexcessive stress concentrations at the point of discontinuity between the compressedand non-compressed areas of each packing cup.

7.26 CHAPTER SEVEN

FIGURE 7.20 Different profiles of packing cupmating surfaces.

Different configurations are used to reduce this stress concentration (Fig. 7.20)with the purpose of smoothing the peak of contact pressure. If the axial load is toogreat, the risk of packing cup fatigue failure is high. The packing cup profilesshould be maintained during reconditioning.

Fretting can occur between the mating surfaces, whereby the initiation point ofa fatigue failure may be reached as two adjacent cups tend to deform in a differentway. The upstream cup has a larger inner diameter (Figs. 7.20, and 7.22) and issubjected to higher pressure because of the pressure drop generated by the sealring. These conditions cause relative movement of the contact faces, and thenfretting, if the preload is not such as to make the two cups behave as a singlepiece. Another factor to be considered in determining optimum load is the tem-perature at which the cylinder is going to operate, since this affects the length ofthe elements, and thus the axial load itself. The compressor cylinder in a polyeth-ylene plant is a complex pressure vessel, due to its geometry and to the variationin the pressure distribution along the packing which makes it necessary to evaluateall the most severe conditions.

FEM analyses carried out on high pressure cylinder components,3 studied asseparate entities, leads to assumptions in determining the actions that the rest ofthe cylinder transmits to the part examined. By considering the whole cylinder,interactions, taking place among all of the components, can be determined withgreater accuracy to establish the stress and deformation states.

The cylinder is considered to consist of elementary components, and each com-ponent is idealized as a spring having an equivalent stiffness (Fig. 7.21).

VERY HIGH PRESSURE COMPRESSORS 7.27

FIGURE 7.21 Cylinder elastic simulation.

In the calculations, each cylinder component is considered under different loadconditions, simulating the actions simultaneously occurring during operation, sothat elastic behaviour can be determined (Fig. 7.22).

The elementary load conditions acting on the packing cups are the effects ofpreloads, gas pressure (viewed as superimposition of a constant and a differentialpressure), shrink-fitting and temperature. The total load and deformation states ofeach cylinder component are obtained under preload, suction and delivery condi-tions.

In order to make a comparison of calculation results with experimental mea-surements, deformation was measured on a cylinder under both static and dynamicconditions by dial gages on the cylinder and strain gages on the tie rods. Staticmeasurements were made of total elastic deformation resulting from the applicationof preloading on both cylinder and valve tie rods. (Total elastic deformation isequal to the interference produced between the tie rods and the rest of the cylinderduring tightening.) The dynamic measurements of deformation (by strain gages)on the cylinder tie rods show that the oscillation of tie rod deformation passingfrom suction to delivery is equal to 52.6 � (microstrains). This means that thefraction of gas thrust acting on the piston section affecting the tie rods is 32%.3

Optimization of Tie Rod Preload. Optimum preload can be obtained consideringaxial stress �a (contact pressure) and /ƒ ratio along the cup radius (Fig. 7.23). is the shearing stress that may cause sliding of adjacent cups and ƒ � 0,2 (as-sumption) is the friction coefficient. Sliding, and thus fretting, occurs when

7.28 CHAPTER SEVEN

FIGURE 7.22 Forces acting onpacking cups: a) Shrink-fitting; b) Tierod preloading; c) Uniform internalpressure; d ) Pressure drop; e) Tem-perature effect.

� /ƒ� � �� a

The pressure distribution along packing cups was considered with a deliverypressure of 300 MPa (43500 psi) in the compression chamber and a differentialpressure of 100 MPa (14500 psi).

When the differential pressure increases, the contact pressure is attenuated at theinner diameter. Moreover, different internal pressures in two adjacent cups resultin different deformations. This causes shearing actions between the mating surfacesthat increase when the differential pressure increases, thus facilitating fretting (Fig.7.23). The gas can infiltrate inside and separate the surfaces. When pressure de-creases during the compression cycle, the surfaces mate once again, passingthrough a sliding stage. The resulting ‘‘hammering’’ and sliding leads to frettingon the surfaces. These phenomena are eliminated when axial stress simultaneouslyexceeds /ƒ and the pressure along the seal surface. The axial preload ensuringthis represents an optimum, taking into consideration an adequate safety factor.

By knowing the main stresses on the cup mating surfaces during suction anddelivery, it is possible to make a strength evaluation (Fig. 7.24).3

VERY HIGH PRESSURE COMPRESSORS 7.29

FIGURE 7.23 Axial and shearing stress on matingsurfaces of cups.

FIGURE 7.24 Main stress distribution on a packingcup contact surface.

7.30 CHAPTER SEVEN

FIGURE 7.25 Ideal stress of packing cup reliefgroove in different operating conditions.

Fatigue Reliability of Packing Cups. The discontinuity between adjacent packingcup pressed and unpressed areas (Fig. 7.20) is one of the most highly stressedregions in high pressure cylinders. It can be affected by high differential pressuresthrough a single cup as the annular shoulder supporting the seal ring is subject topronounced bending, which produces tensile stresses (radial and circumferential)on the high pressure side. Assuming the geometry of Fig. 7.20d, high stress con-centrations may result on the bottom of the relief groove. Calculations providedetailed knowledge of the stress state at this point, by superimposing effects. Themain stresses, determined for suction and delivery, were combined by the VonMises criterion for each condition, thus obtaining the mean Mises stress and itsvariation. These stresses can be increased if stress raisers are present, due to ac-cidental notches on the relief groove (Fig. 7.25).3

7.2.5 Axial Valves Design

General Solutions. In suction-discharge multipoppet valves (Fig. 7.13), particu-larly suitable for large diameters, operating pressures produce very high stresses.Considering the most highly stressed part of the valve, the piece is idealized as arectilinear axis cylindrical body with 6 holes, having two different diameters.24

When operating, this part is subjected to constant pressure on the outer edge (exceptfor the gas pulsations in the line) and to fluctuating operating pressure on the inside,i.e., on the hole edges. There is also a compression in the direction of the axis dueto gas pressure and the axial preload created by tightening the flange tie rodsholding the valve in position.

VERY HIGH PRESSURE COMPRESSORS 7.31

FIGURE 7.26 Cross-section of multi-bored plate.

By the principle of superimposition of effects, the stress conditions generatedby external pressure, internal pressure and axial preload can be considered sepa-rately.

The holes are assumed to be of the through type and have a diameter which isconstant, with the geometry of the valve section unchanged in any plane perpen-dicular to the valve body axis. Without axial stress, the calculation approach bringsup the problem of an elastic body in a plane stress condition. Consequently, theproblem consists of establishing the stress condition due to external and internalpressure in a plate geometrically schematized in Fig. 7.26.

The plate has three axes of symmetry, 60� apart, which correspond to the di-ameters through the hole centers. In this structure, the greatest stresses are on theinner edges of the holes, particularly on the points lying on the axes connectingtwo adjacent holes and on the axes of symmetry. The most interesting points (Fig.7.26) are used to compare different calculations.

The stress condition of this elastic body could be determined through an exactprocedure, i.e., analytically, by solving the elastic problem, or through approximateprocedures using:

• Existing formulas for comparable geometrical bodies

• The finite element method25,26

• Strain gages on the piece boundary

• Photoelastic models

7.32 CHAPTER SEVEN

Solving a plane problem using the elasticity theory,27 means finding the Airy func-tion.

The stress function is complex due to the presence of several boundaries insidethe plate and consequently the resolution of the equation system defining the elasticproblem will also be very troublesome. An analytic solution of a similar case hasbeen found by Kraus.28

Evaluation of the stress distribution on the valve body can also be made usingequations for thick-walled cylinders under external and internal pressure.28 In thecase of cylinders with a central hole, the formulæ are to establish the stress distri-bution in any point of the radial thickness. More complex are the equations forcylinders having eccentric holes,28 giving circumferential stress in any point of theexternal and internal boundary. A further evaluation of circumferential stress canbe made, (only for the points in Fig. 7.26) by utilizing existing studies on stressconcentration factors in plates, whose notches are represented by holes.29 In thiscase, the plate is assumed to be compressed uniformly, as in a solid cylinder, withthe pressure acting on the outside. Variations in the circumferential and radialstresses on the required points referring to the center of the valve body beingknown, the circumferential stresses, resulting from the presence of the holes, canbe determined. Furthermore, holes of different diameters require further simplifyingassumptions.

Strain Gage Method. A model of the plate was equipped with strain gages onexternal and internal surfaces to measure the trend of the circumferential stresseson the boundaries, with pressure acting inside and outside.24 The model was biggerthan the valve, to allow positioning of the strain gages on the internal surface andbecause of seal problems in the passage area of the connecting wires to the straingages. The test pressure value was kept under 30 MPa (4350 psi). To minimizeeffects of systematic and accidental errors of the measuring instruments, the valueof the microstrains undergoing measurement was increased, by adopting a lightalloy model instead of steel, having a normal modulus of elasticity E � 72500MPa (10,512,500 psi) (about 1/3 that of the steel used for the valve). To eliminateuncertainties as to the elastic properties of this material, some specimens were takenfrom the piece the model was made from, to obtain the Young’s modulus andPoisson’s ratio for converting the microstrains into stresses.

FEM Application. The calculations were made with pressure acting separatelyon the external and internal peripheries. It was assumed, according to the symmetryof the system, that there was no rotation in the nodes determining the diameters ofthe half-plate, and that displacement would occur only in the direction parallel tothe circumference. The procedure used for calculation involved finite elements withtriangular elements having three nodal points, with the general element having 6degrees of freedom and a linear shape function,24 whose trend of stresses is shownin the graphs in Fig. 7.27 in relation to pressure.

The trend of circumferential stress with pressure acting on the outside is similaron hole edges. In fact, its lowest values comply with those predicted in points A2.1,A3.1, A2.2 and A3.2. The lowest value (�c /pe � �2.9) is assumed to be at point

VERY HIGH PRESSURE COMPRESSORS 7.33

FIGURE 7.27 Circumferential and radial stresses onplate edge and symmetry axes.

A.3.2, i.e., the internal boundary point of the hole having the smallest diameterand also related to the straight line joining the centers of two adjacent holes. Thehighest value (�c /pe � �1.9) is at point A4.2, i.e., at the smallest hole, toward theplate center and along a symmetry axis. Furthermore, with internal pressure, thecurves of circumferential stresses on the inner edge of the holes show a similartrend, the highest value being point A3.2. The trend of circumferential and radialstresses is alike (Fig. 7.27), both in the case of external pressure and that of pressurein the holes.

The sum of circumferential or radial stresses in the case of external pressureand unit internal pressure is constant and equal to �1, i.e.

(� /p � � /p ) � �1c e c i

The foregoing can be proved analytically for thick cylinders with centered or ec-centric holes, as formulæ exist for stresses along the thickness and at the boundaryrespectively. In any case, if unit pressure exists inside and outside a cylinder, thestress condition is the same at any point of the thickness and the hoop and radialstresses are:

� /p � � /p � �1c r

This is the result of two different loading conditions, with external and internalpressure; the above equation can thus be obtained by the superimposition effect.These statements apply to any type of stress (hoop, radial or direct, according tothe reference axes) involving multiconnected domains, regardless of boundary

7.34 CHAPTER SEVEN

FIGURE 7.28 Comparison of theoretical and experi-mental results on multi-bored plate.

shape, provided the internal pressure is considered on all internal profiles at thesame time.

Comparison of Results. In a polar-type representation (Fig. 7.28), the values arecompared with different methods. The stresses due to internal pressure are brack-eted.24 The trends of the curves determined according to the finite element methodand the experimental measurements are similar, and the stress values are very near.The experimentally determined values, except for the central zone of the smallhole, are slightly higher than those calculated with the finite elements. At the areaof greatest concentration (points A3.1 and A3.2), the results practically coincide.

The use of conventional equations led to results sufficiently in accordance withone another and generally lower than those obtained through the finite elementmethod. This occurs especially at the point of greatest concentration when the thickcylinder formulæ are used. At the same points, according to the theory of notches,the results practically coincide with those obtained through the finite elementmethod and experimental measurements.

Knowledge of the effective stress condition, proper choice of materials and ob-taining a high degree of finite elements in the zones of greatest stress concentrationmakes it possible to arrive at the actual safety coefficient and thus ensure reliabilityagainst fatigue failure.

VERY HIGH PRESSURE COMPRESSORS 7.35

7.3 PACKING AND CYLINDER CONSTRUCTION

7.3.1 Technical Solution for Cylinder Components

Two solutions have been used for this special pressure vessel:

• A hard metal liner (sintered tungsten carbide with 9 percent cobalt binder),shrink-fit into a steel cylinder, on which a piston equipped with special pistonrings (Fig. 7.16) was sliding

• A packing arrangement cup housing the seal rings, with a hard metal plunger(Fig. 7.8)

Although the first solution was providing fairly good results, it was more affectedby plant conditions, low polymers and catalyst carrier as the lubrication was ob-tained by injecting oil into the gas suction stream. The packed plunger solution isless influenced by such factors, considering that the lubricant is injected directlyonto the sealing elements through holes and grooves on the packing cups.

The technological development of sintering WC (11 to 13 percent Co) plungersof large size in one piece, the lower quantity of oil consumed, the excellent per-formance, and other process considerations21 led to preferring packed plungers overliners on the compressors manufactured in the last 25 years.

The selection of materials for components under pressure is very important.Mechanical properties must always be carefully analyzed and, when extreme

fatigue conditions exist, aircraft-quality electroslag or vacuum arc remelted steelsshould be utilized. To obtain adequate fatigue strength of pressure components, itis necessary to use autofrettage when operating pressures are very high.

Sealing surfaces between cylinder components play an important role in achiev-ing good cylinder performance. These are normally flat annular surfaces lapped toa finish of 0.2 microns CLA* and pressed together by tie rods so that their resultingload provides sufficient contact pressure to achieve seal. Since little can be doneto modify the actions the cups are subjected to during operation, care should betaken to prevent the consequences of accidental surface defects by performing localprecompression treatments, such as cold rolling, shot peening, ionitriding etc.

Special attention is required for the surface finishing of elements in direct contactwith the fluid subjected to pulsating pressure. In order to eliminate superficial faultsas much as possible, which could cause fatigue failure, very high grade finishesare required. Tungsten carbide plungers and liners have surfaces with 0.05 micronsCLA; with the additional advantage of reducing to a minimum the coefficient offriction between the moving parts. It is difficult to obtain these low roughnessvalues on the gas passages in the cylinder heads and on the surfaces of steelcylinders in general, without the use of special machinery.

*CLA � Center Line Average.

7.36 CHAPTER SEVEN

With a surface finish of 0.8 microns (32 microin.), fatigue life is reduced by15% as compared to that of a finish of 0.025 microns (1 microin.) It is not necessaryto obtain perfectly smooth surfaces, as it has been proved that finishes of 0.1microns (4 microin.) have no greater fatigue resistance than surfaces with roughnessof 0.025 microns (1 microin.).

7.3.2 Sliding Seals Between Piston and Cylinder at Very High

Pressures

The contact between the sliding parts for adequate sealing is severe for packingand particularly for piston rings. Under normal pressure, as the relative movementis parallel and does not allow perfect lubrication, only a transient condition of filmlubrication and dry friction exists. Oil particles, between the contact points, preventgalling, but to keep the friction coefficient within allowable limits, and to avoidexcessive heat generation, a correct selection of materials (chemical and physicalproperties) is necessary. Experience has shown that the most suitable materials forsealing elements are bronzes, having good wear resistance and mechanical prop-erties.

Cast iron and bronze or various combinations of these metals were used in thepast for piston rings. Special bronzes are still utilized for packing sealing elements,although plastic elements can be used up to 250 MPa (36250 psi) when the processrequires low heat generation to avoid decomposition in the cylinder. Relating tothe plunger material, in the past, nitrided steels were used for plungers in ammoniacompressors up to 100 Mpa (14500 psi). Usually, today piston rods are made ofsteel coated with tungsten carbide (11 to 13% Co) up to pressure of 60 MPa (8700psi).

In polyethylene plants, with more severe pressure conditions and more precari-ous lubrication by white oils, liners or plungers are made of tungsten carbide withcobalt bonding. When the cobalt content is increased, the hardness decreases, butthe toughness increases, and this quality is more important for plungers than forliners. Today, the steel plunger coated with tungsten carbide can be used up to 140MPa (20300 psi), usually on the first stage of secondary compressors.

The sliding surface of plungers and liners should be machined to the maximumdegree of finish obtainable in order to reduce the friction coefficient to a minimum.Values of 0.025 to 0.05 microns (1 to 2 microin.) CLA of roughness are normallyachieved. In case of WC coated plungers, the surface roughness is 0.1 micronsCLA (4 microin.). The surfaces of sealing elements do not require the same highquality, since they are softer and on the plunger they are polished during operation,but still need lapped mating surfaces and more accurate geometry to prevent leaksand failures.

The life of the sealing elements is influenced by other factors. The stroke andrevolutions per minute (RPM) determining the average piston speed influence thelife, since heat generation increases with speed. The RPM are limited by compres-sor size and arrangement, dynamic loads on the foundation, operation of the cyl-inder valves, and pressure pulsation in the gas pipes.

VERY HIGH PRESSURE COMPRESSORS 7.37

The stroke is selected to have a mean piston speed between 2.7 and 3.3 m/s(530 to 650 ft/min). A long stroke is generally desirable since this exposes a longerpart of the plunger out of the packing, for more effective cooling. The life of sealingelements is influenced by the system supplying the oil to the cylinder, the amountand quality of oil, the shape of sealing elements, and the linearity of plungermovement. A continuous film of oil must be applied to the sliding surfaces. Thetype of oil is selected mainly for process reasons (i.e., the need to keep the productpure), and also its lubricating properties. It is current practice to use white oil.

The shape of the sealing elements used is similar to those used in conventionalmachines.

The piston rings solution, with lubricating oil entrained by the gas, needs onlyfew rings for efficient sealing, but also to enable the one most distant from the gas-oil mixture to be lubricated. Each combined piston ring is made of two rings inthe same groove, with a further ring mounted beneath. The ring gaps are positionedout of alignment to give a complete seal effect. On the top of the rings there is abronze insert, improving the anti-friction properties and the running-in.

A packing arrangement is usually composed of 5 elements, for pressures up to350 MPa (50750 psi). In the past, solutions with 3 to 8 sealing elements were alsoapplied. The ring nearest the pressure is a breaker ring of special shape, suitablefor damping the high pressure fluctuations but not designed to provide effectiveseal, as this function is performed by the following ring couples, whose life isconsequently increased.

The amount of oil applied must be controlled accurately, since trouble can arisefrom either excessive or insufficient lubrication. If excessive oil is injected and theseal rings are providing perfect seal, the oil pressure can rise to a value above thatof normal conditions and the contact pressure between rings and plunger couldcause seizure. Of great importance is the linearity of the piston movement, sinceit ensures that the sealing elements will not be subjected to irregular operatingconditions and thus forced to assume an incorrect position in their housing, withconsequent overstressing and reduction in life.

It is necessary to keep the temperature low by cooling the plunger with oilaround it, outside of the main packing. This is important mainly to reduce the riskof thermal cracks on the plunger surface.

7.3.3 Autofrettage of Various Cylinder Components

General Aspects. The use of autofrettage, applied to tubular and vessel-reactors,has been extended to pumps18 and to machines operating particularly in tubular-reactor plants, as it is effective where the probability of fatigue failure is high. Thistechnique allows components to be built using materials with lower mechanicalproperties.

Autofrettage is performed on cylinder heads with combined axial valves, whenhigh pressures are involved, as gas pulsations are still present and fatigue mustalways be taken into consideration. Cylinder chambers and packing cups are ex-cluded, as they can reach adequate prestress levels through shrink-fitting. Packing

7.38 CHAPTER SEVEN

FIGURE 7.29 Surface sealwith conical seat.

cups with axial holes and oil distribution cups require additional prestress onlyinside the lube oil hole. The distribution cup has no shrinkage, and generally hascurved holes normally obtained through a special procedure, such as electro dis-charge machining (EDM). In this case, a proper polishing procedure should beapplied to fully remove the surface modified by local defects.

Autofrettage of injection quills and check valves operating on ethylene second-ary compressor second stages is also common practice when pressures are veryhigh. Cylinder heads with radial valves are shrink-fit and are autofrettaged onlywhen differential pressure between suction and discharge is very high. Autofrettagepressure is determined by operating conditions, geometry, presence of prestresses(due to shrink-fitting), and properties of the material. Autofrettage pressures forhypercompressor cylinder parts range between 500 MPa and 1300 MPa (72500 to188500 psi).30 Autofrettage of axial holes is performed after shrink-fitting of thecup on the finished piece, only upon completion of machining before final lappingof the mating surfaces. In this case, autofrettage pressure has been applied up to1100 to 1300 Mpa (160000 to 188500 psi).

Test Rigs and Seals Arrangement. Few types of seals withstand very high pres-sure applications, due to the fact that the geometries of the cylinder componentsto be autofrettaged are often complex. On polyethylene compressor cylinder parts,seals are restricted to conical seating surfaces, metal gaskets, plastic O-rings andspecial arrangements:30

• The cone solution (Fig. 7.29), typical of high pressure tubing, has been appliedup to 1300 MPa (188500 psi).

• Annealed copper gaskets are used up to 1300 MPa (188500 psi) (Fig. 7.30).

• Viton O-rings are employed for small-diameter seats, tapered (Fig. 7.31) or flat(Fig. 7.32), protected against extrusion by the metallic contact between the parts.

VERY HIGH PRESSURE COMPRESSORS 7.39

FIGURE 7.30 Metal seal.

FIGURE 7.31 Plastic O-ringwith conical seat.

Positive results were obtained on diameters up to 76 mm. (3 in.) and up to 900MPa (130500 psi) for the latter solution.

• Self-sealing arrangements (Fig. 7.33) are used for wider diameters, in order tofollow the bore, subject to considerable strain under high pressures.

These seals are made as follows:

• A seamless plastic O-ring with hardness between 75 to 90 Shore A, with goodsurface finish

• Hard plastic (a polyamide resin) and geometrically precise shoulder rings. Di-mensions have to be carefully checked, as plastics are subject to alteration withthe passage of time.

• Bronze antiextrusion rings with a 45� angle• Bronze rings to preload the seal assembly and to guide the inner core of the

device

In autofrettage of radial valve cylinder heads, similar seals are used and internalmandrels are applied to reduce fluid volume. Axial valve cylinder heads are auto-frettaged (Fig. 7.34) with special seals (Fig. 7.33) to achieve seal on the large innerdiameter which can be accomplished by providing a smooth surface finish and

7.40 CHAPTER SEVEN

FIGURE 7.32 Plastic O-ringwith flat seat.

FIGURE 7.33 Special seal with O-ring.

using great care in assembling the rig to avoid local damage in the seal zone. Aninternal bar reduces fluid volume. The seals are preloaded, the assembly is balancedand no additional support is required for the inner core. Lateral (suction and dis-charge) holes are plugged by flanges using combined metallic and O-Ring seals(Fig. 7.32). Autofrettaged packing cup axial holes (Fig. 7.35) use metal seals (Fig.7.30). The test rig for the oil distribution cups uses axially-directed seal (Fig. 7.30)and radial seal (Fig. 7.31). Autofrettage of injection quills utilizes cone seals (Figs.7.29 and 7.31).

Autofrettage Procedure. In equipments operating at very high hydrostatic pres-sures, the fluid must be able to transmit pressure without undergoing freezing ef-fects, related to fluid properties, operating temperatures and tubing size. Pressuremay increase at the pump and, due to solidification problems within the tubing,may be much lower inside the piece to be autofrettaged.

Brake oils have been used up to 500 MPa (72500 psi) with some drawbacks(i.e., corrosion on pump seal rings caused poor performance). Prexol 201 over-comes solidification problems and gives adequate intensifier plunger seal life, up

VERY HIGH PRESSURE COMPRESSORS 7.41

FIGURE 7.34 Apparatus for autofret-tage of axial valve heads.

FIGURE 7.35 Apparatus for autofrettage of packingcups.

7.42 CHAPTER SEVEN

to 1300 MPa (188500 psi). As oil properties are altered by use at the highestpressures, oil should be changed frequently.

The whole autofrettage process is controlled by resistance strain gage-type trans-ducers to check pressure at pump discharge, close to the piece undergoing auto-frettage and, if critical conditions exist, at the end of the circuit or at the far sideof the cylinder component.

Strain gages on the outer surface of the piece are used when an autofrettageprocedure must be defined for the first time, or in case of complex shapes, andmay detect internal pressure or deviations in mechanical properties. For safetyreasons, dimensional checks are performed after autofrettage.

The inner diameter of axial valve cylinder heads should be checked, to assessthe amount of metal to be removed, which should be as small as possible in orderto preserve the benefits of prestressing. At plastic strain conditions, duration oftests appreciably affect the final results. Pressure should rise slowly to allow strainto take place completely during each loading condition. In short tests, yield pointand ultimate tensile stress are increased while strain decreases. In the case of steel,a pressure rise of 10 MPa (1450 psi) per second is on the safe side. Generally, thetest requires a pressure rise of 5 minutes minimum. Pressure increase is related tothe volume of the fluid in the whole system and its components (tubing and theintensifier). The autofrettage pressure is maintained for 15 minutes (5 minimum)and a slow pressure decrease takes place in about 5 minutes. Slow return to finalconditions eliminates errors in dimensional measurements, allows time to checkthe autofrettage effect, and allows the special seals to return to their original po-sitions in their housings after having undergone severe strain, thus reducing dis-assembly problems.

Very high pressure systems have potential hazards, although risks are not asgreat as when gases are handled, due to the great energy involved (the fluid pos-sesses compressibility and can be trapped inside the system). If gaskets in thehydraulic system fail, the jettisoned particles could cause injury to people or dam-age objects. Fluid leak at high speeds, reduced by the small volumes involved, isanother risk. To prevent air from being trapped in the hydraulic circuit during testrig assembly, a vent valve is temporarily opened at the highest point of the circuitand oil is allowed to drip out, prior to tightening. To reduce risks from storedenergy, the volume of the system is reduced: the piping is made as short as possibleand suitable inner cores are used in large components like cylinder heads. Thecompact system is positioned in a safe area (bunker with fencing around the equip-ment to protect the surroundings). Steel shield between assembly and pump andmetal sheets around the pressure tubes are added protection. The operator’s workstation is separate. Before disassembling any part of the test rig, the pressure isrelieved from the circuit.

Some authors,31,32 advise heat-treating the material at about 250�C for an hourto allow component dimensions (i.e., eliminating flexural stresses without affectingresidual body stresses)33 and the material elasticity to be restored. (Others recom-mend higher temperatures.) At the same or higher temperatures, decarburizingproblems might arise on the surfaces. This is not common practice with polyeth-

VERY HIGH PRESSURE COMPRESSORS 7.43

FIGURE 7.36 Packing assembly.

ylene compressors, as components have proven successful field operation. In anycase, this heat treatment cannot be performed when the tempering temperature ofthe material is lower than the heat treatment temperature.

Axial valve cylinder heads, requiring accurate inner bore dimensions, must bemachined after autofrettage. Remachining is also performed in the seat area quills(oil distribution cup side) and thus the modified prestress level area is quite limited.Appropriate allowances must be considered, and material removal must take intoaccount the reduction in the prestress level.

It is generally advisable to perform autofrettage on finished parts. The combi-nation of autofrettage and shrink-fitting, especially when high ultimate tensilestrength materials are used, is complex. Autofrettage before shrink-fitting is nor-mally carried out on radial valve cylinder heads, allowing use of lower autofrettagepressure, with advantages. Lube oil holes of packing cups are autofrettaged at apressure of 1100 MPa (159500 psi). Autofrettage contributes to increasing theavailability of secondary ethylene compressors which operate in plants with tubularreactors or in general when pressures exceed 200 MPa (29400 psi).

7.3.4 Typical Behaviour of Packings

Packings today consist typically of one (or two) split breaker rings and five radialtangential sealing rings (Fig. 7.36). The rings are made of special bronze alloys,usually with high lead content, uniformly distributed, so as to guarantee sufficientstrength, low friction coefficient and high thermal conductivity, for a rapid dissi-

7.44 CHAPTER SEVEN

pation of the friction heat through the packing cups. The hardness of the ringsvaries from 55 to 80 Brinell (measured with a 10 mm. ball and 500 kg. load).

The plunger on which the sealing elements slide is made of solid tungsten car-bide, with surface finish of 0.05 microns [2 microin.] CLA. The synthetic lube oilof the cylinders has lower lubricating properties than oils used for normal services,since for ethylene polymerization, pollution of the final product must be reducedto a minimum.

Packing performance is greatly influenced by the above parameters and by theefficiency of the breaker rings, whose action is very important, as can be seen byanalysing the operating conditions of a packing. The pressure inside the cylindercan be considered as consisting of a constant portion (suction pressure) and afluctuating portion (the difference between discharge and suction). The static pres-sure distribution tends to overload the last ring (frame side), which has to handlealmost the whole load.23 This is similar to packings, operating at constant pressure,for example on ammonia synthesis compressors. The variable pressure increasesdue to polytropic compression, and then decreases due to the expansion of the gasremaining in the clearance volume, and assumes constant values during dischargeand suction effect.

Breaker rings oppose a rapid pressure increase in the cylinder, limiting gas leak-age and reducing the propagation of the pressure wave towards the seal rings. Theirmost important function, however, is to delay the ‘‘backflow’’ from the packingrings towards the cylinder chamber, when the plunger begins its back stroke. Ifthis action is inadequate, the pressure upstream of the first sealing element willsuddenly drop to the suction value, due to the steep slope of the expansion curve.The resultant of the forces acting on the first sealing ring is suddenly inverted,causing rapid expansion of gas under the radial and especially under the tangentialring, which exerts a stronger sealing action, with the following problems:

• Breakage of the dowel pin between radial and tangential ring

• Breakage of the lips of the tangential cut rings

• Damage to the garter springs of the sealing element

When, after a certain period of operation, the first sealing pair no longer per-forms its function, the problems occur in the second pair and the process of pro-gressive damage continues through the various rings of the packing. To analyzethe operating conditions, behaviour and performance of packings, measurementswere taken at the lube oil injection quills and in the compression chamber (Fig.7.37) of a first and second stage cylinder on a compressor having a capacity of53,000 kg/hr (1945 lb/min), operating in a plant with a vessel reactor. Packingshad a three piece pressure breaker ring, with small circumferential clearance andfive grooves of radial tangential seals (with axial clearance of about 0.15 mm. [.006in.]). The distribution of the pressures along the packing in relation to the crankangle (Fig. 7.37) and during the suction and discharge strokes (Fig. 7.38) is quitesimilar on first and second stage.23

In general, the first three sealing elements are affected by the pressure fluctuationof the cylinder, while the last two are subjected to an almost steady pressure (Fig.

VERY HIGH PRESSURE COMPRESSORS 7.45

FIGURE 7.37 Operating pressures on a 1st and ona 2nd stage cylinder.

FIGURE 7.38 Pressure distributionon the 2nd stage packing during dis-charge and suction stroke.

7.46 CHAPTER SEVEN

FIGURE 7.39 Wear distribution on 1st and 2ndstage packings.

7.38). The pressure variation occurring at the first sealing pair is propagated to thefollowing elements in the proportion of 70% on the second pair, 30% on the thirdand a negligible amount on the two final sealing elements. The steady pressure, atthe external oil injection quill, does not significantly change and therefore about60% should be supported by the last sealing pair, in the hypothesis of labyrinthbehaviour.34 Pressure pulsations, upstream of the suction valve and downstream ofthe delivery valve, may have an influence on the cycle pressures in the cylinder(Fig. 7.37). The pressure breaker rings behaviour appears good since the delayingaction is evident during the compression period and a considerable sealing effectis evidenced in both stages during compression and expansion. The breaker ring,in fact, withstands about 80% of the pressure fluctuation, (100 MPa [14500 psi] inthe second and 70 MPa (10150 psi) in the first stage). The efficiency is higher inthe first stage, due to the greater variability of the specific volume of the gas (5%in the second and 16% in the first stage). This may be partly explained by thedifference between the polytropic coefficient in first and second stage. It should berecalled that when the physical conditions of a gas are close to those of a liquid,the task of the breaker ring is more difficult and its effect is lower.

The fluctuating part of the pressure affects the first three seal rings, with thesecond and third withstanding a differential pressure of 50% and 30% as comparedto the first sealing couple (Figs. 7.37 and 7.38). The steady part of the pressure ismainly supported by the last two sealing elements.

Some packings were dismantled and analyzed after 10,000 to 20,000 hours ofoperation. The wear of each radial and tangential element was compared (Fig. 7.39)

VERY HIGH PRESSURE COMPRESSORS 7.47

and there was a similar wear pattern curve for radial and tangential rings. For firstor second stage, the trend for higher wear is on the first and last elements. Thewear rate is higher in tangential rings as compared with radial ones. On first stage,the first pair did not wear completely, as the dowel broke, due to ‘‘backflow’’ andthen the pressure loaded the second pair, causing accentuated wear. Wear on thetangential ring higher than the amount allowed by the butt gap is frequently ob-served due to non-uniform wear on the rings, resulting from the high pressures andforces acting on them. On the second stage, the ‘‘backflow’’ caused breakage ofthe springs (of the coil type) of the first pair and later breakage of the dowel pinof the second pairs. The work of withstanding the variable pressure was then carriedout by the third sealing element.

The maximum wear on the frame side elements of both stages is due to theconstant pressure to which they are subjected, considering that lubricating condi-tions are not optimal. Wear on the radial ring of the last pair of the first stagepacking is an exception, encountered in other compressors, which can be explainedas follows: The radial rings, subject to steady pressure, tend to remain in theirposition without effecting an appreciable sealing action towards the plunger, butsimply creating a barrier to the pressure at the cuts of the tangential rings. In thezone subject to variable pressure, the first radial rings are forced to exert a sealingaction on the gas that tends to re-enter the cylinder during the suction phase. Thesealing effect is not complete, since the radial cuts allow the gas passage.

A general wear pattern can be derived connected with the pressure distributionalong the packing (Fig. 7.39). The steady portion of the pressure causes a type ofwear with maximum values reached on the frame side sealing ring. The fluctuatingportion of the pressure causes wear with an opposite trend, with the highest valueson the first sealing pair. The resultant wear will be a curve with its maximumvalues at the extremities of the packing. Generally, the theoretical maximum valueis either towards the first ring (pressure side) or towards the last (frame side)depending on the predominance of the fluctuating or the steady portion. The prac-tical wear pattern is different as the ‘‘backflow’’ can make some sealing elementsinefficient. The performance of the sealing elements is strongly influenced by op-erating conditions, lubrication and alignment. The normal plunger runout is within0.075 mm. (.003 in.), as easily measurable by proximity probes, with alarm 0.15mm. (.006 in.) and trip 0.2 mm (.008 in.). Long life of packing rings has beenreported up to 65,000 operating hours, with 180 MPa (26100 psi) final pressure.

7.4 BIBLIOGRAPHY

1. Crossland, B., K. E. Bett, and Sir Hugh Ford: Review of Some of the Major EngineeringDevelopments in the High-Pressure Proc. Polyethyene Process, 1933–1983, Institute ofMechanical Engineering, 1986, Vol 200, Ne A4.

2. Andrenelli, A., ‘‘Reciprocating Compressors for Polyethylene Production at PressuresHigher Than 3000 Atmospheres,’’ Quaderni Pignone 13.

7.48 CHAPTER SEVEN

3. Traversari, A., M. Ceccherini, and A. Del Puglia, Advanced Elastic Analysis of Com-pressor Cylinders for H.P. Low Density Polyethylene Production, ASME Joint Confer-ence of the PVP, Materials, Solar and Nuclear Engineering Division, Denver, Colorado,June 21–21, 1981, Session 0A–6.

4. Traversari, A., and F. Bernardini, ‘‘Aspects of Research on Secondary Compressors forLow Density Polyethylene Plants,’’ Quaderni Pignone 25, June 1978, pp. 123–124.

5. Vinciguerra, C., U.S. Patent 3, 581.583 to Nuovo Pignone S.p.A., January 15, 1969.

6. Andrenelli, A., ‘‘Special Features in Reciprocating Compressors for Polyethylene Pro-duction,’’ Proceedings of the Industrial Reciprocating and Rotary Compressors: Designand Operational Problems, Institution of Mechanical Engineers, Vol. 184, Part 3R, Oc-tober 13–16, 1970, pp. 106–113.

7. Traversari, A., P. Beni P., Approaches to Design of a Safe Secondary Compressor forHigh Pressure Polyethylene Plants, High Pressure Symposium: Safety in High PressurePolyethylene Plants, Tulsa, Oklahoma, March 12–13, 1974.

8. Giacomelli, E., and M. Agostini, Safety, Operation and Maintenance of LDPE SecondaryCompressors, ASME PUP Division Conference, New Orleans, Louisiana, 1994.

9. Manning, W. R. D., ‘‘Ultra-high-pressure Vessel Design, Pt. 1,’’ Chem. Proc. Eng.,March, 1967.

10. Morrison, J. L. M., B. Crossland, and J. S. C. Parry, ‘‘Fatigue Strength of Cylinderswith Cross Bores,’’ J. Mech. Eng. Sci. 1959 1 (N. 3).

11. Parry, J. S. C., ‘‘Fatigue of Thick Cylinders: Further Practical Information,’’ Proc. Inst.Mech. Engrs 1965–66 180 (Pt. 1), 387.

12. Chaaban, A., K. Leung, and D. J. Burns, ‘‘Residual Stress in Autofrettaged Thick-WalledHigh Pressure Vessels,’’ PVP, Vol. 110, 1986, pp. 56–60.

13. Kendall, D. P., ‘‘The Influence of the Bauschinger Effect on Re-Yielding of Autofret-taged Thick-Walled Cylinders,’’ ASME Special Publication, P.V.P., Vol. 125, July, 1987,pp. 17–21.

14. Yang, S., E. Badr, J. R. Sorem, Jr., and S. M. Tipton, ‘‘Advantages of Sequential CrossBore Autofrettage of Triplex Pump Fluid End Cross Bores,’’ P.V.P., Vol. 263, HighPressure—Codes, Analysis and Applications, ASME, 1993.

15. Manning, W. R. D., Design of Cylinders by Autofrettage, Engineering (April 28, May 5and May 19, 1950).

16. Chaaban, A., and N. Barake, ‘‘Elasto-Plastic Analysis of High Pressure Vessels withRadial Cross Bores,’’ P.V.P., Vol. 263, High Pressure—Codes, Analysis and Applica-tions—ASME, 1993.

17. Chaaban, A., ‘‘Static and Fatigue Design of High Pressure Vessels with Blind-Ends andCross Bores,’’ Ph. D. Dissertation, University of Waterloo, 1985.

18. Chaaban, A., and D. J. Burns, ‘‘Design of High Pressure Vessels with Radial CrossBores,’’ Physical 139, 140B, pp. 766–772, North-Holland, 1986.

19. Rees, D. W. A., ‘‘The Fatigue Life of Thick-Walled Autofrettaged Cylinders with ClosedEnds,’’ Fatigue Fract. Eng. Mater. Struct., Vol. 14, pp. 51–68, 1991.

20. Rees, D. W. A., ‘‘Autofrettage Theory and Fatigue Life of Open-Ended Cylinders,’’Journal of Strain Analysis, Vol. 25, pp. 109–121, 1990.

21. Parry, J. S. C., ‘‘Fatigue of Thick Cylinders: Further Practical Information,’’ Proc. Inst.Mech. Eng., 1965–66, 180 (Part I).

VERY HIGH PRESSURE COMPRESSORS 7.49

22. Kendall, D. P., and E. H. Perez., ‘‘Comparison of Stress Intensity Factor Solutions forThick-Walled Pressure Vessels,’’ P.V.P.—Vol. 263, High Pressure—Codes, Analysis andApplications, ASME, 1993.

23. Traversari, A., and E. Giacomelli, ‘‘Some Investigation on the Behaviour of High Pres-sure Packing Used in Secondary Compressors for Low Density Polyethylene Produc-tion,’’ Proceedings of the 2nd Int. Conf. on H.P. Engineering, University of Sussex,Brighton, England, July 8–10, 1975, pp. 57–58.

24. Giacomelli, E., ‘‘Finite Element Method on Polyethylene Compressor Valves Design,’’Quaderni Pignone 26, January 1979, pp. 19–25.

25. Zienkiewicz, O. C., ‘‘Axi-Symmetric Stress Analysis,’’ The Finite Element Method inEngineering Science, (London, Eng.: McGraw Hill, 1971), pp. 73–89.

26. Tottenham H., and C. Brebbia, Finite Element Techniques in Structural Mechanics(Southampton, Eng.: Millbrook).

27. Muschelisvili, Some Basic Problems of the Mathematical Theory of Elasticity, Moscow,1949.

28. Kraus, H., ‘‘Pressure Stresses in Multibore Bodies,’’ Int. J. Mech. Sci. (Pergamon PressLtd., 1962), Vol. 4, pp. 187–194.

29. Peterson, R. E., Stress Concentration Design Factors (New York, N.Y.: John Wiley andSons, 1974).

30. Giacomelli E., P. Pinzauti, and S. Corsi, Autofrettage of Hypercompressor Componentsup to 1.3 GPa: Some Practical Aspects, ASME PUP Division Conference, Orlando,Florida, 1982.

31. Vetter, C., and H. Fritsch, ‘‘Zur Berechnung und Gestaltung von Bauteilen mit Bean-spruchung durch schwellende Innendruck,’’ Chemie Ingr. Tech., 1958, 40 (n. 24).

32. Morrison, J. L. M., B. Crossland, and J. S. C. Parry, ‘‘Strength of Thick CylindersSubjected to Repeated Internal Pressure,’’ Proc. Inst. Mech. Eng., 1960, 174 (no. 2).

33. Giacomelli, E., and P. F. Napolitani, ‘‘Ricerca Sperimentale sul Comportamento degliAccoppiamenti Forzati Albero-mozzo,’’ Thesis, Dept. Mech. Eng., University of Pisa,Italy, 1969.

34. Cosimi, L., ‘‘Il Compressore a Pistone a Secco con Tenuta a Labirinti,’’ Il calore, 1961—N. 3.

35. Faupel, J. H., and F. E. Fisher, Engineering Design, (New York, N.Y., Chichester, Bris-bane, Toronto: John Wiley and Sons, 1981).

36. Whiteley, K. S., Ullmann’s Encyclopedia of Industrial Chemistry, Vol. A21, Section1.5.1, Polyofins, 1992.

8.1

CHAPTER 8CNG COMPRESSORS

Mark EppJenmar Concepts

8.1 INTRODUCTION

The introduction of natural gas as a fuel for automotive and mass transportationhas provided an entirely new application for the compressor. The problems ofenergy supply shortages, poor air quality and high energy costs have contributedto the importance of natural gas as an alternative to crude oil based fuels.

Natural gas is a mixture of gases in which the primary constituent is methane,typically at 85.0 to 95.0 mole percent.

As a transportation fuel, stored natural gas must be compressed for an increasein energy density. The compressor is used to boost the pressure of natural gas andis the primary equipment of the compressed natural gas (CNG) refueling station.

8.2 CNG COMPRESSOR DESIGN

The compressor type used is the multi-stage reciprocating piston compressor. Com-pressor size commonly ranges from 25 to 250 brake horsepower (BHP). The designof the CNG compressor resembles the high pressure air compressor but with someimportant differences.

8.2.1 Suction And Discharge Pressures

Discharge pressures of 3600 to 5000 psig preclude the use of the multi-stage re-ciprocating piston compressor. Suction pressures are site specific and dependent onthe operating pressures of the local gas utility distribution pipeline. Suction pres-sures can range from inches water column to 1000 psig. Most often pressure reg-ulation and metering is supplied by the gas utility providing stable suction pressuresto the compressor. To minimize energy consumption, CNG compressor manufac-

8.2 CHAPTER EIGHT

FIGURE 8.1 Compressed natural gas refueling station (courtesy of IMW AltasInc.).

turers configure compressors specific to the application and suction gas pressureavailable (refer to Fig. 8.2).

The total pressure ratio from suction pressure to discharge pressure determinesthe number of compressor stages used. For the same pressure ratio, a natural gascompressor will generate lower discharge temperatures than an air compressor. Thisis due to the lower specific heat ratio property (k � Cp /Cv) of natural gas relativeto air. For this reason, natural gas compressors of similar technology can operateat higher pressure ratios than air compressors. The gas discharge temperature of acompressor stage is one of the limiting factors determining maximum stage pressureratio. The maximum discharge temperatures allowable are a function of the ac-ceptable operating temperatures of the sealing materials used, including pistonrings, rod rings, o-rings and gaskets. Avoiding high discharge temperatures alsodecreases compression horsepower. To maintain satisfactory discharge temperaturesa suitable number of compression stages must be selected. Table 8.1 provides aguide to the number of compressor stages required for a given suction pressure.There is some overlap of suction pressure ranges. Some compressors, such as thosewith oil lubricated and cast iron piston rings can operate at higher pressure ratiosthan compressors using nonlubricated and special material piston rings such as thefilled TeflonsTM.

CNG COMPRESSORS 8.3

FIGURE 8.2 Compressor brake horsepower vs suction pressure.

TABLE 8.1 Compressor Stages vs Suction Pressure

Suction pressure (psig) No. of stages Discharge pressure (psig)

6� H2O-10 5 3600–50006� H2O-100 4 3600–500080–350 3 3600–5000250–1200 2 3600–50001000� 1 3600–5000

8.2.2 Compressor Sealing

Natural gas is a flammable gas. It has also been identified as an atmospheric green-house gas. CNG compressors are designed to eliminate or severely restrict gasleakage emissions. Uncontrolled leakage may result from random leaks that occurin the piping system or compressor caused by static seal failures. Controlled leakageis expected leakage from compressor rod packings and seals. As industrial emis-sions standards tighten, consideration must be given to CNG compressor manufac-turer’s gas leakage rate data.

8.4 CHAPTER EIGHT

FIGURE 8.3 Pressurized crankcase compressor (courtesy of CompairReavell Limited ).

Pressurized Crankcase. Compressors with pressurized crankcases collect sealleakage gas in the crankcase and recycle it into the suction pipe. No leakage gasis lost to the atmosphere. The crankcase is pressurized at suction pressure. Specialrotating shaft seals prevent gas leakage from crankshaft drive end extensions. Mostpressurized crankcases are limited in use to suction pressures below 250 psig,however compressors with higher seal operating pressures are available.

Pressurized crankcases are most often used on trunk piston type compressors.Trunk pistons have a linear guide and piston as one integral part. There is no rodsealing between the piston and linear guide. Without a linear traveling piston rodand seals (see Atmospheric Crankcase, below), piston ring leakage flows into thecrankcase. To hold leakage gas at suction pressure, the crankcase must be designedas a pressure vessel with heavy rounded walls and internal or external structuralribs (see Fig. 8.3). Some pressurized crankcase compressors use a cantilevered shaftto eliminate one shaft seal. Other components including oil lubrication systems,static seals on inspection plates and cover seals must withstand the elevated pres-sures.

Atmospheric Crankcase. Compressors with atmospheric crankcases commonlyuse double acting cylinders and crossheads. Crossheads allow the use of a pistonrod which moves linearly and compresses both to the head and crank end (see Fig.8.4). The piston rod is readily sealed using a series of rod packings. Rod packingsare assembled in a packing case with gas leakage vented and piped for discharge

CNG COMPRESSORS 8.5

FIGURE 8.4 Atmospheric crankcase compressor (courtesy of Gemini Engine Company).

to atmosphere. New rod seal leakage can be very low and commonly less than0.1% of total cylinder mass flow rates. Most compressors of this type vent the gasat source rather than allowing the gas to leak into the crankcase. The crankcaseoperates at atmospheric pressure, eliminating the need for special shaft seals, gas-kets, and elevated pressure lubrication systems.

The atmospheric crankcase is most suitable for large compressors where designfor pressure containment is difficult. Atmospheric crankcase type compressors us-ing rod sealing also allow compressors to be designed for high gas suction pressuresbeyond what is practical for pressurized crankcase type compressors. In addition,maintenance procedures are less onerous, allowing crankcase inspections withoutdepressurization.

Blow Down Gas Recovery. Similar to air compressors, the natural gas compressormust be depressurized for start up. This necessitates that on shutdown, gas en-trapped in the compressor and piping system must be vented. Unlike an air com-pressor which can be vented to atmosphere, the natural gas compressor must beprovided with a blow down gas receiver tank. This tank must be adequately sized

8.6 CHAPTER EIGHT

to allow the compressor to depressurize and reach a pressure equilibrium suffi-ciently low for compressor start up.

Upon compressor depressurization, valves may operate under sonic or chokeflow conditions during blow down. Sonic gas velocities will quickly erode the seatsand seals of some valves. Sonic flow can be managed by using line orifices, specialvalve seat materials, or specially designed valves which protect seats and sealsfrom direct flow impingement.

8.2.3 Lubrication

Compressor lubrication has become an issue of debate within the CNG industry.Lubricated compressors require lubrication of piston rings, rod packings and valves.Nonlubricated or oil free compressors use special materials for these components,eliminating the need for additional oil injection. Proponents of nonlubricated com-pressors claim that they achieve the highest discharge gas quality. Proponents oflubricated compressors maintain that with well engineered lubrication and filtrationsystems, similar discharge gas quality is attainable. A lubrication oil carry overlimit maximum of 0.5 lb/mmscf at compressor discharge has become a commonindustry standard. This standard can be met using nonlubricated compressors orlubricated compressors with filtration.

In deciding lubricated versus nonlubricated, other factors to consider are outlinedin Table 8.2.

8.2.4 Piston Ring and Seal Performance

The extreme gas pressures exerted in the final stages of a natural gas compressorpresent some unique design problems. Piston ring wear rates increase dramaticallywith increasing stage pressures. High pressure differentials across piston rings con-tribute to ring extrusion between the piston and cylinder clearances. Lowering clear-ances reduces ring extrusion, but increases the possibility of piston contact withthe cylinder wall as the piston wear bands deteriorate. Extreme pressures alsocontribute to high operating PV (the product of surface pressure and velocity)values of piston rings. The result can be high piston and cylinder wear rates. HighPV also generates high ring surface contact temperatures. These temperatures canbe higher than measured gas discharge temperatures resulting in piston ring materialcreep and extrusion. Another less understood factor in piston ring wear is theapparent loss of oil viscosity at high operating pressures.

High pressure static sealing using compliant and porous o-ring materials canresult in seal failure upon rapid decompression. O-ring materials including Buna-N and VitonTM are porous and allow high pressure natural gas to permeate thematerial. If the o-ring is operating at high pressure for some extended time periodand then the compressor shuts down and rapidly decompresses, the gas entrainedin the o-ring will rapidly expand. Failure of the seal is caused by rapid expansionof entrained gas causing bubbles and lacerations in the o-ring material as the gas

CNG COMPRESSORS 8.7

TABLE 8.2 Lubricated vs Nonlubricated Compressors

Lubricated Non-lubricated

Advantages —increased piston ring life—allows use of metallic rings—air cooling or noncooling

systems sufficient—higher pressure ratios and

discharge temperaturesallowable

—fewer stages necessary in somecases

—higher operating speed—reduced capital cost—longer overhaul intervals

—low to nil oil contamination ofdischarge gas

—reduced lubricationrequirements

—less filtration needed—reduced routine maintenance—reduced noise levels with liquid

cooled units

Disadvantages —oil contamination of dischargegas stream

—oil deposits in pressure vesselsreducing capacity to store gas

—oil contamination of on boardvehicle equipment

—increased vehicle emmissions—higher compressor oil

consumption—increased maintenance

requirements on lubricationsystems

—increased noise levels with aircooled compressors

—increased cooling requirements—lower maximum discharge

temperatures—reduced piston ring and rod

packing life—lower pressure ratios and

discharge temperatures required—more stages may be necessary—increased capital cost—lower operational speeds—reduced valve life—shorter overhaul intervals

escapes. High operating temperatures, and pressures along with the presence ofcompressor lubricating oils, seems to exacerbate the problem. The higher durometerseal materials provide some improvement likely due to their lower porosity. Ifsuitable, the use metallic gaskets should be considered.

8.2.5 Other Compressor Design Considerations

Adequate gas aftercooling is key to the satisfactory performance of high demandCNG refueling stations. The cooler the natural gas is when it enters the storagevessels or refueling vehicle, the more dense the fuel, enhancing storage capacity.Final gas discharge temperatures should be a maximum of 20 to 30�F above am-bient air temperatures. Further reductions in temperature will greatly increase af-tercooler cost.

8.8 CHAPTER EIGHT

Compressors used in time filling applications (see Section 8.4.2) operate with alarge variation in discharge pressure. Some compressors require operation abovesome discharge pressure minimum. This minimum pressure is critical to the properoperation of piston rings. Without sufficient back pressure the rings will not seatadequately against the cylinder walls and in some lubricated compressors, oil con-sumption will increase as oil is drawn into the compressor cylinder. To address theproblem, a back pressure regulator can be installed at compressor discharge andset to the manufacturer’s minimum required pressure.

Compressor package noise levels are often critical to the acceptance of an in-stallation by approval authorities. Noise level requirements are often site-specificand set by city and municipal bylaws. Reduced noise levels also enhance fuelmarketing efforts. A commonly specified noise level is 75 dba measured at 10 feetfrom the perimeter of the compressor skid. Most compressor packagers can meetthis noise level with an enclosed and sound attenuated compressor skid package.

8.2.6 Compressor Electrical Systems

Natural gas, being flammable, requires that all electrical equipment and wiringwithin a code specified distance from natural gas compressors and gas containingequipment be explosion-proof. The explosion-proof classification most used in theCNG industry is class 1, division 1 or 2, group D in accordance with National FireProtection Association (NFPA) standard 70, the National Electrical Code. Codessuch as NFPA 52 define the boundaries of explosion-proof areas.

Explosion-proof electrical enclosures and junction boxes are designed to with-stand internal explosions without flame propagation out of the enclosure. They aremetallic and of heavy wall construction making them expensive and cumbersometo access. The compressor skid of Fig. 8.5 shows an explosion-proof disconnectpanel standing to the right of the instrumentation panel. Some alternatives to theuse of explosion-proof equipment include:

• Conventional contact closure instrumentation with intrinsically safe circuitry

• Standard electrical enclosures with air purge systems and failure shutdown inter-locks

• Impenetrable gas tight electrical rooms within the hazardous area with gas de-tection

• Locating electrical equipment remote and outside the hazardous area

8.3 CNG STATION EQUIPMENT

In addition to the compressor, other items of equipment are required to completethe CNG refueling system. The descriptions of equipment that follow are repre-sentative only. The CNG industry has few system design standards. Most instal-lations are uniquely designed to meet a performance specification.

CNG COMPRESSORS 8.9

FIGURE 8.5 Compressor skid package (courtesy of Gemini Engine Company).

8.3.1 Priority Panel

The Fast Fill CNG type refueling station has the compressor filling one or severallarge pressure vessels. The natural gas vehicle (NGV) then refuels its on boardtank from the pressure vessels. In this way, refueling flow rates are maximized andindependent from compressor capacity.

The Three Bank Priority Panel uses a single multi-port valve or multiple valvesto control the flow of discharge gas from the compressor to a series of storagepressure vessels. The pressure vessels are divided into three banks with each bankhaving one or more pressure vessels joined by a manifold. The three storage banksare designated the high, medium and low banks, with the high and low bankshaving the highest and lowest filling priority respectively. The compressor operatesto maintain maximum pressure in the storage banks through the priority panel byfilling the high bank, medium bank and low bank in turn.

If all storage vessel banks are depleted in pressure, most priority panels shift allcompressor discharge flow to feed the refueling vehicles directly. At this stage,unless the compressor has a very large flow capacity, refueling flow rates are slowand equal to the rate of compressor flow.

8.10 CHAPTER EIGHT

FIGURE 8.6 Priority panel (courtesy of IMW Industries Limited ).

8.3.2 CNG Dispenser

While the compressor is maintaining storage bank pressures in accordance withpriority, NGV’s are drawing gas from the CNG dispenser. CNG dispensers resembleliquid fuel dispensers and often accompany them at the same retail service station.

The CNG dispenser includes a special compressed gas meter and two-way se-quencing valves. Upon connecting the special refueling nozzle to the NGV andauthorizing the dispenser, the first sequencing valve S1 opens (see Fig. 8.7). Highpressure gas from the low bank drains into the NGV’s fuel tank which is initiallyat a low or ‘‘empty’’ pressure (e.g. 200 to 500 psig). As the difference in headpressure between the low storage bank and NGV fuel tank reduces, the flow ratedecreases. At a minimum flow rate, as measured by the dispenser meter, sequencingvalve S2 opens. The gas flow rate increases with the increase in head pressure.Again, as the flow rate drops with the head pressure, a minimum flow rate signalsthe opening of sequencing valve S3. When the NGV fuel tank reaches full pressure,the sequencing valve closes, terminating the fill. In this way, multiple vehicles canbe filled consecutively or simultaneously, depending on the number of dispensersprovided.

Refueling flow rates are dependent on how restrictive the piping system is be-tween the pressure vessels and the NGV fuel tank. Commonly the most restrictivepiping is on board the NGV. Since there is no industry standard for on board NGVpiping systems, predicting refueling performance is difficult.

CNG COMPRESSORS 8.11

FIGURE 8.7 CNG dispenser (courtesy of Fueling TechnologiesInc.).

Typical refueling flow rates for passenger cars and light trucks average 300 to500 scfm with maximum flow rates reaching as high as 900 scfm. Refueling flowrates for large commercial, industrial and public transportation vehicles can average1500 to 2500 scfm with maximum flow rates reaching 5000 scfm.

8.3.3 Emergency Shutdown Systems

The CNG station Emergency Shutdown (ESD) System uses fail safe closed valves,strategically located to shut off gas flow in an upset scenario. The ESD valves arelocated in piping systems near pressure vessels, compressor suction and dischargelines, and inside CNG dispensers. Most ESD valves use either pneumatic, spring

8.12 CHAPTER EIGHT

return operators or spring return electric solenoid actuators. The means of initiatingvalve closure include:

• Loss of electric power

• Manually depressing ESD push buttons located in various station locations

• Seismic activity detection devices

• Proximity or limit switch devices sensing motion of impacted equipment

• Vibration sensing equipment

• Gas, fire and heat detectors

• Loss of pneumatic control pressures from plastic air line ruptures caused by fire

8.3.4 Pressure Vessels Storage

Fast fill type CNG stations store compressed gas in one or more pressure vessels.The size, design pressure and configuration of the pressure vessels determine howmuch stored gas can be used for refueling before replenishment by the compressoris required. The CNG industry commonly uses pressure vessels configured in threebanks. Each bank has at least one pressure vessel. Higher capacity installations usemultiple pressure vessels joined by a manifold and perform as one larger volumebank. The CNG dispenser uses a set of valves which open in sequence duringrefueling. Each sequencing valve allows the flow of gas to the vehicle from onebank. By opening the valves in sequence, a greater percentage of gas can be with-drawn from the pressure vessel storage than if all the pressure vessels were joinedby a manifold as a single bank.

Pressure vessel storage full pressures range from 3600 to 5000 psig. Industrystandard NGV fill pressures are 2400, 3000, and 3600 psig at a standard gas tem-perature of 70�F. To complete NGV refueling at least one bank of a pressure vesselstorage must have a higher pressure than the NGV fuel tank final fill pressure.

Storage Utilization. Only a fraction of the total stored weight of gas from fullstorage pressure vessels can be dispensed. At some point, there will be insufficientpressure in the storage vessels and the NGV fuel tank fill cannot be completed. Atthis point, the amount of gas remaining in the pressure vessels is substantial andmay be 50 to 75% of the full amount. Storage utilization is defined as

Total gas weight dispensed/Storage full gas weight � 100%

Storage utilization increases with the number of storage banks used. The increasein storage utilization becomes marginally less with each additional bank. The in-dustry has found the use of three banks to be the best compromise in terms ofcost, complexity and performance.

In addition, storage utilization is highly dependent on storage full pressure andfinal vehicle fill pressure (see Table 8.3). Considerable gains in storage utilizationoccur when maximum storage fill pressures are increased. This allows the use of

CNG COMPRESSORS 8.13

TABLE 8.3 Storage Utilization (SU)*

Maximum storagevessel pressure

(psig)%

SU—single bank

—3600 psig fill

% SU—single bank

—3000 psig fill

% SU—3 bank

—3600 psig fill

% SU—3 bank

—3000 psig fill

3600 n/a 12 n/a 364000 6 17 24 434500 10 21 34 495000 13 25 40 53

Note: The SU values listed were generated with the following assumptions: minimum differentialpressure between the storage bank and NGV fuel tank is 100 psid; isothermal compression and expansion;no compressor replenishment during fill; three equally sized storage bank volumes for the three bankSU values; gas critical temperature of 366�F.; gas critical pressure of 669.84 psia; 70�F. gas temperature;53 psig NGV fuel tank start of fill pressure.

*SU values generated with the assistance of Ralph O. Dowling, P.E., Christie Park Industries, usingthe Institute of Gas Technology ‘‘Cascade’’ computer program.

smaller storage vessel volumes and vessel cost savings. The benefits of higherstorage fill pressures are offset, however, by an increase in compression energycosts and higher compression equipment and maintenance costs.

Other variables affecting storage utilization include

• NGV fuel tank empty pressures

• Dispenser sequencing valve switching set points

• Initial fuel tank gas temperatures

• Heat transfer rates from storage tanks, piping and NGV fuel tanks

• Successive vehicle filling versus periodic filling

• Relative volumes of each storage bank

• Gas critical pressure and critical temperature

8.3.5 Gas Dehydration

New standards for compressor discharge gas quality are making the use of gasdehydration equipment mandatory in many CNG installations. The Society Of Au-tomotive Engineers standard SAE J-1616 specifies maximum allowable compressordischarge gas water content. This standard ensures that NGV fuel tanks will besafeguarded from corrosion and will operate safely for the life of the vehicle.

Gas dehydration equipment is most commonly installed on the suction or finaldischarge line of the compressor or compressor system. Gas dehydration equipmentinstalled on compressor suction lines can incur significant piping line losses. Aminimum pressure loss specification should be included with other process para-meters when sizing and selecting equipment.

8.14 CHAPTER EIGHT

FIGURE 8.8 3 Bank fast fill system.

8.4 CNG STATION SYSTEM DESIGNS

Most CNG refueling station systems are custom designed to meet specific cost andperformance criteria.

8.4.1 Three Line Fast Fill System

The three line fast fill system is commonly used for retail sale of CNG. It is amongthe most costly, but provides the maximum performance, with CNG dispensersproviding fuel at flow rates comparable to liquid fuel dispensers. Fuel flows directlyfrom the pressure vessel storage and is independent of compressor capacity as longas head pressure remains at the pressure vessels.

With the three bank storage, storage utilization is high. This enables the systemto best meet random surges in demand. High storage utilization also allows thecompressor to operate for extended periods of time, with a minimum of stops andstarts.

8.4.2 Time Fill System

The time fill system requires the least amount of equipment and is the least ex-pensive, and no pressure vessels are required. The compressor discharges directly

CNG COMPRESSORS 8.15

FIGURE 8.9 Time fill system.

to the refueling vehicles. Refueling rates are dependent on the number of vehiclesrefueling at once. The system finds application with private vehicle fleets wherefast refueling times are not important and vehicles are parked for an extendedperiod of time during an off shift.

Upon connection of the refueling nozzle to the NGV, a pressure loss in thefeeder line will be sensed by a pressure switch at the compressor. The compressorwill start to compress gas through a time fill control panel. This panel has a pressureregulator and temperature instrumentation with shut off valve to stop the fill whenthe fill pressure is reached.

8.4.3 Single Line Fast Fill System

The single line system is similar to the three line fast fill system, but uses only asingle bank storage. The dispenser is without sequencing valves and the prioritypanel has only one priority.

The use of more than one dispensing hose is not recommended. If two vehicleswith different fuel tank pressures are connected to the same supply line, the refu-eling of one of the vehicles will halt until pressures equalize.

The system is less costly than the three bank system, but storage utilization islow. Surges in demand cannot be met as effectively. Low storage utilization resultsin frequent compressor start and stop operation.

8.4.4 Diverter System

The diverter system is similar to the single line fast fill system, but provides twohose refueling capability. A diverter valve directs all compressor flow to the firsthose authorized. Upon authorization of the second hose, refueling will begin di-rectly from the single bank storage without robbing compressor discharge flow

8.16 CHAPTER EIGHT

FIGURE 8.10 Single line fast fill system.

FIGURE 8.11 Diverter system.

from the first hose authorized. As soon as the fill is complete at the first hose, thediverter valve switches all compressor flow to the second hose.

This system finds application in the refueling of fleet vehicles one after another.The toggling of the diverter valve spaces vehicle filling so that at least one vehicleis always connected to a hose. While one vehicle is moved into position and con-nected to the fueling hose, the second vehicle is nearing fill completion. In thisway, refueling is nonstop and the compressor operates continuously with a mini-mum of starts and stops.

CNG COMPRESSORS 8.17

TABLE 8.4 Daily Refueling Frequency Distribution

Hour end time (a.m.) 1 2 3 4 5 6 7 8 9 10 11 12No. of Vehicles 0 0 0 0 0 0 2 20 5 2 3 8

Hour end time (p.m.) 1 2 3 4 5 6 7 8 9 10 11 12No. of Vehicles 6 2 2 3 10 6 2 2 2 0 0 0

8.5 EQUIPMENT SELECTION AND SYSTEM PERFORMANCE

The following example will demonstrate how to select a compressor and pressurevessel storage for a three line fast fill station. For other refueling system types asimilar approach can be adopted.

Example:A proposed retail CNG refueling station site will have 25 psig regulated and

metered gas available by the local gas utility. Maximum compressor discharge gaspressure will be 3600 psig. The station will be of the three line fast fill type, withmaximum NGV fill pressures of 3000 psig. The proposed CNG refueling instal-lation is forecast to have a filling frequency distribution as per Table 8.4. Theaverage fuel consumption of each vehicle is also determined to be 4.6 gallonsgasoline equivalent per day.

8.5.1 Compressor Selection

Table 8.4 indicates the number of NGVs that will fill up each business hour. Totalamount of gas dispensed each day will be

75 NGVs � 4.6 gal equiv. � 108.7 scf/gal equiv. � 37,500 scf

This is also the amount of fuel that must be compressed daily. A maximumnumber of compressor operating hours per day is arbitrarily set at 8. Fewer oper-ating hours increase compressor size, cost, energy demand charges and interruptedoperation. More operating hours reduce compressor size and the ability to meetrandom increases in refueling demand. The required compressor flow capacity iscalculated.

37,500 scf/8 hrs/60 min/hr � 78 scfm

From Fig. 8.2, a 25 psig suction pressure and 3600 psig discharge pressurerequires 0.48 BHP/scfm. At 78 scfm, the required compressor horsepower is 37.4BHP. A 40 BHP, 4 stage compressor is selected, providing a flow capacity of 83scfm.

8.18 CHAPTER EIGHT

8.5.2 Pressure Vessel Storage Sizing

The filling frequency distribution is critical to the selection and sizing of the pres-sure vessel storage. The hours from 7am to 8am is the busiest with 20 fill ups. Gaswithdrawn from the storage pressure vessels during this hour is calculated.

20 NGVs � 4.6 gal equiv. � 108.7 scf/gal equiv. � 10,000 scf

In this time, the compressor has also operated to refill the storage. To maximizecompressor running duration, control systems do not start up the compressor untilthere is a substantial drop in pressure of the storage. To account for this, it isassumed that the compressor operates for 45 minutes of the hour. Storage replen-ishment flow is calculated.

45 min. � 83 scfm � 3735 scf

In addition, it is assumed that the two vehicles between 6am and 7am did notinitiate compressor operation. This accounts for an additional 1000 scf depletedfrom storage.

The total amount of gas that must be provided from the storage pressure vesselsis calculated.

10,000 scf � 3735 scf � 1000 scf � 7265 scf

The size of the pressure vessel storage can now be estimated. From Table 8.3,the storage utilization factor is 36%. The size of the pressure vessel storage iscalculated.

7265 scf/36% � 20,181 scf natural gas @ 3600 psig

Three pressure vessels each having an internal volume of 22.8 cu. ft are selected.Each vessel provides a storage capacity of 7,082 scf at 3600 psig working pressure,or a three vessel total of 21,246 scf.

8.5.3 Other Equipment

A priority panel is selected and sized for the compressor discharge capacity of 78scfm. Pressure losses through the panel are kept below 50 psid so that the storagepressure vessels are filled to a maximum pressure without compressor shutdown.A two hose metered CNG dispenser is specified so that two vehicles can be filledsimultaneously during peak demand times.

8.6 CODES AND STANDARDS

CNG refueling equipment and installations must comply with numerous codes andstandards. In North America, work is currently underway to further develop codes

CNG COMPRESSORS 8.19

TABLE 8.5 Industry Codes and Standardst

AMERICAN NATIONAL STANDARDS INSTITUTE (ANSI)

ANSI/AGA NGV1 Standard for Compressed Natural Gas VehicleRefueling Connection Devices

ANSI/AGA NGV2 Basic Requirements for Compressed NaturalGas Vehicle (NGV) Fuel Containers

ANSI/ASME B31.1 Power PipingANSI/ASME B31.3 Chemical Plant and Petroleum Refinery PipingANSI/ASME B31.8 Gas Transmission and Distribution Piping

System

AMERICAN SOCIETY OF MECHANICAL ENGINEERS (ASME)

ASME Section VIII, Division 1 and 2 Boiler And Pressure Vessel CodeASME Section IX Boiler And Pressure Vessel Code:

Qualifications Standard for Welding and BrazingProcedures, Welders, Brazers, and Welding andBrazing Operators

AMERICAN PETROLEUM INSTITUTE (API)

API Specification 11P Specification for Packaged ReciprocatingCompressors for Oil and Gas ProductionServices

API Standard 618 Reciprocating Compressors for General RefineryService

API Standard 661 Air-cooled Heat Exchanger for General RefineryServices

NATIONAL FIRE PROTECTION ASSOCIATION (NFPA)

NFPA 37 Standard for the Installation and Use ofStationary Combustion Engines and GasTurbines

NFPA 52 Compressed Natural Gas (CNG) Vehicle FuelSystems

NFPA 54 National Fuel Gas CodeNFPA 70 National Electrical CodeNFPA 496 Purged and Pressurized Enclosures for Electrical

Equipment

SOCIETY OF AUTOMOTIVE ENGINEERS (SAE)

SAE J1616 Recommended Practices for CompressedNatural Gas Vehicle Fuel

t Industry codes and standard compiled with the assistance of Ray Benish, CNG Systems Inc.

8.20 CHAPTER EIGHT

and standards for the industry. The National Fire Protection Association (NFPA)Standard 52 is one of the most important industry standards and invokes otherimportant documents including the ASME code and ANSI standards. Beyond thecodes and standards listed in Table 8.5, state regulations, building codes and mu-nicipal bylaws are routinely enforced.

9.1

CHAPTER 9LIQUID TRANSFER/VAPORRECOVERY

William A. Kennedy Jr.Blackmer/A Dover Resource Company

Gas compressors are often used in the bulk transfer of liquefied gases from railcars or truck transports into a storage vessel. Liquefied gases are products that arecontained at a vapor/liquid equilibrium in closed systems above atmospheric pres-sure. Typical examples are hydrocarbons (propane, butane, propylene, etc.), carbondioxide, refrigerant gases, chlorine, hydrogen chloride, and some solvents. Most ofthese products must be kept free of contaminants like moisture, oil and non-condensables such as air or nitrogen.

While the use of rail cars to transport compressed liquefied gases is a widespreadand safe practice, the process engineer is faced with several system design problemsbecause of the following:

1. The system NPSHA (Net Positive Suction Head Available) is less than requiredby a liquid pump. Top mounted control valves with ‘‘dip tubes’’ are used onthese types of rail cars.

2. The liquid vapor pressure is above atmosphere at ambient temperatures.

3. The system must not be contaminated with moisture, oil, or air.

Unloading a rail car can be handled by a liquid pump, air padding (or othernon-condensable gas), gas compressor or a combination system using a liquid pumpand gas compressor. The problems and merits of each method are discussed below.

9.1 TRANSFER USING A LIQUID PUMP

Cavitation and loss of pump prime are common problems when using liquid pumpsto unload rail cars. Since liquefied gases are stored at their vapor/liquid equilibriumpoint, any reduction in pressure (caused by fluid friction in the pump inlet line),

9.2 CHAPTER NINE

or increase in temperature (caused by heat gain in the pump inlet line), results invapor forming in the inlet piping and/or internal pump cavitation. Either conditionreduces the transfer rate and damages internal pump parts.

Another problem when using a liquid pump is the amount of product left in therail car when it appears to be empty since the dip tubes do not reach all of theway to the bottom of the tank (see Fig. 9.1). In addition, there is product in vaporform remaining in the rest of the rail car. For example, in a typical 11,000 gallontank car, with the dip tube 3 inches from the bottom, there would be about 115gallons of liquid left below the dip tube. Usually there is even more liquid re-maining because a liquid pump will lose its prime before the liquid level reachesthe bottom of the dip tubes. The amount of vaporized product left would dependon the product being transported. A propane tank car on an 80�F day (vapor pres-sure � 144 psia) would still contain 1465 pounds of propane (or 344 gallons whenliquefied) in the vapor space of an 11,000 gallon tank car after all of the liquidhad been removed.

The use of a liquid pump to unload a compressed liquefied gas from a rail carwith top mounted outlets presents the following problems:

1. Extreme difficulty in priming and maintaining the prime due to poor NPSHconditions and likely cavitation problems

2. Low and unpredictable transfer rates due to cavitation in the inlet line and pump

3. Excess noise and internal pump damage due to cavitation

4. Failure to remove all the liquid from the tank car

5. Failure to remove any vapor from the tank car

9.2 AIR PADDING

Another unloading method that will overcome some of the liquid pump problemsis to use compressed air to ‘‘pad’’ the car. A dedicated system designed to supplyoil free air at a pressure greater than the maximum vapor pressure of the liquid inthe tank car is required. Usually the air must be dry (�40�F dew point is typical)to prevent moisture contamination. Nitrogen is sometimes used in place of dry air.While air padding solves the system NPSH problem by pushing the liquid out, itleaves several problems unaddressed and creates others.

1. There is still liquid left below the dip tube.

2. The vaporized liquid is still in the tank car.

3. If the air drying system fails, the resulting moisture contamination can result inproduct quality or system corrosion problems.

4. The most serious problem may be the dilution of the vaporized liquid with air.The presence of a non-condensable gas (air or nitrogen) will cause tank pres-sures greater than the vapor pressure of a pure product. When the rail car is

LIQUID TRANSFER / VAPOR RECOVERY 9.3

ReliefValve

AngleValve

ExcessFlowValve

DipTube

PipeGuide

FIGURE 9.1

9.4 CHAPTER NINE

FIGURE 9.2

later filled with liquid, this may cause relief valves to open unexpectedly re-leasing product to the atmosphere.

9.3 TRANSFER USING A GAS COMPRESSOR

The best solution for unloading rail tank cars is the use of a gas compressor ratherthan a liquid pump or air padding. Figure 9.2 shows a typical schematic of a liquidtransfer operation using a gas compressor. The vapor section of the receiving tankis connected to the compressor suction while the vapor section of the rail tank caris connected to the compressor discharge. A separate liquid line connects the liquidsections of the two vessels. Liquid transfer begins as the compressor transfers vaporfrom the receiving tank to the vapor section of the rail car. In a well designedsystem, the pressure differential developed between the two vessels will be 30 psior less. The process is continued until the liquid level falls below the liquid diptube opening in the rail car. This phase of the operation requires that enough gasbe transferred to displace the volume of liquid leaving the rail car plus the amountof gas condensing into liquid in the rail car. Since the increase in gas temperaturecaused by the heat-of-compression helps keep the gas from condensing, the com-pressor discharge line (leading to the rail car) should be insulated and the com-pressor should be installed near the rail car, ensuring minimum heat is lost fromthe compressor discharge gas. In order to get the remaining product out of the railcar, the system is changed to a ‘‘vapor recovery’’ mode, which is possible with agas compressor but not with a liquid pump or air padding.

Figure 9.3 illustrates the vapor recovery mode. The ‘‘liquid’’ line is closed. Thevapor section of the rail car is connected to the compressor suction and the com-pressor discharge is connected to the liquid section of the receiving vessel. The

LIQUID TRANSFER / VAPOR RECOVERY 9.5

FIGURE 9.3

connection change can be accomplished easily with the use of a multi-port selectionvalve in the piping to and from the compressor. During the early stages of vaporrecovery, the rail car pressure will decrease slightly, causing the liquid below thedip tube in the rail car to vaporize. Once vaporized, it is transferred by the com-pressor into the receiving tank. Bubbling the gas through the liquid phase in thereceiving tank ensures rapid condensation with little increase in receiver tank pres-sure. In extreme conditions, a separate condenser may be required.

After all of the liquid in the rail car has vaporized, the pressure will begin todecrease as more gas is removed. The degree of vapor recovery is usually depen-dent on economics—the value of the gas, the power required to operate the com-pressor and time available to hold the rail car. A rough rule of thumb is to reducethe rail car pressure to 25% of the product vapor pressure.

The use of a gas compressor for unloading rail cars addresses all the problemsnoted above when using liquid pumps or air padding. A well designed compressorsystem will provide years of safe operation with limited down time. The increasedproduct recovery (the liquid below the dip tubes and the vapor in the rail car) willactually reduce the number of rail cars required over a period of time. The NPSHproblems and related cavitation go away and there should be no product contam-ination.

When designing gas compressor systems for liquid transfer/vapor recovery op-erations, some unique system requirements must be considered. An often over-looked, but important system feature is the rated liquid flow of the excess flowvalve on the rail car. The excess flow valves located in the dip tubes, shown inFig. 9.1, are designed to automatically close at a given flow rate to prevent spillagedue to a major line break. Once the allowable flow rates are determined, the sizeof the compressor can be established. An oversize compressor will cause the excessflow valves to close, stopping the unloading operation. Another critical decisioninvolves how low the rail car pressure is to be reduced. This determines whether

9.6 CHAPTER NINE

a single- or multi-stage compressor is required. Careful analysis of the compressoroperating temperature is required. Normally, every effort is made to keep the op-erating temperature of a compressor low, which increases the life of the machine,so water cooling is common in the compressor industry. However, except in ex-treme cases, an air cooled compressor is best used in a liquid transfer operationbecause it is desirable to keep the gas temperature up to help reduce condensationof gas in the rail car during the liquid transfer mode.

The compressor manufacturer can supply performance data to help determinethe time required for liquid transfer, time needed to reduce rail car pressure tovarious levels, power requirements and operating temperatures. These are rathercomplex calculations since the compressor is not operating at steady state condi-tions, and compressor performance varies with product, ambient temperature, tanksizes, piping losses, location of the compressor, etc.

9.4 COMBINATION COMPRESSOR/PUMP SYSTEMS

While the use of a compressor solves many problems with unloading rail cars ofcompressed liquefied gases, there are some limitations that must be observed. Highpressure differentials will decrease the transfer rate. This is usually caused by poorpiping design; great separation of rail car from the storage tank; elevation differenceof two tanks; or metering liquid flow with a high pressure drop meter, i.e., positivedisplacement type meter.

If any of these conditions exist, a combination compressor/ liquid pump systemmay be the best solution (see Fig. 9.4). This is the same as Fig. 9.2, except a liquidpump has been inserted in the liquid line. The NPSH problems caused by the poorpump suction conditions (dip tube and long suction line) are solved by using thegas compressor to increase the rail car pressure with gas from the receiving vessel.With improved suction conditions, the liquid pump can now provide the high dif-ferential pressure required by the system. Once the liquid level drops below thedip tube, the liquid pump is turned off. Removal of the remaining liquid and vaporrecovery take place as shown in Fig. 9.3.

9.5 COMPRESSORS FOR LIQUID TRANSFER/VAPOR

RECOVERY

While there are many variables, typical rail car liquid transfer/vapor recovery com-pressors (Fig. 9.5) will be rather small (up to 60 CFM piston displacement), aircooled and single stage. Larger compressors may be used for multiple rail carunloading. The following design features are common:

1. Cylinder working pressure greater than the maximum expected product vaporpressure plus design system differential pressure

LIQUID TRANSFER / VAPOR RECOVERY 9.7

FIGURE 9.4

FIGURE 9.5

2. Atmospheric vented crankcase design with a filtered pressure oil system to lu-bricate the main bearings and connecting rods

3. Crosshead/piston rod construction allowing for separation of the crankcase fromgas compression area

9.8 CHAPTER NINE

FIGURE 9.6

4. Non-lubricated gas compression construction for oil-free transfer of gas

5. Piston rod seals to control gas leakage and prevent crankcase oil from enteringthe cylinder area. While a single seal per rod may be used, the preferred con-struction is two seals per rod with a closed distance piece allowing for venting,purging or padding between seals. For certain gases (chlorine, vinyl chloride,hydrogen chloride, etc.), a third seal per rod and a second distance piece isrecommended.

6. High temperature switches, high/low pressure switches, high liquid levelswitches in liquid traps, etc., help prevent unexpected equipment problems.

Since the gas is being handled at, or very near, its vapor-liquid equilibrium point,there is always concern with condensation in the piping or in the compressor cyl-inder. To help protect against liquid entering the compressor (which may result insevere damage), several system designs must be considered:

1. A liquid trap should be located as near the compressor inlet as possible. Thetrap must be sized to accommodate any anticipated condensation that couldoccur in the inlet piping. Liquid level alarms, shut-off devices (mechanical orelectrical), mist pads and/or sight gages may be part of the system. Figure 9.6

LIQUID TRANSFER / VAPOR RECOVERY 9.9

shows a typical package including a liquid trap, 4-way valve, strainer and drivesystem.

2. Piping should be designed to prevent condensate from draining into the com-pressor during shutdown.

3. Operating procedures must be established to drain any condensate prior to startup.

10.1

CHAPTER 10COMPRESSED NATURAL GAS FORVEHICLE FUELING

Adam Weisz-Margulescu, P. Eng.FuelMaker Corporation

Air quality is a major public concern. Motor vehicles are a major source of airpollutants that have negative effects on the environment. Faced with unacceptableair quality and growing public concern, governments and industry have taken anumber of initiatives to reduce motor vehicle emissions. The trend is clear: in orderto achieve acceptable air quality motor vehicle emissions standards will becomemore stringent. The natural gas vehicle industry has become the leader in the drivefor clean air. At the same time, due to stringent indoor clean air mandates, fuelpricing and supply problems, the natural gas forklift market has become the fastestgrowing market niche in the natural gas vehicle industry.

Until the development of appliances for compressing natural gas to pressuresrequired for fueling vehicles, the slow-growth in public fueling infrastructure hasmade it difficult for motor vehicles to readily access natural gas fuel. The high costof natural gas fueling equipment is prohibitive for a small number of vehicles.These compact units give a small fleet operator the ability to perfectly size theirfueling requirements to the exact number of vehicles they service. At the sametime, the cost of the fuel station and conversion will be recovered through the fuelprice differential. These appliances can be used as an independent slow-fill gasrefueling appliance to provide compression for up to two vehicles simultaneously,or they can be configured with multiple number of vehicle refueling appliancescoupled together to provide fuel to the fast-fill storage system. The storage systemin turn will provide fast-fill to the natural gas vehicle. For fleets that park theirvehicles indoor, an indoor remote panel is used (Fig. 10.1).

10.1 REFUELING APPLIANCE

The refueling unit is generally a self-contained, oil-free outdoor appliance that willfill a 26.4 U.S. gallon gas cylinder to a pressure of 3000 psig @ 68�F within 8

10.2 CHAPTER TEN

Outdoor Time-Fill

Fast-Fill Storage

Indoor Remote

FIGURE 10.1 CNG fueling systems.

hours, which corresponds to an average flow rate of 1.8 SCFM. The flow rate isroughly the energy equivalent to about 1.1 U.S. gallons of gasoline per hour, de-pending on the energy content of natural gas. Average power consumption is onlyabout 1.3 kW using an electrical supply of 230/208 Volts @ 60 Hz (Fig. 10.2).The appliance is connected to low-pressure gas system from 7 in. water column to2 psig at rated flow. It is usually supplied with one fibre-reinforced high pressurefill hose (second hose can be connected) connected to the unit via a breakawayfitting which allows the hose to be disconnected without damage should the userdrive the vehicle away without disconnecting. The refueling nozzle supplied is

COMPRESSED NATURAL GAS FOR VEHICLE FUELING 10.3

FIGURE 10.2 A refueling appli-ance.

suitable for natural gas ‘‘slow-fill’’ applications. At the completion of each refu-elling cycle, the high pressure gas contained downstream of the compressor isreturned to a blowdown vessel, thus reducing the pressure in the fill hose to ap-proximately 29 psig.

A typical appliance is composed of the following modules (Fig. 10.3):

1. Compression

2. Controls

3. Electronics

The compression module and control module form one compact, integrated unit(Fig. 10.4). The gas flow with the unit ‘‘on’’ is illustrated in Fig. 10.5. When theunit is turned ‘‘off’’ the gas is recirculated as shown in Fig. 10.6.

The blowdown vessel is part of the controls module and will accommodate thevolume of gas contained by the fill hose, refueling nozzle, and the space betweenthe vehicle receptacle and check valve only. This limits the maximum length ofthe fill hose. The maximum length of the fill hose is limited by the NFPA 52 Codeas well, to 25 ft.

10.4 CHAPTER TEN

COMPRESSION MODULE

CONTROLS MODULE

BLOW-DOWNVESSEL

ELECTRONICS MODULE

ENCLOSURE

FIGURE 10.3 Modules within the refueling appliance.

COMPRESSOR

BLOW-DOWNVESSEL

ELECTRICMOTOR

CONTROLS

FIGURE 10.4 Compression and control module.

COMPRESSED NATURAL GAS FOR VEHICLE FUELING 10.5

BLOW-DOWNVESSEL

MOTORSTATOR

MOTORROTOR

COMPRESSIONMODULE

LOW PRESSURESWITCHPRESSURE RELIEF

VALVE

MANIFOLDBLOCK

INLET PRESSURE

HIGH PRESSURE

ATMOSPHERIC PRESSURE

HIGH PRESSURETRANSDUCER

COMBI VALVE

INLET FILTER

FILL NOZZLE

VENT

REDUNDANT PRESSURERELIEF VALVE

BREAKAWAYCOUPLING

FIGURE 10.5 Pressure within control unit when on.

The electro-mechanical controls are mounted on the convection plate, whichrepresents the interface between the blowdown vessel and the compressor (Fig.10.7). The low pressure switch is set to shut down the unit if the inlet pressuredrops below 5 in. of water column (Fig. 10.8). The low pressure relief valve willrelease the pressure into the vent line in case the blow-down vessel is over-pressurized (Fig. 10.9). The high pressure transducer monitors the high pressureoutput from the compressor (Fig. 10.10). It is calibrated for 2900 psig. The pressureis temperature compensated. The temperature sensor is mounted in the inlet airstream and determines the allowable fill pressure for a particular ambient temper-ature. The temperature/pressure compensation feature attempts to fill the storagetank with a constant mass of gas, regardless of the ambient temperature. Thisprevents the vehicle tank from being over-pressurized if the ambient temperaturerises. The convection plate temperature sensor will shut down the unit at 167�Fand the motor temperature switch will turn off the motor at 275�F.

The electronics module controls the operation of the unit. The schematic diagramis shown in Fig. 10.11. Some parameters can be changed by the installer or servicepersonnel in the field via a programming device available. The electronics moduleis interfaced with the user panel. Starting, stopping and monitoring of the unit takesplace at the user panel. It has separate Start and Stop buttons and three indicatorlights.

10.6 CHAPTER TEN

BLOW-DOWNVESSEL

MOTORSTATOR

MOTORROTOR

COMPRESSIONMODULE

LOW PRESSURESWITCHPRESSURE RELIEF

VALVE

MANIFOLDBLOCK

INLET PRESSURE

HIGH PRESSURE

ATMOSPHERIC PRESSURE

HIGH PRESSURETRANSDUCER

COMBI VALVE

INLET FILTER

FILL NOZZLE

VENT

REDUNDANT PRESSURERELIEF VALVE

BREAKAWAYCOUPLING

FIGURE 10.6 Pressure within control unit when off.

10.2 COMPRESSOR

The compression module as shown in Fig. 10.12 is a reciprocating motion type,four-stage, four-cylinder non-lubricated arrangement with the direct-drive rotormounted directly on the drive-shaft. As all reciprocating compressors, this unitoperates on an adiabatic principle: the gas is drawn into the first stage cylinder viathe crankcase, is compressed in the individual cylinders, is moved from stage tostage via integrated gas passages through inlet and discharge valves, and finally ispassed through the fourth stage discharge valve against discharge pressure into thevehicle storage tank. The gas is cooled between stages through the integrated pas-sages by conduction and radiation. The geometry of the compressor and the designof the gas passages between stages will facilitate the dissipation of the heat gen-erated by compression into the surrounding aluminum structure. In turn, the finnedcylinder heads are cooled via forced convection with a separate two-speed fanmounted in the enclosure below the blowdown vessel. In case of blocked ventlines, a pressure relief valve mounted on the compressor housing will release toatmosphere at 145 psig. A high pressure burst disc installed in the fourth stagecylinder head will provide protection if the pressure rises above 3335 psig.

The gas is drawn into the blowdown vessel through the inlet pipe, passingthrough an inlet filter and a combination valve. The blowdown vessel is an integral

COMPRESSED NATURAL GAS FOR VEHICLE FUELING 10.7

MOTOR TEMPERATURESWITCH

LOW PRESSURESWITCH

LOW PRESSURERELIEF VALVE

COMBINATIONVALVE

HIGH PRESSURETRANSDUCER

CONVENTION PLATETEMPERATURE SENSOR

CONVECTION PLATE

FIGURE 10.7 Interface between blowdown vessel and the compressor.

GASINLET

BLOW-DOWNVESSEL

VENT

LOW PRESSURE SWITCH

FIGURE 10.8 Low pressure switch.

10.8 CHAPTER TEN

GASINLET

BLOW-DOWNVESSEL

VENT

LOW PRESSURE RELIEF VALVE

FIGURE 10.9 Low pressure relief valve.

BLOW-DOWNVESSEL

HIGH PRESSURETRANSDUCER

COMPRESSIONMODULE

FIGURE 10.10 High pressure transducer.

10.9

FIGURE 10.11 Electronics control schematic.

10.10 CHAPTER TEN

MANIFOLD BLOCK

4TH STAGE

3RD STAGE

MOTOR ROTOR

2ND STAGE

1ST STAGE

FIGURE 10.12 Compressor.

component system of the unit, designed to reduce the delivery side pressure (in thefueling hose and the space between vehicle receptacle and check valve) from op-erating level to approximately 29 psig. ‘‘Blowdown’’ allows the nozzle to be dis-connected from the vehicle.

Via two holes in the compressor housing the gas enters the back end of the firststage cylinder. The first stage piston is fitted with six valves kept closed by discsprings and activated by differential pressure in the system. During the downstrokeof the piston, the valves open and the gas rushes into the first stage cylinder cavity.As the piston reverses direction, the pressure increases and the valves close, andthe compression cycle is completed. On top of the cylinder, identical valves areinstalled into a valveplate. At the end of the stroke these valves will open due tothe differential pressure, and the gas is pushed through passages in the compressorhousing to stage 2 and subsequently to stages 3 and 4. In the second and thirdstages, the gas enters the compression chamber via valves installed in the cylindersleeves and exits through one similar but larger valve placed in the centre of thecylinder head. Before entering the fourth stage compression chamber, the gas isfiltered again. In order to minimize pulsation, the gas is passed through a damperbefore exiting through the high pressure block. The fill hose has one end attachedto the breakaway coupling and the fill nozzle end connected to the vehicle recep-tacle (Fig. 10.13). During the ‘‘off’’ cycle, the gas is being recirculated into theblowdown vessel through the high pressure block and tube connected to the con-vection plate (Fig. 10.14).

The piston-head clearance is kept to a minimum. But due to clearances necessaryto permit operation and allow valve passages to be incorporated, the piston does

COMPRESSED NATURAL GAS FOR VEHICLE FUELING 10.11

BLOW-DOWNVESSEL

COMPRESSIONMODULE

BREAKAWAYCOUPLINGFILL NOZZLE

INLET FILTER

FIGURE 10.13 Flow during on cycle.

not sweep the entire volume of the cylinder. Hence the actual cylinder capacity islower than the displacement. The volumetric efficiency of the cylinder is:

E � Q /Cv dis

where

Ev is the volumetric efficiencyQ is the total volume through-put per unit of time at suction conditions in CFM

Cdis is the volume swept by all pistons per unit of time in CFM

To improve efficiency, the compression ratio per each stage is kept as close toconstant as possible. To achieve the discharge pressure necessary, the approximateratio/stage is four.

10.3 COMPRESSOR BALANCE

The compressor is driven by a constant speed (1750 RPM) 1.5 HP electric motor.The rotor is mounted directly on the drive-shaft, while the stator is mounted onthe convection plate. Constant air gap is being maintained to minimize temperatureincreases and eddy current losses.

10.12 CHAPTER TEN

BLOW-DOWNVESSEL

COMPRESSIONMODULE

BREAKAWAYCOUPLINGFILL NOZZLE

MANIFOLDBLOCK

FIGURE 10.14 Flow during off cycle.

The drive-shaft is supported by two ball bearings. The crank end of the crank-shaft (drive-shaft) facilitates the conversion of the rotary motion into the recipro-cating motion of the compressor.

The pistons for stages 1 and 3 are mounted in opposite direction on the yoke.The same is true for stages 2 and 4. The two piston/yoke assemblies are installedon the pin end of the crankshaft 90� off to each other in the horizontal plane ofthe compressor. The reciprocating motion is achieved through a set of linear bear-ings riding on a sliding block inside the yoke assembly.

Two counterweights are installed on each side of the yokes to balance the crank-shaft assembly. Both synchronous inertia forces originating in masses with rotatingmotion and inertia forces originating in masses with purely reciprocating motionmust be considered. Since the sum of the reciprocating masses in one direction(stage 1 � stage 3) are equal to the sum of the reciprocating masses in the otherdirection (stage 2 � stage 4), the oscillating forces of this compressor are identicalto a V2/90� engine. For this kind of engine, the oscillating forces can be compen-sated in the counterweights. The following equation has to be satisfied:

M � Mosc cw

where we can approximate:

COMPRESSED NATURAL GAS FOR VEHICLE FUELING 10.13

M � (m � k m ) � dosc rot rec cor-cgosc

and

M � m (top)� d (top) � m (bottom)� d (bottom)cw cw cor-cgcw cw cor-cgcw

where:

Mosc is the moment produced by the oscillating massesMcw is the moment produced by the counterweight massesmrot is the sum of the rotating massesmrec is the sum of the reciprocating masses

dcor-cgosc is the distance from the centre of rotation to the centre of gravity of theoscillating masses

mcw is the counterweight massesdcor-cgcw is the distance from the centre of rotation to the centre of gravity of the

counterweight massesk is a constant percentage factor of compensation for reciprocating masses

and is 0.5 for V2/90� engine mathematical model

10.4 COMPRESSOR COMPONENTS

The main components of the compressor are (Fig. 10.15):

1. Housing

2. Drive unit

3. Piston assemblies

4. Cylinder head assemblies

5. High pressure unit

The housing is made of cast aluminum and has integrated stainless steel tubesto provide the passages from one stage to the next stage. All static seals are naturalgas compatible nitrile elastomers. The geometry and layout of the fins help aircirculation to optimize cooling.

The drive unit has the crankshaft housed by a flange unit via two ball bearings.The flange unit facilitates the attachment of the drive unit to the housing. The twoyoke assemblies are mounted on the pin end of the crankshaft, sandwiched betweenthe two counterweights. The separated rotor is mounted at the free end of thecrankshaft (Fig. 10.16). The bearings in each yoke assembly are well protectedfrom dirt and are lubricated with a high viscosity synthetic grease suitable for aservice temperature range of �40�F to �300�F.

The four piston assembly units are mounted on the two yokes and provide thesequential compression of the gas. The compression of the gas takes place in the

10.14 CHAPTER TEN

FIGURE 10.15 Exploded view of compressor.

four cylinder sleeves mounted in their respective cylinder heads. Sealing is achievedvia non-lubricated sealing elements conceived as integral part of the pistons. Dif-ferential pressure valves for each stage are integrated at both the entry and exit ofeach individual stage to regulate the flow of the gas. All internal and external sealsare made of natural gas compatible elastomers.

These refueling appliances would typically have a service interval of 2250 hours.At that time, the sealing and guide rings are checked and replaced when necessary,all ‘‘O’’ rings are replaced and the drive system is verified and repacked.

10.5 NATURAL GAS AS FUEL

Compressed natural gas as a vehicle fuel has been accepted all over the world.From Canada and U.S.A., where the majority of the installations exist, to Europe,Australia, South-America and Japan, the concept of natural gas as an alternate fuelfor motor vehicles of all kinds has been embraced by more and more people.Considering the overwhelming environmental benefits, cost and availability, thissystem will expand as we approach the 21st century.

COMPRESSED NATURAL GAS FOR VEHICLE FUELING 10.15

FIGURE 10.16 Exploded view of driveassembly.

11.1

CHAPTER 11GAS BOOSTERS

Karl-Heinz BarkMaxPro Technologies

Gas boosters are an alternative to high pressure stationary-type compressors. Theseboosters offer a compact, lightweight design that requires no electrical power orlubrication, thereby providing a more flexible and efficient source for deliveringhigh presssure gas.

Gas boosters will compress gases such as nitrogen and argon up to 15,000 psi,while oxygen can be compressed up to 5,000 psi using special seals and cleaningprocedures. A wide variety of other gases can be compressed including hydrogen,natural gas, ethylene, nitrous oxide, neon, carbon dioxide, carbon monoxide andbreathing air.

In applications where high output pressures are required and the gas supplypressure is low, gas boosters can be operated in series. To achieve higher gas flows,two or more boosters can work in parallel as a unit.

11.1 APPLICATIONS

• Low pressure gas reclaim from storage bottles

• Breathing gas systems for scuba and fire department tanks

• Gas pressure and leak testing

• Charging of accumulators and high pressure inflation bottles for helicopter popfloats

• Boosting gas pressures from oxygen and nitrogen generators

• Nitrogen injection for molding machines

• Leak detection systems

• Low pressure autoclaving

• Cleaning petroleum tanks

• Glass blowing with oxygen

11.2 CHAPTER ELEVEN

• Typical gases—air, nitrogen, helium, oxygen, nitrous oxide, neon, argon, krypton,carbon monoxide, methane, ethylene and natural gas

FIGURE 11.1 Gas booster cross section.

11.2 CONSTRUCTION AND OPERATION

A gas booster consists of a large air driven piston directly connected to a smallerarea gas piston. The gas piston strokes in a high pressure gas section. The gassection contains inlet and outlet check valves. The air drive section includes a spoolvalve and pilot valves that cycle the pistons in both directions. Gas seal assembliesin the high pressure section are vented on the back side to prevent gas from gettinginto the air drive section. Cooling of the gas is provided by routing the cold ex-hausted drive air over the gas barrel section.

GAS BOOSTERS 11.3

11.2.1 Air Drive Head

FIGURE 11.2 Air drive cross section.

11.2.2 Air Spool Valve

The air spool valve is a pilot operated spool that channels the compressed air toeither side of the air drive piston, depending on the position of the spool. In certainoperating conditions with high air consumption, it is possible that the regulated airdrive pressure drops in the back chamber. For this reason, it is important that fullair pressure is available to an unregulated air connection.

FIGURE 11.3 Spool value cross section.

11.2.3 Working Principle

After turning on the air drive, the spool moves to its upper position. Thereby thecontrol line (Sx1) is released. The drive air is now at the pilot value (Vp1) and atthe bottomside of the air piston which now makes a suction stroke.

11.4 CHAPTER ELEVEN

FIGURE 11.4 Air drive logic cross section.

Reaching its upper end position, the air piston switches the pilot valve (Vp1).The spool moves to its start position and the control line (Sx2) is released. The airpiston switches the pilot valve (Vp2). By aid of a logical switching of the controllines, the volume (x) can bleed into atmosphere and the cycle returns. The boosterwill cycle as fast as it is able. To control cycle speed, an air speed valve may beinstalled at the air exhaust connection.

FIGURE 11.5 Air drive logic cross section.

Low Pressure Check Valve Assembly (under 1,000 psi)

FIGURE 11.6 Low pressure check valve cross section.

GAS BOOSTERS 11.5

High Pressure Check Valve Assembly (above 1,000 psi)

FIGURE 11.7 High pressure check valve cross section.

FIGURE 11.8 High pressure piston seal assembly (30:1 booster).

The seal assembly is one of the booster wear parts. This seals the gas barrelwithout letting any gas into the air drive section. The materials of some seals maychange, depending on the gas, the pressure, and the temperature.

11.2.4 Dead Volume

Dead volume is that which does not displace but which must be put under pressurefor the function of the compressor. This volume results, for instance, through bores,tubes, or valve cross sections. The high pressure plunger can completely stroke (inthe pressure direction) and not eject the total gas volume. During suction stroke,the gas expands into the gas barrel until the pressure is equal to or less than thegas supply pressure (ps), at which point only new gas enters the booster.

11.6 CHAPTER ELEVEN

FIGURE 11.9 High pressure cross section.

11.2.5 Exhaust Air as Cooling for the High-Pressure Section

The exhaust air expands after the pressure stroke from the air drive section and theair is guided over the high pressure cylinder for cooling. On two-stage boosters,the connection line between the low and high pressure sections adds cooling.

FIGURE 11.10 Gas end cooling.

GAS BOOSTERS 11.7

11.2.6 Intercooler

The exhaust air from the air drive, used in boosters with a relatively high com-pression ratio, is used for cooling the high-pressure cylinders. Under certain op-erating conditions, it is sometimes necessary to reduce the stroke rate in order toavoid overheating the seals, or connect an additional Intercooler. This intercoolerprovides a longer lifetime of the high pressure piston seals in continuous dutyapplications.

FIGURE 11.11 Inter-stage cooler.

11.2.7 Air Preparation

Version 1

FIGURE 11.12 Air drive schematic to booster (standard).

11.8 CHAPTER ELEVEN

Version 2. For applications with very dry air, when the remaining moisture of thegrease is lost, it is necessary to use an additional oiler.

FIGURE 11.13 Air drive schematic to booster(very dry air).

11.2.8 Pressure Control Filter

The pressure control filter regulator and the ball valve are accessories and notconsidered part of the booster.

FIGURE 11.14 Typical plumbing arrangement for air supply.

GAS BOOSTERS 11.9

11.2.9 Unregulated Pilot Air

The external pilot port must be connected with a separate supply line, otherwisethe fill level of the back chamber is too small. It is possible that the controlled airdrive pressure drops during the operation.

11.2.10 Basic Pressure Relation

Pressure Ratio (pR) pR � pO /pA

Air drive area � air drive pressure↑

Equals↓

Gas piston area � outlet pressure

ExamplePressure ratio 30:1 and air drive pressure90 PSI � 30 � 90 PSI � 2700 PSI outlet pressurefor single acting/single stage booster.

11.10 CHAPTER ELEVEN

Compression Ratio CR � pO /pS

Compression ratio �gas outlet pressure/gas supply pressure

FIGURE 11.15 High pressure checkvalve assembly.

The compression ratio is the ratio between gas supply pressure and gas outletpressure, while the booster is still able to produce a gas flow. If the compressionratio is exceeded, the booster only works into the dead volume.

Stage Pressure Ratio A1 /A2. This is the actual area ratio between the first andthe second stage gas plungers . This only applies to double acting/two stage boost-ers.

GAS BOOSTERS 11.11

FIGURE 11.16 Example of 2-stage pressure ratios.

11.2.11 Suction Pressure Minimum/Maximum

If the suction pressure falls below the minimum stated suction pressure, a two stagebooster would be required. For the single acting/single stage booster, the maximumsuction pressure is lower, so that the air piston does not hammer against the topcap. The maximum suction pressure for double acting/single stage boosters isidentical to the maximum gas outlet pressure. In case of double acting/two stageboosters, the maximum gas supply pressure depends on the air drive pressure.When the gas supply pressure is exceeded, the first pre-booster stage cannot boostthe gas higher and cannot push it to the second stage.

11.12 CHAPTER ELEVEN

11.2.12 Calculation of Outlet Pressure

Outlet pressure (pO) �pressure ratio (pR) � air drive pressure (pA)

FIGURE 11.17 Typical installation diagram single acting /singlestage booster.

Outlet pressure (pO) � pressure ratio (pR) �air drive pressure (pA) � supply pressure (pS)

FIGURE 11.18 Typical installation diagram double acting /single stagebooster.

GAS BOOSTERS 11.13

Outlet pressure (pO) � pressure ratio (pR) �air drive pressure (pA) � (pR2/pR1) � pS

FIGURE 11.19 Typical installation diagram single acting /2-stage booster.

Outlet pressure (pO) � pressure ratio (pR) �air drive pressure (pA) � supply pressure (pS)

FIGURE 11.20 Typical installation diagram double acting /single stage /doubleair head booster.

11.14 CHAPTER ELEVEN

FIGURE 11.21 Typical gas flow curve for 30:1 ratio gas booster.

To find the gas flow, refer to a flow chart similar to Fig. 11.21 of the selectedbooster. The gas flow depends on gas supply pressure (pO) and the air drive pressure(pA). The flow chart above is only for 6 bar air drive. For 4 or 8 bar air drive,another flow chart would be used.

Example: Outlet Pressure � 140 bar and Air Drive � 6 bar

Gas Supply Pressure: 20 bar Gas Flow: 80 L /minN

11.2.13 Selection of a Booster

Boosters are selected based on gas outlet pressure required, gas supply, and the airdrive pressures available. Flow capacity should be checked from a flow chart, asthe example in Fig. 11.21. If the flow capacity is not sufficient, a double actingbooster will be required. If the supply pressure is not sufficient, it would be nec-essary to go to a two stage booster.

Example:

Air drive pressure pA � 6 bar (88 psia)

Working pressure pO � 140 bar (2058 psia)

GAS BOOSTERS 11.15

Gas supply pressure pS � 15 bar (218 psia)

Gas flow required F � 40 LN /min (1.41 SCFM)

Using technical data, a 30:1 ratio unit is the booster that fits these conditions. Referto flow curve to verify flow capability.

11.2.14 Filling a Storage Tank (in a specific time)

Medium Shop Air

Air Drive Pressure (pA) 6 bsar (88 psi)

Supply Pressure (pS) 6 bar (88 psi)

Working Pressure (pO) 80 bar (1176 psia)

Tank Volume 20 Liter (.71 Cu Ft/Min)

Filling Time (t) 20 min

1. Pre-selected booster according to the pressure ratiopR � pO /pA � 80/6 � 13

2. Required volume in tank at 80 bar.VN � V � pO � 20 Liter � 80 bar � 1600 LN

3. Volume in tank at supply pressure.VN1 � V � pS � 20 Liter � 6 bar � 120 LN

4. Volume to be supplied by booster.VN � VN1 � FFill � 1600 L � 120 L � 1480 LN

11.2.15 Average Gas Flow

F� � V / t � 1480 Ln /20 min � 74 LN /min

A booster would be selected with this capacity, based on the performance curves.

12.1

CHAPTER 12SCROLL COMPRESSORS

Robert W. ShafferPresidentAir Squared, Inc.

Initial patents for the scroll concept date back to the early 1900’s. Unfortunatelythe technology to accurately make scrolls did not exist and the concept was for-gotten. In 1972, the scroll concept was re-invented.

The potential and advantages of the scroll compressor over reciprocating com-pressors were immediately recognized by the refrigeration industry. Because of thetremendous pressure for better efficiency of refrigeration compressors in the early’70s, there was a strong incentive to pursue the scroll: the balanced rotary motionreduced noise and vibration; there were no valves to break; and valve noise andvalve losses were eliminated; fewer parts were needed; and rubbing velocities,along with associated frictional losses were lower. Not only did the scroll com-pressor offer improved efficiency, it also had the added benefit of greater reliability,smoother operation and lower noise. Today, scroll compressors are used extensivelyfor residential and automotive air conditioning by many well known companies.

The development of scroll type compressors for air has not been as rapid. Airis much more difficult to compress than refrigerant, especially when oil is not usedfor sealing and cooling. By the ’90s, machine tool technology had progressed tothe point where scrolls could be accurately made and the first dry, oilless scrollcompressor was introduced in January, 1992. The oilless scroll air compressors hadthe same inherent features as the scroll refrigeration compressor when comparedto reciprocating oilless air compressors, durability, reliability, lower noise and vi-bration.

Currently scroll refrigerant compressors are well established as the standard ofthe industry. Scroll air compressors are extending from the initial three and fivehorsepower models into larger and smaller sizes from one to ten horsepower. Figure12.1 shows typical scroll air compressors ranging in size from 1/8 to 1.0 hp.

Recently introduced technology is expected to make scroll air compressors prac-tical in the fractional horsepower sizes.

12.2 CHAPTER TWELVE

FIGURE 12.1 Scroll air compressors from 1/8 to 1.0 HP.

12.1 PRINCIPAL OF OPERATION

The fundamental shape of a scroll is the involute spiral. The involute is the sameprofile used in gear teeth. An involute is a curve traced by a point on a thread kepttaut as it is unwound from another curve. The curve that the thread is unwoundfrom, that is, used for scrolls, is a circle. The radius of the circle is the generatingradius.

A scroll is a free standing involute spiral which is bounded on one side by asolid flat plane, or base.

A scroll set, the fundamental compressing element of a scroll compressor, vac-uum pump or air motor, is made up of two identical involutes which form rightand left hand components. One scroll component is indexed or phased 180 degreeswith respect to the other to allow the scrolls to mesh, as shown in Fig. 12.2.Crescent shaped gas pockets are formed bounded by the involutes and the baseplates of both scrolls. As the moving or orbiting scroll is orbited about the fixedscroll, the pockets formed by the meshed scrolls follow the involute spiral towardthe center and diminish in size (the motion is reversed for an expander or air motor).The orbiting scroll is prevented from rotating during this process to maintain the180 degree phase relationship of the scrolls.

The compressor or vacuum pump’s inlet is at the periphery of the scrolls. Airis drawn into the compressor as the inlet is formed as shown in Fig. 12.2. b, c,and d. The entering gas is trapped in two diametrically opposed gas pockets, Fig.

SCROLL COMPRESSORS 12.3

FIGURE 12.2 Scroll compressor operation.

12.2 a, and compressed as the pockets move toward the center. The compressedgas is exhausted through the discharge port at the center of the fixed scroll. Novalves are needed since the discharge is not in communication with the inlet. Figure12.2 shows the scroll positions as the line connecting the centers of the two scrollsis rotated clockwise, illustrating how gas pockets diminish in size as the orbitingscroll is orbited.

12.2 ADVANTAGES

Scroll refrigerant compressors, air compressors and vacuum pumps have the fol-lowing advantages:

• Scroll compressors can achieve high pressure. The pressure ratio is increased byadding spiral wraps to the scroll. Pressures as high as 100 to 150 psig can beachieved in a single-stage air compressor.

• Scroll compressors are true rotary motion and can be dynamically balanced forsmooth, vibration-free, quiet operation.

• There are no inlet or discharge valves to break or make noise and no associatedvalve losses.

• Scroll compressors can be oil flooded, oil lubricated, or oil free.

12.4 CHAPTER TWELVE

TABLE 12.1 Typical Performance Data of Scroll Air Compressors

Nom. power(HP)

Speed(RPM)

Disch. press.(PSIG)

Air flow(ACFM)

Sound power(dBA@ 1 m)

5.0 3050 120 15.0 593.0 2630 120 9.0 591.0 3450 100 4.0 NA0.3 1750 30 3.0 490.02 3000 10 0.3 39

• Due to the unique orbital motion, the rubbing velocities of the sliding seals aresignificantly less than piston rings or vanes for comparable speeds. Rubbing ve-locities are typically 30 to 50% less, resulting in greater durability.

• Air is delivered continuously, therefore there is very little inlet or discharge pul-sation and associated noise.

• The scroll compressor has no clearance volume that gets re-expanded with as-sociated losses. The compression is continuous.

• Noise levels 3 to 15 dBA lower than other compressor technology are typical.

Table 12.1 gives some typical performance for scroll compressors operating onair.

12.3 LIMITATIONS

Although scroll compressors continue to expand into larger and smaller sizes, thereare limitations. Since the scroll has a leakage path at the apex of the crescent shapedpockets, there are limits to how small a scroll compressor can be as a function ofdischarge pressure. Large displacement scroll compressors become large in diam-eter and the moving or orbiting scroll becomes massive. The maximum centrifugalforce generated by the orbiting scroll gives a practical maximum size in a single-stage scroll.

12.4 CONSTRUCTION

Minimizing leakage of compressed gases within the scrolls is the key to perform-ance in a scroll compressor.

There are two primary leakage paths in a scroll compressor. There is a leakagepath at the apex of the crescent shaped air pockets where the scroll involves are

SCROLL COMPRESSORS 12.5

FIGURE 12.3 Section through involute showing tip seal.

in closest proximity. This leakage is minimized by running the scrolls with a verysmall gap at these points. The size of the gap at the apex of the air pockets is afunction of scroll geometry, and the scroll geometry is a function of the scrollmanufacturing process.

There is also a leakage path between the tip of the involute and the oppositescroll base. Since the involute is relatively long if stretched out, this path is ofprimary importance. This leakage path is sealed by either, running the scrolls veryclose together and using oil to seal the remaining gap or using a floating tip sealas shown in Fig. 12.3. The floating tip seal acts much as a piston ring in a pistontype compressor and bridges the running gap between the scrolls. For oil-freecompressors, the tip seals are made of self lubricating materials.

Driven by a demand from the refrigeration industry, machine tool builders haveimproved the speed and accuracy of scroll manufacture. These new machine toolscan produce finished scrolls in one to five minutes with involute accuracy of 0.0002to 0.0005 inch and with good surface finish. Spindle speeds as high as 30,000 RPMare typical machining scrolls made of aluminum or cast iron. Most of the majormachine tool manufacturers have standard scroll machining centers.

12.4.1 Lubricated Scroll Compressors

Typically scroll compressors used as refrigerant compressors are oil lubricated.Lubrication greatly simplifies the compressor design. Design features include:

12.6 CHAPTER TWELVE

FIGURE 12.4 Typical scroll showing idler shafts.

• Cast iron or aluminum scrolls with no special coatings or surface treatment re-quired

• A simple eccentric drive at the center of the orbiting scroll

• A flat plate thrust bearing to support and locate the orbiting scroll axially

Since refrigerant compressor are hermetically closed systems, no special oilclean up is needed at the discharge. The oil can simply circulate through the re-frigeration system and return to the compressor to seal and lubricate.

SCROLL COMPRESSORS 12.7

12.4.2 Oilless Scroll Compressors

Oilless or oil-free scroll compressors are typically used for air and other gaseswhere the cost of oil clean up is a factor, or where zero oil can be tolerated in thedischarge. Design features include:

• Cast iron or aluminum scrolls coated to improve corrosion and wear resistance

• Tip seals are required for good performance and are made of a self lubricatingmaterial.

• Idler shafts supported by sealed rolling element bearings are used to support theaxial thrust load, locate the orbiting scroll axially and maintain the 180 degreescroll phase relationship. See Fig. 12.4.

12.5 APPLICATIONS

Scroll compressors can primarily be used in those applications where its advantagesare of benefit, specifically low vibration and noise, and durability. Although scrollcompressors can be cost competitive, if cost is the most important factor, alternativetechnology should also be considered.

Some possible applications are given below.

• Residential air conditioning

• Automotive air conditioning

• Process controls

• Pneumatic controls

• Laboratory

• Home health care

• Medical and hospital

• Computer peripherals

• Optical equipment

Scroll compressors can be used where vane or reciprocating compressors areused. They can be dry or oil lubricated.

13.1

CHAPTER 13STRAIGHT LOBE COMPRESSORS

A.G. Patel, PERoots DivisonDivison of Dresser Industries Inc.

13.1 APPLICATIONS

Straight lobe compressors are used for pneumatic conveying of materials, aeratingliquids, extracting gases and vapors, providing low pressure air/gas, superchargingengines and drying materials, etc.

13.1.1 Operating Characteristics

Capacity range: 5 cfm to 60,000 cfm

Pressure range: 15 psi

Vacuum range:

15 in. hgv for conventional compressor27 in. hgv for externally aspirated compressor or liquid sealed0.5 micron as a vacuum booster

Higher pressure and vacuum levels could be achieved through staging.

13.2 OPERATING PRINCIPLE

The more prevalent straight lobe compressors usually have rotors with two or threelobes. The operating principal for a two-lobe compressor is described below.

In the two-lobe compressor, two figure eight rotors are mounted on parallelshafts within an elongated cylinder. A set of timing gears keeps the rotors in syn-chronization. In Fig. 13.1, the lower rotor is presumed to be the drive rotor. As itrotates clockwise, the inlet is created on the right hand side and the discharge iscreated on the left hand side. The driven rotor turns counter clockwise through theaction of the timing gears (not shown). In position 1, the drive rotor is deliveringvolume A to the discharge, while the driven rotor is trapping the volume B betweenthe housing and itself. In position 2, the driven rotor has sealed off volume B fromthe inlet and the discharge. Volume B is basically at inlet conditions. In position3, volume B is being discharged by the driven rotor, while the drive rotor is in theprocess of trapping volume A. The two-lobe compressor discharges four equal

13.2 CHAPTER THIRTEEN

FIGURE 13.1 Two lobe compressor pumping schematic.

volumes of the medium per one rotation of the drive shaft. There is no internalcompression of gas involved. The system resistance determines the head.

13.3 PULSATION CHARACTERISTICS

In Fig. 13.1 position 3, the trapped volume A, which is primarily at the inletpressure condition, is being exposed to the discharge pressure. The higher pressuredischarge medium suddenly rushes in to occupy the volume A. This sudden inrushproduces a pressure pulse.

f � 2�N�Kf � pressure pulse frquency, hz

N � compressor revolution per secondK � number of lobes

In a two-lobe compressor, the pulse frequency is four times the compressor rpm.The amplitude of the discharge pulse is controlled by controlling the rate of pres-sure change of the trapped volume A. In their Whispair� design, Roots Operations,a division of Dresser Industries, uses discharge gas to pre-charge the volume A ina controlled manner to reduce pulsations.

In most of the applications, the use of a discharge pulsation dampner is mandatedto avoid pulsation damage on the equipment down stream of the compressor.

13.4 NOISE CHARACTERISTICS

The discharge pressure pulse is one of the main contributors to noise in a straightlobe compressor. The other contributing factors are gears, bearings and flowinggases. The impeller actions generate varying loads on the bearings. These loadsnot only vary in magnitude during rotation of the impeller, they also change direc-tion causing shock loading that the bearings transfer to the mounting structures.

STRAIGHT LOBE COMPRESSORS 13.3

FIGURE 13.2 Cross section through straight lobe compressor.

The vibrations of these structures radiate noise. For controlling noise, it is notuncommon to enclose the straight lobe compressor in an acoustic housing.

13.5 TORQUE CHARACTERISTICS

The straight lobe compressors have a pulsating shaft torque. The torque pulsationscould be in the range of � 10% of the mean. Stiff couplings like gear type cou-plings are not recommended as they would transmit the torque pulsations possiblycausing damage to the driver.

13.6 CONSTRUCTION (FIG. 13.2)

The main components of a straight lobe compressor are the rotors ➁, the casing➀, the timing gears ➆, the bearings ➄, and the seals ➃.

13.6.1 Rotors

The rotors (2) are nothing more than a set of two toothed gears. The commonprofile for the rotor lobes is involute; cycloidal profile is also used sometimes. The

13.4 CHAPTER THIRTEEN

FIGURE 13.3 PV Diagram For Single Stage Compression

FIGURE 13.4 PV diagram for two stage compression.

shafts are either integrally cast, pressed through, or bolted stub shafts. The clear-ances between the rotors and between the casing and the rotors is held to a mini-mum to reduce leakage flow, the main source of compressor volumetric inefficiency.The rotors are generally hollow; for dusty environments they are plugged to preventrotor imbalance.

13.6.2 Casing

The casing consists of cylinder (1) and end plates (3) also known as head plates.The casing is normally designed for 25 psig rating.

STRAIGHT LOBE COMPRESSORS 13.5

FIGURE 13.5 Suction and discharge arrangement for straight lobe compressor.

FIGURE 13.6 5000CFM straight lobe blower driven by variable frequency driver. Installed ina wasterwater treatment plant. (Roots Division, Dresser Industries Inc.)

13.6.3 Timing Gears

Timing gears maintain the rotor phasing without contact. Timing gears are generallymounted on the shafts with some form of keyless interference fit to permit easytiming of the rotors.

13.6 CHAPTER THIRTEEN

FIGURE 13.7 5000CFM straight lobe blower driven by a Waukesha engine. Installed in a was-tewater plant. (Roots Division, Dresser Industries Inc.)

FIGURE 13.8 1760CFM, 250PSI acetylene product blower (Roots Division, Dresser In-dustries Inc.)

STRAIGHT LOBE COMPRESSORS 13.7

13.6.4 Bearings

Antifriction bearings are generally the bearings of choice.

13.6.5 Seals

The head plate seals are generally labyrinth or piston ring. In air compressors, thearea between the headplate seals and the oil seals is vented to the atmosphere toprevent pressure build-up in the end covers. In gas applications, the vents are closedand mechanical face seals are used in place of oil seals. There are two types ofmechanical seals available: splash lubricated and pressure lubricated. Pressure lu-bricated seals use oil pressure higher than the gas pressure and hence have bettergas sealing ability than the splash lubricated.

13.7 STAGING

Two main reasons for staging straight lobe compressors are for achieving highercompression ratios, and for reducing power consumption.

13.7.1 Higher Compression Ratios

Generally, single-stage straight lobe compressors are limited to a compression ratioof 2.0, or about 15 psi rise on air from an ambient of 14.7 psia. Above this pressurerise, the temperature rise across the compressor becomes excessive. Higher com-pression ratios could be achieved by staging the compressors where discharge gasfrom the each stage is cooled before sending it to the next stage.

13.7.2 Reduction of Power

The straight lobe compressors do not have any internal compression. The powerrequired by a single-stage compressor is represented by a rectangle 1-2-4-3 on PVdiagram as shown in Fig. 13.3.

The air is drawn into the compressor at a constant inlet pressure represented byline 1-2. The trapped volume is instantly compressed to discharge pressure asrepresented by line 2-4. The air is discharged at a constant discharge pressurerepresented by line 4-3. The cycle is completed by line 3-1.

By adding one more stage, power reduction represented by area 2�-4�-4-5 in Fig.13.4 is realized. The first stage draws in air at a constant inlet pressure. The air iscompressed to the intermediate pressure 2�. Since the first stage discharge air vol-ume has been reduced to 4�, the second stage need to have a displacement of only4�. So the work required by the first stage is 1-2-2�-1� and the second stage is 1�-4�-4-3.

13.8 CHAPTER THIRTEEN

13.8 INSTALLATION

Figure 13.5 shows the recommended installation for a straight lobe air compressor.The location of discharge silencer with respect to the compressor flange is verycritical. If distance ‘‘I’’ is not properly selected, there exists a possibility of settingup resonance of discharge gas column. To avoid resonant situation,

ncI ��

4ƒ

where

n � 1,3,5,.......c � velocity of sound in ft /sec � �kgRTf � excitation frequency in Hz � 4 � rotational speed in rev/sec for two-lobe

compressor � 6 � rotational speed in rev/sec for three-lobe compressork � specific heat ratiog � gravity constant � 32.16 ft /sec2

R � gas constant in lb.ft /�RT � gas temperature in �Rankine

For positive displacement compressors, use of relief valves is very important. Anypiping blockage could overload the compressors beyond design pressures.

14.1

CHAPTER 14THE OIL-FLOODED ROTARY SCREWCOMPRESSOR

Hasu GajjarWeatherford Compression

The rotary screw compressor has attracted increased attention in the gas industryduring the last decade as an ideal compressor for low pressure/high capacity op-erations, with low pressure defined as suction pressure at or near zero psig anddischarge pressure at less than 400 psig. Developments are underway by screwcompressor manufacturers to go to higher discharge pressures.

The rotary screw is a positive displacement compressor, like its better knownrelative, the reciprocating compressor. In a comparison between the two, the rotaryscrew gleans honors for its simplicity, low cost, easy maintenance and almost pul-sation-free flow. It takes a back seat to the reciprocating compressor, however, inhandling high pressure (see Fig. 14.1.)

Benefits offered by rotary screw compressors include:

• Simple maintenance

• Low maintenance costs

• Long compressor life

• Full use of driver horsepower

• Low operating expense

• Low purchase price

• High compression ratios (Rc) up to 16 Rc per stage

• Operation at low suction pressure up to 26 inches of vacuum

• Light weight

• Compactness

14.1 TYPES OF COMPRESSORS (see Fig. 14.2)

Rotary compressors may be either positive displacement or dynamic compressors.The positive displacement rotary utilizes either vanes, lobes or screws to literally

14.2 CHAPTER FOURTEEN

FIGURE 14.1 Reciprocating / rotary screw compressors.

FIGURE 14.2 Compressor types.

pack the gas into the discharge line. Dynamic compressors, on the other hand,operate on an entirely different principle. Instead of reducing the volume of thegas to increase its pressure, the dynamic compressor works on transfer of energyfrom a rotating set of blades to a gas, and then discharges the gas into a diffuserwhere the velocity is reduced and its kinetic energy is converted to static pressure.

THE OIL-FLOODED ROTARY SCREW COMPRESSOR 14.3

Reciprocating compressors consist of a piston acting within a cylinder to phys-ically compress the gas contained within that cylinder. They may be either single-acting or double-acting, and can be designed to accommodate practically any pres-sure or capacity. For this reason, the reciprocating compressor is the most commontype found in the gas industry. Each compressor is designed to handle a specificrange of volumes, pressures, and compression ratios.

Compared to the rotary compressor, the reciprocating compressor is more com-plex, and may cost more to maintain. However, its higher efficiency and ability tohandle greater pressures outweigh these disadvantages.

In the selection of a compressor unit, one of the primary considerations, besidespressure-volume characteristics, is the type of driver. Generally, small rotary com-pressors are driven by electric motors, while the larger rotary compressors areusually turbine driven. Reciprocating compressors may be driven by electric mo-tors, turbines (gas or steam) or engines (gas or diesel).

In some types of reciprocating compressors, the power cylinders and compres-sion cylinders are integrated into one unit, and share the same frame and crankshaft.These compressors are referred to as integral units. The power and compressioncylinders of an integral unit may be either horizontally opposed or in a V-configuration with the power cylinders on one bank and the compression cylinderson the other.

Another type of reciprocating compressor is the separable unit. In this typeunit, the prime mover is separate from the compressor, thereby allowing the userto choose the driver best suited to the application. Although this design may beslightly more complex than that of the integral unit, its inherent flexibility oftengives the separable unit an advantage over the integral unit.

A wide variety of compressor designs can be used on the separable unit includ-ing horizontal, vertical, semi-radial and V-type. However, the most common designis the horizontal, balanced-opposed compressor because of its stability and reducedvibration.

14.2 HELICAL ROTORS

The rotary screw compressor consists of two intermeshing helical rotors containedin a housing (see Fig. 14.3). Clearance between the rotor pair and between thehousing and the rotors is .003 in to .005 in. The main rotor (male rotor) is driventhrough a shaft extension by an engine or electric motor. The other rotor (femalerotor) is driven by the main rotor through the oil film from the oil injection; thereis no metal contact.

The length and diameter of the rotors determine the capacity and the dischargepressure. The longer the rotors, the higher the pressure; the larger the diameter ofthe rotors, the greater the capacity.

The helical rotor grooves are filled with gas as they pass the suction port. Asthe rotors turn, the grooves are closed by the housing walls, forming a compressionchamber. Lubricant is injected into the compression chamber after the grooves close

14.4 CHAPTER FOURTEEN

FIGURE 14.3 Typical rotary screwcompressor.

to provide sealing, cooling and lubrication. As the rotors turn to compress thelubricant/gas mixture, the compression chamber volume decreases, compressingthe gas/lubricant toward the discharge port. The gas/lubricant mixture exits fromthe compressor as the compression chamber passes the discharge port. Each rotoris supported by anti-friction bearings held in end plates near the ends of the rotorshaft. The bearings at one end, usually the discharge, fix the rotor against axialthrust, carry radial loads, and provide for the small axial running clearances nec-essary.

After compression, the gas/lubricant mixture enters a multi-stage separatorwhich removes the lubricant from the gas. From the separator, the gas flows to theaftercooler. The lubricant is also cooled, returning to the compressor through athermostatically-controlled valve.

Oil is the lifeblood of a rotary screw compressor. The limited clearance insidethe rotary screw means that without proper lubrication, the screw may experiencehigher than normal wear. Rotary screw compressor operators use a synthetic hy-drocarbon oil of ISO 100, 150 or 220 viscosity. Viscosity is selected based on thespecific gravity of the gas. The gas analysis is very important in oil selection.

During the initial start-up of a unit, gas will dilute the viscosity of the oil. Itshould not be allowed to drop below the minimum recommended value.

Since the rotary screw has a closed oil system, it should use minimal oil. Mostpackagers design the package with oil carryover of five (5) parts per million. If arotary screw compressor loses oil and no leak can be found, then the oil is goingdown the sell line. These conditions mean a scavenging line orifice is plugged ora coalescing filter has collapsed.

The oil filter for the oil injected into the rotary screw is a 10-micron filter. Thefine mesh is needed to protect the bearings and shaft seal. An oil change is rec-ommended only every 8,000 operating hours, unless the oil is contaminated. Aregular oil sampling will help the operator determine when an oil change is needed.

Many rotary screw models are available with internal capacity control and vari-able volume ratio systems, which permit efficient variable load and pressure op-

THE OIL-FLOODED ROTARY SCREW COMPRESSOR 14.5

FIGURE 14.4a Lift valve unloadingmechanism.

FIGURE 14.4b Slide valve unloading mechanism.

eration. Such systems are particularly desirable when constant speed electric motorsare used and varying pressure conditions exist. (see Fig. 14.4a and 14.4b).

14.3 ADVANTAGES OF THE ROTARY SCREW

COMPRESSOR

In many applications, the rotary screw compressor offers significant advantagesover reciprocating compressors.

1. Its few moving parts mean the elimination of maintenance items such as com-pressor valves, packing and piston rings, and the associated downtime for re-placement.

14.6 CHAPTER FOURTEEN

2. The absence of reciprocating inertial forces allows the compressor to run at highspeeds, which results in more compact units.

3. The continuous flow of cooling lubricant permits much higher single-stage com-pression ratios.

4. The compactness tends to reduce package costs.

5. Rotary screw technology reduces or eliminates pulsations, resulting in reducedvibration.

6. Higher speeds and compression ratios help to maximize available productionhorsepower.

14.4 APPLICATIONS FOR THE ROTARY SCREW

COMPRESSOR

A rotary screw compressor package is ideal for numerous compression applications,including:

1. Fuel gas boosting

2. Casing head gas boosting

3. Vapor recovery

4. Landfill and digester gas compression

5. Propane/butane refrigeration compression

6. Compression of corrosive and/or dirty process gases

A rotary screw compressor package can also be used to upgrade existing recip-rocating compressor installations. By boosting low suction pressure, capacity maybe increased at minimum cost with continued use of existing reciprocating equip-ment.

If an application requires large volume/low suction pressure, but discharge pres-sures are greater than the screw can provide, a combination screw/reciprocatingunit with a common driver can be the solution.

14.5 VAPOR RECOVERY

One example of rotary screw utilization is for vapor recovery. Vapor recovery isthe gathering of stock tank vapors and the compression of these vapors into thegas sales line. Capturing these vapors is profitable and environmentally advisable.

The gas vapors are gathered into a common header and fed into a vapor recoveryunit (VRU), which usually includes a suction scrubber, a compressor, a driver, adischarge cooler and separator, and controls for unattended operation. The vaporsare usually rich and wet, conditions which lead to condensate and the washout of

THE OIL-FLOODED ROTARY SCREW COMPRESSOR 14.7

lubricant. Washout causes excessive wear in vanes or piston rings. A rotary screwcompressor does not suffer from these problems for two reasons: there is enoughlubricant injected to take care of washout; and the rotary screw does not requirethe rotors to make contact with the stator.

The sizing of a rotary screw compressor for vapor recovery is extremely im-portant. An oversized unit will operate in the partial load stage or shut down andstart up too often. An undersized unit will not be able to keep up and the ventswill emit vapors into the atmosphere, defeating economy and the effort to maintainclean air.

14.6 SIZING A ROTARY SCREW COMPRESSOR

To size a rotary screw compressor, one needs to know the suction and dischargepressures, the desired capacity, the gas analysis, temperature and the elevation. (SeeEq. 1 for formula to determine capacity and Eq. 2 for formula to determine horse-power.)

EQUATION 1Rotary Screw

Compressor Capacity

ICFM � D3(L/D)(GR)(RPM)(Ev /C)

Rotor Diameter D

Rotor Length L

Gear Ratio GR

Driver Speed RPM

Volumetric Efficiency Ev

Rotor Profile C

EQUATION 2Rotary Screw

Compressor PowerK�1 / KK (P /P ) � 12 1W � P Q � � � WLR 1 K � 1 Ea

Pressures P , P1 2

Gas Flow Rates Q

Gas Properties K

Adiabatic Efficiencies Ea

Mechanical Losses WL

Figures 14.5A and 14.5B show adiabatic efficiency at different pressure ratios,while Fig. 14.6 shows efficiency change with variable volume ratio.

14.8 CHAPTER FOURTEEN

FIGURE 14.5a Adiabatic efficiency (pressure ratio to7).

FIGURE 14.5b Adiabatic efficiency (pressure ratio to 15).

THE OIL-FLOODED ROTARY SCREW COMPRESSOR 14.9

FIGURE 14.6 Efficiency improvementwith variable volume ratio.

15.1

CHAPTER 15DIAPHRAGM COMPRESSORS

G. ReighardHowden Process Compressors, Inc.

15.1 INTRODUCTION

A diaphragm compressor is a specialized piece of equipment used to compressgases when little or no leakage is tolerable. The difference between an ordinarypiston compressor and a diaphragm compressor is in the method of compressionand the accompanying seals. A piston compressor compresses the gas with a mov-ing piston; the piston has a dynamic gas seal in the form of piston rings which arenot leakproof. A diaphragm compressor also has a piston with piston rings, but thepiston moves a volume of hydraulic oil. The oil bends a set of diaphragms up anddown, and the diaphragms compress the gas. Because only static seals are involved,compression is achieved without the escape of gas through a dynamic seal.

15.2 THEORY OF OPERATION

To understand the operation, refer to Fig. 15.1, which shows a typical drive ar-rangement, crankcase, hydraulic system and compression head.

A diaphragm compressor usually has an electric motor as the prime mover, withflexible belts for power transmission. The belts turn a compressor pulley or fly-wheel, which then rotates a crankshaft. Similar to other reciprocating compressors,the crankshaft provides reciprocating motion through a connecting rod on an ec-centric journal. The connecting rod is attached through a wrist pin to a crosshead,which rides in a distance piece or cylinder.

A hydraulic piston is attached to the crosshead. This piston rides in a hydrauliccylinder and is sealed with piston rings. The piston pulses a fixed volume of hy-draulic oil back and forth against the diaphragm set. The oil forces the diaphragmset against the gas head; it is the diaphragms which actually compress the gas.

It is noteworthy that there is a dynamic seal in a diaphragm compressor, but ithas two distinct advantages over a piston compressor:

15.2 CHAPTER FIFTEEN

FIGURE 15.1 Main components of a diaphragm compressor.

1. Because it is on the oil side and does not contact the gas, there is no dynamicgas seal to leak.

2. It is lubricated with oil.

In a diaphragm compressor, the hydraulic oil serves several purposes: in additionto lubricating the running gear, it pulses the diaphragms to provide gas compres-sion, and it provides a cooling effect.

The hydraulic circuit begins in the bottom of the crankcase, which acts as areservoir for lubricating oil. Oil flows into the circuit through a strainer. Whererequired, the oil flow is cooled, usually through a water-cooled heat exchanger.The flow enters the main oil pump and is discharged through a filter. Next the oilis split into two streams, with the bulk of the oil flow going to lubricate crankshaftbearings, connecting rod journals, wrist pins, and sliding surfaces of the crosshead.A small portion of the flow is diverted to the compensating circuit.

The purpose of the compensating circuit is to make up any oil that leaks pastthe piston rings on the hydraulic piston. In this circuit, oil flows from the mainpump to a check valve, through a low-volume reciprocating compensating pump,through another check valve, and into the oil head. However, the makeup oil flowis very large compared to the actual amount of oil lost through piston ring leakage.

During each stroke, the hydraulic oil pushes the diaphragm set into full contactwith the gas head. If leakage past the hydraulic piston rings were not made up, thepulsed oil volume would decrease, and the diaphragm set would not completelycontact the gas head. Continued hydraulic piston ring leakage would have the sameeffect as increasing the volumetric clearance in a piston compressor, with resultinglosses in performance. Therefore the proper operation of this compensating circuitis critical to the performance of the compressor.

DIAPHRAGM COMPRESSORS 15.3

FIGURE 15.2 Internal pressures during compression.

To regulate the makeup oil, a valve is mounted on the oil head to maintainproper oil pressure internally, but also allow any excess oil to flow back into thecrankcase. This valve is known as the hydraulic pressure limiter. It is adjusted todevelop the desired gas discharge pressure in the compression head. The limiter isopened by the development of a peak oil pressure (the limiter pressure), and isclosed by a spring.

On some small models, the function of the compensating pump is provided bydifferential displacement, where the piston displacement is slightly larger than thecavity volume between the gas and oil heads. This allows the diaphragms to touchthe oil head; the additional travel of the piston draws oil into the oil head throughthe oil check valve. However, this approach is limited in its application.

The compression head consists of an oil head bolted to a gas head, a diaphragmset, seals, suction valve(s), discharge valve, valve retainers and bolting. The oilhead contains the hydraulic oil; the gas head contains the gas being compressed,and the diaphragms separate the gas from the oil. The suction and discharge valvesare self-actuating, opening and closing due to differential pressures, allowing gasto enter and leave the head at the proper times.

To understand the relationship of the dynamic pressures inside the compressionhead, refer to Fig. 15.2. This figure shows the pressures developed inside the oilhead during one typical revolution.

At Point A, the hydraulic piston is at top dead center (TDC) and the pressurehas reached its peak. The piston begins its downward stroke, away from the gashead. The oil pressure drops rapidly, as does the gas pressure on the other side of

15.4 CHAPTER FIFTEEN

the diaphragm set. Because the external gas pressure is higher than the internal gaspressure, the discharge valve closes. The remaining gas in the compression headthen expands from discharge pressure to suction pressure. When the internal gaspressure is slightly less than suction pressure (Point B), the suction valve opensand admits fresh suction gas into the head.

As the piston approaches bottom dead center (BDC), an important function oc-curs: the compensating pump injects a small amount of oil into the oil head toallow for piston ring leakage. When the hydraulic piston reaches BDC, the flow ofsuction gas into the head stops (Point C). The diaphragms are now at their closestposition to the oil head.

As the piston begins its upward stroke toward the gas head, internal gas pressureexceeds external gas pressure and the suction valve closes. Gas is now trappedinside the compression head causing the oil pressure and the gas pressure to in-crease simultaneously. When the internal gas pressure exceeds external gas pressure(Point D), the discharge valve opens and gas flows from the head into the dischargepiping. This flow of gas stops when the diaphragm set contacts the gas head, andthe discharge valve closes (Point E). However, the piston continues to travel a smallamount further. As a result, the pressure in the oil head continues to rise althoughthe trapped gas remains at discharge pressure. The hydraulic pressure limiter thenopens and discharges a small amount of oil back to the crankcase. At TDC (PointA), the piston begins to travel away from the gas head. The limiter closes, maintainsthe oil pressure inside the compression head, and the next compression cycle be-gins.

For proper operation of the compressor, the hydraulic pressure limiter mustprovide a peak oil pressure higher than gas discharge pressure. As shown in Fig.15.2, gas compression is intimately tied to the proper operation of the hydraulicsystem.

15.3 DESIGN

Model numbers used by various manufacturers commonly denote the basic crank-case (with a given stroke and rod load); the configuration; and the maximum pres-sure rating of the head(s). Strokes run the range from 1.25 inch through 9 inches;the most popular strokes are 2.5 inches through 5 inches. Configuration of dia-phragm compressors can be varied. Single-stage designs are common, with thehead mounted either vertically or horizontally. Two-stage designs are also common,built in ‘‘L,’’ ‘‘V,’’ and horizontally opposed styles. Three-stage designs are lesscommon, and four-stage systems are unusual. Pressure ratings usually run from150 psig to 15,000 psig. However, compressors have been built outside this range,with some operating at vacuum conditions, and others at 45,000 psig and higher.

Drivers for diaphragm compressors are usually electric motors, ranging from 1HP up to 200 HP. Although purchasers often specify high efficiency motors, theyhave lower slip and higher currents than standard motors. As a result, standard

DIAPHRAGM COMPRESSORS 15.5

efficiency motors are usually the better choice for reciprocating compressor appli-cations.

Belt drives are the most common means of power transmission. A small sheaveis mounted on the motor shaft and a large sheave on the compressor shaft. Thelarge sheave usually doubles as a flywheel, with a heavy rim to provide rotationalinertia for reducing peak motor current.

Crankcases are very similar to those used for piston compressors. The one sig-nificant difference is the provision for shaft-mounted compensating pumps, whichprovide makeup oil to the oil heads to counteract piston ring leakage.

Proper oil filtration is mandatory for successful operation of a diaphragm com-pressor. As with all rotating equipment, bearings may be damaged if fed with dirtyoil. In addition, the diaphragms are susceptible to cracking by bending around dirtor metal particles if the oil is not kept clean continuously. To keep the oil clean,it first passes through a strainer as it leaves the crankcase. After leaving the pump,it passes through a filter, usually of 25-micron rating.

In the past, splash lubrication with slingers or dipping extensions has been pro-vided on some models. However, it has generally been replaced by forced lubri-cation.

Forced lubrication is typically provided by a shaft-driven gear pump. The pumpmay be driven by direct coupling onto the crankshaft, or by a gear attached to thecrankshaft. Auxiliary pumps with electric motors may be provided as an option.Relief valves are fitted to the discharge of these pumps with any overflow beingreturned to the sump in the crankcase.

An oil heater is often required for low-temperature operation. The heater isgenerally an immersion type, installed directly into the crankcase. Oil coolers areoften provided as well; these are typically installed next to the oil pump. In somewide operating temperature ranges, a compressor may have both an oil heater andan oil cooler.

The compensating pump is driven by an eccentric on the crankshaft, and returnedby a spring. The pump has a small plunger sealed to a body with either pistonrings or a tightly-toleranced fit. Check valves are mounted at the suction and dis-charge ports to prevent backflow.

The peak hydraulic pressure is established by the hydraulic pressure limiter. Thelimiter is opened by the peak oil pressure and is returned by spring action. It isusually externally adjustable and has a rugged design, opening and closing up to500 times a minute. Limiters usually have a bypass valve (sometimes external) thatallows the oil head to fill with oil without developing internal pressure. This bypassvalve is designed for use only after the head has been taken apart.

An optional feature recommended for large heads is a set of valves used forfilling the head with hydraulic oil. Filling is done with a separate pump which canbe a hand pump or an auxiliary motor-driven pump.

Selection of the proper lubricant is vital in a diaphragm compressor. For mostapplications, a standard hydraulic or general purpose oil is used, with an ISOviscosity range between 46 and 100 centistokes. Anti-wear and anti-foam additivesare generally used.

15.6 CHAPTER FIFTEEN

FIGURE 15.3 Diaphragm compressor head assembly.

For certain applications, synthetic lubricants such as halocarbon oils are speci-fied, especially in the compression of oxidizers such as oxygen and fluorine. Whenthese synthetic oils are furnished, care must be taken to ensure that all materialsin the hydraulic circuit are compatible with the oil.

For a typical cross-section view of a diaphragm compressor head assembly, referto Fig. 15.3. At the lower end of this assembly, the piston rod is attached to thecrosshead. The piston is assembled into a hydraulic cylinder, guided by rider ringsand sealed with piston rings. While piston rings at one time were made exclusivelyof cast iron, they are now commonly made of specialized filled plastic materials.

The oil head is a rugged component, designed to withstand the peak hydraulicpressure in the system. The hydraulic cylinder is mounted on the crankcase end ofthe head. As the piston pushes oil up through the cylinder, the oil head distributesthe oil evenly underneath the diaphragms through a series of holes or grooves.These holes or grooves must be limited in size, or the diaphragms can be over-stressed by bridging these features. On the side of the oil head facing the dia-phragms is a shallow cavity which limits the deflection and stresses in the dia-phragm set.

The oil head has an inlet port to receive oil from the compensating pump, andan outlet port to discharge oil through the limiter. Because they are pressure-retaining components, thickness of the compression heads (both gas and oil) iscritical; U.S. designs follow the ASME Boiler and Pressure Vessel Code for flatheads. The oil head is sometimes water cooled to limit seal temperature.

The gas head is rugged as well, since it also must withstand the peak hydraulicpressure in the system. On the side of the gas head facing the diaphragms is acavity that matches the one in the oil head. The diaphragms make contact with this

DIAPHRAGM COMPRESSORS 15.7

cavity at top dead center, and the cavity limits the deflection at this point. In thecavity are radial grooves leading to the discharge port at the center; these grooveshelp to sweep gas out of the head during discharge. The suction port is offsetradially from the discharge port. As noted previously, all of these holes or groovesmust be limited in size. On the external face of the gas head, ports are machinedto receive the suction and discharge valves. The gas head is usually water-cooled.

As noted above, both the gas head and the oil head have a shallow cavitymachined into them. Although other designs exist, two of these cavity designs arewell known; they are the ‘‘two-radius’’ and the ‘‘free-deflection’’ approaches. How-ever, a feature common to all cavity designs is a very small center deflection witha large cavity diameter. This ensures that diaphragm stresses are kept within theelastic range. At low pressures, a large cavity is used; such a cavity may be 36inches in diameter with a deflection of 0.5 inch at the center. For high pressures,though, cavities can be quite small. A cavity with a 3-inch diameter may have acenter deflection of only 0.030 inch.

In U.S. design practice, ASME Code allowable strengths and guidelines are usedfor the selection of bolting. High-strength studs are often specified as SA193 GradeB7, with nuts made from SA194 Grade 2H material. Fatigue resistance is of primeimportance due to the high cyclic application of these fasteners.

Many of these compressors are located in corrosive environments such as saltspray from the ocean or in a caustic atmosphere in a chemical plant. Because ofthis, a well designed compressor head will use either plated or coated bolts toprevent rust. While bolting previously made use of cadmium or zinc plating, recenttrends are toward the use of PTFE coatings. These coatings provide lubricity aswell as corrosion resistance.

Although bolted head assemblies are the most common, other methods of headclosure exist. Several of these methods make use of a large body, usually forged,and a large internal nut to retain the compression heads. The internal nut may beclosed with either set screws or by hydraulic pressure.

Diaphragms are flat, circular pieces of sheet metal with a smooth finish. A stackof three diaphragms is commonly used, with each of them serving a differentpurpose. Because it is in constant contact with the process gas, the gas diaphragmmust provide corrosion resistance. The middle diaphragm has slots, grooves, orholes to conduct any leakage from a broken gas or oil diaphragm to the peripherywhere such leakage can be detected. The oil diaphragm, which rarely has a cor-rosion problem, transmits hydraulic pressure to the other diaphragms and providesa barrier to the oil.

Due to tiny differential displacement between the diaphragms as they bend upand down, provision must be made for lubricating the interfaces between dia-phragms. To this end, the middle diaphragm may be coated with a dry film lubri-cant. Alternatively, the use of dissimilar metals can prevent wear on these surfaces.

Seals are critical to the proper operation of these compressors. While earlierversions used metal-to-metal seals with rather high bearing pressures between mat-ing surfaces, the predominant seal in use today is an elastomer o-ring. O-rings arevery forgiving in their ability to seal minor imperfections, and they are available

15.8 CHAPTER FIFTEEN

FIGURE 15.4 Head integrity system.

in many different materials to suit varying process gases. Less common are metalseal rings and metal o-rings, which can be used to seal aggressive process gases.

Because leakage is such an important issue in the application of diaphragmcompressors, most of them are fitted with a head integrity system as shown in Fig.15.4. This system, also known as a leak detection system, will sense any one offour leakage sources:

1. A broken gas diaphragm

2. A broken oil diaphragm

3. A leaking gas seal

4. A leaking oil seal

In the event of a broken diaphragm, the gas or oil will find its way through theslotted or grooved middle diaphragm to the outside of the diaphragms. With aruptured gas or oil seal, the leaking gas or oil will also travel to the diaphragmperiphery. There the leak is contained inside another seal to prevent leakage to theatmosphere. The leak is then conducted to an external port for monitoring by thehead integrity system. This system is composed of four parts: a manual vent valve,a relief valve, a pressure gauge and a pressure switch. The manual vent valve allowsresetting of the switch; the relief valve prevents overpressurization; the pressuregauge allows verification of the leak; and the pressure switch will shut the com-pressor down.

As a rule, valves used in diaphragm compressors are self-actuated, opened bythe flow of suction or discharge gas, then returned and sealed by differential pres-sures. Springs are used to control the valve sealing element and damp out unwantedmotion. The sealing elements are usually flat discs or guided poppets; occasionally

DIAPHRAGM COMPRESSORS 15.9

balls are used. Although some designs require multiple suction valves, most headsuse a single suction valve and a single discharge valve. Seals are usually elastomero-rings, metal gaskets, or metal seal rings. Where high heat is generated duringcompression, valve retainers are fitted with Belleville springs to accommodate ther-mal expansion.

Numerous special configurations of diaphragm compressors have been built.Compressors have been designed with remote head assemblies; the motive hydrau-lic oil is sent from the crankcase to the head through piping. Certain compressorshave been built from light materials such as aluminum where low weight is arequirement. In other variations, air cylinders are prime movers rather than electricmotors. There are many other possible modifications to the basic design.

15.4 MATERIALS OF CONSTRUCTION

Materials used for the crankcase, crankshaft, bearings, connecting rods, wrist pins,and crossheads are very similar to those found in an ordinary piston compressor.However, materials used to manufacture compression heads and valves can varygreatly.

Due to the limited availability of materials, the earliest versions of compressorheads were made from intricate and robust iron castings. However, recent designsmake use of carbon steel plate or forgings. A typical plate specification for oilheads is SA516 Grade 70.

Because gas heads are in intimate contact with the process gas, there are severaldifferent materials used for their manufacture. For inert gas service and lower cost,gas heads may be made of carbon steel plate. For more corrosion resistance, manygas heads are made from stainless steel plate such as SA240 type 304 or 316. Forsevere environments, the selection may range to Monel or Alloy 20. Many othermetals could be suitable providing they meet the structural requirements of thehead design. Along with the oil heads, gas heads are typically machined from plate;forgings are used when dictated by strength or thickness requirements.

For ordinary inert gas applications, carbon steel sheet is adequate as a diaphragmmaterial; however, the majority of diaphragms are made of high tensile-strengthstainless steel, usually type 301 or 316. Other stainless steels such as 17-4 PH arealso used. For added corrosion resistance, Monel or Alloy 20 may be used. Whileother materials are possible, they are sometimes impractical due to limited com-mercial availability in the proper thickness, width, or strength.

Valves for diaphragm compressors are often produced from corrosion-resistantmaterials such as alloy steels and 300 or 400 series stainless steels. As with theother gas-contacting parts, the valves may also be made from Monel or Alloy 20.Sealing elements are sometimes made of specialized plastics such as PEEK orVespel. Springs are commonly stainless steel; Inconel is also a good choice forsprings.

15.10 CHAPTER FIFTEEN

15.5 ACCESSORIES

Because many diaphragm compressors are customized in design, it is common tohave customized accessories as well. These accessories are mounted on a steelbaseplate, which also holds the motor and belt guard.

Because dirt and debris can be very harmful to the diaphragms, a process gassuction filter should be installed. An ideal filter is made of pleated stainless steelmesh with a 10-micron rating. Double suction filters with changeover valves areuseful where production time is at a premium.

Where there is no significant volume of gas in the suction and discharge piping,accumulators are recommended to smooth out compressor operation. Pulsationdampeners tailored to the application are recommended where the pulsation couldbe detrimental to either the process or equipment.

When the process gas may contain moisture, a separator and trap should beinstalled at the suction to each stage and any point where condensation may occur,especially after a cooler. Liquid ingestion can damage not only the diaphragms,but the compression heads as well.

Gas coolers are usually installed at the discharge of each compressor stage.These may be shell-and-tube types, spiral tubes, or tube-in-tube types for smallerflow rates. Intercooling of gas is required not only for protection of seals andequipment, but for efficient operation.

Flow rates on many diaphragm compressors are low enough that tubing canhandle the main flow of gas. At lower pressures, compression fittings are wellsuited. At pressures greater than 5000 psig, however, coned and threaded tubingprovides a very safe joint with a very low leak rate.

When pipe is used, screwed joints may be employed but only with certain pre-cautions. Due to the nature of gases handled (including those that are flammable,pyrophoric, and toxic), only very low leak rates may be acceptable. In those cases,welded joints are preferable. Although socket welds are used frequently, butt weldsare used to meet the most stringent requirements where radiography can verify thesoundness of a joint.

Maintenance joints for piping are very often standard raised-face flanges; how-ever, flat-faced o-ring unions are used in many applications.

To monitor compressor performance, a pressure gauge should be installed at thesuction port and discharge port of each compression head. Very often pressureswitches are also required. These are installed at suction or discharge but rarely atan interstage section. Where final product temperature is critical, a discharge tem-perature switch or transmitter should be used.

For overpressure protection, a relief valve or rupture disc should be installed atthe discharge of each stage, whether interstage or final discharge. Failure to do thiscould result in serious harm to personnel or property damage.

Capacity control is usually provided by some form of gas bypass, which returnsthe excess flow from discharge back to the suction piping. Common bypass meth-ods maintain a constant discharge pressure, provided by an air-operated control

DIAPHRAGM COMPRESSORS 15.11

valve, or a manual back-pressure regulator. If justified by the demand cycle, on-off control can be supplied. With on-off control, there should be only a few startsper hour, and process gas should be vented from the discharge to allow unloadedrestarting.

Variable speed drives are usually not used for capacity control; the varying speedcould play havoc with oil pressure and flow from shaft-driven oil pumps. Mechan-ical valve unloaders are generally not used; the location of valve inlet and outletports directly over the valves would complicate this design.

For protection of the hydraulic system, an oil pressure gauge and pressure switchare usually provided. For added protection, an oil level switch may also be used.These switches are usually wired to shut the compressor down. Water flow switchesare often installed; these are good insurance against accidental loss of coolant.

15.6 CLEANING AND TESTING

Because cleanliness is of extreme importance in the reliable operation of a dia-phragm compressor, its components must be carefully cleaned whether they contactthe gas side or the oil side. Dirt and debris on either side can cause diaphragmfailure. Diaphragm compressor manufacturers have established high standards ofcleanliness for this reason. However, there are some applications that call for evenstricter control of contamination. One of these is oxygen or oxidizer service, whereall gas side components must be free of both debris and oil. The mere presence ofthese contaminants can cause a reaction with the process gas. In addition, thecrankcase and all hydraulic equipment must be free of hydrocarbon oils; ignitioncan occur if the oxidizer contacts these hydrocarbons.

A manufacturer of high-quality compressors will complete not only a mechanicalrun test but a performance test before shipment. The majority of these compressorscan be run at full suction and discharge pressures during test. The actual flow rateis measured, using inert gas (typically nitrogen) to simulate the process gas. Theentire compressor system should be checked for leaks on the gas side, the hydraulicside, and the cooling circuits. In addition, all required nondestructive examinationsuch as liquid penetrant tests and radiographic tests for piping should be completedbefore shipment. These tests should be specified in writing by the purchaser andreviewed by the manufacturer early in the production of the machine.

15.7 APPLICATIONS

Diaphragm compressors are frequently applied where an ordinary piston compres-sor could experience problems due to leakage, gas contamination or pressure lim-itations. Some of the applications where diaphragm compressors are ideally suitedare listed below:

15.12 CHAPTER FIFTEEN

Type of gas Examples

Toxic Boron trifluorideCorrosive FluorineFlammable HydrogenPyrophoric SilaneOxidizer ChlorineRadioactive Uranium hexafluoride

In addition, the applications can provide cost-effective compression where lowcontamination is required, high pressures are developed, or high temperatures willbe handled.

Many different markets have applications for diaphragm compressors. One ofthe largest users is industrial gas production and distribution, where these com-pressors are used to fill cylinders with common gases such as helium, nitrogen andargon. This is a well-established segment where diaphragm compressors are a stan-dard, non-contaminating, reliable method of compression.

Some other areas that make good use of diaphragm compressors include thefollowing mentioned below.

15.7.1 Automotive Air Bag Filling

Gas mixtures are compressed to high pressures to pressure test and leak test gascanisters. The compressed gas then remains in the gas canister to provide actuationof the airbag during an accident.

15.7.2 Tank Car Unloading

Vaporized product from a bulk liquid tank car can be used to pressurize the carand offload it to a storage vessel.

15.7.3 Petrochemical Industries

Gases are produced and distributed throughout a plant to various processes aftercompression. Gases are also recirculated at low compression ratios where onlypiping losses must be overcome.

15.8 LIMITATIONS

Diaphragm compressors typically operate in the range of 300 to 500 rpm. Whilespeeds as low as 100 rpm are possible, provision must be made to maintain oil

DIAPHRAGM COMPRESSORS 15.13

pressure. Speeds of 750 rpm have been achieved in modified diaphragm compres-sors.

Atmospheric suction pressure is common for diaphragm compressors. Low suc-tion pressures such as 2 or 3 cm Hg absolute are also possible, although specialprovisions must be made for degassing the oil in the crankcase sump. In extremeconditions, the suction pressure could be as high as 5000 psig.

Discharge pressures of 2,500 psig are very common; this is typical of manycylinder-filling operations for industrial gas handlers and producers. There are manycurrent applications where discharge pressures of 5,000 to 10,000 psig are routine.Diaphragm compressors have been built with discharge pressures of 45,000 psigand higher. However, such designs must be carefully executed when the processpressures exceed the yield strength of ordinary metals.

Diaphragm compressors can be successfully applied at very small flow rates ofless than one standard cubic foot per minute (SCFM). Typical flow rates lie in therange of 5 to 100 SCFM, although flow rates of 700 SCFM and higher have beenachieved.

Physical size is sometimes a constraint in the design of a diaphragm compressor.While some compressor heads may be only 10 inches in diameter, certain lowpressure heads may have a diameter of 40 inches which can limit the installationin tight quarters. Such large heads may weigh nearly 2000 pounds, which canprovide a challenge when removing the head for maintenance. In addition, thechoice of available diaphragm materials is limited when the diameter exceeds 36inches.

15.9 INSTALLATION AND MAINTENANCE

Installation of a diaphragm compressor should follow the same good practices usedfor any reciprocating compressor. Foundation design should account for vibrationdue to unbalanced forces and moments. These values are available from the man-ufacturer.

Piping design should account for flexibility, vibration isolation and thermal ex-pansion. For large flow rates, pulsation dampeners should be evaluated to avoidacoustic resonance. Where personnel have routine access to the compressor, con-sider guards to prevent contact with discharge lines. These frequently are hotenough to cause burns on unprotected skin.

One of the primary goals of a good diaphragm compressor installation is toprevent contamination of the process gas. Filters should be used to prevent partic-ulate entry; separators are required when liquid could present a problem; and com-ponents must be kept clean during any maintenance work.

Maintenance plans for the compressor should consider: lifting equipment for thegas head and oil head; ability to clean all exposed components on both the gas andoil side; adequate lighting; and accessibility to the crankcase and compressionheads.

15.14 CHAPTER FIFTEEN

PHOTO 1 Burton Corblin two stage 2000 psi diaphragm compressor.

15.10 SPECIFYING A DIAPHRAGM COMPRESSOR

The purchaser of a diaphragm compressor should specify sufficient detail so thatthe manufacturer can provide equipment which meets the requirements safely andefficiently. A thorough specification will contain these key points:

• Required flow rate

• Composition of gas handled

• Special gas conditions such as corrosives, condensibles, and contaminants

• Suction pressure and temperature

• Required discharge pressure and temperature

• Type of cooling available

• Electrical area classification

• Power supply available

• Control voltage and type of controls required

• Site conditions such as ambient pressure, temperature, and humidity

• Preferred materials of construction

• Limitations on envelope size

Because of the current global equipment market, the user should specify appli-cable national or international standards. A design that is approved for one site

DIAPHRAGM COMPRESSORS 15.15

PHOTO 2 Burton Corblin two stage 6000 psi diaphragm compressor.

PHOTO 3 Burton Corblin two stage 8000 psi diaphragm compressor.

15.16 CHAPTER FIFTEEN

may be inadequate for the same service but in a different country. Typical standardsinvoked for the United States markets are:

• ASME B&PV Code for pressure vessels

• ASME B31.3 for piping

• National Electrical Code for wiring

• API 618 for basic compressor construction

In addition, the purchaser should list any of its own in-house standards thatapply, such as those for motors, pressure vessels, and piping.

16.1

CHAPTER 16ROTARY COMPRESSOR SEALS

James NetzelChief Engineer, John Crane Inc.

16.1 INTRODUCTION

The selection of a sealing system for a compressor is critical if satisfactory per-formance and reliability are to be realized. The type of compressor and the methodof lubrication used will determine the type of sealing technology to be applied. Forsome compressors a liquid lubrication system is required, while others will requirea gas lubricated system.

Sealing technology is an evolutionary process. Design concepts and improve-ments in material of construction are some of the most notable achievements inthis field. Sealing systems can be divided into four classes, based on the type oflubrication.

1. Contactinga. Liquid lubricatedb. Gas lubricated

2. Non-contactinga. Liquid lubricatedb. Gas lubricated

16.1.1 Contacting Liquid Lubricated

Seals, both mechanical face-type seals and lip seals, are cooled and lubricated bythe lubricating oil in the compressor. This system is a condition of mixed lubri-cation where the load or contact pressure is partly carried by a fluid film and partlycarried by the mechanical contact between the sealing surfaces. This is the mostcommon sealing system found in industry for all types of rotating equipment.

16.2 CHAPTER SIXTEEN

16.1.2 Contacting Gas Lubricated

The contacting surfaces are designed to run dry with very light contact loads.Cooling and lubrication is achieved from the gas being sealed. This is a conditionof boundary lubrication where the sealing surfaces are in contact, though separatedfrom hard contact by material transfer films. This sealing concept is only appliedto very light duty services.

16.1.3 Non-Contacting Liquid Lubricated

This method of sealing is dependent on a geometry change at the seal interface.Spiral grooves or similar features are incorporated into one of the sealing surfacesto generate hydrodynamic lift to separate the seal faces. This system is generallyused to move a small quantity of liquid lubricant from a low pressure source to ahigh pressure side of a seal. This non-contacting concept is applied to specializedsealing applications to eliminate hazardous and toxic leakage and on those appli-cations where abrasives are present.

16.1.4 Non-Contacting Gas Lubricated

This method of sealing an industrial compressor has become very popular over theyears for it has eliminated expensive oil lubrication equipment. This design is alsobased on the concept of hydrodynamic lubrication and the incorporation of ge-ometry changes to one of the sealing surfaces such as spiral grooves. The onlyheat that is developed is that of shearing gas at the seal interface. Therefore, it isthe most energy efficient sealing system available to industry. This type of systemcan run on the process fluid being sealed or a neutral barrier fluid like nitrogen,purified air, or steam. This type of sealing system, which was designed for com-pressors, is now being applied to all types of difficult sealing applications on ro-tating equipment.

To successfully apply any of these sealing concepts, the following informationmust be considered.

1. Process gas being compressed2. Operating condition

• Pessure• Tmperature• Seed• Buffer fluid (if required)

3. Space available for the seal4. Utility reliability

• Steam

ROTARY COMPRESSOR SEALS 16.3

• Water• Electricity—number of sources• Plant air

5. Disposal of buffer liquids6. Disposal of gas sealants7. Auxiliary equipment

• Controls, alarms, and trips• Direct• Closed loop pneumatic

• Electronic• Dedicated mainframe• Computer

A detailed description of the gas to be compressed is necessary to ensure theproper selection of the sealing system to be used. This includes such items aswhether or not the gas is hazardous or toxic, the effect on materials of construction,and whether contaminants are present. If a buffer fluid is required, then consider-ation must be given to availability, quality, backup, pressure level and cleanliness.

16.2 TYPES OF SEALS

16.2.1 Labyrinth Seals

Labyrinth seals represent the simplest method of sealing a rotating shaft. A seriesof knife edges are designed into either the housing or shaft. The clearance betweenthe knife edge and its mating surface is a closely controlled value to limit leakagefrom the compressor. There is no limit on speed and labyrinth seals can be usedat high temperature. The pressure limit is low and typically limited to 5 psi perknife edge. Leakage from this device is high. When applied to non-hazardousprocess gases, leakage can be vented to atmosphere. When the gas being com-pressed is hazardous to the environment, a buffer gas at higher pressure than theprocess gas, is injected between two labyrinth seals as illustrated in Fig. 16.1.

16.2.2 Carbon Ring Seals

Carbon ring seals are close clearance sealing devices similar to labyrinth seals.These types of seals are primarily used for low pressure, low temperature appli-cations. Seal leakage is lower than a labyrinth seal. To prevent the leakage ofprocess gas to atmosphere, a buffered gas or steam is injected between sets ofcarbon rings. This type of seal may also be used as a pressure breakdown device.There is no limit on shaft speed. This type of seal is illustrated in Fig. 16.2.

16.4 CHAPTER SIXTEEN

FIGURE 16.1 Typical labyrinth seal installation.

FIGURE 16.2 Carbon ring seal.

16.2.3 Bushing Seals

Bushing seals are always used with a buffered oil system to contain gas within acompressor. The oil must be maintained at a pressure of at least 0.3 to 1 bar abovethe process pressure. The oil is always injected between the inner and outer bush-ings, creating the seal. The amount of leakage is always dependent on the operating

ROTARY COMPRESSOR SEALS 16.5

FIGURE 16.3 Bushing seal with oil buffer.

conditions of the compressor and the shaft size of the unit. Leakage of oil to theprocess gas can be 40 to 75 liters (10 to 20 gallons) per day. This leakage can bedegassified and returned to the oil reservoir. Leakage to atmosphere is returned tothe reservoir. Shaft speed for this seal is limited to less than 115 m/s (375 ft/sec).This type of seal may be used to a pressure of 3000 psig. A bushing type seal isillustrated in Fig. 16.3.

16.2.4 Pump Bushing Seal

This type of seal must also be used with a buffer liquid. The buffer liquid may beoil or water. Special designs may allow this sealing device to be used to pressureas high as 5000 psig. Speeds are limited to 115 m/s (375 ft/sec).

Buffer pressure is normally 0.3 to 1 bar greater than the process gas. Leakageis dependent on the operating conditions of the compressor and the shaft size ofthe unit. Static leakage can be high until the shaft begins to rotate. Oil leakage tothe trap can be 4 to 20 liters (1 to 5 gallons) per day. Leakage is degassified andreturned to a reservoir. A typical pump bushing seal is shown in Fig. 16.4.

16.2.5 Circumferential Seals

This type of sealing device uses segmented carbon rings held together with a spring.There may be one or multiple rings within the seal. Each ring is normally capableof pressure to 100 psig. This seal may operate directly in sealing the process gas

16.6 CHAPTER SIXTEEN

FIGURE 16.4 Pump bushing seal.

or a buffer gas supply. Leakage range is 2.8 to 29 l/min (0.1 to 1.03 SCFM), andthe shaft speed is limited to 190 m/s (600 ft/sec). This type of seal is illustratedin Fig. 16.5.

16.2.6 Contacting Seal

Many small oil flooded compressors use conventional contacting seals to containthe oil and the gas being compressed. Refrigeration compressors typically use bel-lows seals and occasionally, o-ring seals. A bellows seal may take the form of anelastomeric bellows or a metal bellows as illustrated in Fig. 16.6 and Fig. 16.7respectively. Most contacting seals of this type are used at speeds to 3600 rpm andpressures of 250 psig. As speeds increase on small oil flooded machines, the sealis held stationary to the unit as illustrated in Fig. 16.7.

On some larger centrifugal compressors a contacting face that requires an oilbuffer is used to seal the compressor. This seal is shown in Fig. 16.8. Here, cleanoil is injected over the rotating mating ring for cooling and lubrication. Oil leakagepast the seal face is captured at an internal drain and separated from the gas. Alabyrinth may be used to break down the pressure at the inboard side of the seal.The oil buffer pressure must be higher than the gas pressure. Leakage of oil canbe as high as 8 gallons per day, and the speed is limited to 115 m/s (375 ft/sec).

16.2.7 Dry Running Non-Contacting Face Seals

Dry running non-contacting seals, as shown in Fig. 16.9, have been used to seallarge industrial compressors since the early 1980’s. This type of seal has become

ROTARY COMPRESSOR SEALS 16.7

FIGURE 16.5 Circumferential seal with segmented carbon rings.

FIGURE 16.6 Elastomeric bellows seal (John Crane Inc.).

the most popular way to seal a rotary gas compressor. The success of this sealdepends on the development of a fluid film at the faces. The non-contacting featureand film development is accomplished by incorporating a lift mechanism into theseal faces. Spiral grooves, Fig. 16.10, have proven to be the most efficient andstable way to achieve a non-contacting seal design. As the shaft begins to rotate,gas is compressed within the seal faces and then allowed to expand across the

16.8 CHAPTER SIXTEEN

FIGURE 16.7 Stationary metal bellows seal (John Crane Inc.).

FIGURE 16.8 Mechanical contact seal with oil buffer.

sealing dam. This generates enough opening force to separate the seal faces by afew nanometers during operation. Since there is no frictional contact, wear is elim-inated and seal life is essentially infinite. A dry running non-contacting seal isdesigned to leak. The small amount of flow helps to remove the heat developedfrom constantly shearing the gas at the seal faces. The amount of leakage is sig-nificantly smaller than other types of seals. The effect of seal size and speed onleakage is shown in Fig. 16.11. Pressure and temperature also have an effect onleakage, as illustrated in Fig. 16.12. Leakage from the seal is vented to a vapor

ROTARY COMPRESSOR SEALS 16.9

FIGURE 16.9 Typical tandem dry running non-contacting seal (JohnCrane Inc.).

FIGURE 16.10 Spiral groove seal face.

disposal system when the gas is hazardous or toxic. Seal arrangement is an im-portant part of any dry running non-contacting seal installation. Operating condi-tions such as the type of gas sealed, pressure, temperature, and speed, as well asabrasive contaminants, are considered in the selection of the seal arrangement.Typically when the process fluid is inert or non-toxic, a single seal is selected, Fig.16.13. When the process gas contains abrasives, a steam flush may be used toprovide a clean environment for the seal. Single seals are limited to 400 psi, 260�C,and 152 m/s.

Tandem seals, as shown in Fig. 16.9, are being used on hydrocarbon mixtures.These types of applications are found on pipeline, chemical, and refinery applica-tions. Typically, operating conditions are limited to 1200 psig, 2600C, and 152

16.10 CHAPTER SIXTEEN

FIGURE 16.11 Dry running non-contacting seal performance: effectof seal size and speed on leakage.

FIGURE 16.12 Dry running non-contacting seal performance: effectof pressure and temperature on leakage.

ROTARY COMPRESSOR SEALS 16.11

FIGURE 16.13 Single dry running non-contacting seal (John CraneInc.).

m/s. Here, two seals are facing in the same direction in the seal chamber. Leakagefrom the seal is vented to a vapor disposal system. A typical control system for atandem seal is shown in Fig. 16.14.

Triple tandem seals have been used to seal hydrogen recycle compressors inrefinery service, with pressures to 2000 psi and temperature of 71�C. Shaft sizeand speed are 92 mm in diameter and 10,250 rpm, respectively. This unit wasoperated continuously for 24 months and the user estimates a 1.7 million dollarsper year savings.

In some cases when a vapor disposal system or vapor recovery system cannotbe used, a hazardous or toxic application may require a double seal arrangement,as shown in Fig. 16.15. Here an inert gas is used between the seals. Typically,plant nitrogen may be used. Nitrogen will leak to the process through the inboardand outboard seals. Leakage rates are normally less than 0.028 m3/min. Doubleseals are normally used on services with pressures to 250 psig and temperaturesfrom �60�C to 260�C, and speeds to 152 m/s.

Dry running non-contacting seals offer the user considerable savings over othertypes of sealing systems.

Sealing technology continues to evolve in solving complex problems defined byindustry. The demands for higher operating pressures required the solution of ex-plosive decompression of O-rings, the solution of secondary seal friction, and thedeflection of seal face materials. The result is a high pressure non-contacting gasseal for pressures to 3000 psig and speeds to 180 m/s, as shown in Fig. 16.16.Here, spring energized polymer seals used with the supporting seal structure tocontrol seal deflection, achieved the intended results.

16.12 CHAPTER SIXTEEN

FIGURE 16.14 Typical emissions control system.

FIGURE 16.15 Typical double seal arrangement (John Crane Inc.).

ROTARY COMPRESSOR SEALS 16.13

FIGURE 16.16 Tandem dry running non-contacting high pressure seal (John Crane Inc.).

FIGURE 16.17 Bi-direc-tional grooved seal face (JohnCrane Inc.).

In certain applications, there is a recognized need for the seal to work in thereverse rotation for an extended period. There are two specific circ*mstances thatcan cause a compressor to run in the reverse direction after shutdown.

• A leaky or ‘‘stuck open’’ discharge valve

• A large volume of gas between the compressor and its discharge valve

This has resulted in optimized bi-directional groove profile shown in Fig. 16.17.Even though this design has optimized bi-directional seal performance, the spiralgroove design still provides a superior level of performance across the operatingenvelope.

Dry running non-contacting seals offer the user considerable savings over othertypes of sealing systems through increased mean time between maintenance andimproved equipment reliability.

16.14 CHAPTER SIXTEEN

16.3 FURTHER READING

1. Netzel, J. P., High Performance Gas Compressor Seals, 11th Internationa Conference onFluid Sealing, BHRA Cranfield Bedford, UK (1987).

2. Shah, P, Dry Gas Compressor Seals, 17th Turbomachinery Symposim, TurbomachineryLaboratory, Department of Mechanical Engineering, Texas A&M University, College Sta-tion, Texas, November 1988.

3. Carter, D. R., Application of Dry Gas Seals on a High Pressure Hydrogen Recycle Com-pressor, 17th Turbomachinery Symposium, Turbomachinery Laboratory, Department ofMechanical Engineering, Texas A&M University, College Station, Texas, November 1988.

4. Atkins, K. E., and R. X. Perez, Influence of Gas Seals on Rotor Stability of a High SpeedHydrogen Recycle Compressor, 17th Turbomachinery Symposiu, Turbomachinery Labo-ratory, Department of Mechanical Engineering, Texas A&M University, College Station,Texas, November 1988.

5. Pecht, G. G., and D. Carter, System Design and Performance of a Spiral Groove GasSeal for Hydrogen Service, 44th Annual Meeting, Society of Tribologists and LubricationEngineers, Atlanta, Georgia, May 1989.

6. Dugar Jr., J. R., B. X. Tran, and J. F. Southcott, Adaptation of a Propylene RefrigerationCompressor with Dry Gas Seals, 20th Turbomachinery Laboratory, Department of Me-chanical Engineering, Texas A&M University, College Station, Texas, September 1991.

7. Morris, J. R., C. G. Stroh, J. F. Southcott, Retrofit of a Steam Turbine with Dry GasSeals, 22nd Turbomachinery Symposium, Turbomachinery Laboratory, Department ofMechanical Engineering, Texas A&M University, College Station, Texas, September1993.

8. Mayeaux, P. T. and P. L. Feltman Jr., Design Improvements Enhance Dry Gas Seal’sAbility to Handle Reverse Pressurization, 25th Turbomachinery Laboratory, Departmentof Mechanical Engineering, Texas A&M University, College Station, Texas, September1996.

17.1

CHAPTER 17RECIPROCATING COMPRESSORSEALING

Paul HanlonC. Lee Cook, A Dover Resources Company

The first seals for reciprocating rods or pistons were of plastic-like materials, forcedto conform to the shape of the seal cavity or stuffing box. This was replaced by‘‘V’’ rings, ‘‘U’’ rings or similar shapes when it was realized that gas pressurecould help supply the force necessary to cause soft materials to seal. This type ofseal is still used in many small compressors.

As machines were built for higher temperatures, pressures and speeds, it broughtout the need for stronger, more wear-resistant materials, and the logical choice wasmetal. Soft ones, such as babbitts, were chosen and used in configurations which,like the plastic materials, were forced to yield or deform to effect a seal. Thesewere still, essentially, slow speed, low-pressure types of seals. In general, theyrequired a large spring or force from the gland to push even the relatively softmetals down into contact with the rod or out against the cylinder.

Following this were pressure-actuated segmental or cut rings of harder metals,such as bronze, cast iron, or hard plastics, which could be made with narrow contactat the rod or cylinder and thus generate less total load and frictional heat. Thesealso ‘‘float’’ with the rod or piston accommodating considerable misalignment orlateral motion.

17.1 COMPRESSOR PACKING

A packing is a seal around a shaft passing through a cylinder head. It consists ofone or more rings contained within a case that is typically bolted to that head.Packing may be as basic as one ring in a case, or it may be an assembly consistingof a number of different type rings in a case that might have provision for lubri-cation, venting, purging, cooling, static sealing, temperature and pressure measure-ment, leakage measurement, and rod position detector.

17.2 CHAPTER SEVENTEEN

FIGURE 17.1 Packing nomenclature.

A typical compressor packing consists of a series of seal rings in which eachring is meant to stop or restrict flow of gas to atmosphere or out into the distancepiece. The rings are held in separate grooves or ‘‘cups’’ within a packing case.Each ring seals against the piston rod and also against the face of the packing cupat a right angle to the rod axis. Rings are free to move laterally along with the rod,and free to ‘‘float’’ within the grooves.

A basic packing arrangement consists of: 1) a pressure breaker that functions asa flow restricter (rather than a true sealing ring); 2) several seal rings that are meantto stop flow or leakage into the vent; and 3) a vent control ring that prevents gasfrom leaking into the distance piece from the vent.

Nomenclature for compressor and packing is given in Fig. 17.1. The packingillustration shows some elements that are not in all packing. Where the packingand other seals are located in a compressor cylinder is shown in Fig. 17.2.

In addition to the cylinder pressure packing is a wiper packing, which preventsoil from escaping along the rod out of the crankcase, and then a partition packing,in double distance piece machines, to prevent leakage between the distance pieces.The partition and wiper packing are under light pressure differential, but in com-pressors where very low loss of gas to atmosphere is required, these packings mustprovide a tight seal.

A packing assembly which incorporates wiper and distance piece all in thepressure packing is shown in Fig. 17.3. This type of packing allows for a verycompact arrangement of the cylinder, but with somewhat greater opportunity forgas leakage into the crankcase, or crankcase oil leakage into the packing case. Itwould be most suited to lubricated or possible semi-lubricated cylinders.

RECIPROCATING COMPRESSOR SEALING 17.3

FIGURE 17.2 Seals in a typical compressor cylinder with double distancepiece.

FIGURE 17.3 Compact packing incorporating distance piece and wiper into thecylinder packing case.

Even though seal rings do not provide a direct leak path, a vent to carry leakageaway from the packing is necessary in most applications, since slight imperfectionsin the rings, or misalignment of ring, case, or shaft mating faces may allow somesmall volume of gas to blow-by.

Gas flow past a series of rings creates varying pressure differentials across in-dividual rings, but because of rapid rise and fall of pressure within the compressorcylinder and because of low flow by the best sealing rings, this ‘‘labyrinth’’ effectin packing rings is usually insignificant.

Pressure drop is highest across rings nearest the pressure when the set is new.As packing wears, the downstream rings see more and more pressure drop as theleak paths of rings increase with age. A ‘‘reverse’’ drop exists across some rings

17.4 CHAPTER SEVENTEEN

FIGURE 17.4 Plot of instantaneous pressures within a pack-ing case.

during the suction stroke; that is, gas will flow back out of the case toward thecylinder during that portion of the stroke. All this is illustrated in the ‘‘computergenerated’’ curves shown in Fig. 17.4.

Pressure drop through a series of rings is highest across the one ring that formsthe best seal. In packing sets containing well-made rings which fit the rod andgrooves properly, the ring nearest the cylinder will, initially, carry almost the fullpressure drop. As this ring wears, or changes for any reason, the load will shift toone of the other rings, usually the next ring in line. The pressure drop may distributeacross a series of rings in almost any manner. The individual rings in a packingset wear, essentially, one-at-a-time, so the number of rings in the set influencespacking life but has little effect on leakage.

17.2 BREAKER RINGS

Breaker rings, the simplest form of packing rings, are designed to restrict or controlflow rather than effect a tight seal. In type P, the flow controlling orifice is the gap

RECIPROCATING COMPRESSOR SEALING 17.5

FIGURE 17.5 Type P and PA packing rings.

that is formed at the segment ends. In a type PA breaker, the orifice is formed bythe clearance between the ring bore and rod. Type P and PA are illustrated in Fig.17.5. The performance of both rings is very similar. However, a type PA breakerprovides lower rod loading than a P, at the expense of a more difficult to controlorifice area.

The most important function of breakers is to retard rapid expansion of gas fromwithin the packing case back into the cylinder during the suction stroke. On theintake portion of the stroke, gas contained within the packing case tends to reversedirection and flow toward the cylinder where pressure is dropping rapidly to suctionpressure levels. Without some restriction to this flow, an ‘‘exploding’’ action of therings may occur causing premature ring failure and damage.

Pressure breakers are not required in all packing. They are generally not neededat pressures below 300 psi and are not required when the seal rings themselves actto restrict backflow.

Pressure breakers may be manufactured from almost any material, but thosematerials with a low thermal coefficient of expansion and high stiffness are pref-erable for a stable orifice area. Metal is usually superior to plastic in this respect;however, breakers can be made satisfactorily from some of the high strength plas-tics.

17.3 PACKING RING TYPE BT

The BT packing ring (Fig. 17.6) is a true sealing ring which is made up of aradially cut ring (facing the high pressure side) and a second, butt / tangent cut ring.The individual rings are doweled together so that the inner butt cuts of the tangen-

17.6 CHAPTER SEVENTEEN

FIGURE 17.6 Type BT packing ring.

tially cut ring are offset, or staggered, between the radial cuts of the first ring inthe pair. In this manner, gas passage by or through the ring is prevented.

In order for these rings to operate satisfactorily, it is necessary that both fit therod perfectly. They must contact each other at their mating faces and the tangentring must lie flat against the groove side face.

In addition to this, all sealing edges at the bore must be sharp and square. Ifthese edges are beveled or rounded, they form a path for gas flow from the radialcut in the first ring to the radial portion of the cut in the tangent ring. If thetangential edges are not square, they form a passage from the outside toward theradial cut at the bore. All other edges are generally given small bevels to assistlubrication between the contact faces. Under ordinary circ*mstances, lubricationserves to help the seal function because it fills up minute crevices. This type ofring is single acting, or directional, in that it seals pressure from one side only.

17.4 PACKING RING TYPE BD

The BD packing ring (Fig. 17.7) is double acting, meaning it will seal pressurefrom either direction. It consists of two butt / tangent cut rings doweled so the radialportion of the cuts are staggered, blocking any flow path for leakage. All featuresimportant for establishing a tight seal with the BT ring, such as square sealingedges and proper face contact between rings and the rod and/or cup, are alsoimportant for sealing with the BD ring.

17.5 COMMON PACKING RING CHARACTERISTICS

The P, BT, and BD are the most common types of packing ring in general use.Numerous variations of these three exist, but sealing principles involved are gen-

RECIPROCATING COMPRESSOR SEALING 17.7

FIGURE 17.7 Type BD packing ring.

erally the same and the conditions affecting proper operation are common to alltypes.

Packing rings are made in segments for two reasons: 1) for installation over therod; and 2) to allow free radial movement down against the rod. Free radial move-ment allows for slight size variations and also provides a means to accommodatering wear. Both spring and gas pressure loading cause rings to contract or moveradially inward toward the rod.

All types of packing rings are manufactured with an initial end clearance ofsufficient size that no adjustment is required throughout their useful life. Whenthey have worn to a point where the ends butt, they are normally discarded. Inmost rings, end clearance could be adjusted to maintain the proper opening. How-ever, it is seldom practical to rework such a ring after it has operated in a buttedcondition. The bore will be worn out of round, and merely recreating end clearancewill not correct poor rod contact.

17.6 PACKING RING MATERIALS

Lubrication and gas pressure are two factors that influence selection of ring ma-terial. Packing may operate at conditions that vary from full or normal lubricationall the way to dry or nonlube service. The common material used in packing fallinto two categories:

1. Metallic—(typically bronze, cast iron, or to a diminishing extent, babbitt)which requires some lubrication, but may be used at very high pressure

2. Nonmetallic—(typically carbon-graphite, TFE (polytetrafluoroethylene), or oneof the other plastics). The important advantage of nonmetallics is their abilityto run in poorly lubricated applications.

17.8 CHAPTER SEVENTEEN

Carbon-graphite and TFE blends work well in the complete absence of lubri-cation, but are somewhat limited insofar as the pressure at which they can be useddue to their low strength (compared to metallics). Filled TFE blends are good toapproximately 800 psi; but, with the addition of a backup, or anti-extrusion ring,can be used at much higher pressures. Carbon-graphites are moderately strong, butsomewhat brittle, and therefore limited to approximately 1500 psi.

Plastic is the preferred material for tangent cut rings which require a high degreeof conformability. All rings must conform at their joints and around the rod inorder to establish a good seal, but some types will begin to leak slightly as theywear or as they change size due to thermal expansion. A good ring material is onethat is not excessively stiff relative to the pressure acting on it.

Nonmetallic materials, including the new ‘‘high performance’’ plastics and theirblends with fillers, are the most commonly used materials in the manufacture ofmodern packing rings. Metallics are principally useful at very high pressure, or asanti-extrusion rings, where strength or rigidity is an important requirement.

17.7 LUBRICATED, SEMILUBRICATED AND

NONLUBRICATED PACKING

Packing rings made with TFE filled or blended with other materials (includingother plastics) can now be used in many applications including those with less thanfull lubrication. By definition, lubricated packing receives just the amount of lu-bricant required for long life. Semilubricated packing is that which receives eitherreduced lubrication through a lubricator, or, in the event there is a short distancepiece, minimal lubricant carry-over from the crankcase. Nonlubricated packing ispacking installed in systems where double distance pieces, rod oil slingers, or someother means is used to prevent any lubrication from reaching the rod rings.

TFE is the material used most often for packing installed under conditions wherelubrication is impaired or less than normal. Generally, this would be in the presenceof corrosives, diluting liquids, or high temperatures. The sealing principles of allTFE ring types are virtually the same as those previously described. Due to theirinherent flexibility, TFE rings have the added advantage of immediate sealing with-out requiring break-in.

Ring types TR and BTR (Fig. 17.8) are designs that include nonmetallic ringsplus a rigid back-up ring. The back-up ring is made slightly larger than the rod. Ithas butted ends and does not grip (or grips lightly) the rod under pressure loading.Its function is to prevent extrusion of the softer nonmetallic ring and also, undersome conditions, aid in conducting heat away from the rod surface through thelight contact. Usually back-up rings are made of metal, but they can also be man-ufactured from the stronger plastics.

At pressures above 800 psi, type TR rings are the preferred alternative to thestandard BT sealing ring. To obtain a better seal where there is insufficient pressure

RECIPROCATING COMPRESSOR SEALING 17.9

FIGURE 17.8 Packing rings (various types).

to properly actuate the TR ring, type BTR rings may be used. The BTR is limitedto a pressure of about 2500 psi. Above this pressure, deformation or extrusion mayoccur into the gap of the butt / tangent ring.

To overcome sealing problems with the TR and deformation of the BTR, atangent cut may be combined with an upstream radial cut ring. This is the type C(Fig. 17.8) or when a backup is added, the type CR. These styles are most usefulwhen applied above 2500 psi.

The basic TFE ring set for pressures below 800 psi consists of BT rings to sealcylinder pressure with a double-acting BD ring downstream of the vent. This ar-rangement is the same for nonlubricated or fully lubricated cases. When the pres-sure exceeds 800 psi and the application is full or semi-lubricated, the arrangementshould be as follows:

1. One breaker ring type P

2. BTR or TR rings in intermediate grooves

3. A BD ring beyond the atmospheric vent

17.10 CHAPTER SEVENTEEN

Unless some special condition exists, the P and BD rings should be metal, and theBTR or TR rings a combination of metal-TFE. For best sealing of vent gas, theBD ring should be TFE.

The type P ring in this case will have an added function. Along with preventingbackflow, garter spring breakage, etc., the fact that it is in contact with the rodaround the entire circumference (without heavy pressure loading) allows it to func-tion as a means of conducting heat. BD rings of metal may serve the same purpose.

17.8 PACKING RING TYPE TU

The TU ring is essentially the same as the TR, except the radially cut ring in theTR has been replaced with an uncut ring, which can be either plastic or metal.

When stiffness of the U ring is low compared to the pressure acting against thering, it will collapse inwardly, maintaining a seal even as it wears. With properchoice of material in the TU ring, it can be made to seal low pressure (suction)with the tangentially cut ring, and high pressure (discharge) with the uncut ring.The TR ring can function in the same manner, but lacks the almost perfect sealcharacteristics of the uncut ring in the TU.

An added benefit with an uncut ring is reduced contact pressure between thering bore and the rod. Compressive stress in the ring acts counter to gas pressureagainst the ring outside diameter, so there is lower ring-to-rod loading than therewould be with a tangentially cut ring.

To prevent extrusion of the soft plastic sometimes used in the U ring, an addi-tional back-up ring can be added to form the TUU style (Fig. 17.8). Typically thesecond U ring would be metal, or a very rigid plastic.

With proper choice of materials for the three rings in the TUU, each ring canbe made to seal only over a particular pressure range. Thus wear and heat gener-ation can be divided over the individual rings to give better performance and longerlife.

The lower leakage and reduced wear that are advantages of the TU or TUU ringare somewhat offset by difficulty of installation. The rings must be installed overthe rod end, and with an entering sleeve that is no larger than rod diameter asshown in Fig. 17.9.

17.9 THERMAL EFFECTS

When rings expand circumferentially due to temperature increase, there are usuallyleak paths created at the joints. The effect is similar whether this occurs in a truetangent-cut T ring such as in the TR, or in a butt / tangent ring such as in the BT.

A T ring is less likely to leak when its joint is covered by another upstreamring. This is the construction used in the Type C.

Contraction due to lower temperature rarely occurs, but if it does, it is muchlike having an undersized ring or oversized rod.

RECIPROCATING COMPRESSOR SEALING 17.11

FIGURE 17.9 Installation of compressor rod through packing rings.

All the high temperature effects can be minimized by adding an upstream ra-dially cut ring to block leak paths through the T ring. This addition is found in theC or CR ring arrangement. These ring styles are free of unsupported areas whereextrusion can occur, so they’re suitable for higher pressures than a BT or BTR.

One method to minimize the tendency toward breakage and lack of conforma-bility of both butt-tangent and true tangent, or T rings, is to use ‘‘bridge’’ joints asillustrated in WB and E style (Fig. 17.8). The shorter, sturdier segments make theWB style suitable for service in situations where the elevated temperature andpressure may cause other style of rings to leak or break. Handling and installationof WB or E rings may present problems due to the greater number of segmentsinvolved. As with other style of rings, the E and WB may be used with back-uprings to prevent extrusion along the rod.

17.10 UNDERSIZED RODS

If a rod is undersize, but true in circularity and without taper, most rings still forman effective seal because bore contact will be in the center of each segment and atthis point, the cut in each ring is overlapped by its mate. There is normally not aproblem if undersize does not exceed .002 inch per inch of rod diameter. When arod is undersized, some additional time is required for break-in before a packingwill give the best seal.

17.11 OVERSIZED RODS

When packing rings have a somewhat smaller bore than rod diameter, segmentstouch only at each end, leaving the center away from the rod. This is directly in

17.12 CHAPTER SEVENTEEN

FIGURE 17.10 Effect of rod misalignment and taper onleakage.

line with the cut, or joint, of the mating ring so there is a passage for gas flowalong this line. This condition, if not too severe, will also be corrected by wear-in.

One problem that may occur with either an undersized or oversized rod is thatlubrication may be blown off the rubbing surfaces by the passage of gas. Thesubsequent ‘‘dry contact’’ may result in high friction, high temperature or rapidwear.

17.12 TAPERED RODS

In the presence of lubricating films, which help fill (or block) very small leak paths,a packing can function adequately with some slight rod taper. Generally, taper isfound at one, or both, ends of the ring travel area, the rest of which is relativelystraight. The effect of the rod passing through the packing ring from the taperedto the straight portion and back, is wear at ring edges. This is due to the ringbearing directly on one edge while over the tapered section of rod and on the otherwhile over the straight section. This dual edge wear leaves a gas passage along thebore from one radial cut to the other. The effect of taper or misalignment of therod surface on leakage is illustrated in Fig. 17.10.

Tapered rods also cause cyclic flexing of garter springs. If this flexing is exces-sive, it can lead to spring breakage.

RECIPROCATING COMPRESSOR SEALING 17.13

17.13 PACKING LEAKAGE

If the complete packing, that is case plus rings, is considered there are three ele-ments past which leakage can occur: gasket, cup faces and rings.

Conventional gaskets, which are generally soft metal, such as copper, aluminum,or pure iron, will basically give zero leakage if proper dimensions and smoothsurfaces are applied. However, there have been some improvements in this recentlyusing spiral wound gaskets and in a few instances, o-rings. In general though, toaccommodate misalignment and discontinuities in the surface at the bottom of thestuffing box, the solid metallic gasket has been satisfactory.

The second element, case faces, can be made 100% leak free by the use of eithera sealant or an o-ring applied between the mating surfaces. With this, and withproper uniform torque applied to the flange bolting, cup faces can be brought to apoint where essentially no flow occurs between them.

The third element, rings, are probably what receive the most attention whentrying to control leakage. Rod rings, since they do leak slightly, can act as a lab-yrinth or more likely as a labyrinth through which most of the pressure drop occursacross just a few rings. Changes in the rings due to pressure and temperature, andalso the cyclic nature of the pressure, make it very likely the pressure drop willoccur, for the most part, across only one ring. The pressure level, as it typicallymight occur across each ring in a 5-ring set, would be as illustrated in Fig. 17.4.

This was calculated on the basis of small orifices in new rings, larger leak pathsfor used rings, and equal volume between the rings. Pressures have been measuredin actual packings and it has been determined that pressure distribution can occurin almost any fashion, but in general, will agree with what is illustrated by thesecurves. Efforts could then logically be directed at reducing leakage by 1) increasingthe number of rings in the case or 2) designing and manufacturing individual ringsthat present the smallest orifice size.

Packings operating satisfactorily will leak at an average rate somewhere betweenzero and .2 scfm (standard cubic feet per minute). In general, packings that areconsidered to be unsatisfactory will be above .5 scfm. Current rings in use are,theoretically, very close to zero leak seals. The leakage that does occur by them,when they are properly manufactured and applied, by actual measurement falls inthat zero to .2 scfm range, with the average generally about .1 scfm.

Most of the leakage that occurs by rings, flows through the joints due to ‘‘misfit’’within the ring itself, or past the side or bore of the ring due to misalignment atthese surfaces. Leakage past the ring due to less than perfect surface finish doesalso occur, but this is a minor leak path, except in those instances where the ringscause an increase in roughness or finish of the mating surface. No doubt someleakage also takes place due to manufacturing errors or a lack of quality. Theprimary reasons for leakage by rings usually is 1) misalignment between packingcase and rod; and 2) temperature changes that distort the relative position betweenthe ring and the rod, the ring and the case, or the ring segments themselves.

Misalignment, or as it is sometimes described, ‘‘run-out,’’ between the rod andcase, is generally measured by slowly moving the rod back and forth through its

17.14 CHAPTER SEVENTEEN

stroke and measuring lateral movement with an indicator. This can also be doneelectronically when the machine is running by the use of an analyzer and trans-ducers to instantaneously pick up the rod position. Packing rings are able to ac-commodate lateral motion in that they can float within the case and, in general,exhibit little leakage as a result of this motion. However, angular motion (or themotion caused by a bent or temperature deflected rod) is detrimental and causesthe sealing surfaces to open up leak paths as in Fig. 17.10.

There is one other type of misalignment that is important and that is the angularrelation between case and rod. Usually this would be checked by measuring thesquareness between the face of the flange and the rod. Correction to bring the caseinto alignment would be made by proper torquing of the flange bolting.

A rise in temperature of the rings, which is usually the result of frictional heat,can cause the rings to lift away at the bore or can cause separation at tangent cuts.High, uneven heating of the rod can also cause ‘‘bowing’’ of the rod, which willhave the same affect as misalignment. Typically, the way high temperature resultsin leakage at the cuts and bore is shown in Fig. 17.11.

High temperature is probably the most destructive condition that can occur in apacking. Aside from the distortion that it causes, it may also lead to breakdown ofthe mating faces between the ring and rod, or the ring and case. All of these thingsultimately lead to leakage and short packing life.

17.14 RING LEAKAGE AT LOW PRESSURE

Relative to the potential sealing problems that occur in higher pressure compres-sors, the sealing problems in low pressure (50 psi or less) compressors would seeminsignificant. Wear and packing life may not be major problems, however, obtaininga good seal between packing ring and rod, and especially between the ring andcup face, may be difficult.

There are two reasons for this. The first is because of the relative stiffness ofconventional seal rings. As the pressure differential increases across a ring, someof the leak paths will be decreased as the ring deforms. Using materials with lowmodulus of elasticity, such as plastics, will improve the seal. However, even plasticsare relatively rigid when sealing against very low pressure, such as when suctionis close to atmospheric pressure.

The second reason for leakage at low pressure is loss of ring contact with theflat cup face. The pressure and frictional forces acting on a ring is as illustrated inFig. 17.12. Frictional forces acting in a direction away from the cup face may causethe rod to drag a packing ring away from the cup. When this occurs depends onring size, coefficient of friction, and the pressure level. For ‘‘normal’’ size rings,which are well lubricated, approximately 50 psi differential pressure is required toovercome the effect of friction, and hold them against the cup.

In a compressor, pressure at the packing vent is normally well under 50 psi, sogood practice dictates the use of a double-acting ring to minimize leakage fromthe vent into the distance piece. This ring functions by forming a reasonable seal

RECIPROCATING COMPRESSOR SEALING 17.15

FIGURE 17.11 Leak paths in packing rings.

FIGURE 17.12 Pressure and friction forces acting on a packing ring.

17.16 CHAPTER SEVENTEEN

FIGURE 17.13 Side loaded packing rings.

regardless of which face it rests against. However, there is an instant during strokereversal when even the double-acting ring will leak, and in order to improve onthis it is necessary to use rings which are spring loaded in the axial direction, asillustrated in Fig. 17.13.

The advantage of ring types AT or WAT is the almost equal axial and radialload provided by the spring. If these loads are not equal, or very nearly equal, thering can either ‘‘hang’’ in the groove and thus leak, or be pulled from one face tothe other by the frictional force.

17.15 PROBLEMS ASSOCIATED WITH LOW SUCTION

PRESSURE

In a compressor handling gas which would be undesirable to contaminate with air,and in which suction pressure is below atmospheric pressure (pressure within thecylinder falls to vacuum), air may pass back through the packing and into thecylinder. Either double-acting rings or those spring loaded against the cup face will

RECIPROCATING COMPRESSOR SEALING 17.17

reduce leakage, but neither will eliminate it completely due to minor leak paths atring surfaces and insufficient gas pressure to make the ring conform.

One solution is to introduce gas at low pressure at the vent. Gas that enters thecylinder will be drawn from this rather than air from the atmosphere. Gas pressurein the vent need be only a few psi above atmospheric pressure.

Further loss of vent gas to the distance piece can be minimized with doublevents, that is, a pressured vent, plus a vent to atmosphere with a ring between them.This double vent arrangement will control gas leakage into the distance piece to atleast the same degree as with a single atmospheric vent.

When it is impractical to use a source of gas slightly above suction pressure,then gas at full discharge pressure may be used. This will increase leakage bothtoward the cylinder as well as out the atmospheric vent. It also puts a higherpressure load on the ring between the vent and the distance piece, or between thetwo vents, and may cause more frictional heat. This is the result of two rings loadedat high pressure, when normally only one ring would carry a high differential.

Everything discussed to this point assumes the gas used to exclude air was thesame as that going through the compressor cylinder. There are circ*mstances whereit is more practical to use a gas other than the process gas being compressed. Theusual choice of a vent gas is an inert gas such as nitrogen. If nitrogen is used andpressure at the vent is less than discharge pressure, then gas in the vent or thedistance piece will probably be a mixture of inert gas and process gas. Gas dis-charged from the compressor cylinder may also contain a small quantity of theinert gas.

17.16 PROBLEMS ASSOCIATED WITH LOW LEAKAGE

REQUIREMENTS

In addition to low suction compressors, where entry of air should be avoided, thereare a number of applications where any loss of gas to the atmosphere must beprevented. This is true for toxic or dangerous gases, very expensive gases, or inprocesses where it is desirable to maintain a constant quantity of gas in the system,such as within a refrigeration cycle.

There are several methods that will accomplish the goal of minimizing leakage.One way is to use a double-vented packing, with buffering gas introduced at con-stant pressure to the outer vent instead of the inner vent. The ‘‘buffering’’ gas isusually inert or at least can be tolerated as emission. Leakage from the main sealingrings flows out the inner vent in addition to some flow of buffering gas. The lossto atmosphere of the gas being compressed is almost zero and the mixture of thetwo gases from the inner vent can be recovered.

Another way to prevent leakage is much like the method used to prevent airfrom entering the cylinder during vacuum conditions. Buffering gas is introducedthrough the packing vent at a pressure which exceeds the compressor dischargepressure. The result is a gas mixture in the cylinder as opposed to one in therecovery vent. Depending on buffering pressure, one or more rings may be used

17.18 CHAPTER SEVENTEEN

between the buffer inlet and the distance piece. A second vent may be used torecover buffer gas or minimize leakage into the distance piece.

17.17 EFFECT OF RING TYPE ON LEAKAGE CONTROL

In each of the low pressure vent arrangements previously described, double-acting(BD) rings are normally used. When the requirements call for very low leakage,one of the axially loaded type of rings would normally be substituted. Axial loadedrings may be used for control of gas flow toward the cylinder, or into the vent ordistance piece, as well.

When confronted with low pressures, another possible control method is to use‘‘soft’’ packing or a lip seal. The result will be a tighter seal than with conventionalrings. However, packing life may be somewhat shorter due to a limited resistanceto, and compensation for, wear. In many reciprocating machines, lubrication ismarginal, and when this is coupled with significant rod ‘‘float,’’ there may be rapidwear on soft plastic seals. This soft seal arrangement, though not 100% effective,might be chosen for gases such as ammonia, propane, or methane. In general, theescape to atmosphere of these gases may be tolerated to a greater degree comparedto gases such as vinyl chloride, chlorine, or hydrogen sulfide.

The quantity of leakage with any of the ring types or with lip seals can only beestimated based on experience and empirical data. Leakage paths through packingrings occur not by design, but due to tolerances, alignment, or various other char-acteristics of the compressor and ring itself. Although it would appear that flowrate would be directly related to pressure differential, this is not the case as ringsoften conform and effect a better seal at high pressure.

Under normal conditions and with most gases, leakage from the cylinder or outany of the vents will be on the order of 0.1 scfm. As factors which cause leakageprogressively get worse (misalignment, dirt, poor finishes, poor lubrication, etc.),or with lighter gases such as hydrogen or helium, leakage rates can be expected toincrease by two to four times. This is just a guide based on measured flow ratesat various conditions. If a more accurate flow rate is required, it must be obtainedby test and measurement.

17.18 LEAKAGE CONTROL WITH DISTANCE PIECE

VENTING

Another method to prevent both air entry into the cylinder and/or gas leakage isto close, but vent, the distance piece rather than the packing case. To accomplishthis, the conventional packing arrangement, less the atmospheric vent, may be used.It is also necessary to provide a positive seal at the partition packing in doubledistance piece machines, or for the wiper packing in a single distance piece ma-

RECIPROCATING COMPRESSOR SEALING 17.19

FIGURE 17.14 Distance piece venting to control leakage to atmosphere.

chine. To reduce air contamination, the distance piece vent is used to supply gas,whereas when it is required to control leakage, the distance piece vent will be usedto recover gas. This type of buffering for both single and double distance piecesis illustrated in Fig. 17.14.

In either case, one type of partition or wiper packing seal arrangement consistsof side-loaded rings between which a buffering liquid (oil) or, more commonly,

17.20 CHAPTER SEVENTEEN

gas, is injected. When oil is used, it is generally taken from the crankcase. Part ofthe leakage past this seal goes back into the crankcase, while part must be recoveredfrom the distance piece to also be re-piped to the crankcase. In the event gas isused, it must be one that is tolerated in the crankcase and suitable for mixing withthe recovered gas. When two distance pieces are used, the second one can bepressurized to serve as the buffer.

In nearly every instance where gas is used in the distance piece to controlleakage, the process pressure is very low which usually requires the use of axiallyloaded rings. The basic principle remains the same in all applications: the preven-tion of gas flow in one direction along some particular path is accomplished byestablishing pressure conditions that cause gas to flow in the opposite directionalong that same path.

17.19 STATIC COMPRESSOR SEALING

In some applications, after a compressor stops, it is desirable to maintain gas, underpressure, within the cylinder. Rod packing will generally leak slightly more whenrod motion is stopped as compared to when it is moving. This is due to a numberof factors: loss of oil which filled the leak paths; changes in the ring shape as thering cools; and changes in rod alignment as the temperature changes.

The cylinder may be sealed by essentially an uncut, conformable ring which isforced against the rod by a piston that encircles the rod. Actuation occurs whenpressurized gas is admitted to the piston. The piston, when actuated, wedges theseal ring inward against the rod. The shape of the seal is such that pressure fromwithin the cylinder will cause the seal to move away from the rod when actuatingpressure is lowered. A typical packing case containing this static seal is illustratedin Fig. 17.15. The pressure required to actuate the seal is one-half, up to fullcylinder pressure.

After the compressor has stopped, a valve would be opened, admitting pressur-ized gas behind the internal piston. Pressure must be maintained on the piston foras long as it is desirable to seal the cylinder. De-actuation would take place whenpressure on the piston is reduced, allowing the springs to push the piston backaway from the seal. The seal itself would then lift from the rod surface. A vent toatmosphere (or some other low pressure area) must be located downstream of theseal in order for seal actuation to occur or for seal release. This can be adaptedfor pressures up to approximately 2000 psi. The seal itself is made of relativelysoft synthetic rubber for pressures up to 700 psi or TFE for pressures above that.

17.20 COMPRESSOR BARRIER FLUID SYSTEMS FOR

FUGITIVE EMISSIONS CONTROL

Although far down the list of offenders for total air pollution emissions, compres-sors have higher leak rates than most other industrial equipment. There is no federal

RECIPROCATING COMPRESSOR SEALING 17.21

FIGURE 17.15 Static seal arrangement in a packing case.

regulatory limit for compressor leakage. It is indirectly established by the limit onthe allowable concentration of VOC (volatile organic compounds) measured nearthe leak source.

Federal regulations consider 500 ppm (parts per million) to be ‘‘no detectableemissions.’’ The regulations require that any compressor not in compliance withthat emission level must have a barrier fluid (gas or liquid) system installed on itsseal.

A ‘‘barrier’’ system is one in which a non-VOC liquid, or gas, is forced to flowinto the seal in a direction opposite to that of the leakage. The barrier fluid or gasblocks the escape of leakage to atmosphere from the compressor seal or packing.The system can be installed in one of two ways:

1. A fluid, usually inert, is injected to form a barrier seal between the process gas,and atmosphere. The fluid pressure must be maintained slightly above the pres-sure upstream of the seal.

2. More commonly, a barrier gas is applied between a set of ‘‘barrier seals’’,usually WAT or AL rings as illustrated in Fig. 17.16. The barrier gas is held ata pressure exceeding the pressure in the vent which carries leakage away fromthe compressor seal.

On reciprocating equipment the motion of the rod will carry fluid, usually oil,in the form of a thin film under the seal face and out to atmosphere where emissionsof gas carried in the oil may be released. The oil film on the rod surface absorbsgas while in the cylinder due to the relatively high gas pressure, and then releasesthis gas to atmosphere when the rod moves out of the packing. On non-lube ap-

17.22 CHAPTER SEVENTEEN

FIGURE 17.16 Typical purged packing.

plications, gas molecules can be carried out of the packing in the rod surfaceirregularities.

In either case, a small quantity of gas may escape the barrier seal and becomefugitive emissions outside the packing flange. These may measure as much as 200ppm, but generally are much lower. Gas transported by the rod surface becomesimportant only when allowable emissions approach zero.

17.21 WIPER PACKING

In addition to wiping oil from the rod surface and returning it through a drain backto the crankcase, wiper packing also has a sealing function. Pressure pulses fromthe crosshead, acting as a piston, may cause a ‘‘breathing’’ action through the wiperthat will cause it to leak oil over into the distance piece. There can also be leakageof gas from the distance piece into the crankcase. The seal rings, as indicated inFig. 17.17, must minimize both these leakages.

The seal and wiping function can be combined into one groove if it is necessaryto seal only the crosshead pressure pulse. This single groove would normally con-tain a butt tangent cut ring paired with two wiper rings. Compared to the threewiper ring combination, this ring sacrifices some ability to scrape oil effectivelyfrom the rod, but it is sufficient for slow speed compressors.

To wipe oil from the rod surface requires an apparent contact pressure betweenring and rod of about 50 psi (controlled by the garter spring). Lower pressure tendsto leave a thicker film, while high pressure may allow rapid wear of ring edge orrod surface. Ring to rod fit and contact is the most important factor in wiper packingperformance.

RECIPROCATING COMPRESSOR SEALING 17.23

FIGURE 17.17 Typical wiper packing arrangement.

From a wiping standpoint, metal or hard plastic works best for the wiper ring.However, seal rings, if made of a softer, more conformable plastic (typically filledTFE), offer the best performance from a wear, friction, and sealing standpoint.

The wiper packing case should have a drain(s) shielded from oil spray or splashthat results from crosshead motion. The force of this oil thrown up by the crossheadcan, in some instances, block free drainage away from the wiper rings. Establishinggood open drains as well as proper ring/rod contact becomes more important onthe smaller, higher speed, compressors.

17.22 HIGH PRESSURE (HYPER) PACKINGS

‘‘Hyper’’ is generally taken to mean over 10,000 psi. (Compressor discharge pres-sure might go above 100,000 psi.) At these pressure levels, fluids are usually actingvery much like liquids in that compressibility is low. The type of rings used to sealthese pressures are similar to those used in lower pressure compressors, but ringdesigns and materials must be selected to withstand high ‘‘compressive’’ cyclicpressures.

The problems (wear, friction and heat) caused by high contact pressure betweenring and plunger are normally overcome by using ring sets that act partly as alabyrinth, and thus spread the pressure drop across several rings. Life of hyperpackings is increased also by high lubrication rates plus, in some cases, coolant(oil) flow across the rod downstream of the packing.

The other principle problem in hyper packings is the containing of very highcyclic pressure within the case, which is essentially a thick-walled pressure vessel.Particular attention has to be paid to stress concentrations, such as holes or notches,

17.24 CHAPTER SEVENTEEN

FIGURE 17.18 High pressure packing with compounded packing cups and oil circulatingaround plunger and case.

FIGURE 17.19 High pressure packing with discharge pressure surrounding thecase.

that might raise stress beyond acceptable levels. Compounding of cups, autofret-taging, or pressure loading the outside of the case are typical ways to ensure longlife of the case parts. Typical high pressure packing is shown in Figs. 17.18 and17.19.

17.23 COMPRESSOR PISTON RINGS

Although sealing principles for rings on the piston are the same as those in thepacking, their construction is somewhat different. In normal compressors, the re-quirement for sealing at the piston is not as stringent as it is in the packing. Infact, there is some reduction in wear if piston rings do leak slightly and thus

RECIPROCATING COMPRESSOR SEALING 17.25

FIGURE 17.20 Piston ring types.

distribute the pressure drop over more than one ring. The predominant type of jointfor double-acting cylinders is the angle, or butt cut as in Fig. 17.20. For single-acting cylinders where leakage is more important, a seal joint is sometimes used.Regardless of the joint style, a large percentage of compressors use segmentalrings—either two- or three-piece. The segmental type allows a ring with moreradial thickness, which exerts less load against the cylinder wall than a radiallythin one-piece ring.

Choosing the number of piston rings to use is, to some degree, an art. Thequantity, no doubt, influences one thing of primary importance—ring life, andattempts have been and are being made to put this in to a good relation. However,at the moment, the number of rings selected for most applications is based essen-tially on experience. A guide for number of sealing rings generally used is includedwith Fig. 17.21.

17.24 COMPRESSOR RIDER RINGS

In some lubricated applications, and all nonlube ones, it is necessary to use aseparate bearing, or rider ring(s), on the piston. This can be metal or plastic andserves only to keep the piston from contacting the cylinder. The rider must be madewide enough to keep bearing pressure between rider and cylinder very light, since

17.26 CHAPTER SEVENTEEN

FIGURE 17.21 Typical piston ring arrangementsand number of rings required versus pressure dif-ferential.

tolerance for wear will be less than for piston rings. This is because even with arider, relatively little clearance separates the piston and the cylinder, and no morethan this can be worn from the rider before piston and cylinder come into contact.

One major problem with riders is preventing them from pressure actuating likethe sealing rings. They are usually notched on the sides or across the face and, insome instances, grooved or drilled in such a manner that they will not trap gas andthus seal like piston rings. They can be made either with a cut, as shown in theillustration, or uncut. Both of these types have advantages and disadvantages. Theuncut ring is more difficult to install, will not tolerate even moderate temperatureincreases, but is slightly less prone to act as a seal as long as it remains tightagainst the groove bottom. A cut ring is easily installed, has room for expansioncircumferentially, and has the advantage of large end clearance, through which gascan readily flow.

The rider supports piston weight plus one-half rod weight. This load is consid-ered to be carried by the projected contact area of a 120� arc. Loading is usuallyacceptable if kept below 5 psi for nonlubricated cylinders. For lubricated service,American Petroleum Institute Standard 618 limits rider loading to 10 psi, but thishas been extended to 50 psi successfully in a number of applications.

17.25 PISTON RING LEAKAGE

The average compressor has from two to six piston rings. The most common ringjoint is an ‘‘open type’’ butt, or angle cut as in Fig. 17.20. Leakage wise, these are

RECIPROCATING COMPRESSOR SEALING 17.27

FIGURE 17.22 Instantaneous pressure between piston rings.

about the same. There is some slight advantage to the angle cut, but this is oftenovershadowed by the other factors affecting leakage.

Nearly all the leakage occurs through the joint since this is the only point in thering where there is a definite opening or orifice. The opening is a rectangularpassage with one dimension equal to the ring gap and the other to the pistonclearance. This path is subject to wide variation—it will be almost zero whenpositioned at bottom of the piston, changing to maximum when at the top. It alsoconstantly increases as the ring wears. Both of the leak path dimensions are afunction of cylinder diameter, so in general, leakage can also be related to cylinderdiameter.

Pressure distribution across the rings has been analyzed and measured and, fora two-ring piston, would look as illustrated in Fig. 17.22. For additional rings, thisbecomes more complicated, but in essence pressure within the ring pack cyclesthrough a range somewhere between suction and discharge, resulting in a differ-ential across the rings, first in one direction and then in the other.

Leakage through the rings then is not a result of steady pressure drop, butchanges constantly. Leakage can be expressed however, as an average flow of gasduring any particular compression cycle. A representation of approximate leak ratesis pictured in Fig. 17.23. Quantity wise, there can be large variations. For example,.03 scfm in a small cylinder all the way up to 40 in a very large one.

In a double-acting cylinder this is not actually leakage, as gas is not lost. Itsimply passes from one side of the piston to the other. It is really a loss only fromcompressor discharge capacity. So, a better way to look at this is as a percentagechange leakage causes to cylinder volumetric efficiency. For new rings in lubricatedapplications, loss of V.E. with open joint rings will be about .5% up to approxi-mately 3%.

17.28 CHAPTER SEVENTEEN

FIGURE 17.23 Average leakage by pis-ton rings (for light gases in a double actingcylinder at ratio of 4).

Rings in nonlube cylinders suffer in two respects. First, no oil is present toreduce leak paths, and second, piston clearances are larger. Both of these have theeffect of increasing leakage by roughly three times. To recover the loss of capacity,seal joint rings are often used as in Fig. 17.20. These rings have no theoreticalleakage paths, plus leakage remains, essentially constant during the life of the ring,that is, until the gaps open. Based on tests, it is a good assumption these styles ofrings will reduce leakage, when compared to open gap rings, by as much as 90%.

17.26 COMPRESSOR RING MATERIALS

The trend to plastics has not completely left metals behind. For lubricated service,time-proven bronze and cast iron are still commonly used materials. These aregood simply because they are excellent bearing materials. They have the ability tocarry and hold lubricant because of their porosity, the chemistry or structure tosupply their own lubrication when oil is lacking, and heat transfer properties toquickly carry frictional heat away from the rubbing surface.

To replace these metals with plastics with equally good properties requires se-lection from an almost infinite number of plastic-filler or plastic-plastic composites.The first plastics that made successful rings were the phenolic and cloth laminates.These are resistant to many chemicals, will work under marginal lubrication, andare relatively inexpensive. The other important group has been the low-friction, butweaker, plastics blended with a strengthening filler or another stronger plastic. Inthis last group, there have been only a few with frictional properties good enoughto run without lubrication.

RECIPROCATING COMPRESSOR SEALING 17.29

It is difficult to put plastics in categories, but the most useful as related tocompressors might be described as thus:

*Higher friction plastics needing at least some lubrication:

Polyimide (PI)

Poly(amide-imide) (PAI)

Polyetheretherketone (PEEK)

Polyphynylene Sulfide (PPS)

Polyamide (Nylon)

Phenolic-Cloth laminates

Low-friction materials capable of running without lubrication:

TFE plus strengthening and wear reducing fillers

PI plus friction reducing fillers

PEEK with friction reducing fillers

This is just a general grouping of the materials, but indications are that from thesecome most of the best, or most common, seal ring materials.

The properties of these materials influence the types of piston and packing ringsused. For example, the relatively low yield strength of TFE blends has dictated theuse of Type TR rings; the high elongation and ‘‘plastic memory’’ of TFE allowsits use in stretch-on riders, while the strength and stiffness of some newer plasticsmake them useful for BT or M rings or as anti-extrusion rings. This, plus the factthat compressors face such a variety of conditions, is the reason there may neverbe universal ring ‘‘standards’’ in material or configuration. As new materials comealong, the rings applied to compressors are designed around material properties, aswell as operating conditions.

17.27 SEAL RING FRICTION

More than any other characteristic, friction serves as an indicator of how wellcompressor seals are performing. Like wear, this is very dependent upon lubrica-tion. A certain amount of power must be put into a compressor to overcome sealring friction, but as indicated in Fig. 17.24, this is relatively low compared to thepower needed for gas compression. These curves are based on normal size pistonand rod packing rings.

Power needed to overcome ring friction will usually be only about .5% to 2%of the compression HP. Essentially, all the frictional horsepower changes to heat

* All these materials have friction reducing fillers.

17.30 CHAPTER SEVENTEEN

FIGURE 17.24 Power required (heat generated) to overcome ringfriction versus ring diameter.

and, if not conducted away from the packing or piston rings, can cause wear andleakage. To illustrate the affect of this heat, the approximate 1.6 HP (68 BTU/Min.) as shown, which might be generated on a 3 inch rod, will cause approxi-mately 100�F rise in four minutes if not conducted away. The principle ways toreduce friction are proper lubrication, low friction materials, and narrow rings.

17.28 COOLING RECIPROCATING COMPRESSOR PACKING

One of the critical, if not most critical, factors in obtaining good service fromcompressor packing is proper cooling. A primary source of heat is from the workrequired to overcome frictional resistance of the seal rings.

This is influenced by material selection, ring dimensions, characteristics of thecompressor, and operating conditions. The relation between cooling requirementsand the various influencing factors is not known precisely. What follows is intendedto serve as a guide, indicating when special cooling is required and to help in sizingthe equipment needed to provide the cooling.

Low friction materials, such as TFE blends, or carbon graphite, have made itpossible for packing and piston rings to operate without lubrication. Frictionalcharacteristics of these materials are good, but not nearly as good as when lubri-cation is used. Configuration of the seal rings affects this somewhat, but with mostdesigns considerable frictional heat is generated.

The primary purpose of cooling packing is to remove heat generated due tofriction between seal rings and the rod. Nearly all the work done to overcomefriction converts to heat at the ring and rod mating surface. This heat is transferredto the case, gas passing through the cylinder, distance piece, and the crankcase.

RECIPROCATING COMPRESSOR SEALING 17.31

FIGURE 17.25 The most common methods for cooling packing cases.

Examples of methods to cool cases are shown in Fig. 17.25. Coolants in suc-cessful applications range from oil, circulated only by convection, to special fluidschilled and pumped through the case. In some instances, gas is blown through thecase or over the rod for cooling.

Currently, the best available method to affect cooling is to use a case withinternal channels through which water or a water anti-freeze mixture is circulated.Oil is not often used because it is ineffective at removing heat compared to water,or water with anti-freeze.

Factors affecting generation of heat and heat flow vary from compressor tocompressor, making accurate predictions of the quantities involved very difficult.A general method of calculation, coupled with certain assumptions, is a startingpoint that can be modified by empirical data gathered in actual field installations.

This will provide reasonably accurate results for most applications. Estimatingthe coefficient of friction is difficult in any event, but especially difficult for ap-plications with less than full lubrication.

When a compressor is lubricated and pressures are relatively low, friction loadscan be estimated fairly accurately. However, at low pressures, cooling is frequentlynot required. At higher pressures, the lubricant film separating the ring and rodsurfaces is, at best, partially effective and the coefficient of friction is more difficultto determine without actual operating experience and empirical data.

17.32 CHAPTER SEVENTEEN

17.28.1 Heat Generation

In a packing case containing several rings, most of the pressure drop will be acrossone ring. For calculation purposes, the heat generated by friction can be consideredto be totally from one ring carrying the entire pressure drop. A pressure dropdistributed in any manner over a complete set of rings generates essentially thesame heat.

For purposes of simplifying the calculations, it can be assumed that the coeffi-cient of friction is independent of load and contact area. The work required toovercome friction and the heat generated is:

Work� (F)(2)(S) (17.1)

Revolution

(F)(FPM)BTU/MIN � (17.2)

777

where: F � Force required to move rod against friction (lb.)S � Compressor stroke length (In.)

FPM � Average rod speed (Ft/Min.)

Velocity of the rod is not constant throughout the stroke, but again, the coefficientof friction, f, can be estimated on the assumption that it is independent of velocity.

Friction force, F, is dependent upon the coefficient of friction, ring dimensionsand average pressure, Pa, acting on the ring. Reasonably accurate results can beobtained using mean pressure between suction and discharge. A more accuratecalculation of friction force can be made using an average pressure, Pa, as follows:

1 nPs(Pd)(n) � (Ps)(2 � n)� � � �Pd

Pa � (17.3)2(n � 1)

where: Pd � Compressor discharge pressure (psia)Ps � Compressor suction pressure (psia)n � Gas constant

The various ring configurations found in packing cases can be broken down intofour groups based on the load exerted against the rod. At a given pressure andwidth, W, each group exerts a different load due to the type of cut between seg-ments. The friction force for various ring types is shown in Fig. 17.26, as relatedto pressure and ring dimensions.

The coefficient of friction can vary over a broad range as illustrated in Fig.17.27. The lower figures correspond to well-lubricated surfaces, while higher applywhere dirt and/or abrasives are present. When ƒ exceeds approximately 0.3, ac-companied by high pressure, the packing is usually unable to function and can betotally destroyed. At very high frictional resistance, it becomes nearly impossibleto get rid of the heat generated or to maintain a reasonable seal.

RECIPROCATING COMPRESSOR SEALING 17.33

FIGURE 17.26 Friction loading for various packing ring types.

FIGURE 17.27 Coefficient of friction for various materials and levels oflubrication.

The value for ƒ, along with ring dimensions, operating pressures and rod speedcan be used to calculate BTU/Min. generated by the seal rings. (From Eq. 17.2).)

17.28.2 Heat Transfer to Gas

The heat generated is dissipated through several means. For most compressors, thetwo major paths are:

17.34 CHAPTER SEVENTEEN

1. Through the case or case coolant

2. Through the gas flowing in the cylinder

Heat is lost to gas passing through the cylinder when the rod, warmed by friction,moves into the cylinder and releases some of its heat to the inlet gas at suctiontemperatures, and also during a portion of the discharge stroke.

There are several formulas, or empirical relationships, used to describe flow ofheat from the rod into the gas. One which might be used is Eq. (17.4), for calcu-lating the surface coefficient for gas passing over a smooth surface.

75Vdhc � .05 k (17.4)� �u

where: hc � Film coefficient (BTU/Hr-Ft2-�F)k � Thermal conductivity (BTU-Ft/Hr-Ft2-�F)V � Gas velocity (Ft/Hr)u � Gas viscosity (Lb/Hr-Ft)d � Gas density (Lb/Ft3)

The total heat flow, Q, into the gas, may be expressed as

(hc)(�T)(D)(S)Q � (17.5)

5500

where: Q � Heat Flow (BTU/Min.)�T � Temperature difference between rod and gas (�F)

D � Rod diameter (In.)S � Stroke length (In.)

OR.75(k)(D)(S) (d)(FPM)

Q � (Tr � Ts) (17.6)� �5000 u

where: Tr � Rod temperature (F)Ts � Suction gas temperature (F)

The rod is not a flat surface with gas flowing exactly parallel to it, gas velocityand direction of flow vary widely from point to point on the surface of the rod,and rod temperature and area of exposure are constantly changing as well. Essen-tially then, the calculation of heat flow is an approximation.

In making this approximation, values can readily be assigned to everything ex-cept the rod temperature, Tr. Rod temperature is one of the conditions to be con-trolled with cooling. Using the maximum value of rod temperature will give themaximum heat flow, both into the gas and the case.

If the value is lower, the heat transfer is lower, and the rod temperature willtend to rise. Therefore, it is logical to base heat flow predictions on maximum

RECIPROCATING COMPRESSOR SEALING 17.35

allowable rod temperature. In general, nonlubricated machines can run with rodtemperatures as high as 250�F. In lubricated machines, the limitations is approxi-mately 150�F.

17.28.3 Coolant Requirements

When heat flow into the gas exceeds heat generated, no separate liquid coolant isrequired. Experience indicates that, unless total heat to be removed from the caseexceeds 20 BTU/min. per inch of rod diameter, it is not necessary to providecoolant.

Once it is established that coolant is required, it is necessary to determine re-quired coolant temperature and amount of coolant flow. Usually, one gallon perminute per inch of rod diameter provides sufficient velocity through most cases toensure good heat transfer. The increased flow for larger diameter rods absorbs theincreased heat generated and also compensates for larger coolant passages. Largerrod diameters generally have larger cases and thus more room for coolant passages.

It is difficult to find a good correlation between calculated thermal resistance ofa packing case and observed heat rejection rates. Because of this, coolant temper-atures are determined by first setting the temperature of the coolant leaving thecase at about 90�F and then calculating the inlet temperature.

For example: If 200 BTU’s per minute are to be removed from a particularpacking and circulation is two gallons (16.6 pounds) per minute, there are 16.6pounds of water available to absorb the heat. Dividing 200 by 16.6 yields a tem-perature rise of 12�F. Subtracting this from 90�F exit temperature gives a maximumallowable inlet temperature to achieve this of 78�F. A definite temperature differ-ence between coolant and rod is required for any given amount of heat to beconducted from the case. Using the method previously outlined, it is apparent thatthere are instances where rod temperatures will vary from the 250�F or 150�F levelfor un-lubricated and lubricated service.

17.28.4 Materials

The influence of materials on heat generation is illustrated in a general way in Fig.17.27. In addition to frictional properties, heat transfer characteristics also affecttemperature control. These two parameters are not the only basis for choosing amaterial to be used for packing, as strength, resistance to the medium, cost, andwear resistance are also important.

At the extremes of lubrication, choice of material is limited. With full lubrica-tion, metals such as bronze or cast iron are best. Plastics such as phenolic, nylonor TFE may be used due to conditions other than heat transfer characteristics. Fornonlube service, filled TFE is usually the first choice. Filled polyimides are alsoexcellent but costly, while some of the less expensive plastics do not have thefrictional properties to allow them to be effective for nonlube service.

17.36 CHAPTER SEVENTEEN

FIGURE 17.28 Examples of coolant calculations.

Between these two extremes, compressors operate in mini- or semi-lube serviceor, as shown in Fig. 17.27, ‘‘poorly lubricated.’’ In this type of service, it is moredifficult to select optimum material to provide the lowest operating temperaturedue to the overlapping performance of metals and non-metals. For example, at acertain level of lubrication, metal rings will operate at a satisfactory temperaturelevel. However, with a slight change of conditions, nonmetallic rings may performbetter. Metals transfer heat faster and can run in conditions where the coefficientof friction is a bit higher, whereas nonmetallics require low friction for optimumresults. It is sometimes possible to realize best properties of both materials bycombining nonmetallic seal rings with a metallic backup ring, which not only acts

RECIPROCATING COMPRESSOR SEALING 17.37

as an anti-extrusion ring, but aids the nonmetallic ring, by using its contact withthe rod to conduct heat away from the ring-rod interface.

Figure 17.28 contains two examples of calculated coolant requirements. Due togeneralizations and assumptions made, the results are approximations, as statedpreviously. However, designs often are put into practice in the field without benefitof even these rough calculations. Since many problems experienced with compres-sor packing stem from inadequate cooling, the method outlined here should helpeliminate those problems.

Many machines operate under conditions that do not exactly match the assump-tions or descriptions used. They have features, or use materials, that could changeto some degree the calculated values of either heat generation or heat flow. Forexample, in a compressor with large clearance volume, the temperature in thecylinder may have an effect not allowed for in the calculations. Units which haveshort strokes will have a very limited amount of heat flow into the gas and a moreconcentrated input of heat to the rod than normal. (A good approximation of thisis to ignore the heat calculated from formula (6), and plan on removing all the heatthrough the case.) There are also materials and material-lubrication combinationswhich provide a different coefficient of friction than found in the coefficient offriction chart. The area designated as ‘‘poorly lubricated’’ is actually a broad range,and to assign one value for the coefficient may be an oversimplification.

18.1

CHAPTER 18COMPRESSOR LUBRICATION

Glen Majors, P.E.C.E.S. Associates, Inc.

Lubrication of compressors must accomplish one or more of the following:

1. Reduce friction between moving parts

2. Carry heat away from bearing surfaces

3. Prevent corrosion both during operation and when compressor is stopped

4. Reduce gas leakage between seal faces and close clearances

In rotary screw compressors, oil is used to remove the heat of compression ofthe gas, seal the rotors, and lubricate the bearings.

In the frames of reciprocating compressors, the crankcase oil lubricates the bear-ings, carries away bearing heat, reduces friction, and prevents corrosion.

In reciprocating compressor cylinders, the oil is a once through operation de-signed to reduce friction and wear as well as preventing corrosion.

18.1 ROTARY SCREW COMPRESSORS

Figure 18.1 shows a typical piping flow diagram for an oil-flooded screw com-pressor. Oil is injected directly into the compressor intake at a rate of 0.25 to 0.50gpm/bhp. The discharge gas stream is a mixture of oil and gas at 185 to 200 �Fflowing into a series of separators and filters which reduces the oil content to around2 ppm. The discharge air pressure on the oil reservoir permits oil flow in thisoperation without use of a pump.

Screw compressor manufacturers have their own unique temperature controls forpreventing water condensation. For this reason, they have proprietary oil specifi-cations for best operation. They use different synthetic fluids or combination ofsynthetic fluids for controlling oxidation, oil emulsions, water separation, and cor-rosion.

18.2 CHAPTER EIGHTEEN

FIGURE 18.1 Flow diagram—air /oil systems rotary screw compressor.

18.2 RECIPROCATING COMPRESSOR CRANKCASE

In reciprocating compressor crankcases (Fig. 18.2), the oil pump delivers a contin-uous flow of 40-45 psi oil to the main and connecting rod bearings in order toreduce friction, and carry away heat. Oil sump temperature is usually maintainedat 135 to 160 �F to prevent moisture condensation. The pump picks up oil fromthe crankcase, passes it through an oil filter and thermostatically controlled coolerand back into the main bearing header.

Compressor manufacturers generally recommend for the crankcase an SAE 30to 40 lube oil with rust and oxidation (R&O) inhibitors. If a high viscosity oil isused, it will reduce the oil flow to the bearings causing hotter bearing surfaces.Low viscosity oils may be inadequate to lubricate the compressor cylinders orpacking in those units using crankcase oil for the dual purpose. on Figure 18.3�Ashows the operating temperature range for crankcase oils, while on Fig. 18.3�Bshows the oil pump cavitation region for those oils on a cold start.

18.3 COMPRESSOR CYLINDERS

Compressor cylinder lubrication is completely different in that oil passes ‘‘oncethrough’’ the cylinder with no recycling. Successful operation depends upon un-interrupted, continuous, metered flow to a cylinder bore and piston rod.

COMPRESSOR LUBRICATION 18.3

FIGURE 18.2 Oil flow diagram—compressor crankcase.

The gases being pumped range from air, sweet gases, sour gases, refrigerationgases, entrained hydrocarbon-liquid gases, and liquid water-entrained gases. Thesegas properties affect the lubrication by oxidation, corrosion, chemical reaction,water washing, dilution, and gas absorption.

The pressures range from vacuum to as high as 60,000 psi. Temperatures rangefrom as low as �60 �F to as high as 400 �F. The piston rings, packing rings, andvalves may be either metallic or non-metallic.

18.4 LUBE OIL SELECTION

All of the above conditions require consideration before selecting a compressorlubricating oil. With proper attention to the selection, the life of the wearing partscan be extended several years. With ineffective lubrication, the life may be onlyminutes.

18.4.1 Oil Viscosity

Any oil selected must have sufficient viscosity at operating temperatures to keepthe moving parts from coming into contact with each other and to minimize wearif abrasive particles pass through the system. There are two different temperaturesthat must be considered for oil selection: a) ‘‘cold flow;’’ and b) cylinder dischargetemperature. Cold flow temperature should not be confused with the ‘‘pour point’’in oil properties. Cold flow is that temperature at which oil pumps cavitate orplungers fail to consistently fill on the suction stroke. Regardless of the oil selected,

18.4

FIGURE 18.3 Flow diagram—air /oil systems rotary screw compressor.

COMPRESSOR LUBRICATION 18.5

the cold flow limit occurs at the 6,000 to 10,000 SUS viscosity range (Fig.18.3 ).�B

The oil viscosity selection is always made on the basis of operating temperatureor on the maximum cylinder discharge temperature. If that oil then has a cold flowproblem in cold weather, heaters and insulation must be added to the oil reservoirand meter pumps.

18.4.2 Minimum Oil Viscosity

When lubricating oil reaches the viscosity equivalent to water, the oil film no longersupports dynamic loads resulting in rapid failure. This minimum viscosity is rec-ognized as about 36 SUS (Fig. 18.3 ).�C

18.4.3 Gas Absorption

All petroleum base compressor oils will absorb gases. The higher the gas pressure,the more gases will be absorbed into the oil. The oil then becomes less viscous inthe compressor cylinder. This gas dilution effect is hard to accurately measure and/or predict without time-consuming laboratory tests using the actual gas streamcomponents elevated to the operating cylinder pressure and temperature. A labo-ratory test using natural gas at 980 psi pressure showed that one gallon of oilabsorbed 0.75 gallons of gas when de-pressurized. A somewhat reasonable andpractical way to offset this gas dilution effect is to select an oil having 5 to 10SUS higher viscosity at operating temperature (See Fig. 18.3 ). The oil supplier�Dhas temperature viscosity curves (as in Fig. 18.3) for all compressor oils underconsideration. The suggested upgrade in viscosity of 5 to 10 SUS around cylinderoperating temperatures generally requires the selection of the next higher SAEgrade of oil.

18.4.4 Liquid Hydrocarbon Dilution

Many compressors and particularly field gas gathering units encounter hydrocarbonliquids in the gas stream. Petroleum base lube oils are also hydrocarbons and willbe diluted or washed away by gas stream liquids. The magnitude of this dilutionwill vary as liquid carryover usually occurs in slugs. There are two choices: a)remove the liquid hydrocarbons from the gas stream; or b) select the highest vis-cosity oil.

18.5 OIL ADDITIVES

No amount of flood lubrication will solve an oil quality problem. Various oil ad-ditives are often required to overcome unusual operating conditions.

18.6 CHAPTER EIGHTEEN

18.5.1 Water Displacing and Metal Wetting Additive

The majority of compressor cylinder wear problems result from water carryover inthe gas stream. When water reaches the compressor cylinder or is chemicallyformed inside the cylinder, ‘‘water washing’’ causes the oil to float away leadingto drastic wear. A synthetic polar-type additive (not animal fatty oil) that has metalwetting and water displacing properties may be used to minimize the effects ofwater.

18.5.2 Corrosion Inhibitors

Small amounts of CO2, H2S, chlorides, and other potentially corrosive gases canbe successfully handled with ‘‘standard’’ compressor components, providing thegas stream is absolutely dry. If any moisture is present, then either: a) corrosionand chemical resistant materials in all components touched by the gas; or b) afortified corrosion inhibited compressor oil may be used. The corrosion inhibitorsshould be combined with the water displacing and metal wetting additives discussedabove. These additive combinations promote an oil film that tightly adheres to allmetal surfaces even in the presence of water. The object is to let the oil be thesacrificial agent to neutralize the acids and protect the critical metal parts.

18.5.3 Oxidation Inhibitor

Oxygen reacts with the hydrocarbon molecules of lube oil to form a brownishcrystalline volcanic-ash type deposit that cannot be dissolved with petroleum sol-vents or cleaners. Oxidation rates double for every 18 �F increase in temperature.Normal R&O inhibitors are adequate for compressor crankcase oil operating at 140�F, but totally inadequate for air compressor cylinders operating over 300 �F. Aslittle as 2% excess 02 in a gas stream will cause serious ash type build up in amatter of weeks. In order to handle this problem, the compressor oil must befortified with a high-temperature, anti-oxidation inhibitor.

18.5.4 Anti-Foam Additive

Lube oil leaving a compressor cylinder may be highly agitated in a foamy ‘‘may-onnaise’’ state that will pass through liquid knock out traps. If the oil has to beremoved from the gas stream, the oil must be fortified with a 3 to 5 ppm activeanti-foam inhibitor to quickly break down the gas bubbles.

18.5.5 Anti-Emulsion Additive

At high discharge gas temperatures, the aerated oil combined with moisture formsa black ‘‘soap’’ deposit on the inside of the pipes and inside the cooler tubes. Toovercome this problem, an anti-emulsion additive should be used.

COMPRESSOR LUBRICATION 18.7

18.5.6 Viscosity Index (VI) Improver

All engine-type motor oils have VI improver additives for cold starts and coldweather operation. Figure 18.3 shows how oil viscosity changes with temperatureand how 60 VI to 150 VI oils might be compared. These VI improvers servepractically no useful purpose in compressor cylinders. They do, however, make itpossible for lubricator pumps to operate at considerably colder temperature withoutheaters (Fig. 18.3 ).�B

18.6 OPTIMUM LUBRICATION

Figure 18.4 gives empirical guidelines for optimum quantity of oil for variouscompressor cylinders operating in different gas streams, with different ring mate-rials, under low-to-high pressures, and in a wide range of speeds.

‘‘Optimum’’ lubrication gives years of compressor life, while ‘‘starved’’ lubri-cation produces rapid wear and short life. ‘‘Over lubrication’’ gains little in oper-ating life and requires more oil. Figure 18.5 illustrates the compressor componentlife with various lubrication rates.

There are various lube oil rate formulas or guidelines proposed by compressormanufacturers, oil suppliers and seal manufacturers. They provide an estimate forquantity of oil to lubricate gas transmission type compressor cylinders. These for-mulas are similar in that they are based on total swept surface area to be lubricated.

No formula or graph can cover all possible conditions, pressures, speeds, gases,and ring materials. Figure 18.4 graphically covers a broad range in cylinder sizes,compressor speeds, pressures, and ring materials. The oil usage for optimum lu-brication is given in pints per day per cylinder for PTFE-equipped cylinders. Forother cylinders with different rings and different gas streams, the appropriate mul-tiplier is listed on the graph.

18.7 OIL REMOVAL

When sensitive downstream catalyst is involved, oil carryover from compressorcylinders may be objectionable. To overcome this problem: a) the compressorshould be converted to non-lubricated construction; or b) adequate oil removalequipment should be installed. Field experience with the following devices willpermit inexpensive removal of lube oil from gas streams:

Percentage Of Oil Removed From Stream1. Regular lube oil with no anti-foam additive with KO (knock out) Traps 16%2. Oil with anti-foam additives � KO trap 40%3. Oil with anti-foam additive � aftercooler � KO trap 84%4. Oil with anti-foam additive � aftercooler � KO trap � coalescing filter 96%5. Oil with anti-foam additives � aftercooler � KO trap � coalescing filter

� molecular sieve 99.6%

18.8 CHAPTER EIGHTEEN

FIGURE 18.4

COMPRESSOR LUBRICATION 18.9

FIGURE 18.5 Compressor seal life vs. oil usage.

18.8 NON-LUBE (NL) COMPRESSORS

There are certain compressor applications where no oil can be tolerated in the gasstream. To be most effective, these compressors require PTFE piston rings, packingrings, wear bands, and nonmetallic compressor valve parts, plus a discharge gastemperature under 275 �F. They also require double distance pieces and a slingerring on the rod between the cylinder and the frame in order to prevent crankcaseoil migration along the piston rod. If a very small quantity of oil gets into the NLcompressor cylinder, ‘‘twilight zone’’ operation occurs in that area between non-lube and minimum lube where the ring and the packing life may be only a fewweeks. Figure 18.5 is a representation of various degrees of lubrication up to‘‘over’’ lubrication.

18.9 SYNTHETIC LUBRICANTS

A relatively small percentage of compressors are lubricated with synthetic lubri-cants. They are more expensive, have special properties not found in petroleumoils, and some have excellent fire resistant properties while others enter into thereaction of the gas process. Sometimes the synthetics attack paints, gaskets, o-ringsand form corrosive acids in the presence of water.

Table 18.1 compares the properties of the most common synthetic lubricantswith mineral oil and their compatibility with compressor components.

18.10 CHAPTER EIGHTEEN

TABLE 18.1 Comparison of Synthetic Lube Oils

Min

eral

Oil

Poly

isob

uten

esPo

lyal

phao

lefin

Alk

ylat

edA

rom

atic

sPo

lyal

kyle

negy

cols

Perfl

uoro

alky

leth

ers

Poly

phen

ylet

hers

Dic

arbo

nxyl

icA

cid

Est

ers

Neo

pent

ylPo

lyes

ters

Tri

aryl

Phos

phat

ster

rial

kyl

Phos

phat

ster

sSi

licon

ils

Viscosity Temp. Behavior(VI)

M P V M V M P V V P E E

Low Temp. Behavior(Pourpoint)

P M E G G G P E V M E E

Liquid Range M P V G G E P V V V G EOxidation Stability (Aging) M M V M G E V V V V M VThermal Stability M M M M G E E G V V G VEvaporation Loss, Volatility M M V G G E G E E V V VFire Resistance, Flash Temp. P P P P M E M M M V V GHydrolytic Stability E E E E G E E M M M G GCorrosion ProtectionProperties

E E E E G P M M M M M G

Seal Material Compatibility G G V G G E G M M P P GPaint and LacquerCompatibility

E E E E M V M M M P P G

Miscibility with Mineral Oil E E E E P P G V V M M PSolubility of Additives E E V E M P V V V E E PLubricating Properties G G G G V E E V V E M PToxicity G E E P G E G G G V M EBiodegradability M P G P E P P E E V V PPrice Relation AgainstMineral Oil

1 4 4 4 8 500 400 8 8 8 8 60

E ExcellentV Very GoodG GoodM ModerateP Poor

18.10 COMPRESSOR LUBRICATION EQUIPMENT

Reciprocating compressors require equipment that can reliably and consistentlyinject small quantities of oil under pressure to different locations on the cylinderand packing. There are two basic systems in general use: a) pump-to-point, and b)divider block.

COMPRESSOR LUBRICATION 18.11

FIGURE 18.6

18.10.1 Pump-To-Point

These metering pumps are driven from either the main compressor or from anelectric motor. Figure 18.6 shows a cut-away view of an individual lubricator pumpthat goes into a 5 to 18 compartment unit. Each compressor cylinder may have 2to 6 oil injection points. The no-flow/shut-down device is to prevent compressoroperation when there is no oil flowing. These pumps come in different sizes, dif-ferent pressure ratings, and have adjustable outputs.

18.10.2 Divider Block System

This system (Fig. 18.7) uses one adjustable output pump and various sized dividerblocks to meter a specific amount of oil to multiple cylinder locations. Like any

18.12 CHAPTER EIGHTEEN

FIGURE 18.7

COMPRESSOR LUBRICATION 18.13

other lubricator system, it must have a no-flow shut-down device to prevent com-pressor operation when no oil is flowing. Reliable operation can only be achievedwhen ‘‘balancing valves’’ (Fig. 18.7) are in each divider block discharge line andmanually adjusted for higher than the highest cylinder pressure.

18.10.3 Cylinder Check Valves

Each oil injection point on compressor cylinders requires a check valve (Fig. 18.6)to be installed close to the cylinder to prevent gas back-flow into the oil system.The check valve should be installed in the vertical up position so as to have aliquid ‘‘oil leg’’ covering the ball check to prevent gas leakage and air binding ofthe metering system.

18.10.4 Balancing Valves

Figure 18.7 shows a cut-away view of an adjustable balancing valve used in dividerblock systems. All are set slightly higher than the highest cylinder pressure. Bal-ancing valves should be installed with the outlet up; otherwise, they will trap gasesand cause ‘‘soft pump’’ operation.

18.10.5 Air Binding

The biggest operational problem with divider block systems is ‘‘air binding.’’ Airand gases may get entrained in the oil supply, do get injected into it during lubri-cator reservoir filling, and do flow back through improperly installed cylinder checkvalves. These troubles can be overcome by making the lubricator system self-venting. Gases seek the highest point; therefore the piping and devices should beinstalled so that oil always flows up with no downward tubing loops.

19.1

CHAPTER 19PRINCIPLES OF BEARING DESIGN

Hooshang Heshmat, Ph.D.H. Ming Chen, Ph.D., P.E.Mohawk Innovative Technology, Inc.

19.1 NOMENCLATURE

Unless noted otherwise, the following symbols are used throughout the text.

Units

A Area (in.2)AMB Active Magnetic BearingB Damping coefficient (lbf-s)/ inB (�B) /2�ND(L /D)(R /C)3 � (�B) /�L(R /C)3

C Radial clearance (in.)Cm Smallest clearance for � � 0 (in.)CM Largest clearance for � � 0 (in.)CSB Compliant Surface BearingD Diameter of bearing for journal (in.)E Elastic modulus (psi)F� Frictional force (lb)G Mass flow rate (lbm/s)G G /1/2 �a ULC (�)Gx Turbulence coefficient in x or � (�)Gz Turbulence coefficient in z or r direction (�)G� Turbulence coefficient for viscous shear (�)H Power loss (hp)K Spring coefficient (lb/in.)K K /2� NL (R /C)3 (�)KB Structural stiffness of CSB (lb/in. / in.)L Width of bearing (in.)

� in the z direction in journal bearings� in the r direction in thrust bearings

MCR Critical mass for journal bearing stability (lbm)CRM (MCRN) /2� L(R /C)3

N Revolutions per unit time (rpm) (�)P Unit load (psi)

� (W /LD) in journal bearing (lbf/ in.2)� (W /A) in thrust bearings (lbf/ in.2)

19.2 CHAPTER NINETEEN

Units

Q Volumetric lubricant flow (in.3 /s)z �Q (Qz /QzF) Level of starvation (�)

Qz , Qr Side leakage of lubricant (hydrodynamic) (in.3 /s)Q1, Qin Flow in at leading edge (in.3 /s)Q2 Flow out at trailing edge (in.3 /s)Q2P Flow out at trailing edge due to pressure gradient (in.3 /s)R Radius of bearing or journal (in.)R1 Inner radius (in.)R2 Outer radius (in.)R Perfect gas constant (ft-lbf/ lbm-�R) (�)Re Reynolds number (�)

� (�R�h /�) in journal bearings� (�r�h /�) in thrust bearings

REB Rolling Element BearingsS Sommerfeld number (LD�N /W) (R /C)2 � 1/W (�)T Temperature (�R or �F)T Temperature rise (T � Ti) (�R or �F)U Linear velocity (in. /s)W Load (lb)WCR Critical load for journal bearing stability (lb)

CRW (WCR /W)(C�2 /g) (�)W � (W /LD�N)(C /R)2 in journal bearings (�)

� (W /R22��) (h2 /L)2 in thrust bearings

b Tapered fraction of thrust bearing (�)c Specific heat of lubricant (BTU/�F or �R)d Amount of center offset or preload (in.)e Eccentricity (in.)ƒ Friction coefficient (F� /W) (�)g Gravitational constant (32.174 ft/s2)h Film thickness (in.)hmin Minimum film thickness (in.)h11 Value of (h1 � h2) at R1, 0) (in.)hp Film thickness over pivot (in.)h2 Film thickness at end of fluid film (in.)h Dimensionless film thickness (�)

� (h /C) for journal bearings� (h /h2) for thrust bearings

hN Nominal film thickness (in.)h* (h /) (�)hN* (Hn /) (�)h1* (h1 /) (�)h2* (h2 /) (�)lo Half length of bump in angular direction (in.)

PRINCIPLES OF BEARING DESIGN 19.3

Units

m Preload (d /C) (�)n Number of pads in bearing (�)p Pressure (psi)pa Ambient pressure (psia)ps Supply pressure (psi)r Radial coordinate (�)r (r /R2) (�)s Distance between bumps (pitch) (in.)t Time, foil thickness (s, in.)w Specific weight (�)x, y Rectangular coordinates (�)z Axial coordinate (�)� Bearing compliance:

3 32p s l 2p s la o a o2 2(l � � ); (l � � )� � � �CE t h E t2

Angular extent of bearing pad (rad or deg.) (deg. or rad) p Angular extent of pad from start to pivot (deg. or rad) s Fluid film arc (�2 � �1) (deg. or rad)

p ( p / ) (�) Taper (in.)� Circumferential taper (h1 � h2) (in.)r Radial taper at � � 0, (h11 � h12) (in.)� Eccentricity ratio (e /C) (�)�m (e /Cm) (�)� Angular coordinate (deg. or rad)�S Start of bearing pad (deg. or rad)�p Location of pivot (deg. or rad)�E End of bearing pad (deg. or rad)�2 End of hydrodynamic film (deg. or rad)�min Location of hmin (deg. or rad)� Lubricant viscosity (lbf-s/ in.2)� Poisson’s ratio (�)� Density of lubricant (lbm/in.3)� Attitude angle (�min � �) (rad)�L Load angle (deg. or rad)� Angular velocity (rad/s)�i Threshold instability frequency (rad/s)�n Natural frequency of system (rad/s)

i� (�i /�) (�)� 12� (�N /pa)(R /C)2 (�)

19.4 CHAPTER NINETEEN

Units

Subscripts

a AmbientE Endr RadialF Full filmR RingS Startxx Force in the x direction due to a displacement in the x directionxy Force in the x direction due to a displacement in the y directionyx Force in the y direction due to a displacement in the x directionyy Force in the y direction due to a displacement in the y direction� Friction1, 2, 3 Lobe 1, 2 or 3

19.2 COMPRESSORS AND THEIR BEARINGS

From the standpoint of speed and pressure heads one can, in a general fashion,classify compressors as follows:

• Reciprocating—low speeds generating both moderate and high pressures

• Centrifugal—high speeds and moderate pressures

• Axial flow—very high speeds and low pressure

This picture of compressor operation is portrayed in Fig. 19.1. The temperaturesof the compressed fluid are usually kept below 600�F and for this intercoolers areoften required. The drives employed are shown in Fig. 19.2, along with compressormass flows; the flows are high at low speeds and low at the higher speeds. Thusbearings in compressors operate at speeds up to 30,000 rpm and, in some unusualapplications such as in cyrogenic pumps, may reach speeds of 100,000 rpm.

19.2.1 Bearings in Reciprocating Compressors

A generic picture of the use of bearings in reciprocating compressors is shown inFig. 19.3. The unit contains four sets of bearings, each subject to different operatingconditions. The main shaft bearing is the most conventional, its position and sizepermitting a proper supply of lubricant. It runs typically in the range of 125 to 500rpm, driven usually by a steam turbine. Next comes the crankshaft bearing whichis the most heavily loaded, this being due to the variable forces exerted on it duringthe power stroke; its speed, too, is variable during each cycle. Then there is thewrist pin bearing at the end of the connecting rod undergoing an oscillatory motion.

PRINCIPLES OF BEARING DESIGN 19.5

FIGURE 19.1 Approximate range of application ofvarious compressors.

FIGURE 19.2 Operating conditions of centrifugal compressors.6

19.6 CHAPTER NINETEEN

FIGURE 19.3 Schematic of bearing locations in reciprocating compressors.

The crosshead usually has a bronze bushing operating in the boundary lubricationregime.

19.2.2 Bearings in Centrifugal Compressors

By far the most commonly used compressors are of the centrifugal type, rangingfrom simple fans with pressures of no more than a few psi to multistage unitsemploying intercoolers and often gear trains linked to electric motors or gas tur-bines. A typical relation between volume flow and speed would be as follows:

Volume, cfm Speed, rpm

3,000 10,00012,000 6,00040,000 3,60090,000 2,700

Since high cfm also implies large shaft sizes the actual bearing linear speeds donot vary much for the different conditions listed above.

From the standpoint of bearings, centrifugal compressors can be subdivided intothe following groups:

Single Stage with Overhung Impellers. These are shown in Figs. 19.4a and 19.4band although different in construction they produce similar effects on the journaland thrust bearings, namely misalignment. Naturally, the one with no bearing out-

PRINCIPLES OF BEARING DESIGN 19.7

a. Unsupported Overhung Impeller

b. Single Bearing Overhung Impeller

c. Two Bearing Impeller Shaft

FIGURE 19.4 Single stage centrifugal compressors.

side the drive would be more severely misaligned. Due to its overhung construction,the unit would also be more prone to vibration and instability. The preferred con-struction is that shown in Fig. 19.4c which has an additional bearing at the outboardend of the shaft.

Multistage Compressors. Typical bearing locations in multistage compressors areshown in Fig. 19.5. Here there is no overhung mass and unless the shaft is severelybowed there should be no misalignment. In the high speed units, couplings, electricmotors and gear sets are used introducing external excitation forces in addition topossible unbalance forces. These come from the power line frequencies, the gear

19.8 CHAPTER NINETEEN

FIGURE 19.5 Multistage centrifugal compressors.

teeth, from misalignment problems with the coupling, and occasionally even frompedestal vibrations.

The greatest complexity arises in accommodating the generated axial forces.Where large thrust loads are present, an attempt is usually made to reduce themby the use of a balancing piston. A schematic of such an arrangement is shown inFig. 19.6. Still there is always a net thrust load present which must be carried bya properly designed thrust bearing. Often there are two such bearings, one activeand one inactive; the first is designed to carry the steady load while the other ismeant to accommodate any dynamic loads. This is made possible by having theshaft float axially some 10 to 20 mils, thereby transferring the thrust load from theactive to the inactive bearing. In some cases the thrust load may actually reverse

PRINCIPLES OF BEARING DESIGN 19.9

FIGURE 19.6 Thrust loads in centrifugal compressor.

itself, in which case two thrust bearings are needed for supporting a thrust in eitherdirection.

19.3 GENERAL BEARING PRINCIPLES

Five kinds of bearing can be considered candidates for use in compressors, eachpreferable for a particular set of operating conditions. From a tribological stand-point, these can be grouped as follows:

Fluid Film Bearings. These bearings carry the imposed load on a fully developedfluid film, be it a liquid or gas. To this group belong the various hydrodynamicjournal and thrust bearings which generate support pressures by virtue of the rel-ative motions between the surfaces; and hydrostatic bearings whose load capacityis provided by an externally supplied high-pressure fluid.

Elastohydrodynamic Bearings. These bearings operate on a combination of hy-drodynamic pressures and forces generated by deflections of the elastic bearingsurfaces. Bearings in this category are the compliant surface (or foil bearings), androlling element bearings.

Magnetic Bearings. The third kind considered here is a unique support system,known as the magnetic bearing. In this device the load is carried on forces gen-erated by an electromagnetic field in the bearing structure.

19.10 CHAPTER NINETEEN

FIGURE 19.7 Four generic kinds of bearings.

The basic elements of these various fluid film bearing designs are sketched inFig. 19.7. In the following subsections, the theoretical principles of bearing oper-ation will be reviewed briefly. Sections 19.3.0 through 8.0 will provide the practicalaspects of bearing design and application.

19.3.1 Hydrodynamic Bearings

Figure 19.8 shows a generalized sketch of a bearing consisting of a moving and astationary surface. The two surfaces are separated by a fluid film of variable thick-ness. As the lubricant is sheared through the clearance from inlet to outlet, itsvelocities, pressures, temperatures and viscosity undergo considerable variationswhich bear directly on bearing performance.

Incompressible Lubrication. For bearings using incompressible lubricants, thebasic mathematical expression that relates performance to the bearing’s geometricaland operational parameters is the Reynolds differential equation given by

3 3� h �p � h �p �h� � 6 (19.1)� � ��

�x � �x �z � �z �x

When solved, the Reynolds equation yields the pressure field p(x,z), as well as the

PRINCIPLES OF BEARING DESIGN 19.11

FIGURE 19.8 Schematic of a hydrostatic bearing.

pressure gradients (�p /�x) and (�p /�z) in the bearing. By integration one thenobtains

• Load capacity

L B

W � � � p (x, z)dxdz (19.2)0 0

• Frictional force and power loss

L B h �p �UF � � � � � dxdz: H � F U (19.3)� � � ��

0 0 2 �x h

• Component flows in the x and z directions

L 3h �p hUQ � � � dz (19.4a)� � � �x

0 12� �x 2

B 3h �pQ � � dx (19.4b)� �z

0 12� �z

Compressible Lubrication. For a bearing lubricated by gas, the Reynolds equa-tion is similar but because of gas compressibility a density parameter now makesan appearance, namely

3 3� �h �p � �h �P �(�h)� � 6U (19.5)� � ��

�x � �x �z � �z �x

The basic differences between gas and liquid lubricated bearings are:

19.12 CHAPTER NINETEEN

FIGURE 19.9 Comparative viscosity of various fluids.

• The load capacity depends on the prevailing ambient pressure, whereas it doesnot with incompressible fluids.

• In liquid lubricated bearings, there is often cavitation at the end of the fluid film;there is no cavitation in gas films.

• Opposite to that of liquids, gas viscosity rises with a rise in temperature.

• Film thicknesses in gas bearings are one or two orders of magnitude smaller thanwith liquid-lubricated bearings; this is due to the much lower viscosity of gases,(see Fig. 19.9). For the same reason, frictional losses in gas bearings are consid-erably lower.

• No special arrangements for lubricant supply are required.

PRINCIPLES OF BEARING DESIGN 19.13

FIGURE 19.10 Values of turbulence coefficients.

Effects of Turbulence. The above equations are all for laminar flow, i.e., whenthe lubricant velocity is below a Reynolds number of about 1,500, where theReynolds number is given by

Re � �R�h /� (19.6)

Should the flow in any region of the film exceed the above value, then lubricantflow would be reduced and both power loss and temperatures would rise. TheReynolds equation that defines turbulent bearing operation is given by:

3 3� h �p � h �p dhG � G � 6U (19.7)� � �� x z�x � �x �z � �z dx

where the functions Gx , Gz and G� (G factor) are given as a function of Re numberin Fig. 19.10. Thus the G factors are a function of the turbulence level (i.e., Gfactors are a function of the Reynolds number). The function G� is a multiplyingfactor of the power loss given by Eq. (19.3) (i.e., G�F�).

Stability. Rotordynamics plays a crucial part in determining the critical speeds,vibrational amplitudes and possible instabilities in rotating machinery. Since thefluid film possesses both stiffness and damping properties, it affects considerablythe overall characteristics of such a system. Moreover, each bearing possesses four

19.14 CHAPTER NINETEEN

spring and four damping coefficients which must be known to determine the effectof bearings on a rotordynamic system. The origin of these eight coefficients derivesfrom the fact that a load imparted either along x or y produces a journal displace-ment in two perpendicular directions; conversely a journal motion either along xor y generates incremental forces in two perpendicular directions. The eight stiff-ness coefficients thus generated are defined by

�F �Fx xK � � B � �xx xx�e �ex x

�F �Fx xK � � B �x y x y�e �ey y

�F �Fy yK � � B � �y x y x�e �ex x

�F �Fy yK � � B � �yy yy�e �ey x

where the e’s represent displacement and velocities. The terms with subscriptsexx and yy are called colinear and those with xy and yx cross-coupling coefficients.These eight springs and dashpots are schematically represented in Fig. 19.11.

The dynamics for a rotor bearing system is then determined by the set of twodynamic equations

K x � K y � B x � B y � Mx � 0 (19.8a)xx xy xx xy

K x � K y � B x � B y � My � 0 (19.8b)yx yy yx xy

where the dotted quantities denote velocities and the double dot are accelerations.The solution of this set of equations yields two important quantities with regard

to system stability

• Threshold instability frequency �i

• Critical mass, MCR

The highest rotor mass M that a bearing will support before becoming unstable isthen given

M � MCR system stable

M � MCR system unstable

The threshold instability frequency �i gives the vibrational frequency at the onsetof stability. Given �n as the natural frequency of the system, we then have

If �i � �n system is stable

If �i � �n system is unstable

PRINCIPLES OF BEARING DESIGN 19.15

FIGURE 19.11 Dynamic coefficients of a journal bearing.

The two quantities MCR and �i are determined from the eight coefficients as follows:

2 2 2M � (Z /� ) � Z /4� � (19.9a)CR i i

K B � K B � K B � K Bxx yy yy xx xy yx yx xyZ � (19.9b)B � Bxx yy

1 / 2K K � Z(K � K ) � K K � Zxx yy xx yy xy yx� � (� /�) � (19.9c)� �i i B B � B Bxx yy xy yx

19.3.2 Hydrostatic Bearings

There are several distinct advantages to the use of hydrostatic bearings, namely

• They can operate at low or zero speeds without affecting the load capacity. Theycan therefore be easily started under load.

• Due to the depth of the fluid pocket which is one or more orders of magnitudehigher than in hydrodynamic films, they have very low drag losses.

19.16 CHAPTER NINETEEN

The above merits are counteracted by some inherent disadvantages:

• They need an external pump or some other source to supply the pressurized fluid;thus even though the bearing power loss is low, the pumping power is part ofthe energy expenditure.

• Due to the depth of the pocket, they are prone to turbulence in the fluid.

• They require a compensation system, that is, a regulatory mechanism to adjustthe fluid pressure in the pocket in conformity with changes in the imposed load.

Since the pockets containing the pressurized fluid are very deep, there is usuallyno significant hydrodynamic effect. The film thickness can be considered constantand so (�h /�x) in Eq. (19.1) becomes zero. Thus the Reynolds equation for hydro-static bearings reduces itself to a Laplace equation

2 2� p � p� � 0 (19.9)2 2�x �z

The proper boundary conditions are determined by the supply pressure and theform of compensation used in the system.

The most common restrictor used for compensation is either an orifice or acapillary. Referring to Fig. 19.12, the relation between the supply pressure ps, thepocket pressure po, and the ambient pressure pa is for an incompressible fluid givenby

a. For orifice compensation

1 / 22 3C �a p � p �h (p � p )D s a o a� (19.10)� �2 2� 6� ln (R /R )2 1

b. For capillary compensation

4 3(p � p )r (p � p ) hs o 0 0 a� (19.11)4l 3 ln (R /R )2 1

Using po obtained from the above relations, one can subsequently calculate load,film thickness and the flow in the bearing.

19.3.3 Compliant Surface Bearings

The compliant bearing combines features of fluid dynamics and elastic responsewhich make for a number of unique features of this device. It also accounts for itsgreater analytical complexity since, in addition to the Reynolds equation, one mustconsider the corresponding mechanical response of its surfaces. Given the largenumber of possible configurations, no single deflection equation can be written forthem all; rather each family of compliant surface bearings will have its own set of

PRINCIPLES OF BEARING DESIGN 19.17

FIGURE 19.12 Elementary configuration of a hydrostatic bearing.

characteristic expressions, which together with the Reynolds equation will providethe necessary solution.

There are multiple advantages to the use of compliant bearings.

• Due to their ability to yield under load, they perform well at high speeds and athigh temperatures.

• By introducing friction between the compliant and rigid surfaces, Coulomb damp-ing can be introduced.

• Compared to either fluid film or rolling element bearings, they have very lowpower losses.

19.18 CHAPTER NINETEEN

FIGURE 19.13 Extension domi-nated compliant surface bearing.

• They can operate with either liquid or gas lubrication. By virtue of their abilityto deflect, the difference between performance with a liquid or a gas is not aspronounced as in rigid bearings.

One of the major disadvantages is the high starting torque due to rubbing. Thisproblem can be alleviated by applying coatings to the mating surfaces.

The two major groups of compliant bearings are those in which the dominantmode of deformation is extension and those where bending is the main mode. Quiteoften both modes are present. A model of the tension dominated configuration isgiven in Fig. 19.13 where a highly flexible foil is stretched between fixed fulcrums.Here the imposed bearing load is supported by the radial component of the tensionforces; the load capacity can be further increased by imparting to the foil a preloadtension. Figure 19.14 shows a bearing belonging to the second category. The figurepart (b) shows one segment of the surface consisting of a strip of foil supportedon a compliant subsurface. The corrugated subsurface rests on the rigid bearingshell.

19.3.4 Rolling Element Bearings

Most of the literature, not to speak of handbooks, on ball and roller bearings isbased on the premise that there is metal-to-metal contact between the races andthe rolling elements. Under load, the ball or roller is compressed to form a circular,elliptical or rectangular contact area, generating conventional Hertzian stresses. Inreality, however, the contact area is covered with a lubricant film, albeit severalorders of magnitude smaller than in hydrodynamic bearings. Under these condi-tions, as was asserted in the opening paragraph of this chapter, there is superim-posed onto the Hertzian stresses a hydrodynamic pressure field. These combinedeffects produce what is called an elastohydrodynamic pressure distribution alongwith a finite film thickness, whose basic shapes are given in Fig. 19.15. The cal-culation of these pressures, film thicknesses, power loss and so on, must, as in the

PRINCIPLES OF BEARING DESIGN 19.19

FIGURE 19.14 Bending dominated compliant surface bearing.

case of compliant bearings, be based on the use of the Reynolds equation in con-junction with the elasticity equations as they pertain to the particular geometry ofthe bearing.

The more significant attributes of rolling element bearings are as follows:

• They can start under load and operate well at lower, including zero, speed.

• When on the point of failure, they will continue to operate for some time pro-viding an opportunity to shut down the machine.

• They can support both radial and axial loads.

The main shortcoming of rolling element bearings is that, depending on speed andload, they have a finite life span. They must, therefore, be periodically replaced,unlike hydrodynamic bearings which can operate indefinitely. They also requiremore installation space and are noisy.

Given the complexity of the elastohydrodynamic solutions, design and perform-ance calculations of REB’s are based on empirical relations, related primarily tothe fatigue properties of the structures involved. Since fatigue failure is a functionof level of stress and number of cycles, the viability of an REB can thus be relatedto rotational speed of the machine, shaft size and bearing loading. The relationbetween the first two parameters, known as the DN curve, is shown in Fig. 19.16.

19.20 CHAPTER NINETEEN

FIGURE 19.15 Elastohydrodynamic behavior of rolling elements.

This limit is imposed by the dynamics of the spinning balls or rollers and therotating races and cages. Thus, regardless of load this DN limit ought not beexceeded. The longevity of a given bearing when operated under the limitations ofFig. 19.16 does depend on the imposed load. This dependence is given by

�31.67 � 10 WDL � (19.12)� �10 N W

where

PRINCIPLES OF BEARING DESIGN 19.21

FIGURE 19.16 Limits in ball bearing DN values.

L10 � is the predicted life of the bearing carrying a 90% probability of survivalN � shaft speed, rpmW � load on the bearing, (lbf)

WD � the dynamic load, (lbf) a bearing will endure for one million revolutions

and

� 3 for ball bearings�

� 3.3 to 4.0 for roller bearings

The value of L10 is influenced by a host of additional factors such as size andnumber of rolling elements, kind of materials used, the bearing’s angle of contact,lubrication method, surface finish, and others.

19.3.5 Magnetic Bearings

Figure 19.17 shows basic designs of radial and thrust AMB’s. These contain astator wound with coils to create the magnetic field and a rotor which has ferro-

19.22 CHAPTER NINETEEN

FIGURE 19.17 Basic designs of magnetic bearings.

magnetic laminations or solid materials to interact with the magnetic field. In aradial bearing, it is common to have two sets of opposing coils with a sensor toprovide feedback of rotor position along two axes. In a thrust bearing, position ismaintained by a set of stationary coils on either side of the runner. Since each pairof poles acts independently, it is sufficient to illustrate the action of one set to makeclear the operation of the bearing as a whole. The attractive force on a rotor, asshown in Fig. 19.18, is given by

2F � (I /C)

where F is the magnetic force and I the current. With attractive poles, as the rotormoves toward the poles, the force on this face increases while on the opposite polesit decreases; thus without control the system is unstable leading to metal-to-metalcontact. With a sensor and feedback system, current is decreased on the approach-ing side and increased on the opposite to force the rotor back toward the center.Direct feedback control is non-linear and not responsive enough; this is remediedby the introduction of a large bias current compared to which the regulating currentis small.

The above outlined arrangement of displacement feedback is, however, not suf-ficient to control resonances. For this, the system must account not only for dis-placement but also for rotor velocities. Thus a feedback for velocity sensor is alsorequired, or a provision to convert the recorded displacements into velocities.

A major advantage of AMB’s is that stiffness and damping can be varied, unlikein any other bearings where they are fixed for a given design. With such control,optimum performance can be obtained over a wide range of operating conditions.Moreover, this flexibility offers means for virtual rotor balancing to counteract

PRINCIPLES OF BEARING DESIGN 19.23

FIGURE 19.18 Elements of AMB’s servo control.

residual unbalance in the system. The system can even account for pedestal vibra-tions once they are measured and fed into the control circuit of the bearing.

All the varied bearing designs are combinations of three principles of magneticoperation

• Attraction by the use of electromagnets

• Repulsion by the use of permanent magnets

• Reluctance using permanent magnets

Figure 19.19 illustrates these principles. Part A) shows the attraction system whichhas been applied in a number of machine designs employing five active servocontrols. The repulsion principle illustrated in part B) yields a radially stable bear-ing by means of passive magnets, but is axially unstable and requires at least oneactive control. In the reluctance design shown in part C), the magnetic circuitalways seeks a geometry so as to align itself with the edges of the rectangularsalient pole faces. In the configuration shown, axial stability is achieved at theexpense of radial instability that must be overcome by an active control. Part D)is shown not because it represents another principle, but because using permanentmagnets to energize the air gaps and electromagnets for control yields a metastablesystem that can operate at almost zero control power when disturbance loads are

19.24 CHAPTER NINETEEN

absent; and it produces a linear force versus current which simplifies the servocontrol design.

Attraction Electromagnets. These are by far the most widely used. A straight-forward approach is to use two sets of orthogonally disposed magnet pairs tocontrol the rotating shaft, as shown in Fig. 19.19. This approach controls x and yas well as the two angular directions. The axial direction must be controlled byeither an active or passive bearing. With today’s materials these electromagnets canbe quite compact. Unit loadings of 58 lb/in.2 per electromagnet pole face can berealized with silicon steel; and 116 lb/in.2 with iron-cobalt-vanadium alloys. As anexample, to provide an active radial magnetic bearing capable of supporting a 100lb. Static load with a stiffness of 100,000 lb/in. on a 2 inch shaft diameter wouldcall for a 2 inch long bearing.

Radial Repulsion Design. One radially passive design is shown in Fig. 19.20.Here multiples of radially polarized permanent magnets of alternating polarizationare stacked axially with matching sets so that the disks are in repulsion with thehousing. This provides a radially centering force. However, the bearing is axiallyunstable and requires a servo-controlled axial magnet. The bearing has limitedstiffness; Fig. 19.20 shows that for a stiffness of 100,000 lb/in. such a bearingwould be 20 inches long. Furthermore, the bearing does not by itself develop muchdamping and the introduction of eddy currents is required to provide radial damp-ing.

Reluctance Designs. A radially passive bearing using multiple concentric ringson a stator and rotor is shown in Fig. 19.21. The design uses permanent magnetsto energize the radially passive gaps but electromagnetic power can be used aswell. Here the ferromagnetic circuit will seek a geometric arrangement so as tominimize total magnetic ‘‘reluctance.’’ This design is radially stable and it willmaintain a uniform centering force, provided the axial magnetic gaps have an activeservo control. Its greatest disadvantage is that the maximum radial stiffness is lowcompared to the axially destabilizing stiffness. Consequently, to achieve good radialstiffness, large axial electromagnets are required.

19.4 CONVENTIONAL BEARINGS

The bearings described in the present chapter are the most commonly used bearingsin rotating machinery. These are oil lubricated, mostly babbitted journal and thrustbearings which, when properly designed and maintained, will last throughout thelife of the machine. The parameters that determine the adequacy of a bearing designare described first, following which equations, tables and charts supply the numer-ical values of these parameters for various bearing configurations and various setsof operating conditions.

PRINCIPLES OF BEARING DESIGN 19.25

FIGURE 19.19 The direction stabilities of magnetic bearings

19.26 CHAPTER NINETEEN

FIGURE 19.19 (Continued )

PRINCIPLES OF BEARING DESIGN 19.27

FIGURE 19.20 The radial repulsive magnetic bearing.

FIGURE 19.21 The ‘‘reluctance’’ type magnetic bearing.

19.28 CHAPTER NINETEEN

19.4.1 Bearing Parameters

The Minimum Film Thickness. All discussion of bearing performance includesthe term ‘‘load capacity’’ by which is usually meant the load a bearing can supportat a given minimum film thickness. The minimum film thickness is important be-cause it gives an indication of the following:

• The likelihood of physical contact between the mating surfaces which may leadto failure

• The intensities of the peak pressures and temperatures which tend to rise steeplywith a decrease in hmin

• The reserves available in the bearing to accommodate any unexpected increasein load or sudden shaft excursions

There is no fixed value for a satisfactory hmin. It depends upon a number of factorsincluding size of bearing, nature of application, operating conditions, degree ofreliability required, and others. Naturally, in no case should hmin be smaller thanthe sum of the asperities of the two mating surfaces.

The Maximum Temperature. The importance of knowing the value of the filmmaximum temperature, Tmax, is often on a par with that of hmin. While too small,an hmin can cause damage by physical contact, excessive temperatures cause failureeither by softening or melting the bearing surface, and this can occur even whenthere is an ample film thickness. Tmax usually occurs near the trailing edge of thebearing pad. In aligned journal bearings, this Tmax occurs on the axial centerline;in thrust bearings, it occurs near the outer radius where both linear speed and thecircumferential path of the lubricant are largest.

Temperature Rise. It is common practice in industry to use T as a criterion ofbearing performance, this quantity being the difference between the bulk temper-ature of the oil discharging from the bearing and the oil supply temperature.

While monitoring T may be helpful in spotting sudden changes in bearingbehavior, it is a poor indicator of the magnitude of Tmax. Two bearings may havethe same T, yet two radically different values of Tmax, and if a bearing is to failbecause of excessive temperature, it will be Tmax that would initiate the failure.

Thus, while T remains a useful overall indicator of the amount of total heatgeneration and of any untoward changes in bearing behavior, it cannot representor replace the crucial quantity Tmax.

19.4.2 Journal Bearing Performance

For a journal bearing with the nomenclature as sketched in Fig. 19.22, the per-formance quantities of interest can be calculated as follows:

PRINCIPLES OF BEARING DESIGN 19.29

FIGURE 19.22 Conventional 2-axial-groove bearing.

• Film thickness. For an aligned journal it is

h � (h /C) � 1 � � cos (� � �) (19.13)

• Sommerfeld number and load parameter. The Sommerfeld number, given by

2S � (�N /P) (R /C) (19.14a)

has traditionally been the most important parameter. However, a more convenientquantity is the inverse of S, here called load parameter, given by

2 2W � [P / (�N)] (C /R) � [W / (LD�N)] (C /R) (19.14b)

where P � (W /LD) is the unit loading. What this parameter says is that anycombination of P, �, N, C and R, such as to leave the value of W unchanged,would result in the same bearing eccentricity ratio � and attitude angle �.

• Minimum film thickness. This is the smallest distance between the journal andbearing surfaces and is given by:

hminh � � (1 � �) (19.15)min C

19.30 CHAPTER NINETEEN

What is normally referred to as load capacity related to the load W which thishmin can support.

• Friction coefficient. This is the ratio between the frictional force and bearing load(W). It is normally expressed in the form of:

F�ƒ � (19.16)W

• Power loss. This, of course, can be obtained from the value of F� , namely:

H � F R� � ƒWR� (19.17)�

However, the power loss is often given directly in the form of

HCH � (19.18)3 2 3� �N LD

In Eq. (19.18), the quantity by which H is normalized represents the power lossin an unloaded concentric journal bearing, i.e, one in which � � 0. It is knownas the Petroff equation.

• Flow. In a bearing with a single or a multi-pad arrangement, flow of lubricantQ1 enters at the leading edge; an amount of lubricant Qz is lost from sides of thebearing; and flow Q2 leaves at the trailing end of the pad and adheres to themoving surface in most cases. The adhered flow, Q2, is carried to the next padand/or the bearing convergent section. Thus, the net amount of lubricant to bereplenished is Qz. The latter is referred to as side leakage. Clearly we must alwayshave:

Q � Q � Q1 2 z

All of these flows are given in dimensionless form as:

Q � Q / (�NDLC /2) (19.19)

the denominator representing the flow in an unloaded, concentric bearing, i.e., at� � 0 (for which case Qz � 0 and Q1 � Q2).

• Temperatures. For isothermal conditions, a bulk temperature rise can be estimatedfrom the values of power loss and side leakage, namely:

HT � (T � T ) � (19.20)av 1 cwQz

The parameters �, ƒ, 1, z and T , which serve to evaluate the various bearingQ Q max

performance items, are to be obtained from a solution of aforementioned gov-erning equations for the specific geometry and specific operating regimes of thebearing under consideration.

• The problem of viscosity. In most of the expressions, � appears either as a vari-able, or as one of the normalizing quantities. Since in practice viscosity varies

PRINCIPLES OF BEARING DESIGN 19.31

throughout the fluid film, the question arises as to what value to assign to � whenquantitatively evaluating bearing performance. Without going into much detail,several approaches are possible.

a) Inlet viscosity: � � �1 � const. This is the approach most widely used be-cause it is the simplest; it also introduces the largest errors. In this approach,a viscosity, �1, corresponding to the known inlet temperature, T1, is used forall calculations. This may be acceptable for cases where the T is expectedto be low. Even then, it should be kept in mind that in most applications, agiven variation in T produces a much more pronounced variation in � so thata small T may still produce appreciable variations in viscosity.

b) Average viscosity: � � �av � const. The overall aim in this approach isto assume an average temperature, Tav, which yields levels of power loss andside leakage such that when used in Eq. (19.20), the calculated Tav, will bethe same as the assumed one. The steps involved here are as follows:

1. Assume a Tav � T1 which then specifies �av.2. Using the above �av, calculate H and Qz.3. Determine Tav from Eq. (19.20).4. If the assumed Tav from step 1 differs from the calculated Tav in step 3,

assume a different Tav and repeat procedure.5. Continue until the assumed Tav equals the Tav calculated from Eq. (19.20).

Figure 19.23 shows the procedure for arriving at a correct Tav. Plotting theassumed Tav versus the calculated Tav from Eq. (19.20), one can, after several trials,arrive at the correct result which is a point lying on the 45� line. While a correctconvergence may require four or five trials, Fig. 19.23 shows that drawing a straightline through the first two guesses may yield an approximate Tav sufficient for manyapplications.

The use of �av based on the above approach is a very useful and efficaciousmeans for calculating bearing performance, and it provides results of good accu-racy.

Types of Bearing Used. Compressors employ at least half a dozen types of jour-nal bearings. Essentially all of these designs consist of partial arc pads having acircular geometry. The differences are mainly in the number and arrangement ofthe pads and in whether or not the centers of curvature of the pads coincide withthe geometric center of the assembled bearing. This will become clear during dis-cussion of the individual bearing types.

Circular Bearings. The most common journal bearing is what is often referredto as a ‘‘2-axial-groove bearing,’’ portrayed in Fig. 19.24. Its bore is circular andeach of its two identical pads may span anywhere from 120� to 160� in angularextent. A variation of this bearing, shown in Fig. 19.24b, is called the ‘‘overshotgroove bearing.’’ The bottom pad is identical to that of part (a); however, the toppad is cut circumferentially by a deep channel.

The rationale for the overshot groove is to increase the amount of oil flow. Thisit does. However, by flooding the upper half, it also increased the power losses. In

19.32 CHAPTER NINETEEN

FIGURE 19.23 Method of calculating temperature rise.

general, since the load is carried primarily by the bottom pad, the overshot groovein circular bearings does not affect hmin or Tmax one way or another.

Circular bearings, made up of more than two pads, are called 3, 4, or 5 axial-groove bearings. Similar to the 2 axial-groove bearings, the individual pads in thesedesigns are separated by oil grooves with the load passing midway through thebottom pad.

Circular bearings are used extensively since they are easy to manufacture, toinstall, and to repair. Their performance is good as long as stability is not a problem.The angular extent of the pads can be reduced down to 120� without penalty, theload capacity being about the same for all 360� � � 120�. If the bottom pad arcis reduced below 120�, a deterioration in load capacity sets in which acceleratesrapidly when arcs of less than 80� are used.

As is true for most bearings, the smaller the (L /D) ratio, the lower the loadcapacity, through a low L /D, by increasing eccentricity, improves a bearing fromthe standpoint of stability.

Table 19.1 gives the characteristics of 2, 3 and 4 axial-groove bearings.

PRINCIPLES OF BEARING DESIGN 19.33

FIGURE 19.24 The ‘‘overshot’’ journal bearing.

Elliptical Design. A journal bearing which has an increased capability to suppressinstability is the elliptical bearing shown in Fig. 19.25. This bearing looks muchlike the 2 axial groove bearing, but the two lobes are assembled so that their centersof curvature are not coincident. Each lobe has been displaced inward, this displace-ment, expressed as a percentage of the machined radial clearance, being denotedas ellipticity, or ‘‘preload.’’ In effect, then, even for operating at the geometricbearing center, both lobes have eccentricities greater than zero. Larger amounts ofellipticity increase the pad eccentricities and thus provide more stable operation.The design is penalized by higher friction losses, higher flow rates, and reduced

19.34 CHAPTER NINETEEN

TABLE 19.1 Performance of Axial Groove Bearings21

L/D �

2-Groove

� S 1Q

3-Groove

� S 1Q

4-Groove

� S 1Q

1-1/2 0.20.40.60.80.9

6251422923

0.4350.1790.09430.0370.0167

0.1650.2900.3500.3200.290

6749362720

0.990.370.150.050.019

0.110.2050.290.390.40

8072492518

1.90.710.2450.2590.0222

0.0810.160.290.380.37

1 0.20.40.60.80.9

6453452822

0.7140.2750.1250.0410.019

0.270.430.560.460.43

6950372620

1.330.480.1870.0590.022

0.160.300.4350.0590.022

7972492519

2.040.870.300.070.025

0.12

0.390.510.53

1/2 0.20.40.60.80.9

6453422422

2.100.800.310.0820.031

0.320.560.7150.7250.695

7254392720

3.001.060.3850.1030.033

0.2450.470.680.921.04

8072492519

4.231.70.550.110.035

0.200.420.670.840.90

1/4 0.20.40.60.80.9

7057432720

7.942.861.060.2560.074

0.360.670.860.930.87

7456412820

9.613.301.170.270.0735

0.300.6250.901.171.29

7972492519

11.64.51.30.230.73

0.2720.560.891.151.22

load capacity at low eccentricities. At high eccentricities, the behavior of the ellip-tical bearing approaches that of the circular design. The bearing is commonly usedbecause it is effective and is easy to manufacture; with shims placed at the hori-zontal split, the bearing is given a circular bore; then the shims are removed yield-ing the desired ‘‘elliptical’’ geometry.

In order to properly understand and handle the elliptical bearing, the followingcentral fact must be stressed. While, as is customary, journal positions are referredto the geometric center of the bearing (� and �), the quantities that count, i.e., theparameters that determine load capacity, hmin, etc., are the eccentricities and attitudeangles with respect to the lobe centers 01 and 02.

The relation between the bearing parameters and the two lobe parameters are,referring to part (b) of Fig. 19.25, as follows:

2 2 0.5� � (� � m � 2� cos �) (19.21a)1

� sin ��1� � sin (19.21b)� �1 e1

PRINCIPLES OF BEARING DESIGN 19.35

FIGURE 19.25 Geometry and nomenclature in elliptical bearings.

2 2 0.5� � [� � m � 2�m cos �] (19.22a)2

� sin ��1� � � � sin (19.22b)� �1 �2

where:

e e e d1 2� � , � � , � � , m �1 2C C C C

Thus, for a bearing with a certain ellipticity ratio m, when bearing eccentricity and

19.36 CHAPTER NINETEEN

attitude angle (� and �) are given, all other quantities can be determined from theforegoing relationships.

It should be noted here that in all the normalized quantities, the machined bear-ing clearance C is the relevant parameter. Also, the value of hmin, by virtue of whatwas said above, is determined not by � and �, but by the eccentricity of either theupper or lower lobe. If the shaft center is above the horizontal centerline (and, aswill be seen later, this is possible) then hmin is located in lobe No. 2 and hmin isdetermined by:

h � C(1 � � ) (19.23a)min 2

� � 3� /2 � � (19.23b)min 2

If, as happens in the majority of cases, the shaft center is below the horizontalcenterline, then the relevant equations are

h � C(1 � � ) (19.24a)min 1

� � � � � (19.24b)min 2

A convenient quantity in dealing with elliptical bearings is to introduce a bearingeccentricity ratio based not on C, but on the minor clearance Cm. Thus, since

C � (C /C) � 1 � m (19.25)m m

we have for this new eccentricity ratio:

� � (e /C ) � � / (1 � m) (19.26)m m

The usefulness of the above expression lies in the fact that as in circular bearings,the journal cannot travel in the vertical direction beyond �m � 1. (It can do so inother directions.) It is thus possible to plot the loci of journal center for all valuesof m against a common vertical scale, as shown in Fig. 19.26. As seen, at loweccentricities, the shaft center is often above the horizontal centerline locating thebearing’s hmin in the upper lobe. The plot includes, for comparative purposes,m � 0, which corresponds to a circular bearing.

The general performance characteristics of the elliptical bearing are given inTable 19.2 and Fig. 19.27. These are given for the entire practical range of (L /D)ratios and for ellipticity ratios from 0.25 to 0.75. Since m � 0 represents a circularbearing and m � 1 is the limit for possible ellipticity ratios (at m � 1, there iscontact between the surfaces), the plots cover the entire spectrum of elliptical bear-ing design.

Unlike the case of circular bearings, the introduction of an overshot groove inelliptical designs has a telling effect on performance. In essence, an extensiveovershot groove destroys the effectiveness of the bearing as an elliptical design,approximating it to a circular bearing of clearance C.

PRINCIPLES OF BEARING DESIGN 19.37

FIGURE 19.26 Locus of shaft center for elliptical bearings.23

Three-Lobe Design. The 3-lobe bearing represents a further accentuation of thefeatures that characterize the elliptical design. It is more stable than the circularand elliptical varieties, but due to its lower average clearance and smaller arc ofbottom lobe, it shows higher losses and lower load capacities than the two otherdesigns.

As the name implies, the conventional 3-lobe design consists of three pads eachof about 80� to 120� in angular extent, with the bottom lobe placed symmetricallyabout the vertical load. The bearing is shown schematically in Fig. 19.28. Allremarks made in connection with the elliptical bearing regarding the relationships,usage, and importance of the bearing and lobe parameters hold here too, thoughclearly the quantitative relations will be somewhat different. Thus, the relationbetween the parameters of the geometric center (�, �) and of the individual lobesare here as follows:

2 2 0.5� � [� � m � 2�m cos �] (19.27a)1

� sin ��1� � sin (19.27b)� �1 �1

19.3

TABLE 19.2 Performance of Elliptical Bearings23

L/D �m

m � 1/4

� �1,2 S zQ

m � 1/2

� �1,2 S zQ

m � 3/4

� �1,2 S zQ

1-1/2 0.20.40.60.80.91.01.2

11090623832

——

0.330.390.610.810.90——

0.5720.1850.0900.03330.0107——

0.170.290.350.3050.29——

9898927053——

0.520.560.590.740.85——

0.6250.3130.1560.0510.024——

0.230.250.330.3330.30——

87757575—7570

0.750.1780.820.8350.840.850.895

0.250.110.0450.0340.030.0290.019

0.270.2750.2950.300.300.300.30

1 0.20.40.60.80.91.2

10590683530

—

0.320.390.590.810.90—

0.8340.3050.1200.0400.019—

0.2250.4120.5460.4360.430—

9590876748—

0.520.540.600.750.80—

0.4150.2740.1550.0560.024—

0.3220.370.440.470.43—

858081797865

0.750.770.790.810.940.90

0.2850.1430.0870.06070.01550.0202

0.410.410.410.440.440.45

1/2 0.20.40.60.80.91.01.2

10090823830——

0.310.390.510.810.90——

2.00.570.290.0710.0305

——

0.2750.530.720.720.69

——

9085836548——

0.510.540.610.760.86

——

1.30.670.320.110.040

——

0.520.570.670.720.675

——

80807575757567

0.760.780.820.830.840.850.90

0.530.260.0850.0670.0580.0530.030

0.680.690.720.730.730.740.76

1/4 0.20.40.60.80.91.01.2

10095623028——

0.310.410.610.810.90——

7.153.330.960.240.074

——

0.420.590.940.930.93

——

9085807045——

0.510.5450.620.740.875

——

5.552.320.9450.3770.080

——

0.560.720.8250.910.875

——

75757575757568

0.760.780.800.830.840.850.88

1.070.7150.4880.2600.1700.1300.091

0.930.960.970.980.981.001.00

Note: Wherever � � 90, �1,2 denoted �2; otherwise it denotes �1.

PRINCIPLES OF BEARING DESIGN 19.39

FIGURE 19.27 Power loss in elliptical bearings.23

0.5�2 2� � � � m � 2�m cos � � (19.28a)� � ��2 3

2� � sin (� /3 � �)�1� � � sin (19.28b)� �2 3 �2

19.40 CHAPTER NINETEEN

FIGURE 19.28 Geometry and nomenclature of three-lobe bearings.

0.5�2 2� � � � m � 2 �m cos � � (19.29a)� � ��3 3

4� � sin (� /3 � �)�1� � � sin (19.29b)� �3 3 �3

Another detail to be noted is that although C is the machined clearance in allthree lobes; when assembled, this dimension does not physically appear in thebearing. The largest concentric clearance, which occurs at the junction of the threelobes, is less than the machined clearance C, and will here be denoted by CM. Itis given by

C � (C /C) � (1 � m /2) (19.30)M M

whereas m, as before, is given by (1 � m).CFigure 19.29 shows the locus of shaft center in a 3-lobe bearing of 100� arc

extent. Since, as seen here, the shaft never rises above the horizontal centerline,the minimum film thickness will always be located in the bottom pad, and is givenby

h � (1 � � ) (19.31)min 1

Table 19.3 and Figs. 19.29 and 19.30 give the performance characteristics of the3-lobe bearing for three (L /D) ratios and two ellipticity ratios. Together with the3-groove circular bearing given in Table 19.1, which represents the case m � 0, a3-point variation in m is provided from which performance for intermediate valuesof m can be obtained by cross plotting.

PRINCIPLES OF BEARING DESIGN 19.41

FIGURE 19.29 Locus of shaft center for three-lobe bearings.24

It was said previously that the 3-lobe bearing is usually chosen for its superiorstability characteristics and following is a brief illustration of its features vis-a-visthe elliptical bearing. Figure 19.31 shows the stable and unstable regimes plottedagainst Sommerfeld number for the two bearing types. Each of the constant linesgives the locus of the operation of a bearing with a fixed geometry as its speed isvaried. The bearing parameter, �, is given by

2 0.5�LD R W

� � � � � �2�w C CM

which is independent of rotor speed and describes a certain bearing geometry. Asspeed is increased, the bearing will, via S, proceed along a line of constant � andeventually enter the unstable region. The parameter � is most sensitive to bearingdiameter and lobe clearance and less so to the length, L, and viscosity, �. A moveto a higher value of �, i.e., to a more stable region is accomplished by eitherincreasing �, increasing L, increasing D, or decreasing C. Because the ordinateparameter �(MC /W)0.5 also depends upon the clearance, changes in C will followthe slightly inclined dashed lines—toward the left if C is increased, toward theright if C is reduced. At light loads and small clearances, the 3-lobe bearing isbetter than the elliptical bearing. Under heavier loads, the elliptical design is themore stable bearing. It should, however, be kept in mind that it is precisely thelow load range that is the troublesome region of bearing stability.

19.42 CHAPTER NINETEEN

TABLE 19.3 Performance of Three-lobe Bearings* 24

L/D �m

m � 1/2

� �1 S Q

m � 2/3

� �1 S Q

1 0.20.40.60.81.0

4253555030

0.580.630.710.8150.965

0.450.180.100.0480.0063

0.1250.1850.200.2350.28

5050504540

0.710.750.810.850.945

0.210.120.0710.0390.0095

0.180.1850.200.210.23

1/2 0.20.40.60.81.0

4555555030

0.570.630.710.8150.905

0.840.400.200.0840.011

0.2650.310.3350.4250.50

5052504540

0.710.760.810.860.945

0.430.210.110.0540.0125

0.3550.350.380.410.465

1 0.20.40.60.81.0

4545454030

0.5750.650.7450.8450.965

2.51.00.410.130.021

0.370.510.540.610.75

6255585244

0.700.750.800.860.945

1.160.590.330.120.025

0.530.530.530.5740.58

*For m � 0 see Table 19.1.

When a bearing is absolutely stable, the whirl ratio approaches zero and Fig.19.31b shows the variation of the whirl ratio at the threshold of instability. Thewhirl ratios with the 3-lobe and the elliptical bearings share similar characteristics.They both rise sharply at S � 0.1 � 0.2 and remain fairly constant thereafter. Theelliptical bearing which is the less desirable for lightly loaded applications is seento have a whirl ratio in excess of 0.5, thus a worse ratio than the 3-lobe bearing.The whirl ratio is an important parameter in determining the stability threshold fora flexible rotor which is always lower than that for a rigid rotor. Thus, Fig. 19.31bcan be viewed as the highest possible stability that can be achieved with thesebearings.

Tilting Pad Bearings. Unlike the previously considered designs, the tilting padbearing is a generic name which covers many permutations. Its primary character-istic is that the individual pads are not fixed in position, but are pivot-supported sothat during operation not only does the shaft move in response to operationalconditions, but so do the pads, and each pad in a different fashion. A general pictureof a pivoted shoe bearing is shown in Fig. 19.32. The complexity of the design ispartly evidenced in the configuration of a single pad given in Fig. 19.32b.

Several things ought to be noticed. In the first place, the criterion of hmin as ameasure of load capacity somewhat loses its meaning here since this hmin is not a

PRINCIPLES OF BEARING DESIGN 19.43

FIGURE 19.30 Power loss in three-lobe bear-ings.24

fixed distance; rather the film thickness over the pivot, hp , is a geometrically fixedpoint. Under excessive load, given that the pad at hmin can yield whereas at hp itcannot, failure is more likely to occur at hp. Thus, the critical quantity here isperhaps hp rather than hmin. The next thing to realize is that the center of curvatureof the pad is not fixed in space; when the pad rocks above the pivot, its center ofcurvature moves either in a positive or negative angular direction, shown in Fig.19.32b by ��. Next, should the preload be too low, some of the pads on the topof the bearing may become unloaded, in which case, as shown in Fig. 19.33, thefluid film frictional moment about the pivot will make the leading edge of the padscrape against the journal and cause ‘‘flutter,’’ obviously an undesirable contin-gency. The condition that the top pads not be unloaded is dictated by the amountof preload and shaft position; the lower the preload and the higher �, the morelikely that some of the pads will become unloaded. Figure 19.34 gives a samplegraph, in terms of �m and m, when a pad is likely to be unloaded. In this respect,loading between the pads, when the journal may reach �m � 1, is a more undesirablemode of operation.

The number of possible design parameters and operating modes in a tilting padbearing is large. Some of these design options are:

• Number of pads, 3 � n � 8

• Angular extent of pads, including the option of a variation of for various pads

19.44 CHAPTER NINETEEN

FIGURE 19.31 Stability characteristics of el-liptical and 3-lobe bearings.1

• Load vector passing between pads or over a pad

• Central or eccentric pivot location, i.e., a choice of value for ( p / )

• (L /D) ratio

• Preload, m � 1 � (Cm /C)

• Pad inertia, which often determines the ability of the pad to follow or trackjournal motion.

PRINCIPLES OF BEARING DESIGN 19.45

FIGURE 19.32 Tilting pad journal bearing.

19.4.3 Thrust Bearings

Much of what has been said previously about journal bearings applies also to thebehavior of thrust bearings. It thus remains only to point out the differences thatarise due to the different geometry of a thrust bearing shown in its generic elementsin Fig. 19.35.

Thrust bearings are simpler to handle in that no cavitation occurs and in that itis sufficient to solve only for one pad (for a parallel runner, all pads are identical).The geometry of the film, on the other hand is more varied. The film shape in

19.46 CHAPTER NINETEEN

FIGURE 19.33 Unloaded tilting pad.

journal bearings is more or less universal, namely that prevailing between twoeccentric circular cylinders. In thrust bearings—it can be anything—shapes withone or two directional tapers, with or without flats, crowned profiles, pocket bear-ings, and finally tilting pad designs. Another simplification with thrust bearings isthat no instability problems, such as occur with journal bearings, arise in theiroperation. There is, thus, no need to evaluate stiffness and damping.

The Reynolds equation for thrust bearings has to be written in polar instead ofrectangular coordinates. In parallel to journal bearings, turbulence is accounted foron a point-by-point basis, here a function of r as well as �

3 3� rh G �p 1 � h G �p rz x� � 6 (19.32)� � �� 2�r �� (L /R )�r � r � 2

where Gx , Gz are the turbulence coefficients in the � and r directions respectively,both functions of the Reynolds number given by:

Re � �r�h /� � ƒ(r, �)

The expressions above differ from those for the journal bearing in that they havea dependence on r. This is due to the variation of the velocity profile and flowwith r and to the film thickness being a function of both coordinates, r and �.

Tapered Land Bearings. The simplest tapered land bearing is one which has aconstant angular taper, or:

h(�) � h � (1 � � / ); � (h � h ) (19.33)2 � � 2 1

with its geometry as shown in Fig. 19.35. This equation, independent of r, is valid

PRINCIPLES OF BEARING DESIGN 19.47

FIGURE 19.34 Regime of unloaded pads in a five-pad tilting pad bearing.18

for a bearing surface with a circumferential taper alone. As will be shown later,the exact shape of the fluid film between fixed values of h1 and h2 does not affectthe results appreciably. Thus, by their simplicity, the one-dimensional taper solu-tions provide a useful key for evaluating the performance of thrust bearings ingeneral.

The several crucial parameters in journal bearings are , (L /D) and (e /C). Par-allel quantities appear in thrust bearings, namely, , the angular extent of the pad;(L /R2); and (h2 /�) with � (like C) being a geometric quantity and h2 being thetrailing film thickness at which the bearing is run. It should be also noted that here

h � h (19.34)min 2

Solutions for the tapered land bearing are given in Table 19.4, where:

19.48 CHAPTER NINETEEN

FIGURE 19.35 Elements of tapered land thrust bear-ing.

Q � (Q /�R NL ) (19.35)r r 2 �

is the side leakage, the index R1 indicating the leakage along the inner radius, andR2 indicating the leakage along the outer radius. The total side leakage is then

Q � [Q � � Q � ] �R NLr r R r R 2 �1 2

The leakage out the end of the pad, Q2, is given by:

Q � 0.5�NLh (R � R ) � Q �R N (19.36)2 2 1 2 2P 2 �

where the first right-hand term is the shear flow and does not involve any computerobtained coefficients. The value of 2P can be obtained from Table 19.4 by sub-Qtracting r from ( ).Q Q � Qr 2P

Table 19.5 shows the relative load capacities and friction of three different thrustbearing configurations. One is a plane slider, i.e, an inclined rectangular block; thesecond, a slider with an exponential film profile; and the third is the tapered landgeometry of Eq. (19.33). As seen, the results for a given value of (h1 /h2) are nearlyidentical, confirming the assertion that once h1 and h2 are fixed, the exact variationin h between these values is not of great importance.

In all of the above results, it should be noted that P is the unit pressure givenby:

19.4

TABLE 19.4 Solutions for Tapered Land Thrust Bearings25

All values are for single-pad

LR2

�

(deg)

2�N L� �P 0

at R1 at R2

rQ�

2pQ

r � (r � R1) /L� � � /

Center of pressure

� rH�

2 4��N R2

1 /3

1/2

1/4

1/8

80554030

1.4231.1800.9470.870

0.3210.2570.2250.211

0.08550.7140.06520.0635

0.02780.02470.02380.0242

0.340.320.280.235

0.350.320.290.245

0.350.320.290.235

0.360.330.290.25

0.400.440.810.75

0.470.440.400.36

0.470.440.410.36

0.480.450.410.37

0.870.840.810.75

0.870.840.790.74

0.870.830.780.70

0.850.810.750.67

0.640.0250.610.605

0.710.690.670.66

0.780.760.740.73

0.830.8150.7950.78

0.370.450.490.51

0.370.470.500.51

0.410.450.5050.52

0.4650.500.510.565

2.441.6851.200.95

3.942.702.001.57

5.964.253.232.54

8.516.234.883.91

19.5

TABLE 19.4 Solutions for Tapered Land Thrust Bearings25 (Continued )

All values are for single-pad

LR2

�

(deg)

2�N L� �P 0

at R1 at R2

rQ�

2pQ

r � (r � R1) /L� � � /

Center of pressure

� rH�

2 4��N R2

1 /2

1/2

1/4

3/8

80554030

1.721.4941.4351.489

0.4020.35850.3520.370

0.11380.10620.10800.1103

0.04020.03990.04230.0470

0.230.190.1450.11

0.230.190.150.11

0.240.200.150.11

0.250.200.160.11

0.4050.360.310.20

0.410.330.310.26

0.420.270.320.27

0.420.280.320.27

0.750.690.610.57

0.740.610.600.53

0.720.650.560.49

0.700.620.530.44

0.620.610.600.59

0.6850.670.6550.65

0.7550.7350.720.71

0.810.780.770.765

0.480.510.530.55

0.460.520.530.55

0.480.520.540.56

0.500.530.550.57

2.901.961.471.13

4.723.332.491.92

7.325.294.0653.18

10.818.066.305.01

19.5

2/3

1/2

1/4

1/8

80554030

2.2402.1852.3202.590

0.5380.5370.5780.653

0.15980.16550.18200.2085

0.05990.06490.07370.0861

0.120.0820.0520.033

0.130.0840.0530.034

0.130.0870.0550.035

0.140.090.0560.036

0.350.2950.2450.200

0.350.300.250.20

0.360.300.250.21

0.3650.310.250.21

0.600.530.480.44

0.580.510.450.40

0.560.460.400.38

0.530.440.350.29

0.610.600.590.59

0.670.660.650.645

0.7350.720.710.705

0.790.780.7650.75

0.500.550.580.61

0.510.560.590.61

0.530.570.600.62

0.550.580.610.63

3.062.121.571.20

5.073.592.702.07

8.005.704.433.46

12.078.986.945.47

19.52 CHAPTER NINETEEN

TABLE 19.5 Performance of Thrust Bearings with VariousFilm Configurations25

� Plane slider* Exponential slider** Sector pad***

2 2PL h2P � 4��R2

2.002.502.85

0.08100.1130.135

0.08190.11370.135

0.08260.1060.125

Fh2F � 4��R2

2.002.503.04

0.660.740.84

0.810.8750.95

0.780.8250.88

*h � �x**h � k1e

***h � h2 � (1 � � / )

P � W /Area � 360W / [n �L(R � R )]T 2 2

where is in degrees, WT is the total load on the thrust bearing and n the numberof pads. Also it should be noted that the data for flow and power loss in Table19.4 are for a single pad so that the total flow and losses are

Q � nQ H � nHT pad T pad

Composite Tapered Land Bearings. A more practical and preferred thrust bearinggeometry is a tapered land bearing having tapers in both the circumferential andradial directions with a flat portion at the end of the film. Its advantages are: (1) ithas higher load capacity; (2) has lower side leakage and, (3) at low speed andduring starts and stops it provides a flat surface for supporting the load, thus min-imizing wear. The geometry of such a bearing is shown in Fig. 19.36. Its filmthickness is given by:

h � h � [(h � h ) /L](r � R )11 11 12 1

h � [(h � h ) /L� (r � R ) � h11 11 12 1 2� � (19.37)� �b

for 0 � � � b

h � h constant for b � � � 2

Normalizing all h’s by h2 and all radii by R2 we have:

PRINCIPLES OF BEARING DESIGN 19.53

FIGURE 19.36 Composite tapered land bearing.

� r � (L /R ) � l �2h � h � (h � 1) � 1 � (19.38)� � � �11 11 rb (L /R ) b 2

for 0 � � � b

h � 1 for b � � �

The expression for has, as seen, three arbitrary parameters:h

• 11 � (h11 /h2) � the dimensionless maximum film thickness at the lower lefthcorner

• r � (h11 � h12) /h2 � the radial taper along the leading edge � � 0

• b � the friction of tapered

In an optimization study in which both load capacity and lower power losseswere considered, the following desirable proportions for the above three parameterswere arrived at:

h � 3.0 � 0.5 b � 0.811 r

Physically, the above numbers imply a maximum film thickness at (R1, 0) of threetimes the one over the flat; an outward decrease in film thickness at the leadingedge half that of h2; and a flat portion equal to 20% of the pad’s angular extent.The performance of such a bearing for the case of a 40� bearing pad an (OD /ID)

19.54 CHAPTER NINETEEN

TABLE 19.6 Composite Tapered Land Thrust Bearings22s (R2 /R1) � 2; � 40�, h11 � 3,r � 0.5; b � 0.8

Re1

2Wh24�R �1

H *hc 24 2R �1

Q /R12h2�

at � � 0 at R1 at R2

HW�h2

500 0.1920.1820.175.0168.0151

3.923.883.783.683.42

1.581.581.591.591.60

0.2960.2940.2930.2920.290

0.4370.4450.4510.4560.469

17.618.318.518.719.1

1500 0.3370.3070.2890.2750.240

8.457.937.597.316.63

1.611.621.621.631.64

0.3240.3210.3190.3180.314

0.4550.4650.4710.4760.490

21.521.621.821.922.3

3500 0.5670.4990.4630.4350.369

15.614.013.21.25

11.2

1.631.641.641.651.66

0.3390.3340.3310.3290.325

0.4620.4750.4820.4880.504

23.223.223.323.423.7

*Hc includes losses over a 10� oil groove. All results are per individual pad.

ratio of 2 is given in Table 19.6. The table provides data for both turbulent andlaminar operation.

The following comments will, perhaps, be useful:

• The values of the Reynolds number

Re � �R �h /�1 1 2 1

• The losses as represented by HC in column 4 include the losses over a 10� oilgroove; the losses H over the pad only can be obtained from the last column inTable 19.6.

• The flow QIN represents the inflow at � � 0. The outflow will, be given by:

Q � Q � (Q � Q )2 IN R R1 2

• The lowest value of Re1 given is 500. This value is close to laminar operation.

• For the total bearing, the values of W, HC, Q and H should all be multiplied bythe number of pads.

Tilting Pad Bearings The comments made about the tilting pad journal bearingregarding its complexity and large number of parameters apply equally well to thethrust bearing. However, in the case of a pivoted thrust pad such as the one shown

PRINCIPLES OF BEARING DESIGN 19.55

FIGURE 19.37 The hydrodynamics of a tilting pad thrustbearing.

in Fig. 19.37, an additional complication overshadows the other difficulties; thereis theoretically no solution to a planar centrally pivoted sector. This can be deducedfrom the pressure profile sketched in Fig. 19.37a. Such a profile must always beasymmetrical with respect to the center of the pad; an asymmetrical pressure profilewould impose a moment about the pivot tending to align the pad parallel to therunner. However, a parallel pad produces no hydrodynamic pressures, thus makingthe working of such an arrangement impossible. Yet such centrally pivoted, planarsurface thrust bearings are widely used and they perform exceedingly well.

Various theories have been advanced and stratagems employed to explain theworkings of these bearings and obtain a solution to the problems. Among theseare:

• Thermal or density wedge—The variation in viscosity or density of the oil isoften credited with generating hydrodynamic forces in the parallel film. At best,such effects produce forces which come nowhere near the heavy loading sup-ported by such bearings.

19.56 CHAPTER NINETEEN

• Thermal and elastic distortion of the pad—As shown in Fig. 19.37b, thermal andelastic stresses may crown a pad, so that in essence it produces a convergent-divergent film. In that case, it is possible for the resultant load to pass throughthe pivot and the pad can support a load. However, such bending can occur onlywith very thin pads or extremely high temperature gradients. Yet such bearingsperform satisfactorily even with very thick pads and under conditions of minimalheat generation.

• Incidental effects—There are a number of incidental features which may play amore important role than the above theoretical explanations. Among these are:

• Machining inaccuracies on the faces of both runner and bearing and roundedoff edge at entrance to the pad, which in effect constitute a built-in taper

• Misalignment between runner and pads during assembly or during operation• Pivot location not exactly at 50% of pad angular extent

These factors would combine to generate hydrodynamic forces and they areperhaps the most likely explanation for the satisfactory working of tilting pad thrustbearing.

19.5 LOW-SPEED BEARINGS

One of the requirements in the bearing described in the previous section is a properlubrication system. This includes a pump delivering oil at 10 to 50 psi supplypressure with all the accompanying equipment such as oil tank, filters, piping, sumpand cooling arrangements. When the bearings run at relatively low speed involvinglow power dissipation and therefore low bearing temperatures—as in fans, blowersand some compressors—one can simplify the system by employing oil-ring lubri-cation. This consists of a self-contained oil delivery package placed adjacent to thebearing which dispenses with all the auxiliary equipment required for a more de-manding operation.

Figure 19.38 shows the components of an oil-ring lubrication setup. The ring,riding on the top of the exposed shaft, is a sort of viscous drag device that lifts oilfrom the sump and deposits it on the shaft. It is clear that in comparison to apressurized supply system where the oil is distributed along an axial groove, herethe amount of oil lifted is not sufficient to provide the bearing with a complete oilfilm, and therefore an important parameter in oil ring operation is the amount ofoil the bearing receives relative to what it needs for a full film. This is called thestarvation ratio and is given by

Q � Q /Qz z zF

where Qz is the side leakage under starved conditions and QzF is the side leakagefor a full film.

PRINCIPLES OF BEARING DESIGN 19.57

FIGURE 19.38 Oil-ring lubrication system.

19.5.1 Regimes of Operation

The value of starvation ratio depends on shaft and ring speeds. Due to the centrif-ugal effects of the rotating ring and attached oil one can distinguish four regimesof ring behavior, as shown generically in Fig. 19.39. The characteristics of theseregimes are as follows:

Regime I. At the low end of journal rotation, there is contact between ring innersurface and the journal, and the linear speeds of the two mating surfaces are aboutthe same. There is thus a linear rise in ring rpm with the rpm of the journal. Theoil delivered by the ring rises throughout this regime. At the upper end of Regimel, ring speed and oil delivery reach a local maximum.

Regime II. At the beginning of this regime, direct frictional drag yields to a stateof boundary lubrication between ring and journal. Due to this, slippage occurs andring speed drops. Since the speed has decreased, so too does the amount of oildelivered by the ring. However, with further rise in journal speed, a full hydrody-namic film is established between journal and ring. The reduced viscous friction(the friction coefficient may drop from 0.1 to 0.01) and the larger film between the

19.58 CHAPTER NINETEEN

FIGURE 19.39 Oil ring behavior as function of journal speed.15

mating surfaces bring about a rapid increase in both ring speed and oil delivery.Once again, at the upper end, a local maximum in ring speed is achieved. Oil flow,however, at the end of this regime is an absolute maximum and represents thehighest possible oil delivery by the ring.

Regime III. The drop in ring speed and oil delivery following Regime II is as-sociated with the onset of ring oscillations in the plane of rotation. While smalloscillations already appear during the trailing portion of Regime II, the values of�� become, within a short span, very large, bringing about a drastic reduction inoil delivery. While, due to these planar oscillations, the ring speed drops onlyslightly, the oil delivery is affected to such a point that at the end of this regime itapproaches asymptotically zero. The angular swing of the ring at its maximumvalues can be of the order of �5� to �10� with an oscillatory frequency equal tothat of ring rotational frequency.

Regime IV. This regime, essentially beyond our interest, is characterized by con-ical and translatory vibrations of the ring. While the oscillatory motion abates andthe ring speed once again tends to increase with journal speed, oil delivery isessentially zero. The frequency of both the conical and translatory (or axial) vi-brations is that of ring rotational frequency. Starting with the oscillatory vibrations

PRINCIPLES OF BEARING DESIGN 19.59

FIGURE 19.40 Full and starved fluid films.

and proceeding through the two other modes of instability, the violent motion ofthe ring causes splash and a throw-off of oil from the surface of the ring, and partlyalso from the journal, so that little oil reaches the bearing.

Figure 19.40 presents the hydrodynamics of a starved journal bearing vis-a-visa full film or flooded condition. For a fixed load, speed and supply oil temperature,the deviations of a starved bearing from one operating with a full fluid film are asfollows:

• The film starts later and terminates earlier, that is �1 � �IF and �2 � �IF, producingin essence something similar to a partial bearing, though the upstream, and some-times also the downstream, boundary conditions are different.

• The eccentricity increases, producing smaller values of hmin.

• The attitude angle decreases, yielding a more vertical locus of shaft center.

• Since oil supply is equivalent to side leakage, there is a reduction of bearing sideleakage and consequently an increase in fluid film temperatures. This is somewhatmitigated by a reduction in power loss due to a shorter extent of the fluid film.

Table 19.7 gives a set of solutions for a wide range of loads and levels ofstarvation. It is seen that the effects of starvation are much more pronounced atlight and moderate loads, which are due to the fact that, at heavy loads, the fullfilm extends over a narrower arc and the pressure gradients at Q1 being higher, alower amount of Q1 is required to form a film. The loci of shaft center, both forconstant oil supply values 1 and for constant loads, W, are given in Fig. 19.41. ItQ

19.60 CHAPTER NINETEEN

TABLE 19.7 Theoretical Performance of Starved Journal Bearings16

� � const; � 150�; (L /D) � 0.93

W %Qz � �, degs 1Q zQ �1, deg z, degs

0.491 00.93.1

12.029.053.0

100*

1.00.903.808.625.446.272.081

036

11182878

0.100.200.400.600.800

1.03

0..899 � 10�3

.309 � 10�2

.0122

.0289

.0534

.100

180175171163155144105

01322406086

150

1.965 0.0.72.8

12.430.350.2

100*

1.00.906.818.657.516.395.285

059

17263757

0.100.200.40.600.800

1.03

0.208 � 10�2

.0817

.0357

.0875

.162

.289

180172167155144129105

016295782

101150

9.825 0.1.56.4

15.628.060.0

100*

1.00.914.846.793.753.702.672

1419243137

0..100.200.300.400.600.809

0..659 � 10�2

.0291

.0697

.125

.267

.445

100168158148139122105

025466982

108132

34.39 0.4.8

19.438.761.3

100*

1.00.929.896.881.073.866

01117212326

0..100.200.300.400.560

0.0192.0802.162.253.413

180160144131120105

038737986

110

98.25 012.938.766.193.8

100*

1.0.954.947.946.945.944

01216171818

0..100.200.300.400.423

0.0463.138.235.335.357

180149131118107105

0507087

100101

*Full fluid film.

PRINCIPLES OF BEARING DESIGN 19.61

FIGURE 19.41 Locus of shaft center at different levels of starvation.15

L /D � 0.93; � 150�

is seen that starvation displaces the locus of shaft center inward of the full filmline, i.e., towards higher eccentricities and lower values of attitude angle �.

From the above and the parametric studies described in Section 19.9 the follow-ing conclusions can be drawn:

• Except at very low speeds, most oil ring bearings operate under starved condi-tions.

• The load capacity of oil ring bearings, first increases then decreases with risingshaft speed.

• The locus of shaft center of oil ring bearings is much closer to the vertical axisthan in full film bearings.

• An optimum in the (L /D) ratio exists in oil ring bearings which ranges from 0.6to 0.8.

• The effects of starvation are much more pronounced at low and intermediateloads than at high loadings.

19.62 CHAPTER NINETEEN

19.6 HIGH-SPEED AND HIGH-TEMPERATURE BEARINGS

This chapter will consider bearings suitable for operation at extreme speed andtemperature ranges. These two parameters may occur either together or indepen-dently, that is, although usually high speed implies high temperatures, the reverseis not always so. One can have lower or moderate velocities, but the environmentmay be such that the bearing will be exposed to high temperatures and the fluidfilm, the lubricant and bearing materials must be able to cope with it. The otherimportant consideration in high-speed bearings is that of stability. As will be seenbelow, the likelihood of bearing instability, known as half-frequency whirl, riseswith rotational speed. This becomes particularly intense when speeds twice thenatural frequency of the system are reached.

The kinds of bearings that are possible candidates for such applications are gasbearings, either hydrodynamic or hydrostatic; compliant surface geometries; andmagnetic bearings.

19.6.1 Gas Bearings

The differential equation governing the behavior of gas bearings is that given byEq. (19.39). For liquids, � � constant and the density terms fall out of the equation.In gas bearings, it varies with both pressure and temperature. In most cases, theperfect gas equation is applicable, or

P� RT (19.39)

�

Two factors make the gas film in bearings isothermal; one is the low heat gen-eration; the other is the high thermal capacity of the bearing shell as compared tothe tiny volume of gas in the film. We therefore have

� � RT � P � const � P (19.40)

and Eq. (19.39) becomes

3 3� ph �P � ph �p �(ph)� � 6U (19.41)� � ��

�x � �x �z � �z �x

All the solutions given subsequently are based on this expression with the properboundary conditions applied to each specific geometry.

As was pointed out in Section 19.3, unlike with liquids, gas bearing behaviordepends on the ambient pressure. Thus, for example load capacity increases witha rise in pa. A new dimensionless parameter now makes an appearance whichgoverns gas bearing behavior given by:

PRINCIPLES OF BEARING DESIGN 19.63

26�� R� � (19.42)� �P Ca

called the Bearing number. Thus, along with geometry and such variables as(L /D) ratio, load, speed, etc., the value of p, or, in dimensionless form, �, consti-tutes now an additional input.

Full Circular Bearings. These bearings are the most commonly used if for noother reason that they are easy to manufacture, requiring no grooves or holes forlubricant supply. In obtaining a solution it is only required that at the sides of thebearing the hydrodynamic pressures fall to ambient pressure p, in most cases theatmosphere, Pa. Figures 19.42 and 19.43 give the load capacities and frictionallosses for full (360�) gas journal bearings for a range of (L /D) ratios from 1/2 to2 and for the entire spectrum of possible � values. It can be shown that when� → 0, the gas bearing solution approaches that of a liquid; thus the solutions inthe figures comprise cases from liquid lubricants to gases of very high compress-ibility. The reason that the (L /D) ratios range as high as 2 is to compensate for theinherently low load capacity for gas bearings.

Non-Circular Geometries. As was pointed out in Section 9.4, elliptical and 3-lobe geometries are often resorted to because of their higher stability characteristics.This is particularly desirable with gas bearings which tend to become unstable athigh speeds. The solutions given in Section 19.4.2 for these bearings are for cen-trally loaded cases, that is when the load vector passes midway through the bottomlobe. However, this is not the optimum mode of loading; better results can beobtained when the bearing is so positioned in the housing that the load is made topass through the bottom lobe at an angle �L, see Fig. 19.44, called the load angle.

Load Capacity. There is a rather large number of independent parameters whendealing with noncircular gas bearings. Assuming even, as was done here, that thespace or slots between the individual lobes occupy a negligible portion of the arc,i.e., assigning to the elliptical bearing two arcs of 180� span each, and to the 3-lobe bearing, three symmetrical (they do not have to be equal) arcs of 120� each,we are still left with five independent parameters, namely

p � p[(L /D), m, � , � , �]B B

A solution for any set of these five parameters will yield the load capacity in theform of the Sommerfeld number S, and the line of action of the resultant force, orload angle �L with respect to the geometry of the bearing.

Tables 19.8 to 19.12 give the results with regard to load capacity and some ofthe other bearing performance characteristics. It should be kept in mind that sinceload capacity means the relation between Sommerfeld number and minimum filmthickness, this hmin is provided not by the bearing eccentricity which is unrelatedto the surface curvature, but by the value of one of the lobes, i.e.

19.64 CHAPTER NINETEEN

FIGURE 19.42 Load capacity of full (360�) gas journal bearing.7

h � C(1 � �) (19.43)min

In order to obtain this hmin, we must search from among the two or three lobes themaximum lobe eccentricity ratio. The values of � listed in the tables and figuresare these maximum eccentricity ratios. These most often occur in the bottom lobe.In the few cases when the maximum � occurs in Lobe No. 2, this can be identifiedin the tables from the fact that for the elliptical bearing this would require � �90�; and for the 3-lobe bearing � � 60�.

While in a circular ungrooved bearing the direction of load application is im-material, this is not so in the case of non-circular designs. The most common modeof bearing operation is with the load vector parallel to the vertical line of symmetry.

PRINCIPLES OF BEARING DESIGN 19.65

FIGURE 19.43 Friction in full (360�) gas journal bear-ings.7

This is the natural way of mounting the bearing and it is also useful in that itenables two-directional rotation. However, this is not necessarily the optimum ar-rangement. Applying the load at various angles to the vertical centerline wouldyield different values of bearing performance. Somewhere an optimum angle existsfor the direction of load application and these are shown in Tables 19.9 and 19.11.In practice it means that depending on the parameters S and �, the bearing shouldbe rotated with respect to the load vector anywhere from a few degrees to as muchas 25� and nearly always in the clockwise direction, in order to obtain the maximumload capacity.

Figure 19.45 summarizes graphically some of the data contained in the tables.Table 19.12 is a practical summary of the various implications contained in thepreviously discussed results. In practice, one is usually confronted with the givenrequirements of speed, load, ambient conditions, etc. In other words, S and � arefixed. Given these parameters, Table 19.12 shows what eccentricities one can obtainby using a circular or non-circular design.

Stiffness Characteristics. As was done with load capacity and friction, the stiff-nesses of the various bearings will be considered at identical Sommerfeld numbersfor all the designs. This means that they will be evaluated at different values of S.This is pertinent from a practical viewpoint since the designer wants to know whatthe stiffness of the bearing will be under the given conditions of load, speed, etc.

19.66 CHAPTER NINETEEN

FIGURE 19.44 Nomenclature for non-circularbearings.

regardless of where the journal positions itself in the bearing clearance as a con-sequence of the imposed operating conditions. Since shaft displacement in differentdirections produces different responses, here the displacement will be consideredin the direction of the load vector. Thus here the definition of the spring constantis given by K � (dF /de), where F is the response force to a displacement alongthe load line. Table 19.13 and Fig. 19.46 give the results. We see immediately theprofound improvement in stiffness in the non-circular over the circular design. Inthe region of low eccentricities where instability usually occurs (low load, highspeed), the value of the spring constants for the elliptical and 3-lobe designs arenearly an order of magnitude higher.

PRINCIPLES OF BEARING DESIGN 19.67

TABLE 19.8 Centrally Located Elliptical Gas Bearings26

L /D � 1 m � 1/2

�B

�B at � �

1/2 1 3

� at � �

1/2 1 3

� at � �

1/2 1 3

0.10.20.30.40.45

7575705030

60605030—

302720——

0.530.580.670.820.92

0.560.620.730.87—

0.590.680.79——

1019252214

9161813—

5.7.57.5——

�B

S at �

1/2 1 3

at �G

1/2 1 3

� �E

1/2 1 3

0.10.20.30.40.45

0.2830.1350.07720.03410.0147

0.2500.1170.06250.0270—

0.2820.1280.700——

0.0790.07030.0455

�0.02040.0412

0.1270.1250.06200.0444—

0.1220.1010.0717——

3.283.413.704.546.27

3.283.403.764.90—

3.213.373.86——

Special Design. Several unorthodox configurations which have in the past beenused on high-speed equipment, including automotive gas turbines, are bearings withgrooved surfaces and foil bearings. Figures 19.47a and 19.47b show a herringbonegrooved journal bearing and two versions of spirally grooved thrust bearings. Inboth designs, the bearing or runner surface consists of a lattice of grooves andridges. From a hydrodynamic point of view, the geometry essentially consists of aseries of step bearings though, unlike with conventional steps, these are at an angleto the direction of motion. One of the achievements of such a design is that thefluid is being driven away from the edges of the bearing, minimizing side leakageand raising load capacity. By a proper orientation of the grooves, the fluid can bepumped away from either the inner or outer periphery or from both edges. Theadvantages of these bearings also lie in the fact that, whereas an ordinary geometryhas poor stability characteristics for a concentric shaft position (� � 0), the her-ringbone bearing is superior to a conventional bearing at low eccentricities. Thesedesigns can, of course, be used also with liquid lubricants.

Hydrostatic Bearings

Thrust Bearings. Hydrostatic gas bearings are subject to an instability calledpneumatic hammer. It is therefore necessary that their recess volume be kept to aminimum. Referring to Fig. 19.48, this means that r1 and are small. The entrance

19.68 CHAPTER NINETEEN

TABLE 19.9 Optimally Loaded Elliptical Gas Bearings26

L /D � 1 m � 1/2

� B �B � � S �L G

1/2 0.10.20.30.40.45

8080808080

0.530.570.630.690.73

1120283537.5

0.2970.1430.08790.05810.0474

�3�4�7

�10�13

0.07980.07350.06080.04080.0279

1 0.850.100.1750.200.290.400.475

80807575758075

0.520.530.570.5750.640.690.77

9111720263536

0.3620.3080.1600.1490.08880.06190.0411

�12�12�9

�13�12�18�19

0.1370.1310.1240.1200.09950.07530.0204

3 0.090.110.22

808075

0.520.530.60

101221

0.4490.3360.163

�23�23�21

0.1980.1960.168

flow area 2�r1h from the recess into the clearance will then become more restrictivethan the orifice area (�dS

2 /4) in which case the bearing is said to be inherentlycompensated. With an inherently compensated bearing the recess pressure po willequal the supply pressure ps and the drop (ps � p1) across the bearing film isgoverned by the equation:

2 / � ��1 / �2� p p1 1m � C A p � (19.44)� �� D o s (� � 1)RT p ps s

where m is the mass flow of the gas in lbm/s; Ao is the entrance throat area 2�r1hin in.2; T is the gas temperature in �R; and � is the ratio of specific heats.

To avoid pneumatic hammer gas thrust, bearings must be designed with inherentcompensation. For a design with an (r1 /r2) ratio of 0.1. Figures 19.49 and 19.50provide appropriate design charts, given in terms of a parameter B defined as

1 / 212�A C 2�RT ln(r /ro D 1 2B � (19.45)�� 3h p � � 1 �a

The chart in Fig. 19.49 presents the dimensionless flow, m�, for various values of� (ps /pa) while Fig. 19.50 gives load capacity. Chart 5-10 offers values of bearingp

stiffness K.

PRINCIPLES OF BEARING DESIGN 19.69

TABLE 19.10 Centrally Located Three-lobe Gas Bearings

L /D � 1 M � 1/2

�B

�B at � �

1/2 1 3

� at � �

1/2 1 3

� at � �

1/2 1 3

0.10.20.30.4

70676353

444237—

0.57(2)*0.64(2)0.71(2)0.81

0.560.640.730.85

0.580.660.76—

112(2)106(2)99(2)23

8.414.918.317.2

7.111.713.5

�B

S � �

1/2 1 3

at � �G

1/2 1 3

at � �F

1/2 1 3

0.10.20.30.4

0.2930.1340.07340.0370

0.3010.1350.07340.0352

0.4370.1940.106—

0.03580.03680.03700.0314

0.09020.08600.07730.0550

0.07360.06750.0575—

3.623.864.30—

3.603.824.25—

3.553.764.13—

*(2) indicates that minimum film thickness occurs in right-hand lobe.

TABLE 19.11 Optimally Loaded Three-lobe Gas Bearings26

� �B �B � � S �L G

1/2 0.10.20.30.4

60606060

0.560.620.700.78

9162226

0.2840.1280.07200.0418

973

�5

0.03580.03640.03620.0336

1 0.0850.100.1750.200.280.300.400.455

5555606060606060

0.550.560.610.620.680.700.780.83

14.51621222628

0.3850.3000.1650.1400.08930.08100.04770.0347

1.51

�4�5�6.5�8

�13�17

0.05800.09020.05640.08620.05210.07900.04250.0359

3 0.100.2250.30

505060

0.570.670.70

81522

0.4440.1710.121

�6�7

�17

0.1170.06550.0578

19.70 CHAPTER NINETEEN

TABLE 19.12 Comparison of Load Capacity of Various Gas Bearings; (L /D) � 1 Valuesof � for Given � and S

� sm � 0

Circular

Ellipticala m � 1/2

�L�� Optimum

3-lobea m � 1/2

�L � 0 Optimum

1 0.3650.1620.8660.0381

0.20.40.60.8

0.54 (�170)0.59 (�48)0.67 (�12)0.815 (�2)

0.525 (�162)0.56 (�40)0.635 (�6)0.77 (�4)

0.55 (�175)0.615 (�54)0.70 (�17)0.84 (�5)

0.545 (�172)0.605 (�51)0.685 (�14)0.815 (�2)

3 0.3650.1620.0860

0.250.4750.655

0.57 (�132)0.65 (�37)0.75 (�14)

0.535 (�114)0.59 (�24)0.685 (�4)

0.595 (�38)0.68 (�43)0.80 (�22)

0.57 (�128)0.645 (�36)0.755 (�15)

a Numbers in parentheses refer to percentage reduction in load capacity from a circular design.

FIGURE 19.45 Load capacity of symmetrically loaded gasbearings.26

PRINCIPLES OF BEARING DESIGN 19.71

TABLE 19.13 Values of � K /2�LN (C /R)3 26K

For L /D � � � 1

� Sm� 0

Circular

m � 1/2

Elliptical

�L � 0 Optimum, �L

3-Lobe

�L � 0 Optimum, �L

1 0.3650.1620.08660.0381

2.85.4

12.887.2

26.229.442.496.0

10.2—

26.471.6

22.428.637.4

115.6

—20.026.4

152.6

3 0.3650.162

5.56.8

20.025.8

26.431.2

16.446.2

—40.4

FIGURE 19.46 Spring constants for symmetrically loaded gasbearings.26

19.72 CHAPTER NINETEEN

FIGURE 19.47 Special bearing designs.

FIGURE 19.48 Hydrostatic gas thrust bearing.

PRINCIPLES OF BEARING DESIGN 19.73

FIGURE 19.49 Mass flow rate in hydrostatic thrust bearing.34

FIGURE 19.50 Load capacity of hydrostatic gas thrust bearing.34

19.74 CHAPTER NINETEEN

FIGURE 19.51 Stiffness of orifice and inherently-compensated hydrostatic thrustbearing.34

To use the charts for design purposes one first needs to know value of ps todetermine B for the maximum obtainable stiffness from Fig. 19.51. From Fig. 19.50one then determines the r2 that will carry the required load W. The value of (h /r2)is set within the limits of 0.5 � 10�3 � (h /r2) � 2 � 10�3. With r2 and h established,the actual dimensional values of stiffness k and flow rates can be calculated fromFigs. 19.49 and 19.50. Refinements are possible by a few more iterations.

Journal Bearings. Typical configurations for journal bearings are shown in Fig.19.52a and b. The former is an inherently compensated design; the latter has anorifice restrictor. Here, too, the recess must be small, of the order of 10% of anincompressible fluid pocket. Capillary restrictors are not used because they causepneumatic hammer.

The analysis of these bearings is very complex and possible only with numericalmethods. A typical set of performance curves for an L /D � 1/2 is shown in Figs.19.53 and 19.54. The first shows stiffness as a function of a restrictor coefficient�s for various ratios of (ps /pa). This �s is similar to the B parameter in thrustbearings for it represents the ratio of fluid film resistance to the resistance of therestrictor. The parameter appearing in the coordinates is defined as

2 � (d /4hr ) (19.46)1

which gives the ratio of the throat area for an orifice restrictor to the throat area

PRINCIPLES OF BEARING DESIGN 19.75

FIGURE 19.52 Two bearing geometriesof hydrostatic gas journal bearings.

represented by the restriction of the bearing film. Its inclusion in the figures permitsone to use these charts for both modes of restriction.

The K values presented are the center stiffness of the bearing (� � 0). Since thestiffness remains essentially constant up to � � 1/2, load capacity of the bearingcan be calculated from W � �CK; or since it is not recommended that the bearingsoperate at higher eccentricities, the load capacity is given by W � 0.5 CK whereK is obtained from Fig. 19.53.

19.6.2 Complaint Surface Bearings (CSB)

In high-speed, high-temperature applications the CSB’s have the advantage of de-veloping higher load capacities than with fixed geometry gas bearings. Since CSB’shave a complex structure consisting of a spring-like substructure with an overlyingflexible surface, there exists a great variety of permutations on any given design.The presentation here will start with two basis models of a journal and a thrust

19.76 CHAPTER NINETEEN

FIGURE 19.53 Stiffness of a hydrostatic gas journal bearing.34

FIGURE 19.54 Flow in a hydrostatic gas journal bearing.34

bearing, to be followed with some more elaborate geometries. In all cases thelubricant will be that of air.

Foil Journal Bearing. The solution of this bearing is based on Eq. (19.39), cou-pled with additional expressions accounting for the elastic behavior of the top andbottom surfaces. The journal bearing is portrayed in Fig. 19.55 and its solution isbased on the following postulates.

PRINCIPLES OF BEARING DESIGN 19.77

FIGURE 19.55 Configuration of a foil journal bear-ing.

• The stiffness of the foil is uniformly distributed around the circumference and islinear with the amount of deflection.

• The foil is assumed not to ‘‘sag’’ between bumps but to follow the deflection ofthe bumps.

• In response to the hydrodynamic pressures, the deflections are local, i.e., theydepend only on the force acting directly over a particular point.

19.78 CHAPTER NINETEEN

FIGURE 19.56 Minimum and nominal film thicknesses.

Under the above conditions the variation in h is due to the eccentricity e andthe deflection of the foils. We then have:

h � C � � cos (� � � ) � K (p � p ) (19.47a)o 1 a

where K1 is a constant reflecting the structural rigidity of the bumps, given by:3

�C 2p s la o 2K � ; � � (l � � ) (19.47b)� �1 p CE ta

K1 is then the compliance of the bearing with the quantities, s, lo and t portrayedin Fig. 19.55c.

The Nominal Film Thickness. In rigid journal bearings, the minimum film thick-ness is a clear and fixed quantity. It occurs at the line of centers and its value isconstant across the axial width of the bearing. Also, generally, the film thicknessanywhere is constant in the z direction. Since in our case pressures cause propor-tional deflections of the bearing surface, the film thickness in the interior ofthe bearing, where pressures are highest, will be larger than at the edges (z ��L /2); also since the maximum pressures occur near the line of center, the filmthickness in the interior at � � �0, are larger than at angular position � � �N. Figure19.57 shows a three-dimensional film thickness plot for a 120� pad in which, whilefilm thickness at the edge (z � L /2) is small over most of the pad area, the surfacehas been deflected into much larger values of h.

For these reasons, a nominal film thickness hN will be defined as the minimumfilm thickness that occurs along the bearing centerline, i.e, at z � 0 at variousvalues of � as shown in Fig. 19.58. While hmin for the rigid case occurs at � �180�, with increasing values of �, the value of this hmin, or our hN, shifts downstreamand increases in value; at � � 5, it is twice the value of the rigid case and hasshifted downstream by nearly 100�. This should be kept in mind later on, whenload capacity, i.e., the W � hN relation is plotted; an increase in load while in-creasing � may also produce an increase in the nominal film thickness.

PRINCIPLES OF BEARING DESIGN 19.79

FIGURE 19.57 Film thicknesses in a 120� bearing pad.

FIGURE 19.58 Location of nominal film thickness.9

Active and Effective Bearing Arc. Compliant foil bearings suffer a penalty intheir ability to generate hydrodynamic pressures whenever the pad arc commencesin a diverging region. The effect can be seen in Table 19.14 which show that byshifting in a 360� bearing the line of centers from 180 to 270�, there was a loss inload capacity of nearly 30% as well as a reduction in hN.

19.80 CHAPTER NINETEEN

TABLE 19.14 Effect of Load Angle in 360� Bearings9

� � 0.6; (l /d) � � � � � 1; �1 � 0, �E � 360�

�o �L � �2 Pmax hN W � 102 T � 10

020�

45�

60�

90�

180�

220�

245�

270�

—163.1�

141.6�

129.8�

107.2�

33.1�

�11.9�

�41.9�

�72.9�

—4�

11.6�

20.2�

27.2�

33.1�

28.1�

23.1�

17.1�

—32�

74�

95�

142�

240�

272�

300�

325�

01.0181.0871.1331.2011.2531.2451.2281.201

0.400.410.480.520.580.620.620.610.58

01.04

11.521.440.056.854.950.040.1

—42.938.133.927.224.623.723.725.5

In designing a foil bearing, if the eccentricity is fixed for the particular appli-cation, it is best to start the bearing at �S � � (for a vertical load); if the eccen-tricities are liable to vary, some compromise value of �S � 0 can be chosen.

Performance Characteristics. There are six geometric, structural, and opera-tional parameters relevant to a foil journal bearing. These are , �, (L /D), �, �L,and number of pads. There is also the eccentricity ratio and the attitude angle �,the latter tied to the load angle �L. A set of standard conditions consisting of

(L /D) � � � � � 1; � � 0.6

is used, and any parametric variation commences from this set of reference values.The Full Bearing. Table 9.15 gives a detailed listing of the performance of a

vertically loaded (�L � 0) full 360� bearing as a function of (L /D), �, and �. Noteshould be taken of the fact that the start of the bearing, that is �s is so chosen asto avoid idle (p � ps) regions at the upstream portion of the bearing. In effect, thisrequires that �s � �. The case of nonvertically loaded foil bearings �L � 0, isgiven in Table 19.15. Some of the noteworthy points emerging from these tabula-tions are:

• Effect of �. While in terms of � there is a drastic drop in load capacity with amore compliant bearing, in terms of hN there is actually an increase in loadcapacity.

At large values of �, � � 10, the load the bearing can support is low, due tothe fact that the flexible foil deflects sufficiently to maintain high film thicknesseseven at large eccentricities. Thus from a design standpoint, it may be advisableto use high compliance bearings at low loads; high loads, however, can be sup-ported only with bearings of low values of �. In highly compliant bearings (par-ticularly at high L /D ratios), an increase in eccentricity may produce an increasein hN, a phenomenon opposite to rigid bearings where hmin is the inverse of �.

PRINCIPLES OF BEARING DESIGN 19.81

TABLE 19.15 Performance of � 360� Foil Journal Bearing9

� � 1; �L � C

� � � � �1 �2 � � maxP Nh � 102W � 10T

0.3 015

1020

63.559.048.560.034.0

81.587.0

100.5114.0114.0

L /D � 0.51.0461.0431.0371.0251.017

0.700.720.800.850.94

4.44.23.22.92.1

9.349.158.538.097.54

0.6 015

1020

40.036.032.030.027.0

62.076.097.0

105.0114.0

1.251.1441.0731.051.033

0.400.510.680.7950.90

17.913.78.36.14.2

15.8513.938.197.336.54

0.9 015

1020

12.019.021.021.021.0

52.071.091.099.0

108.0

3.731.331.121.0771.048

0.100.410.640.760.91

157.334.714.89.86.3

26.113.89.88.57.3

L /D � 1.0

0.3 015

1020

37.049.036.028.020.0

97.0104.0117.0120.0132.0

1.1731.1071.0611.0411.025

0.700.770.941.041.14

27.923.714.810.36.37

22.721.218.617.516.5

0.6 015

1020

36.033.028.525.020.0

77.095.0

112.0117.0120.0

1.5391.2531.1141.0741.046

0.400.620.901.0551.22

94.956.828.819.412.2

31.124.619.116.915.0

0.9 015

1020

13.021.022.021.519.0

59.086.094.0

108.5127.0

4.8501.4341.1541.1031.063

0.100.520.861.051.26

504.5102.842.927.817.2

58.228.119.516.714.4

19.82 CHAPTER NINETEEN

TABLE 19.15 Performance of � 360� Foil Journal Bearing9 (Continued )

� � 1; �L � C

� � � � �1 �2 � � maxP Nh � 102W � 10T

L /D � 1.5

0.3 015

52.043.029.021.0

103.0113.0119.0141.0

1.2181.1521.0761.048

0.700.821.031.13

70.053.228.518.3

33.430.426.424.8

0.6 015

35.032.026.022.0

88.0104.0120.0137.0

1.7311.3111.1351.084

0.400.681.001.18

208.9112.052.034.1

45.634.326.323.1

0.9 015

14.023.023.0

68.095.0

112.0

5.3001.4851.184

0.100.560.96

298.9179.774.2

85.139.226.7

• Effect of �. The performance of a foil bearing as a function of � conforms tothe familiar pattern of compressible lubrication. After an initial rise in withWan increase in �, the load capacity, both in terms of an increase in as well asWa rise in N, tends to flatten off and approach an asymptotic value. The torque,hhowever, rises almost as a linear function of the increase in �. The more com-pliant bearing shows lower power losses due to the prevailing higher film thick-ness.

The Multipad Bearing. The 3-pad design consists of three 120� arcs; the 5-paddesign has five 72� arcs. In each case, the vertical line of symmetry bisects thebottom pad, so that �L � 0 represents a load passing through the midpoint of thebottom pad. Tables 19.16 and 19.17 give a spectrum of solutions for the perform-ance of the 3-pad bearing and these results show the following:

• Variation with load angle. Because of the cyclic nature of this bearing (symmetryfor each 120�) there is much less variation in either W or T with a shift in loadangle. In particular, there is no acute loss of load capacity when the line of centerspasses between pads. The optimum load angle for � � 1 is �L � �10�; for � �5 it is �L � �14�. The improvement in load capacity over that of central loading(�L � 0) is of the order of 10 to 15%.

• Variation with number of pads. Figure 19.59 shows the variation of 1-, 2-, and3-pad bearings as a function of load angle. The plot shows clearly a drop in loadcapacity with the number of pads, i.e., with a drop in extent of bearing arc .As seen, the optimum for the 360� bearing occurs at �L � 0, at which point the

PRINCIPLES OF BEARING DESIGN 19.83

TABLE 19.16 Performance of a Three-pad Bearing (L /D) � � � 1, � 20� 9

� �1 �L � maxP � 102W T � 10

0.3 40210217220225245273

�140.07.2

�2.3�2.3�5.2

�10.0�17.4

79.237.227.027.729.855.077.6

1.0731.0721.0751.0791.0821.0881.077

12.112.713.714.114.615.012.6

21.421.821.922.022.021.521.4

0.6 29180200

2202245270

�145.044.1

�2.6�10.6�17.0�25.5

69.244.130.629.448.064.5

1.1881,1331.1971.2151.2841.185

24.025.237.229.834.928.7

27.818.627.728.829.027.4

0.9 15194210230245260

�145.00.0

�10.8�14.1�14.7�26.2

50.916.319.2

333.950.553.8

1.4971.3401.3751.5721.4121.463

59.369.576.974.352.455.3

62.934.745.771.877.356.6

� � 5

0.3 38210214220225245275

143.05.10.0

�5.3�8.6

�13.3�11.1

74.935.134.334.736.451.773.9

1.0491.0381.0401.0431.0451.0531.050

0.017.527.878.318.609.078.18

20.721.121.121.221.220.820.7

0.6 12180205220245270

�145.055.0

3.6�9.7

�16.3�23.1

67.455.528.630.348.7466.9

1.1041.0481.0771.1031.1211.106

15.712.616.118.318.415.9

25.416.525.326.727.225.4

0.9 25200203210230245260

164.03.50.0

�4.3�16.3�18.9�21.5

61.023.523.023.733.746.158.5

1.1781.1221.1191.1581.1981.2021.186

24.425.326.328.129.718.225.2

46.534.436.241.667.172.153.7

19.84 CHAPTER NINETEEN

TABLE 19.17 Mode of Load of 3-Pad Bearing9

(L /D) � � � 1; � 120� eachCentral Loading �L � 0; Optimum Loading

� � � W �L � W

1 0.3 37.5 13.8 �10 55.0 15.01 0.6 28.5 36.0 �10 29.0 39.81 0.9 16.0 68.0 �10 18.5 78.05 0.3 35.0 7.8 �14 53.0 9.05 0.6 30.0 17.0 �14 41.0 18.65 0.9 23.5 26.2 �14 30.0 29.8

FIGURE 19.59 Performance of multipad bearings.8

torque also reaches it minimum value. The 3-pad bearing, as said previously,reaches an optimum at �L � �10�; whereas the 5-pad bearing reaches an opti-mum at �L � �15�.

Stiffness. Table 19.18 gives the values of the four spring coefficients for twovalues of compliance, the limiting case of � � 0, and � � 1. The � � 0 casediffers from a rigid gas bearing in that the subambient pressures are eliminatedfrom the pressure profile. A comparative evaluation of the stability characteristicsof the 1- and 3-pad bearings is, of course, best done in a study of a rotordynamicsystem, particularly when the cross coupling components vary not only in magni-tude but also in sign. However, the following items can be deduced from the tab-ulated � data:

PRINCIPLES OF BEARING DESIGN 19.85

TABLE 19.18 Values of Spring Coefficients8

(L /D) � �; �L � 0

� � � W xxK xyK yxK xxK

� � 360�

0.6 0 35.7 0.951 1.920 �0.125 �2.345 3.2370.75 0 24.1 1.894 3.416 �1.166 �3.989 8.9810.9 0 12.8 5.055 7.202 �6.024 10.151 44.5930.6 1 32.1 0.568 1.129 0.174 �0.693 1.1300.75 1 26.3 0.7833 1.231 0.0254 �0.686 1.3780.9 1 21.4 1.028 1.268 �0.098 �0.627 1.602

3-pad-120� each

0.6 0 26.0 0.635 1.123 �0.092 �2.05 2.6350.75 0 17.4 1.321 2.102 �0.752 �3.710 7.4320.9 0 8.6 3.695 4.728 �3.344 �8.768 37.1030.6 1 25.5 0.359 0.5702 0.0451 �0.758 0.8010.75 1 20.5 0.511 0.673 �0.017 �0.821 1.0510.9 1 16.3 0.689 0.759 �0.057 �0.855 1.274

• When plotted against W the Kyy’s are about the same for both designs, whereasthe Kxx’s are lower for the 3-pad configuration.

• With the more compliant case, the K’s tend to level off with a rise in eccentricity,the values of the coefficients approaching the structural stiffness of the system.

In general, the advantage of compliant bearings in the area of stability is thatlevels of stiffness can be selected by the designer via a proper combination ofstructural and hydrodynamic stiffnesses. Thus, instead of making the bearing’s in-ertia and support suit the inherent stiffnesses of purely hydrodynamic bearings, thedesigner may try to tailor and adjust bearing stiffness to the demands of his rotor-dynamic system.

Foil Thrust Bearings. Figure 19.60 shows the configuration of the thrust bearingconsidered next, which resembles that of a conventional tapered land design. Allthe postulates stated in connection with the journal bearing apply here as well,except, of course, that the film thickness is different. This is now given by

h � h � g(r, �) � C(p � p )2 a

where geometric function:

g(r, �) � (h1 � h2)[1 � � /b ] for 0 � � � b

g(r, �) � 0 for b � � �

19.86 CHAPTER NINETEEN

FIGURE 19.60 The geometry of compliant surfacethrust bearing.

Geometric Optimization. As shown in Table 19.19, the maximum pressurechanges vary little with an increase or decrease in or the value of h1. The tablealso shows that when the total number of pads possible for a given value of isaccounted for in the calculation of the total load capacity, there is little differencein the choice of a particular arc length. The effect is shown in Fig. 19.61 for botha relatively stiff and soft bearing. In both cases, the nominal film thickness doesnot vary with . The total load capacity in a full 2� thrust bearing shows a max-imum somewhere between 45� and 50�. The effect of the proportion of ramp isshown in Fig. 19.62. For a relatively stiff bearing, the optimum is about 70%,which is close to the case of rigid bearings. For the more compliant case, theoptimum is 50%. For high values of �, the optimum value of b recedes to valuescloser to 40%. It can be seen that near the highest values of W, the nominal film

PRINCIPLES OF BEARING DESIGN 19.87

TABLE 19.19 Effect of on Bearing Performance9

(L /R 2) � 0.5; b � 0.5

1h �* �* n � 102W � 103T maxp TOT � 102W

2.5 4 1.2 30456075

1286

0.2590.4300.5730.686

4.196.098.029.98

1.02881.03201.03291.0331

3.123.443.443.30

3.0 3-1/3 1.0 30456090

12864

0.2570.4350.5880.808

4.135.977.81

11.58

1.02931.03341.03491.0349

3.083.483.533.23

4.0 2.5 0.75 30456090

12864

0.2380.4150.5740.814

4.015.827.56

11.08

1.02851.03360.03591.0372

2.863.323.443.26

thickness is also at its highest, thus reinforcing a general load capacity optimumfor compliant bearings at about b � 0.5.

The effect of varying 1 is given in Table 19.20. It shows that while the valuehof changes little with a variation of 1, the nominal film thickness goes up˜ ˜W happreciably, doubling in value for a doubling of h1. Thus, in terms of customaryload capacity criteria, the highest values of l seem desirable.h

To summarize, the optimum geometry for a bearing with the common OD toID ratio of 2 is:

˜ � 45�, b � 0.5, h � 101

Performance Characteristics. The performance of a compliant foil bearing forthe optimized parameters of � 45� and b � 0.5 are given in Table 19.21 for awide range of parameters 1, �* and �*. In terms of h2 normalization the range ofh� extends to nearly 1000 and that of � to over 60. Figure 19.64 is a performanceplot in terms of the basic variables involved in the bearing. The drop of loadcapacity with an increase in film thickness and with a decrease in the value of �are trends known from other studies of gas bearings. What is particularly note-worthy in Fig. 19.63 is the effect of � on load capacity. While at moderate �’shigh values of � yield the highest load capacity, at high � the optimum � is someintermediate value, in our case �* � 1. Note should be taken that all quantities,i.e., �*, �*, and are all normalized by the geometric ramp height ; and thath*Nthe Fig. 19.63 plots contain implicitly various values of h1. The relation between

1 and N is given in Fig. 19.64. This graph can be used to determine various ramp˜ ˜h hheights for different points of Fig. 19.63. The 1 � N graphs support the conclusion˜ ˜h h

19.88 CHAPTER NINETEEN

FIGURE 19.61 Effect of on pad and totalload.8

of the previous section as to the desirability of using high values of 1 since theyhyield high nominal film thicknesses. It also shows that the higher �� and �� are,the higher the film thickness.

Finally, Fig. 19.65 gives a plot of the spring constant for the bearing. The stiff-ness of the bearing is, of course, a function of both the structural stiffness asrepresented by KB and of the hydrodynamic film stiffness. Since they are in parallel,

PRINCIPLES OF BEARING DESIGN 19.89

FIGURE 19.62 Effect of extent of ramp on per-formance of CS thrust bearing.8

TABLE 19.20 Effect of 18h

� 45� L /R 2 � 0.5, b � 0.5 �* � 1.0, �* � 10

1h � 102W � 10T Nh * � 103K

10 8.169 44.5 5.106 11415 8.626 72.2 7.675 11617 8.730 83.3 8.730 11619 8.811 94.5 9.730 11720 8.845 100 10.265 122

high loads would tend to flatten the values of K for the softer bearings, leavingessentially the structural stiffness KB as the dominating spring constant.

Advanced CSB Designs. The construction of CSB’s lends itself to a number ofmodifications that can enhance a particular performance characteristic in accord-ance with operational requirements. Due to their analytical complexity and space

19.90 CHAPTER NINETEEN

FIGURE 19.63 Load capacity of CS thrust bearing.8

limitations, they cannot be discussed to any extent but a mere listing of some ofthem will give an idea of the range of possibilities latent in this group of bearings.

CSB’s with Variable Direction Stiffness. The bump foil design can be manip-ulated to provide a wide range of desirable dynamic properties. One such arrange-ment to vary the stiffness in both radial and circumferential directions is shown inFig. 19.66. The stiffness gradient permits the formation of a variable hydrodynamicwedge in accordance with variation in load or speed. As speed increases, the par-ticular arrangement can be made to increase film convergence which enhancesstability precisely when it is needed. In one such application, an advanced air-lubricated journal bearing reached speeds of 135,000 rpm carrying a unit load ofclose to 100 psi. These advance bearings are capable of operation above rotors’bending critical speeds (super-critical operation), which is beyond any hydrody-namic bearing capabilities.35

Much of the above applies also to thrust bearings. A proper thrust bearing ge-ometry is one that has a taper in the circumferential direction followed by a flat

19.9

TABLE 19.21 Compliant Foil Thrust Bearing Performance � 45�, B � 0.5, (L /R 2) � 0.5

�*

�* � 0

� 102W *Nh � 10T * � 103K

�* � 1

� 102W N*h � 10T * � 103K

�* � 4

� 102W N*h � 10T � 103K

� � 20

� 102W N*h � 10T * � 103K

1 � 2h

0.1 0.014 1.0 0.024 0.314 0.104 1.001 0.024 0.314 0.014 1.004 0.024 0.321.0 0.144 1.0 0.241 3.24 0.145 1.011 0.24 3.20 0.147 1.046 0.23 3.35

10.0 0.632 1.0 2.40 38.6 1.52 1.114 2.27 31.5 1.214 1.326 2.04 17.520.0 3.33 1.0 4.79 76.4 2.736 1.197 4.34 45.5 1.828 1.461 3.78 18.840.0 6.246 1.0 9.50 125.0 4.238 1.276 8.21 51.5 2.406 1.574 7.05 16.4

1 � 5h

0.3 0.192 0.25 0.35 12.2 0.204 0.268 0.341 14.0 0.206 0.316 0.31 2.3 0.152 0.452 0.24 5.241.0 2.343 0.25 3.50 171.0 1.833 0.378 2.72 77.7 1.164 0.538 2.07 29.8 0.513 0.834 1.43 6.92

10.0 22.2 0.25 33.5 1230.0 6.633 0.635 17.3 104.0 2.697 0.905 12.9 26.1 0.854 1.15 10.2 3.6420.0 34.66 0.25 65.2 1730.0 8.135 0.71 30.8 95.7 3.362 0.978 28.6 19.740.0 46.4 0.25 127.0 2060.0 9.231 0.758 57.0 78.0 3.612 1.015 44.9 14.7 0.915 1.18 38.8 1.16

1 � 10h

0.1 0.66 0.111 1.63 91 0.661 0.161 1.30 61.1 0.571 0.192 1.15 40.5 0.464 0.234 0.98 25.01.0 8.818 0.111 16.1 1,120 2.170 0.307 7.81 113.0 2.309 0.38 6.50 64.8 1.619 0.485 5.38 35.6

10.0 60.38 0.111 150.0 6,120 8.109 0.566 44.5 114.0 5.345 0.695 37.5 56.7 3.323 1.825 32.3 25.020.0 86.84 0.111 292.0 8,240 9.457 0.630 79.5 95.6 6.020 0.785 68.0 45.0 3.627 0.88 59.8 18.5

1 � 20h

0.1 2.084 0.0526 6.60 575 1.103 0.16 3.54 90.0 0.843 0.162 2.91 52.2 0.623 0.209 2.39 29.71.0 22.35 0.0526 64.6 4,720 3.876 0.282 18.3 128.0 2.705 0.364 14.8 70.6 1.83 0.404 12.1 37.8

10.0 134.8 0.0526 605.0 26,600 8.845 0.54 100.0 117.0 5.674 0.666 83.6 56.2 3.467 0.790 71.7 24.320.0 185.5 0.0526 1179.0 34,200 10.24 0.596 179.0 97.5 6.280 0.722 152.0 44.0 3.733 0.835 113.0 17.7

19.92 CHAPTER NINETEEN

FIGURE 19.64 Relation between 1 and N.8h h

portion. A CSB can be constructed with a foil possessing stiffening elements atthe trailing edge, as shown in Fig. 19.66b. The stiffening elements placed betweenthe top and bump foils provide a variable stiffness gradient from the leading totrailing edge yielding the desired converging shape.

CSB’s with Controlled Coulomb Damping. A foil bearing can be constructedto improve internal damping and thus enhance its stability characteristics. This canbe done by affecting the Coulomb damping due to the relative motion between thetop and bump foil surfaces, as well as between the bump foil and the housing (seeFig. 19.67). This relative motion occurs, of course, when the bearing is loaded andthe foils are radially deflected. To improve the friction characteristics of this relativemotion, the rubbing surfaces are sputter coated with copper, silver, or some otherhigh friction material. Sometimes the surfaces of the journal and mating top foilare coated with dry lubricants to minimize friction on start-up and shutdown. Tofurther enhance stability, the bump foil can be circumferentially split along axiallines to improve alignment and axial compliance. A single pad design of this varietyhas carried unit loadings up to 100 psi.

CSB’s with Cantilevered Leaves. A bending dominated foil bearing is the can-tilevered leaf type design. A journal bearing of this type is shown in Fig. 19.68a.Here each leaf is preformed with a specific radius to induce a desirable film profile.The thrust bearing variety is shown in part b. It is essentially a thin plate withsprings mounted below it which is separated by a backing plate from a foil assem-bly plate to which the leaves are attached. The plates are in the form of annularrings and the leaves in the form of annular sectors. The leaves should be thin

PRINCIPLES OF BEARING DESIGN 19.93

FIGURE 19.65 Stiffness of compliant foil bearings.8

enough to permit considerable flexibility but still thicker than the hydrodynamicfilm.

19.6.3 Magnetic Bearings

To illustrate the potential of magnetic bearings, a specific design example will befollowed through. It will provide orientation and a guide for general cases wheretheir use is contemplated, particularly with regard to controlling instability andresonances at high speeds.

General Principles. Practical AMBs are mostly the attractive type. Radial AMBsgenerally adopt an 8-pole stator configuration as shown in Fig. 19.69. Both thestator and journal consist of laminations of ferromagnetic material. The journal isshrunk on a shaft without windings. The use of laminations reduces eddy current,which not only causes power loss, but degrades the dynamic performance of thebearing. The stator poles are separated into four quadrants. In each quadrant, the

19.94 CHAPTER NINETEEN

FIGURE 19.66 Variable support stiffnessin compliant bearings.

FIGURE 19.67 Mechanism for Coulomb damping in foil journal bearing.

PRINCIPLES OF BEARING DESIGN 19.95

FIGURE 19.68 Garrett self-acting compliant foil bearing.

electromagnetic windings are wound in such a way that the magnetic flux circulatesmainly inside the quadrants so that each quadrant of poles can be controlled in-dependently.

Magnetic force is proportional to the ratio current to air-gap squared (Fig. 19.70).To support a load in a controlled axis (Fig. 19.71), unequal steady state or biascurrents are induced in opposite pairs of poles, such that

2 2 2W � ƒ(I � I ) /C (19.48)1 3

where I1 � I3

ƒ � a magnetic pole constant for a given number of windings.

The bias current produces an I2R loss, which is a major power loss in an AMB.However, the total resistance in the current path is not large; the AMB loss is ingeneral insignificant compared to fluid film bearings. The journal floating in themagnetic field due to its bias currents alone is unstable. Linearized feedback controlis achieved by making the air gap large relative to the journal’s vibrations. Forstable operation, the journal motion must be sensed and corrected instantaneouslyand continuously by superimposing a small control current to each bias current.

19.96 CHAPTER NINETEEN

FIGURE 19.69 An 8-pole configuration of an active magneticbearings.

FIGURE 19.70 Nonlinearity of magnetic force.2

PRINCIPLES OF BEARING DESIGN 19.97

FIGURE 19.71 An independently controlled axis.

For example, as shown in Fig. 19.71, when the journal moves up by a smalldisplacement, the current in the top quadrant will be reduced to a small amount, i,and the bottom quadrant increased by i. The control currents produce a net down-ward force, F, which pulls the journal back to the center. From sensing Y to pro-ducing F, a series of AMB components are involved, namely sensor, controller,power amplifier and electromagnets.

AMB Components

Electromagnets. For a given maximum load including static and dynamic loads,the AMB physical size is determined by the saturation flux density of the lami-nation material. For the 8-pole configuration,

5 2F � 5.75 � 10 A B (19.49)max p s

where Fmax � maximum load, NAp � surface area per pole, m2

Bs � saturation flux density, Weber/m2

The maximum value of the flux density in the linear range which is about 90% ofthe actual Bs value should be used in applying Eq. (19.49). Choosing the axiallength Lp , the circumferential pole width is Ap /Lp. The radial dimensions can be

19.98 CHAPTER NINETEEN

determined from a given shaft diameter at the AMB. For sizing, the followingguidelines should be followed:

• The cross-sectional area at any point of the flux path is not less than Ap.

• Adequate wiring space is provided.

• The axial length is no greater than the journal OD.

• As a rule, the air gap should be 10 times the expected journal vibration.

The pole surfaces are the most effective areas for heat dissipation via convection.The ampere-turns per pole is fixed for a given ferromagnetic material; the optimalchoice of winding turns, Mt is a trade-off of total current and inductance load, L,to the power amplifiers. The latter is proportional to ApC which is a crucial2Nt

parameter causing control delay and bearing instability.More than 8 poles can be designed for the stator, such as 16 or 24 evenly spaced.

A large number of poles saves radial space because it localizes flux circulation.The coil pairs can be in series or parallel to a power amplifier with the same trade-off.

Power Amplifiers. Converting a low power control voltage signal to a highpower control current and actuating the electromagnets requires power amplifiers.Two types are commercially available the linear and the pulse-width-modulation(PWM) type. The linear amplifier applies the control signal to a power transistorin an ‘‘active mode.’’ The transistor continuously regulates the current through thewindings from a DC source, Vs, with the current directly proportional to the controlsignal. The PWM type applies the control signal to generate high voltage pulsesat a fixed frequency above audible range. The on-time period of each pulse isproportional to the input signal. The voltage pulse train produces current to thewindings. The PWM type is electrically noisy and needs its own filters. The powertransistors operate in a ‘‘saturation mode’’ with much less power loss.

There are three requirements for the power amplifiers. First, the control current,i, cannot be larger than the bias current. Second, the inductance of the electromag-nets causes the control current to diminish and delay above a certain frequency(cut-off frequency). The PWM amplifiers usually apply their own current feedbackto increase this frequency. Third, the value of Vs /L, called the current slew ratelimit, is the maximum amperes per second that the amplifier can provide.

Sensors. Three displacement sensors prove to be practical: the capacitanceprobe, inductance, and eddy current probe. Each has its advantages and disadvan-tages, but all relate the small distance between the stationary sensor and the rotatingshaft to an output electrical signal in volts. A low-pass filter is usually included inthe sensor conditioning device to eliminate high frequency noise, including its ownFM carrier. This filter, similar to the power amplifier cut-off characteristics, maycause a significant time delay in the frequency range of interest. A phase-leadcircuit implanted in series in the feedback loop can reduce the delay.

Using displacement probes, journal velocity sensors are not needed in feedbackcontrol. Different analog circuits, such as a differentiator with a low-pass filter, and

PRINCIPLES OF BEARING DESIGN 19.99

FIGURE 19.72 A single-axis control diagram.

phase-lead circuits have been used to produce a pseudo velocity from the displace-ment measurement.

An analog surrogate called a velocity observer, instead of differentiating dis-placement, integrates journal force (equivalent to acceleration) to obtain velocity.The output of any pseudo velocity circuit is a combination of displacement andvelocity signals. Thus, its feedback not only produces damping, but also contributesto the stiffness.

AMB Stiffness and Damping. From the previous discussion, a practical singleaxis control can be represented by the block diagram of Fig. 19.72. A radial AMBneeds two independently controlled axes like this, while a thrust AMB needs onlyone.

A second-order, low-pass filter was assumed to be part of the sensor though itcould have been a fourth-order or other type of filter. Gp is the sensor sensitivity;e.g., 1000 V/in. (40 V/mm). A phase-lead circuit is applied in series here forcompensating the time delay caused by the inductance loads to the power ampli-fiers. One may set the phase-lead parameter ‘‘a’’ to be equal to the amplifier cut-off frequency, �a. Thus a system ‘‘zero’’ cancels a system ‘‘pole’’ in the 3-plane.This does not improve the current slew rate of the amplifier, but does increase thedamping-to-stiffness ratio around �a. The other phase-lead parameter ‘‘b’’ is set inthe range of 5a � b � 10a.

19.100 CHAPTER NINETEEN

FIGURE 19.73 AMB stiffness and damping—a numerical example.2

The AMB stiffness and damping of this controlled axis can be calculated byusing the equations below with S equal to j�.

�F /Y � K � j�b � �K (i /Y) � K (19.50)i m

i /Y � (Ts)(Tc)(Tp)(Ta) (19.51)

where� � excitation frequency, rad/s

Ts � Ga� / (S2 � �nS � � )2 22n n

Tc � �Cd � Ce�o / (S � �o) � C S / (S � �v)v

TP � (b /a)(S � a)(S � b)Ta � Ga�n / (S � �n)

The equations indicate that both K and B are functions of excitation frequency�, not rotational speed. Numerical results are plotted in Fig. 19.73 using the AMBdata. The frequency axis in this plot is normalized with respect to 50 Hz which isthe average of two rigid-body critical speeds of a rotor. The amplitude is normalizedwith respect to (GpCeKiCd � Km).

At the low frequency range where the integral control dominates, the plot showsnegative damping values. This should not cause alarm, however, since mechanicalsystem resonances seldom exist in that low range. At the high frequency range,especially where the first two bending criticals exist, negative damping can causeresonances. This is discussed below.

PRINCIPLES OF BEARING DESIGN 19.101

Rotor-AMB System Dynamics

System Design Guidelines. AMBs are generally less stiff than rolling elementor hydrodynamic oil-film bearings. Therefore, the first two system criticals haverelatively rigid mode shapes, and their vibrations are easily controlled. The thirdand fourth criticals with bending mode shapes must be given careful considerationin high speed turbomachines.

Taking the rotor model in Fig. 19.74 as an example, its critical speed map showsthat the rotor operates between the third and the fourth criticals. Two identical 8-pole AMBs are chosen to support the rotor with dimensions in Fig. 19.73. The firstissue is finding the best method for determining the stiffnesses. In this case, thestiffness per bearing can be made 1000 lb/in. or 10,000 lb/in. (1.75 � 105 N/mor 1.75 � 106 N/m). The answer depends on rotor shock load. To take 1 g shock,this rotor of approximately 100 lb (45 kg) moves radially 50 mils and 5 mils (1.25mm and .125 mm) respectively, for the lower and higher stiffnesses. The catcherbearing is set at 10 mil (0.25 mm) away from the rotor for a designed air gap of20 mils (.5 mm). To avoid pounding the catcher bearing when shocked, the higherstiffness is chosen.

Reviewing the mode shapes at the chosen stiffness, Fig. 19.75 reveals that thereare sufficient relative displacements at the bearings for control of the first andsecond modes. The third and the fourth modes are lacking the displacement at onebearing. To help control the third mode, the displacements sensor is mounted atthe outboard side of each AMB where the sensor sees more than only the centermotion.

The second design issue is to determine how many bending modes should becontrolled. To keep the control electronics relatively simple, the frequency rangewith acceptable control response is limited by two factors, the inductance load andthe filtering delay. It is imperative to have an adequately damped bending modebelow the operating speed (the third mode in this case), because of the unbalanceexcitation during traversing the critical. The bending mode immediately above theoperating speed (the fourth mode in this case) should be 15 to 20% away in fre-quency. However, it still can be excited by harmonics as the rotor is going up inspeed, or by a shock load. But less damping is required for controlling this mode.

The higher bending modes normally are less likely to be excited. The rotormaterial damping is a source to resist the minor, or occasional excitation. Oil-filmbearings always provide positive damping but there is no guarantee of this forAMBs. The control current at the high critical frequency may lay behind the dis-placement measurement, or the probe may be at the wrong side of the AMB. TheAMB may become a small exciter for that mode. When it happens, a band-rejectfilter for the excitable mode can be inserted in series in the feedback loop to blockthe control at that modal frequency.

For the example herein, the power amplifier and the sensor low-pass filter areassumed to have the cut-off frequencies at 500 and 5000 Hz, respectively. Applyingthe normalized stiffness and damping of Fig. 19.73, the normalized frequency of1.0 to 50 Hz, which is between the first and the second criticals as read from the

19.102 CHAPTER NINETEEN

FIGURE 19.74 Characteristics of the rotor model.2

PRINCIPLES OF BEARING DESIGN 19.103

FIGURE 19.75 Rotor critical mode shapes.2

map. The values of �B /K for the lower four modes range from 0.2 to 0.6, whichis adequate for properly designed vibration modes. More damping can be achievedby increasing the value of Cv.

Rigorous Dynamic Analysis. After component sizing and cursory analysis, rig-orous system analysis is needed to prove the expected rotor vibration behavior.Considering the fact that the AMB stiffness and damping are functions of excitationfrequency, the state vector of the conventional rotor model is extended to includethe state variables of the AMBs. The mathematical rotor model is the same as theconventional model including sections of shaft with specified ID, OD, length, andconcentrated masses and inertias. The model for each bearing would be the bearingstation number, the measurement station number, and the key parameters of Fig.19.73.

Using this electromechanical model, the lower four damping frequencies of therotor running at 15,000 rpm were computed and are presented in Table 19.22. Thefirst three modes are adequately damped because the associated log decrementvalues are all significantly above 0.4. The latter is a damping value generally ac-cepted for a rotor system supported in oil-film bearings. The fourth mode has alog decrement value of 0.06 without considering the rotor material damping. Itshould be acceptable since it is much higher in frequency that the third mode andthe operating speed.

19.104 CHAPTER NINETEEN

TABLE 19.22 Damped Natural Frequencies of Forward Modes2

Rotor Speed � 15,000 rpm; Cross Coupling Stiffness (Kxy) at Wheel

Mode

Kxy � 0

Frequency(cpm)

Logdecrement

Kxy � �4000 lb/ in(�7 � 105 N/m)

Frequency(cpm)

Logdecrement

1st 2,318 1.05 2,374 �0.002nd 5,263 2.20 5,623 2.193rd 11,154 0.89 11,144 0.884th 34,156 0.06 34,156 0.06

In Table 19.22, the cross-coupling stiffness produces a destabilizing seal effectat the wheel, but it only affects the first mode damping. The reason for this is thatonly the first mode shape has significant lateral displacement at the wheel. Therotor/AMB system can sustain a value of 4000 lb/in. (7 � 105 N/m) before be-coming unstable.

Figure 19.76 presents an unbalance response at the third critical speed using thesame electromechanical model. It indicates that the response peak is well dampedand far away from the operating speed of 15,000 rpm. The peak dynamic currentwas calculated to be 0.45 (0-peak) at 11,500 rpm. It specifies that a current slewrate no less than 500 A/s must be provided by the power amplifier design.

19.7 CRYOGENIC APPLICATIONS

Due to the nature of the fluid, machinery employing cryogenic fluids such as liquidoxygen or liquid hydrogen, use predominantly rolling element bearings. These ma-chines run at extreme speeds, are heavily loaded and do not permit the use ofconventional lubricants. In all of these applications, wear of the bearing is thelimiting factor so that the bearings have a very short life. Since REB’s suffer fromDN limits, they often are unable to run at the high speeds demanded for givenrotor diameters. An additional problem with REB’s is their high stiffness and nearzero damping. The low viscosity of the process fluid makes squeeze film dampersineffective and the low temperatures prevent the use of elastomeric damping. In-troducing some of the novel type bearings discussed earlier offers a possibility ofeliminating or ameliorating this critical situation in cryogenic turbomachinery.

The performance will be studied under the conditions of using liquid oxygen asthe process fluid as well as the lubricant. In actual applications, such as turbopumps,these fluids are usually at very high pressures ranging from several hundred psi toperhaps 10,000 psi and this will constitute the ambient pressure for the bearings

PRINCIPLES OF BEARING DESIGN 19.105

FIGURE 19.76 Unbalance response at 3rd critical speed.2

in use. Generally the lubricant should be treated as a compressible fluid. However,a parametric study of journal bearings shows that load capacity is a strong functionof ambient conditions up to about a pa � 2,000 psi; thereafter there is very littledependence on pa. This is in conformity with the previously stated fact that a � →0, a compressible fluid acts as a liquid. Thus in some cases the use of the incom-pressible equations, which are much simpler, is justified.

19.7.1 Compliant Surface Bearings

Journal Bearings. Two designs will be considered, a full (360�) and a 3-pad(120�) bump foil bearing.

The Full 360� Bearing. Studies conducted for three different foil bearings in-dicate the following:

• W increases with bump stiffness.

• hN decreases with stiffness.

• At an intermediate stiffness (41 � 103 lb/in.), the foil deflection is of the sameorder as the Hn.

• Power loss rises slightly with stiffness.

19.106 CHAPTER NINETEEN

FIGURE 19.77 Three-pad foil journal bearing for SSME (space shuttle enginerotor) L � D � C � 2.25 � 3.5 � 0.0015 in., XKB � 40,960 lb / in. / in.

� � 10 mil, �4 � 4, �l � 6

• The vertical stiffness Kyy approaches that of Kxx at bump stiffnesses below 50,000lb/in. / in. of the fluid film.

Based on the above, a stiffness of 40 � 103 which corresponds to a foil thicknessof 6 mils seems to be an optimum yielding a reasonable W at low deflections.Under these conditions, the structural stiffness dominates the overall bearing stiff-ness.

The 3-Pad CSB. One of the major parameters to be looked into here is theangular extent of the pad, or the number of pads. In the present 3-pad 120� con-figuration, actually only two of the pads would be loaded. The other parameter tobe investigated is the load angle. This is particularly relevant when there is arotating load in the bearing.

• Steady Load. Figure 19.77 shows the configuration of the 3-pad bearing withthe load in the present case directed midway of the bottom pad. Bearing per-formance at operating speed is shown in Table 19.23 and Fig. 19.78. Load ca-pacity increases exponentially with a decrease in hN but the power loss is insen-sitive to it. The spring coefficients seem to have an inverse linear dependence onhN which contributes much to bearing stability.

• Variable Load Angle. This parameter was studied under the fixed condition of� � 0.9 and a speed of 29,830 rpm. The results, shown in Table 19.25 and inthe additional plots, reveal the following:

• Maximum load capacity is obtained for �L � 195�.

19.1

TABLE 19.23 Three-Pad Foil Journal Bearing Performance12

(n � 29,830 rpm)LOX at 191�R and 2200 psia, Load at �L � 180�

L � D � C � 2.25 � 3.5 � 0.0015 in; Bump Foil Thickness: tlower � 6 mil; tupper � 4 mil

�

AA(�)

W(lb)

(mil)Pmax

(psig)Power loss

(hp)

Dynamic bearing coefficients(lb / in � 106)

Kxx Kyx Kxy Kyy

� 212.0 620.0 1.33 192.0 11.40 1.040 �1.300 0.45 0.5000.6000 210.1 834.8 1.26 216.8 11.44 1.000 �1.202 0.40 0.620

� 1.22 0.9800.8000 207.8 1151.9 1.17 286.9 11.69 0.950 �1.062 0.28 0.7500.9000 206.7 1307.5 1.12 320.8 11.94 0.940 �1.064 0.26 0.790

� 1.11 0.9200.9990 204.8 1463.6 1.06 350.0 12.41 0.910 �1.104 0.20 0.8500.9995 204.8 1463.6 1.06 350.0 12.41 0.900 �1.105 0.21 0.801

� 203.0 1637.0 1.03 391.0 0.855 �1.130 0.18 0.890� 1.02 13.00� 200.8 2158.0 0.95 487.0 0.850 �1.200 0.135 0.955� 198.0 2720.0 0.89 589.0 0.850 �1.300 0.085 0.970� 3000.0 0.87� 0.83 700.0 0.00 0.985� 196.0 0.81� 0.79 0.850 1.000

19.108 CHAPTER NINETEEN

FIGURE 19.78 Performance of cryogenic 3-pad foil bearing.12

PRINCIPLES OF BEARING DESIGN 19.109

TABLE 19.24 Three-Pad Foil Journal Bearing Performance vs. Load Angle �L12

LOX at 191�R and Pa � 2200 psia; N � 29,830, � � 0.9

�L

(deg)AA

(deg)W

(lb)hN

(mil)Pma �(psig)

Powerloss(hp)

Dynamic bearing coefficients(lb / in � 106)

Kxx Kyx Kxy Kyy

120 234 903 1.90 278 12.00 1.15 �0.43 1.15 0.44*132 227 914 1.94 258 13.25 1.27 �0.66 0.98 0.38*144 218 967 1.98 234 14.25 1.40 �0.84 0.78 0.33

150 216 975 2.03 222 15.00 1.43 �0.95 0.68 0.30*156 212 1040 1.59 234 13.25 1.4 �1.05 0.59 0.35

165 208 1105 0.92 255 10.00 1.51 �1.13 0.43 0.52*168 207 1180 1.00 267 10.50 1.43 �1.0 0.38 0.57

180 206 1307 1.12 320 11.00 0.98 �1.06 0.27 0.78*192 217 1422 1.32 395 10.60 0.32 �0.6 0.05 0.87

195 219 1451 1.40 406 10.70 0.15 �0.55 0.02 0.92*204 239 1180 1.50 374 10.75 0.32 �0.48 0.50 0.82

210 247 1050 1.74 347 10.80 0.47 �0.40 0.77 0.69*216 248 1026 1.72 338 11.10 0.61 �0.41 0.84 0.68*228 241 967 1.81 305 11.90 0.90 �0.42 0.98 0.54

240 235 906 1.90 279 12.80 1.15 �0.43 1.15 0.44

*Extrapolated values.

• hN is smallest when �L � 168�.• The power loss here is 12 hp which compares with 11 for the steady load.

Total variation in W over the entire 360� span circumference is some 500 lb andof hN one mil. Since a change in film thickness of 0.5 mils corresponds to a changein load capacity of 2,400 lb, a dynamic load from zero to a peak value of 2,400lb at a fixed load angle would produce a journal orbit of 1/2 mils radius. This isquite an acceptable disturbance.

Thrust Bearings. From past studies, a compound thrust bearing emerges as themost promising design. Its geometry will be � 45� with an (R2 � R1) � 2 andwith a KB � 40,960 lb/in. / in. Varying in this design, the value of hN, from 3 to16 the load capacity shows a maximum at hN � 14. This is three and a half timesthe value in rigid bearings. Next, a variation in the extent of taper was conductedunder different stiffnesses. Table 19.25 summarizes the performance of the bearingfor the optimized variables which covers a range of operation from 1,000 to 30,000rpm and ambient pressures from 30 to 2,200 psi. Satisfactory performance underall conditions is indicated by the rather healthy values of hN which never fallsbelow 0.3 mils and in most cases stay above half a mil.

19.1

TABLE 19.25 Performance of Thrust CFB Under Lox Conditions12

(8 pads at 45� each, R1 � R 2 � h2 � 1.25 in. � 2.5 in. � 0.0002 in.; 1 � 14, KBR � 40, 950 lb/ in2,htL � 4 mil; tU � 6 mil, s � 0.5, g � 1.5)K K

Caseno.

N(rpm)

(psia)

psi lbhN

(mil)�

(mil / in) H /Pad KBS KBE Re no. Remarks

1 29,830 2,200 260 3,835 1.23 1.9 2.1 20,480 61,440 17,685 The Re No. is computedfor a 4-mil entrance gap

2 25,000 1,900 236 3,472 1.14 1.74 1.5 20.480 61,440 15,5883 20,000 1,400 211 3,104 1.07 1.57 1.01 20,480 61,440 12,6184 14,000 1,012 187 2,752 0.96 1.4 0.8 20,480 61,440 7,9785 11,000 900 168 2,472 0.92 1.3 0.4 20,480 61,440 —6 8,000 800 149 2,200 0.83 1.14 0.24 20,480 61,440 4,2877 4,000 500 108 1,560 0.65 0.84 0.08 20,480 61,440 2,144 Turbulent (inlet film)8 4,000 500 73 1,080 0.52 0.6 0.045 20,480 61,440 1,000 Super Laminar (hN)9 2,000 370 38 536 0.37 0.3 0.01 20,480 61,440 800 Laminar

10 1,000 370 21.7 320 0.3 0.2 0.003 20,480 61,440 400 Laminar11 1,000 370 12.5 184 0.53 0.6 0.002 3,530 1,059 400 Upper bump foil is

considered (i.e. lowstiffness)

PRINCIPLES OF BEARING DESIGN 19.111

FIGURE 19.79 Hybrid CSB’s for cryogenic applications.

Hybrid Bearings. If the purely hydrodynamic CSB does not meet the operationalrequirements, then a combination hydrodynamic-hydrostatic CSB can be used. Nearzero speeds, the high pressure fluid would have to be taken from a reservoir untilthe unit starts generating its own high pressure supply.

Journal Bearings. The essence of a hydrostatic CSB fed through the rotatingshaft is shown in Fig. 19.79. An LOX solution is here obtained for a 4-pad bearingwith dimensions D � L � C � 3.8 in. � 2 in. � 0.002 in. with an orifice dimensionof 0.056 in. This unit provides a 50% drop across the orifice, yielding a value ofpo of 250 psi and a load capacity of 2,000 lb. If a 2,000 psi supply pressure isavailable, such a bearing would carry a load of 5,100 lb at a value of hN of aboutone mil.

Thrust Bearings. The thrust bearing design analyzed is one with R2 � R1 �3.5 in. � 2.5 in. shown in Fig. 19.79. Using 8 orifices gives more or less squarebearing pads which is an optimum arrangement. Three parameters determine theperformance, namely

2 1 / 2 3(R /R ); p � (p /p ); � � 6�na (pv) /p h2 1 s s a s s N

For the present (R2 /R1) � 1.4, the load capacities for several values of ps and �s

are listed in Table 19.25. As seen, in order to meet a 6,000 thrust load over therange of 0 to 12,000 rpm, a supply pressure of some 3,000 psi is needed. For sucha value of ps and a 6,000 lbs load the other performance items would be

Flow:Axial stiffness:Angular stiffness:

Q � 1.7 gpm6K � 2.4 � 10 lb/in.z

6K � 0.96 � 10 lb-in. /rada

To sum up the geometry and operating conditions of this bearing would be asfollows:

19.112 CHAPTER NINETEEN

TABLE 19.26 Thrust Bearing Forces asa Function of Supply Pressure12

(R1 /R 2) � 1.4; pa � 250 psia

pa (psia) ps /pa �s W (lb)

1000 4 0.74 16502000 8 0.57 4620

300 12 0.49 6040

R � R � h � 3.5 � 2.5 � 0.0005 in.2 1 min

8 orifices 0.05 in. in diameter

(p /p ) � 12 or p � 3,000 psias a s

�7� � 0.25 � 10 reynes�4 2 4� � 10 lb-s / in.

19.7.2 Hydrostatic Bearings

For this section, the following special symbols will be used:

A � area of feeding recess � ld, in.2

a � radius of orifice hole, in.ac � radius of orifice feeding hole chamber, in.aF � radius of orifice feeding hole, in.C � radial clearance, in.

CD � orifice discharge coefficientD � diameter, in.d � circumferential length of feeding recess, in.e � eccentricity of journal, in.

G�,Gz,GR � turbulent viscosity correction factors�G dimensionless flow � �2 /C3(Ps � Pa)m

� �G dimensionless flow � (Ps � Pa)DPRGz3m� L (1 � Y) /C2

GRADPS � turbulence parameter or fluidic Reynolds number � (Ps � Pa)C3 /

R�s�s

GRADP � modified turbulence parameter � (GRADPS) PRD /L � (1 � Y)gc � acceleration due to gravity � 386 in./s2

h � local bearing film thickness, in.hR � depth of feeding recess, in.

�h dimensionless thickness � h /CL � bearing lengthl � axial length of feeding recess, in.

lF � depth of orifice feeding hole, in.

PRINCIPLES OF BEARING DESIGN 19.113

�m mass flow rate, lb-s2/ in.n � number of recessesN � rotational speed, rpmP � pressure, lb/ in.2

�P dimensionless pressure � (P � Pa) /(Ps � Pa)R � radius, in.r � coordinate in radial direction from feeding holes, in.

Ren � Reynolds number � UC /vs

t � time, sU � surface velocity of journal, ipsu � velocity in circumferential direction, ips

�u mean total circumferential velocity, ips�u dimensionless circumferential velocity � (�s /Ps � Pa)

1 / 2uup � mean circumferential velocity due to pressure gradient, ipsV � fluid volume, in.3

� � velocity normal to bearing surface, ipsW � load, lb

�W dimensionless load, � / (Ps � Pa)LDWw � velocity in axial direction, ips

�w mean axial velocity, ips�w dimensionless axial velocity � (Ps � Pa)

1 / 2w�X circumferential recess length ratio � nd /�D�Y axial recess length ratio � l /L

z � coordinate in axial direction, in.� � eccentricity ratio � e /C� � dimensionless axial coordinate � z /R� � coordinate in circumferential direction, rad� � inertia parameter � C(GRADP)2Gs

2 /R(GRADPS)PR

� � rotational speed of journal, rad/s� � absolute viscosity, lb-s/ in.2

� � kinematic viscosity; in.2 /s�� dimensionless kinematic viscosity � � /�s

� � fluid mass density, lb-s2

�� dimensionless density � � /�s

Subscriptsa � ambient conditionsF � film conditionR � recess conditionr � radial direction from feeding holes � supply conditionsz � axial direction� � angular direction (circumferential)

Since the cryogenic process fluid is usually available at very high pressures, a

19.114 CHAPTER NINETEEN

FIGURE 19.80 Full hydrostatic journal bearing.

naturally attractive solution is to use fully hydrostatic bearings. The design chosenis a full 360 orifice compensated journal bearing. The continuous circumferenceprovides a higher load capacity than a design with a number of discrete pads; aschematic of the bearing is shown Fig. 19.80. Due to the high speeds, the flow isassumed to be turbulent and a function of both the rotation and fluid velocity inthe film. The density and viscosity of the fluid will vary here also with pressureaccording to

2h G �P�u � � U /2 (19.52a)� R��

2h G �Psw � (19.52b)� �z

The turbulence level in a bearing can be due either to high rotation or to high filmvelocities induced by the pressure gradients, or both. In the last two cases, aniterative procedure is required in obtaining a solution since the pressure gradientsare not known a priori. Concerning the variation of density and kinematic viscositywith pressure, this is approximated by the following isothermal relationships

P � Pa� � � � (� � � ) (19.53)s s a P � Ps a

P � Pa� � � � (� � � ) (19.54)s s a P � Ps a

where the subscripts s and a indicate conditions at supply pressure and ambientpressure, respectively. Since for LH2 and LO2 bearings, � and � vary at most, onlyon the order of 20% from supply pressure to ambient pressure, this variation canbe approximated quite well by the linear relations given in the foregoing.

Inertia forces result in a decrease in the static pressure when fluid acceleratesand a corresponding increase in static pressure when fluid decelerates. In the LH2

PRINCIPLES OF BEARING DESIGN 19.115

and LO2 bearings, the principal effect of inertia forces is that of a sudden decreasein static pressure at the edge of each bearing recess caused by the acceleration offluid from relative stagnant conditions in each recess to a condition of high velocityin the thin bearing film. In the present analysis, this decrease in static pressure atthe axial edge of each recess is calculated by means of the following relationship.

2P (edge of recess) � P � �w /2 (19.55)R

where PR � recess pressure�w mean local velocity in axial direction in bearing film at edge of recess

The relationship used to calculated static pressure at the circumferential edge ofeach recess is

2P (edge of recess) � P � �u /2 (19.56)R

where u is the mean velocity in the circumferential direction in the bearing film atthe edge of the recess. In hydrostatic bearings, attainable load and stiffness areindependent of lubricant viscosity. Hence, it was anticipated for the LH2 and LO2

bearings that once turbulence was fully established, load and stiffness would beessentially independent of the level of turbulence.

Although load capacity is relatively insensitive to turbulence, bearing mass flowrate depends strongly on the level of turbulence. In order to generalize the effectsof turbulence and other operating parameters on flow rate, the following formula-tion for dimensionless flow was developed.

m� L(1 � Y)xDimensionless flow, G� � 3C (P � P )DP Gs a R z

The parameter

3GRADP � (p � p ) � p C � � (1 � Y)s a R s s

provides an index of the axial flow Reynolds number. A plot of Gz versus GRADPis given in Fig. 19.81. The dimensionless flow parameter � is independent ofGPR and � and of the variables L, D and over the range of 0.5 � L /D � 1.5 andY0.2 � � 0.6. Also, inertia effects are ignored here since they were found to haveYlittle effect on load capacity and flow rate.

In hydrostatic bearings designed for maximum stiffness at � � 0, load capacityincreases linearly with � out to values of � � 0.7. Consequently, bearing load dataare presented here in the form of W /� which is roughly independent of � for valuesof � � 0.7.

Bearing flow rate tends to decrease slightly as � increases, the decrease amount-ing to about 10% at � � 0.7. Bearing flow design data presented are for � � 0.

Effects of journal rotation on bearing flow and load capacity are neglected forthe design data, i.e., the design charts pertain to purely hydrostatic bearings. Forall anticipated operating conditions of the LH2 and LO2 bearing, the mode of op-eration was predominately hydrostatic. Also, the level of turbulence was alwaysdominated by the pressure flow rather than by rotational shear.

19.116 CHAPTER NINETEEN

FIGURE 19.81 Turbulent viscosity relationship.32

Compressibility of liquid hydrogen and liquid oxygen was taken into account inthe bearing analysis. However, this compressibility is so slight as to have a negli-gible effect on the steady-state performance of the bearings.

An approximately optimum design configuration was chosen for these bearingsconsidering both load capacity and flow rate. The design chosen was

L /D � 0.65

n � 6

�X 0.5

�Y 0.4

�PR 0.5

Design Charts

a. Effect of L/D Ratio. The effect of L /D on dimensionless stiffness /� isWshown in Fig. 19.82a. The decrease in with L /D is typical of all hydrostaticWbearings. Corrected dimensionless flow � is independent of L /D, the effect ofGlength to diameter ratio being taken account of by the inclusion of the ratio L /Din the expression �.G

The reason that /� decreases with L /D in hydrostatic bearings is that as L /DWincreases, circumferential flow in the bearing film becomes more significant. Thistends to reduce load capacity because it tends to equalize the pressures in thevarious recesses.

The dimensionless variables /� and � somewhat obscure the effect that aW Gchange in bearing length has on the real load W and the real flow, m. In fact, if

PRINCIPLES OF BEARING DESIGN 19.117

FIGURE 19.82 Effect of L/D ratio on load and stiffness.32

the variables C, �, D, and e are kept fixed, the ratio of real load to real flow, W /in will increase quite steeply as L /D increases. To show this effect, L /�D dividedWby the reduced dimensionless flow is plotted whereG

m�sG � (19.57)2C (P � P )s a

The resulting curve is shown in Fig. 19.82. Note that one of the more effectiveways of designing a hydrostatic bearing to have a large load capacity with lowflow rates is to make L /D large.

b. Effect of Recess Pressure Ratio R. The most significant design parameterPwith respect to optimization of load and stiffness is the recess pressure ratio R.PThe influence of R on dimensionless stiffness is shown in Fig. 19.83a. As can bePseen, maximum stiffness (load) occurs at R � 0.55. It should be mentioned thatPthis curve of /� versus R is characteristic for a bearing with turbulent flowW P(GRADP � 3000) and with an orifice restrictor. For the case of laminar flow in

19.118 CHAPTER NINETEEN

FIGURE 19.83 Effect of recess pressure ratio on dimension-less load-to-flow ratio and dimensionless stiffness.32

the bearing film, maximum load would occur at R � 0.586, which is still veryPclose to R � 0.55.P

Corrected dimensionless flow, �, is independent of R, the effect of pressureG Pratio being taken into account in the parameter �, itself.G

Actual flow, , will increase as R increases. Because of this effect, the maxi-m Pmum value of the ratio of stiffness to flow does not occur at R � 0.55, but ratherPat a lower pressure ratio ( R � 0.375). This is illustrated by the curve shown inPFig. 19.83a.

Recommended design practice for LH2 and LO2 hydrostatic bearings would beto select R between 0.375 and 0.55. However, certain special requirements, suchPas limitations on flow rate may dictate the use of pressure ratios lower than R �P0.375.

c. Effect of Axial Recess Length Ratio � 1/L. The influence of the parameterYY on dimensionless stiffness is shown in Fig. 19.84b. As would be expected, /�Wincreases with .Y

Corrected dimensionless flow � is essentially independent of over the rangeG Y0.2 � � 0.6 due to the inclusion of the factor (1 � ) in the expression �.Y Y G

PRINCIPLES OF BEARING DESIGN 19.119

FIGURE 19.84 Effect of (axial recess / length) ratio on load andstiffness.32

Since actual flow increases with as does the actual load, W, it is of interest toYsee how the ratio of load to flow rate varies with . This is shown by the curve inYFig. 19.84a. Note that the ratio of actual load to actual flow improves as the axiallength of the feeding recess is reduced. Choice of an optimum recess length woulddepend on how much flow one was willing to sacrifice to obtain an increase inload capacity. It will be shown that bearing stability considerations also enter intothe selection of optimum recess dimensions. This will be discussed in a subsequentsection.

d. Effect of Circumferential Recess Length Ratio, � nd/�D. DimensionlessXstiffness increases as the circumferential recess length is reduced, at least for valuesof � 0.30, Fig. 19.85b. The physical reason for this is that as the land widthXbetween pockets decreases ( increases), flow can more readily pass from oneXrecess to the next, thereby tending to equalize the pressure in the different recesses.

The value is one of the few parameters which influence the value of theXdimensionless flow �, another parameter being n, the number of recesses. TheGvariation of � with is shown in Fig. 19.85a.G X

19.120 CHAPTER NINETEEN

FIGURE 19.85 Effect of circumferential recess ratio onload and stiffness.32

e. Effect of Number of Feeding Recesses, n. The dimensionless flow � in-Gcreases very slightly with number of recesses n in the range from 4 to 8 recesses,Fig. 19.86a. Dimensionless stiffness increases somewhat in going from 4 to 6recesses, but increases very little going from 6 to 8 recesses (Fig. 19.86b). Thequestion of how many recesses to have in a bearing will depend primarily onwhether the gain in load with increase in n is worth the added manufacturingcomplexity.

One point in favor of using a greater number of recesses is that it minimizesthe effect that different directions of loading can have on load capacity. Otherinvestigators report that there can be as much as a 25% difference in bearing loadcapacity depending on whether the load line passes through the center of a recessor between recesses. However, this study indicates only a slight change (�5%) inload with load direction in a bearing with four or more pockets.

PRINCIPLES OF BEARING DESIGN 19.121

FIGURE 19.86 Effect of number of recesses on dimen-sionless flow and dimensionless stiffness.32

19.8 LUBRICANTS AND MATERIALS

This section is not meant to enter into a discussion of the very extensive field ofbearing lubricants and materials, but merely to provide the basic data required inthe use of the equations and tables given in previous sections.

19.8.1 Lubricants

The major functions of a lubricant in a bearing is to provide a fluid film at theinterface; to convect the heat due to viscous dissipation; and to wet the surfacesduring stops and starts when there is no full film at the interface. In a hydrodynamicbearing, the most important property in fulfilling the above functions is the vis-cosity. The level of generated hydrodynamic pressures and hence the load capacity,as well as all other performance characteristics such as temperatures, flow, powerloss, etc., all depend very strongly on lubricant viscosity. Since viscosities are listed

19.122 CHAPTER NINETEEN

in a great variety of units, Table 19.27 is provided to facilitate conversion fromone system to any other.

The oils used on most compressors are similar to those in turbines and gear sets.These are shown in Fig. 19.87 along with other common SAE grade oils. Some ofthe more pertinent characteristics of these oils are as follows:

Thermal conductivity: 0.08 BTU/(hr ft2 �F)/ft [0.14 Joules/(sec-m-�C)]

Specific heat: 0.4 BTU/(lb �F) [2.52 K Joules/(Kg-�C)]

Heat of vaporization: 80 BTU/lb (187 K Joules/Kg)

Specific gravity: 0.88 at 60�F (16�C)

Flash point: 410� to 470�F (210� to 243�C)Pour point: �10�F (�23�C)

If the operating temperatures exceed 300�F or fall below �10�F, a shift to syntheticlubricants may be required and some such candidates are listed in Table 19.27. Toincrease the resistance and longevity of petroleum oils during prolonged usage,additives are often desirable and a list of such additives for particular contingenciesare given in Table 19.29.

19.8.2 Bearing Materials

Selection of bearing materials for specific applications involves a scrutiny of thefollowing characteristics: (1) compatibility; (2) embeddability and conformability;(3) corrosion resistance; and (4) compressive and fatigue strength. In hydrodynamicbearings, the most relevant items are the allowable maximum pressures before thematerial begins to deform or flow, and the value of Tmax it can endure. For com-pressive strength, an alloy with intermediate strength is desirable; an alloy too lowin strength is prone to extrude under load, while too strong a metal, being brittle,may crumble under impact loading. Fatigue strength is particularly important inapplications with dynamic loading in order to prevent the formation of cracks orsurface pits. The use of a thin soft layer bonded to a hard backing metal oftengives the desired combination of fatigue and compressive strength; in such cases,however, the fatigue strength of the bond itself requires attention. When a materialhas low corrosion resistance, difficulties can be minimized by using oils with goodoxidation inhibitors and by maintaining low bearing temperatures.

Babbitts. The most common bearing materials are babbitts, either tin-based orlead-based. The detailed properties of babbitts are given in Table 19.30. Babbittscan operate under conditions of boundary lubrication or dirty operation. They haveexcellent compatibility and non-scoring characteristics and are outstanding in tol-erating errors in construction and operation. Their deficiencies with regard to fa-tigue strength can be improved by using an intermediate layer of high-strengthmaterial between a steel backing and a thin babbitt layer. Many of these, knownunder the name of trimetal bearings, use the following construction: (1) a low-

19.1

TABLE 19.27 List of Synthetic Lubricants36

Type

Kinematic viscosity, cs

210�F 100�F �65�F

Flashpoint,

�F

Pourpoint,

�F

Approximatecost pergallon Typical uses

Diester:Turbo Oil 15 3.6 14.2 12,600 430 �90 $10.00 MIL-L-7808 high load capacity, high temperature jet

engine oil.Low volatility aircraft hydraulic and instrument oil.

MIL-0-6085 3.5 13.5 10,000 450 �90 10.00 Aircraft hydraulic fluid for alternator drives.MIL-0-6387 4.6 15.8 5,000 410 ��80 —

Phosphate:Tricresyl phosphate 3.8 30.7 — 465 — 3.60 Low flammability hydraulic fluid for diecasting

machines.Nonflammable aircraft hydraulic oil.

Skydrole 3.85 15.5 �20,000 355 70 12.00 Nonflammable hydraulic oil for diecasting machines,punch pressures, etc.

Pydraul F-9c 5.8 54 — 430 �5 3.75 Air compressors.

Silicone:SF-96 (40) 16 40 850 600 ��100 30.0 Low-torque aircraft oil bearings, air craft hydraulic and

damping fluid.SF-96 (300) 122 300 7,000 605 ��55 30.00 Heat transfer, hydraulic, and damping applications.SF-96 (1,000) 401 1,000 20,000 605 ��55 30.00 Heat transfer, hydraulic, and damping applications.DC-710 40 275 — 575 �10 40.00 Heat transfer, high-temperature trolley bearings.

Silcate:OS-45 3.95 12.4 2,400 — ��85 20.00 Wide-temperature-range aircraft hydraulic fluid.Orsil BF-1 2.4 6.8 1,400 395 ��100

19.1

TABLE 19.27 List of Synthetic Lubricants36 (Continued )

Type

Kinematic viscosity, cs

210�F 100�F �65�F

Flashpoint,

�F

Pourpoint,

�F

Approximatecost pergallon Typical uses

Polyglycol:LB-140X 5.7 29.8 — 345 �50 2.40 Water-insoluble oils used for internal-combustion engines.LB-300X 11.0 65.0 — 490 �40 2.40 (Prestone Motor Oil), high temp. bearings in ovens andLB-650X 21.9 141.0 — 490 �20 2.40 furnaces and gears.50-HB-55 2.4 8.9 — 260 �85 2.40 Water-soluble oils used in wire drawing, metal forming,50-HB-280X 11.5 60.6 — 500 �35 2.40 and some machine tools.50-HB-2000 72 433 — 545 �25 3.00Hydrolube 300N — 666.3 — None �55 2.50 Water-polyglycol mixture used as non-flammable

hydraulic fluid in die-casting and machine tool work.

Chlorinatedaromatics:Aroclor 1248 3.1 48 — 380 20 2.30 Die-casting machines and high-pressure compressors.Aroclor 1254 6.1 470 — None 50 2.30

Polybutenes:No. 8 7.9 72 — 310 �40 — Electrical oils, hydraulic and shock absorbing fluids,No. 20 106 3,600 — 410 10 1.05 kilns, and ovens, refrigerator compressors.No. 128 4,000 — — 450 70 1.40 High pressure compressors.

Fluorolubes:Fluorolubes FS 1.10 3.52 — None — 300.00 Equipment handling liquid oxygen, concentratedFluorolubes S 4.6 24.1 — None — 300.00 hydrogen perioxide, etc. Density of approximately 1.8

grams/cc.Process and natural gas compressors.

19.1

100.00050.00020.00010.000

5.0003.0002.0001.000

50030020015010075504030

109.08.07.06.05.0

4.0

3.0

-20 0 20 40 50 80 100 120 140 160 180 200 220 240 260 280 300

Kin

emat

ic V

isco

sity

, Cen

tisto

kes

SAE 50

SAE 40

SAE 30

SAE 20 WSAE 10 W Heavy Steam Cylinder Oil

Grade 1010 Jet Engine Oil

Light Spindle Oil

Light Turbine and Electric Motor Oil

Medium Turbine Oil

T, Fo

FIGURE 19.87 Viscosity of petroleum oils.

19.126 CHAPTER NINETEEN

TABLE 19.28 Viscosity Conversion Factors

Multiply By To obtain

Stokes (cm2 /sec) Density (g/cm3) Poises (gm/cm-sec)Poises 100 CentipoisesCentistokes Density (g/cm3) CentipoisesCentipoises 1.45 � 10�7 Reynes (lb force-sec/ in2)Centipoises 2.42 � 10�9 (lb force-min/ in2)Centipoises 5.6 � 10�5 (lb mass in-sec)Reyns (lb forc-sec/m2) 6.895 � 103 Pascal-sec (N-sec/m2)Centipoises 10�3 Pascal-sec (N-sec/m2)

TABLE 19.29 General Types of Additives with TypicalChemical Compositions36

Function Typical chemical type

Oxidation inhibitor PhenolicsDithiophosphate

Detergent Calcium petroleum sulfonate

Rust inhibitor Organic acidsSodium petroleum sulfonate

Wear preventive Trieresyl phosphate

Boundary lubrication Chlorinated naphthaleneSulfurized hydrocarbon

Viscosity index improver Polyisobutylene

Pour-point depressant Polymethnerylate

Defoaming agent Silicone oil

carbon-steel back; (2) an intermediate layer of copper or bronze; and (3) an overlayof lead-base babbitt from 0.001 to 0.020 in. thick. The intermediate layers increasethe mechanical strength of the babbitt bearing and also provide reasonably goodbearing surfaces in cases the thin babbitt surface layer is destroyed in operation.

Non-Babbitt Bearing Materials. Other common bearing materials used, when-ever babbitt cannot be employed are:

• Bronze. Bearing bronzes may be grouped into lead bronzes, tin bronzes, andhigh-strength bronzes. The strength and high-temperature properties generallyimprove as one proceeds from the high-lead to high-tin to various high-strengthbronzes. However, there is a loss in the compatibility properties as the amountof lead decreases. For this reason, it is generally advisable to use the highest lead

19.1

TABLE 19.30 Composition and Physical Properties of Babbitts30

Tin-base babbitts

AlloySpecificgravity

Composition, %

Cu Sn Sb Pb

Yield point*

psi

66�F 212�F

Ultimatestrength*

psi

66�F 212�F

Brinellhardness

68�F 212�F

Meltingpoint

�F

Completeliquefaction

�F

1 7.34 4.56 90.9 4.52 None 4400 2680 12,850 6050 17.0 8.0 433 7002** 7.39 3.1 39.2 7.6 0.03 6100 3000 14,900 8700 24.5 12.0 466 6693** 7.46 8.3 83.4 8.3 0.03 6800 3100 17,600 9900 27.0 14.5 464 792

4 7.52 3.0 75.0 11.6 10.2 5550 2150 18,150 8900 34.5 12.0 363 5835 7.75 2.0 65.5 14.1 18.3 2150 2150 18,060 8750 22.5 10.0 358 565

Lead-base babbitts

AlloySpecificgravity

Composition, %

Cu Sn Sb PbAs

(max)

Yield point*

psi

66�F 212�F

Ultimatestrength*

psi

66�F 212�F

Brinellhardness

68�F 212�F

Meltingpoint

�F

Completeliquefaction

�F

6(e) 9.33 1.5 20 15 63.5 0.15 3800 2050 14,550 8060 21.0 10.6 358 5817(f) 9.73 0.50 10 15 75 0.60 3550 1600 15,650 6150 22.5 10.5 464 5148 10.04 0.50 5 15 80 0.20 3400 1760 15,600 6150 20.5 9.5 459 522

10 10.07 0.50 5 15 83 0.60 3550 1850 15,450 5450 17.6 9.0 468 50711 10.28 0.50 — 15 85 0.25 3050 1400 12,800 5100 15.0 7.0 471 50412 10.67 0.50 — 10 90 0.25 2800 1250 12,900 5100 14.5 6.5 473 498

15(g) 10.05 0.5 1 15 82 1.40 21.0 13.0 479 53816(f) 9.88 0.5 10 12.5 77 0.20 27.5 13.6 471 49519 10.50 0.50 5 9 95 0.20 15,600 6100 17.7 8.0 462 495

**In composites.***Babbitts predominantely used by electric utilities (ASTM alloy B23).

19.128 CHAPTER NINETEEN

content and the softest bronzes while still retaining the necessary strength andload-carrying capacity.

• Silver. Silver bearings normally consist of electro-deposited silver on steelbackings with an overlay of 0.001 to 0.005 in. of lead. Indium is usually flashedon top of the lead overlay for corrosion protection. Silver bearings have outstand-ing metallurgical uniformity, excellent fatigue resistance and thermal conductiv-ity, can carry very high loads, and can operated at high temperatures. Althoughthe lead coating helps to relieve problem of poor embeddability and conforma-bility, silver bearings are not recommended for applications where misalignmentand dirt are present.

• Aluminum. Aluminum bearing alloys offer excellent resistance to corrosion byacidic oils, good load-carrying capacity, superior fatigue resistance, and goodthermal conductivity. A smooth machine finish of the running surface is recom-mended along with a clean lubricant, a shaft hardness of 300 Brinell or higher,and a large enough clearance to allow for the high thermal expansion of thealuminum. Sometime the aluminum is overlaid with a thin coating of lead babbitt.This overlay assists in making up for the otherwise poor embeddability and con-formability characteristics of the aluminum.

The range of temperatures that these various bearing materials, as well as someother materials, can endure is given in Table 19.31.

19.9 DESIGN CONSIDERATIONS

In practice, a designer must obtain quantitative data to ascertain on the one handwhether the bearing will meet his operational requirements, and on the other handfind out what the power losses, flows, temperatures, etc. will be to properly planthe layout of the facility. In Sections 19.3 to 19.7, the graphs and tables offer valuesfor the performance of various bearing designs. These, however, do not exhaustthe information required for rational design. What is needed is some orientationhow the various geometrical and operational parameters affect bearing operationand how to go about improving or even optimizing a given bearing design. Thefollowing paragraphs should offer some guidance as to how to go about approach-ing this task.

19.9.1 Performance Parameters

The expressions required for calculating the more important items of bearing per-formance are the following:

• Film thickness. For an aligned journal, the film thickness is given by

h � (h /C � 1 � � cos (� � �)) (19.58)

19.1

TABLE 19.31 Approximate Temperature Limitations of Various Bearing Materials36

19.130 CHAPTER NINETEEN

The attitude angle � is defined as the angle between the line centers—a linepassing the centers of bearing and journal—and the load vector. When the treat-ment is restricted to vertical loads, � denotes the angle between location of hmin

and the vertical and therefore the importance of � lies in that it determines thelocation of hmin.

• Sommerfeld number (load parameter). The Sommerfeld number, given by

2�N R

S � (19.59a)� �P C

has traditionally been the most important parameter. However, a more convenientquantity is the inverse of S, here called the load parameter, given by

2 2P C W CW � � (19.59b)� � � ��N R LD�N R

where P � (W /LD) is the unit loading. What this parameter says is that anycombination of P, �, N, C, and R such as to leave the value of unchanged,Wwould result in the same bearing eccentricity ratio, �, and attitude angle, �.

• Minimum film thickness. The is the smallest distance between the journal andbearing surfaces and it is given by:

hminh � � (1 � �) (19.60)min C

What is normally referred to as load capacity relates to the load, W, which thishmin can support.

• Friction coefficient. This is the ratio between the frictional force and bearingload. It is normally expressed in the form of:

R (R /C)F�ƒ �� C W

The general shape of ƒ as a function s is given in Fig. 19.88. The region ofsudden rise in ƒ denotes the limit of hydrodynamic lubrication, followed by aregime of ‘‘boundary lubrication’’ characterized by partial contact between themating surfaces.

• Power loss. This, of course, can be obtained from the value of F� , namely

H � F � R � � � ƒ � W � R � ��

H HH � � (19.61)� � 3 2 3H [� �N LD /C]0

The quantity by which H is normalized, represents the power loss in an unloadedconcentric journal bearing, i.e., one in which � � 0. It is known as the Petroffequation.

PRINCIPLES OF BEARING DESIGN 19.131

FIGURE 19.88 Behavior of friction coefficient in fluid filmbearings.

• Flow. An amount of lubricant, Q1, enters the bearing at the leading edge; anamount, Qs leaks out the two sides of the bearing (one-half Qs at each side), andan amount Q2 leaves the trailing end of the pad. In most cases, since a journalbearing extends over circumference (2�), Q2 is not discharged outside but reen-ters the next oil groove, so that the net amount of lubricant to be made up froman outside source is Qs. The latter is referred to as side leakage. Clearly we mustalways have

Q � Q � Q (19.62)1 s 2

All of these flows are given in dimensionless form as:

QQ � (19.63)

�NDLC

the denominator representing the flow in an unloaded, concentric bearing, i.e., at� � 0 (for which case Qs � 0 and Q1 � Q2).

The above flows, Q1, Qs, and Q2 are what may be called hydrodynamic flowsinduced by the shearing action and pressure gradients of the fluid film. Qs is theminimum amount of oil to be delivered to the bearing to maintain a full fluidfilm with all its potentialities. In practice, designers supply more than this re-quired minimum, using a supply pressure ps � pa. The effect of the supplypressure, usually of the order of 10 to 30 psig, can be ignored as far as bearinghydrodynamics are concerned.

• Temperature rise. A bulk temperature rise can be estimated from the values ofpower loss and side leakage, namely

19.132 CHAPTER NINETEEN

HT � (T � T ) � (19.64)av 1 c wQp s

• Dynamic coefficients. The dimensionless stiffness is given by

2K � (K /2�NL)(C /R)

while the damping coefficient reads

3B � (�B /�L)(C /R)

from which the dimensional values of K and B can be obtained.

The coefficients �, ƒ, 1, 2, and which serve to evaluate bearing perform-H, Q Q K Bance are obtained from solutions of the Reynolds equation for the specific geom-etries and operating conditions of the various bearing designs. Many such solutionswere given in Sections 19.3 through 19.7.

19.9.2 Bearing Configuration

The behavior of a bearing is naturally a function of its geometry. However, evenfor a given design there are a number of variables that will affect its performance.Among the more known parameters are the L /D and C /R ratios and the degree ofpreload. Of the less familiar ones one can cite load orientation, the geometry ofthe oil grooves or the relative proportions of a bearing’s geometrical elements.

Journal Bearings. Although one often hears about the use of full, that is, 360�arc bearings, it is very rarely that such sleeves are employed in machinery. Mostjournal bearings consist of two or more pads separated by horizontal oil groovesmaking them in fact partial bearings, used either singly or in tandem. The numberand distribution of these angular pads on bearing performance is one of the moreimportant considerations in bearing design.

Partial Bearings. Whenever a single pad of an angular extent � 2� is used,it is called a partial bearing. When is very small, its load capacity is low, asillustrated in Figs. 19.89 and 19.90. However, soon a limit is reached at about �140� beyond which no further gains are registered. The reason for this asymptoticbehavior is due to oil cavitation at the trailing end of the pad where the pressuresdecrease close to or even below ambient pressure. Thus, if a partial bearing is usedthere is no need to go beyond a 140� arc. The effect of temperature in partialbearings is a combination of two phenomena. The higher the arc the longer thedissipation path and the higher the temperatures; however, a longer arc producesthicker films and thus less heating. Consequently, as shown in Fig. 19.91, a cross-over point occurs; at high loads low values of are preferred, if low T’s aredesired; at low loads a longer arc is preferred.

Grooved Bearings. Partial bearings are not used extensively. The most commondesigns are grooved bearings which consist of a number of pads arranged in tandemby cutting axial oil grooves around the 360� circumference. There is a great variety

PRINCIPLES OF BEARING DESIGN 19.133

FIGURE 19.89 Effect of bearing arc on load capacity.21

of such designs, the most common being a 2-pad bearing with two grooves at thehorizontal split. Others may have 3, 4 or 6 grooves forming the same number ofindividual pads. The more grooves the lower the load capacity, as shown in Figs.19.92 and 19.93. Thus, if load capacity is the primary objective, a 2-groove bearingis best; however, those with a larger number of grooves are somewhat more stable.Related to the above is the fact that any hole or disruption in the bearing surfacewill reduce the load capacity. Figure 19.94 shows the effects on the pressure profileof cutting a slit or circular hole in the loaded part of a bearing. The larger theincursion, the more drastic the reduction in the hydrodynamic pressures whichtranslates directly into reduced load capacity.

Tilting Pad Bearings. The primary characteristic of this family of bearings isthat the individual pads are not fixed but are pivot-supported so that during oper-ation not only does the journal move but so do the pads and each in a differentfashion. A general picture of a tilting 3-pad bearing is shown in Fig. 19.95. Thestructural and analytical complexities of these bearings are more than compensated

19.134 CHAPTER NINETEEN

FIGURE 19.90 Effect of bearing arc on load capacity.21

by their great reliability and the fact that they have no rival in their stability char-acteristics.

The number of possible design parameters and operating modes in a tilting padbearing is very large. Some of them are discussed below.

a. Number of pads. Table 19.32 gives a comparison of a 3-pad versus a 5-padcentrally pivoted bearing having zero preload. When the load is in line with thepivot, the 3-pad design has a higher load capacity but the reverse is true whenthe load direction is between the pads. For loads of engineering interest the 5-pad design consumes less power.

b. Pivot location. In order to assure two-directional rotation and for ease of as-sembly, most tilting pad bearings are centrally pivoted. However, a 10% or 15%displacement of the pivot in either direction would not significantly alter thegeneral performance, a slight preference being a downward shift.

c. Preload. From many standpoints a high preload is desirable. Its effect on pre-venting the scraping of the top pads has been discussed previously and fromthis standpoint an m of at least 0.5 is required. High preloads also yield higherstiffness and damping. However, the penalty is that the film thickness over thepivot and often also the absolute hmin is reduced. Likewise, the power losses andtemperatures rise with an increase in preload.

d. Mode of loading. In general, the shaft eccentricity will be lower when loadedover the pivot. It is characteristic of tilting pad bearings that, regardless of

PRINCIPLES OF BEARING DESIGN 19.135

FIGURE 19.91 Effect of bearing arc on value of hmin.31

whether the load vector is over the pivot or between the pads, the locus of shaftcenter is along a vertical line which has a direct beneficial effect on stability.Results for the two modes of loading on stiffness and damping are given in Fig.19.96 for a bearing of zero preload. As seen, both the spring and dampingcoefficients are lower for the between-pads mode of loading.

Oil-Ring Bearings. As pointed out previously, oil ring bearings operate understarved conditions. It is thus the main task of the designer to find ways to increaseas much as possible the amount of oil delivered to the bearing surface. Some ofthe important parameters that play a role in accomplishing it are geometry shapeof contact surface, weight, the material and size of the ring relative to the shaft. Inan experimental study, a series of rings portrayed in Table 19.33 was tested withthe purpose of both increasing the flow of lubricant and of extending the regimeof stable ring operation. The conclusions reached were as follows:

a. An optimum ring shape is one with a quasi-trapezoidal cross-section and a seriesof straight teeth at the contact surface shown in Table 19.33 as Ring No. 2.

b. The best ring material is bronze with a weight of 0.135 lb per inch of ringcircumference.

c. For bearing diameters in excess of 6 in., dual rings are recommended.

19.136 CHAPTER NINETEEN

FIGURE 19.92 Load capacity of grooved bearings.27

d. An anchored spring leaf inserted between the ring and journal raises the amountof oil delivery and extends the ring’s region of stable operation. One such sta-bilizer is shown in Fig. 19.97.

Load Angle. Bearing loads are usually directed midway of a pad or betweengrooves. However, improved performance can be obtained by shifting the loadvector toward the trailing edge of the bearing pad. A comprehensive mapping ofthe effects of shifting the load vector around the circumference of a 2-groovebearing is shown in Fig. 19.98. Normally the load would be straight down, that isalong �L � 0. However, as seen in the figure by moving the load toward the trailingedge, improved performance is obtained for the entire range of bearing operation.At low loads an optimum occurs at a load of �L � 10�; at high loads the value of�L is some 30�. The lowest load capacity would occur at a load angle of 60� fromthe midway point. Supplementary data is given in Table 19.34, where it is seenthat the worst angular position results in a load capacity reduction of 70 to 80%.Similar data for a 3-groove bearing has been given in Fig. 19.92. Achievement ofan optimum bearing position requires no special effort. It is sufficient to rotate thebearing in the housing the required 10� to 30� to obtain this. Attention should onlybe given to the oil delivery path since now the oil grooves would no longer be atthe horizontal split. This can be taken care of by cutting a short oil supply channelon the outside of the bearing shell.

PRINCIPLES OF BEARING DESIGN 19.137

FIGURE 19.93 Comparisons of 2- and 4-axial groovebearings.

Misalignment. It was pointed out in an earlier section that an overhung impellerwill cause bearing misalignment. As shown in Fig. 19.99, in severe misalignmentthe journal at one end may find itself in the upper half of the bearing even thoughthe load is downward. As a consequence, a fluid film and hydrodynamic pressuresmay develop in both the lower and upper portions of the bearing. Stretching fromthe end where the hydrodynamic film is at the bottom, this film will wrap itself inhelical fashion around the entire bearing circumference. In all cases the load ca-pacity, that is the value of h for the imposed load, will be drastically reduced.

Thrust Bearings. Unit loads in thrust bearings are higher than in journal bearingsand consequently their hmin will be smaller. But it should also be realized that,except for a bearing with a flat at the end, hmin in thrust bearings occurs not alonga line as in journal bearings but at a point, namely the outer downstream edge ofthe pad. This point is also where Tmax will occur and again it will be higher thanin journal bearings. This is due to the low value of hmin but also to the higher linearvelocities of the runner at the outer radius of the pad.

19.1

FIGURE 19.94 Effect of a slot and a hole on hydrostatic pressure.

PRINCIPLES OF BEARING DESIGN 19.139

FIGURE 19.95 A tilting 3-pad journal bearing.

TABLE 19.32 Relative Load Capacity 3-and 5-Pad Bearings29

On-pivot load

3 pads 5 pads

Load betweenpivots

3 pads 5 pads

20 0.72 0.82 1.42 0.9740 0.79 0.87 1.58 1.0560 0.80 0.90 1.60 1.0980 0.82 0.92 1.61 1.10

100 0.83 0.93 1.62 1.11

Tapered Land Bearings. A conventional tapered land bearing was shown inFig. 19.35. There are three parameters here; the taper (h1 � h2), the pad arc andthe (L /R2) ratio. The angular extent also determines the number of pads in a thrustbearing. Table 19.35 shows the results of an optimization study giving the valuesof (h1 � h2) and for the entire range of (L /R2) ratios. From this an optimum setof design parameters can be obtained for a particular application. It is worth notingthat in general the optimum configuration is that which yields nearly square bearingpads.

An improved version of a plain tapered land bearing is one with a flat surfaceat the trailing end, as shown in Fig. 19.36. The additional merit of this design isthat upon starting and stopping, the runner rides on a flat surface reducing wear.

19.140 CHAPTER NINETEEN

FIGURE 19.96 Effect of mode of loading on bearing stability in a 4-pad tilting pad bearing.

Here a new parameter is the ratio of the tapered to the flat portion. The plot in Fig.19.100 shows such a variation from 60% to 100% taper, the latter being the taperedland bearing discussed previously. The load capacity peaks at a taper value of about80% of the pad arc, that is the tapered portion should be four times that of the flat.Interestingly the value of (power loss/ load capacity) achieves a minimum at thesame point.

Misalignment. In properly operating thrust bearings, the load carried by eachpad is the same. When the shaft and consequently the runner is misaligned, this isno longer true and some of the pads are much more heavily loaded than the other.A pictorial representation of this situation is given in Fig. 19.101. As seen, theloads carried by the heavily loaded pads as well as their maximum temperaturescan be 10 times as high as the ones located opposite them where the runner isfurthest from the pads. The values of h in the two sets of pads will be of the sameratio. The span of severity of bearing operation goes up with the number of padsused in the misaligned bearing. Thus, if misalignment is expected, one should notuse more than 4 to 6 pads.

Hydrostatic Bearings. In a conventional hydrostatic bearing portrayed in Fig.19.102, the load capacity is given by

2 2�R (p � p ) [1 � (R /R ) ]2 o a 1 2W �2 ln (R /R )2 1

There are therefore two parameters that determine the level of W; (po � pa) and

PRINCIPLES OF BEARING DESIGN 19.141

TABLE 19.33 Oil Ring Configuration15

(R2 /R1). The variation of load with these quantities is shown in Fig. 19.102. Asseen no optimum for load capacity occurs; it rises with p and drops with a risein (R1 /R2). A minimum occurs in the power loss, but power loss in a hydrostaticbearing is not of great concern and, when it is, it is due not to bearing geometrybut to the onset of turbulence in the fluid.

19.142 CHAPTER NINETEEN

FIGURE 19.97 Configuration of oil ring stabilizer.15

19.9.3 Qualitative Guidelines

In selecting design parameters, it must be kept in mind that the choice often de-pends on the size of the bearing. Small bearings, less than 2 in. in diameter, cantolerate relatively lower values of hmin, higher unit loads, P; and operate close toisothermal conditions, whereas larger bearings require larger values of hmin, lowervalues of P, and tend to run close to adiabatic conditions. On the other hand,(C /R) ratios must be higher for small bearings. With this as an introduction, Table19.36 gives some typical design practices in the field of journal bearings. Theperformance characteristics of one’s design should fall somewhere within the rangeof values listed in the table.

Nearly all the bearing data given here are for bearings operating under laminarconditions. Should turbulence set in, the operating characteristics will change. Onemay expect turbulence when the bearing Reynolds number reaches a value between750 and 1500. The higher the Reynolds number, the more intense will be the effectof turbulence. Table 19.37 shows what will be the impact of the turbulent regimeon the major items of bearing operation.

PRINCIPLES OF BEARING DESIGN 19.143

FIGURE 19.98 Effect of load angle on load capacity in two-groove bearing.37

TABLE 19.34 Effect of Load Angle on Load Capacity inConventional Two-Groove Bearing13

L /D � at �L � 0W

Worstcondition

�L WW at Worst �L� �W at � � 0L

0.5 0.6 3.1 50 1.05 0.320.95 83 55 14.5 0.175

1.0 0.6 8 52 2 0.250.95 115 60 20 0.17

19.144 CHAPTER NINETEEN

FIGURE 19.99 Hydrostatic forces and films under misalignment.

PRINCIPLES OF BEARING DESIGN 19.145

TABLE 19.35 Optimum Pad Arrangement25

L /R 2 h1 /� , deg Number of pads

1/3 1 �30 �101/2 �30 �101/4 35 91/8 40 8

1/2 1 40 81/2 45 71/4 50 61/8 60 5

2/3 1 50 61/2 60 51/4 80 41/3 �80 4

FIGURE 19.100 Effect of extent of taper (or flat).13

19.146 CHAPTER NINETEEN

FIGURE 19.101 Effects of misalignment in thrust bearings.28

PRINCIPLES OF BEARING DESIGN 19.147

FIGURE 19.102 Performance of incompressible hydro-static bearing.

TABLE 19.36 Typical Design Limits for Journal Bearings

Minimum film thickness 0.001–0.01 in. (0.0025 to 0.25 mm)Temperature rise Up to 80�F (27�C) (on babbitt)Maximum temperature Up to 300�F (150�C) (on babbitt)Loads 500 psi (3.4 MPa)L /D ratio 0.25 to 1.0C /R ratio 0.001 to 0.002Preload, m 0.25 to 0.75Bearing arcs 150� to 60� for fixed pad

80� to 30� for tilting padInlet oil temperature, T 80�F to 130�F (27� to 55�C)

19.148 CHAPTER NINETEEN

TABLE 19.37 Effect of Turbulence onBearing Performance

Reynolds number a parameterRe � �R�h /u

Regimes● Re � 750 Laminar● 750 � Re � 1500 Transition● Re � 15000 Turbulence

Effects of turbulence on bearingperformance

Item Effect

Load capacity �

Oil flow �

Power loss �

Temperatures �

Stiffness and damping � or �

�-Increase; �-Decrease.

In a more comprehensive way, Table 19.38 provides a guide in which directiondesign modifications should head in order to ameliorate unsatisfactory results in achosen design. Finally, Table 19.39 offers a cursory look at the relative advantagesand disadvantages in choosing journal bearings of different designs.

19.1

TABLE 19.38 Effect of Design Parameters on Journal Bearing Performance

Code: (�) means increase magnitude of parameter to achieve effect in left-hand column.(�) means decrease magnitude of parameter to achieve effect in left-hand column.

Example: To decrease temperature rise, one or more of the following can be done:decrease L /D ratio, increase C /R, decrease oil viscosity, etc.

Objective L /D C /R Geometry ViscosityPreload,

m Arc,

Supply oilpressure, ps

To decrease temperature rise (�) (�) Elliptical (�) (�) (�) (�)b

To reduce power loss (�) (�) or (�) Circular (�) (�) (�) (�)To reduce Tmax (�) (�) Elliptical (�) (�) (�) or (�) No effectTo increase oil flow (�) (�) Elliptical (�) (�) (�) (�)To improve stability (�) (�) See (a)

below(�) or (�) (�) (�) No effect

To increase load capacity (�) or (�) (�) Circular (�) (�) (�) No effectTo avoid turbulence (�) or (�) (�) 3-lobe (�) (�) (�) (�)Stability (�) (�) Tilting

Pad(�) or (�) (�) (�) No effect

a)The stability of a journal bearing increases in the following order: circular, pressure, elliptical,3-lobe, tilting pad.

b)Apparent effect only.

19.1

TABLE 19.39 Characteristics of Various Journal Bearings Journal Bearing SummaryTable

Bearing type Advantages Disadvantages Comments

Axial Groove 1. Easy to make2. Low cost

1. Subject to oil whirl Round bearings are nearlyalways ‘‘crushed’’ to makeelliptical or multi-lobe

Elliptical 1. Easy to make2. Low cost3. Good damping at critical speeds

1. Subject to oil whirl at highspeeds

2. Load direction must be known

Probably most widely usedbearing at low or moderatespeeds

Three andFour Lobe(TaperedLand, etc.)

1. Good suppression of whirl2. Overall good performance3. Moderate cost

1. Some types can be expensiveto make properly

2. Subject to whirl at high speeds

Currently used by somemanufacturers as standardbearing design

Pressure Dam(Single Dam)

1. Good suppression of whirl2. Low cost3. Good damping at critical speeds4. Easy to make

1. Goes unstable with littlewarning

2. Dam may be subject to wear orbuild up over time

3. Load direction must be known

Very popular withpetrochemical industry. Easy toconvert elliptical over topressure dam.

Hydrostatic 1. Good suppression of oil whirl2. Wide range of design

parameters3. Moderate cost

1. Poor damping at critical speeds2. Requires careful design3. Requires high pressure

lubricant supply

Generally high stiffnessproperties used for highprecision rotors

Tilting Pad 1. Will not cause whirl (no crosscoupling)

2. Wide range of designparameters

1. High cost2. Requires careful design3. Poor damping at critical speeds4. Hard to determine actual

clearances5. High horsepower loss

Widely used bearing to stabilizemachines with subsynchronousnon-bearing excitations

PRINCIPLES OF BEARING DESIGN 19.151

19.10 REFERENCES

The selection of the following references was made with the intent of providingsources from which additional data could be culled for bearing design purposes.

1. Allaire, P. E., D. F. Li, and K. C. Choy, ‘‘Transient Unbalance Response of Four Mul-tilobe Journal Bearings,’’ Journal of Lubr. Technology, Trans. ASME, July 1980.

2. Chen, H. M., ‘‘Active Magnetic Bearing Technology: A Conventional RotordynamicApproach,’’ 15th Leeds-Lyon Symposium on Tribology, September 1988.

3. Chen, H. M., ‘‘Magnetic Bearings and Flexible Rotor Dynamics,’’ STLE Annual Meetingat Cleveland, Ohio, May 9–12, 1988.

4. Chen, H. M., et al., ‘‘Stability Analysis for Rotors Supported by Active Magnetic Bear-ings,’’ 2nd International Symposium on Magnet Bearings, July 12–14, 1990, Tokyo,Japan, pp. 325–328.

5. Chen, H. M., ‘‘Design and Analysis of a Sensorless Magnetic Damper,’’ presented atASME Turbo Expo, June 5–8, 1995, Houston, Texas, 95GT180.

6. Compressor Handbook, Gulf Publishing Co., Book Division.

7. Gross, W. A., ‘‘Gas Film Lubrication,’’ John Wiley, 1962.

8. Heshmat, H., J. A. Walowit, and O. Pinkus, ‘‘Analysis of Gas-Lubricated CompliantThrust Bearings,’’ ASME Paper 82-LUB-39, 1982.

9. Heshmat, H., J. A. Walowit, and O. Pinkus, ‘‘Analysis of Gas-Lubricated Foil JournalBearings,’’ ASME Paper 82-LUB-40, 1982.

10. Heshmat, H., and J. Dill, ‘‘Fundamental Issue in Cryogenic Hydrodynamic Lubrication,’’Proc. AFOSR/ML Fundamentals of Tribology Workshop (February 1987).

11. Heshmat, H., ‘‘Analysis of Compliant Foil Bearings with Spatially Variable Stiffness’’presented at AIAA/SAE/ASME/ASEE 27th Joint Propulsion Conference, June 24–26,1991, Sacramento, CA, Paper No. AIAA-91-2101.

12. Heshmat, H., ‘‘A Feasibility Study on the Use of Foil Bearings in Cryogenic Turbo-pumps,’’ presented at AIAA/SAE/ASME/ASEE 27th Joint Propulsion Conference, June24–26, 1991, Sacramento, CA, Paper No. AIAA-91-2103.

13. Heshmat, H., and P. Hermel, ‘‘Compliant Foil Bearing Technology and Their Applicationto High Speed Turbomachinery,’’ 19th Leeds-Lyon Symposium on Thin Film in Tribol-ogy—From Micro Meters to Nano Meters, Leeds, U.K., Sept. 1993, D. Dowson, et al.(eds) (Elsevier Science Publishers B.V., 1993), pp. 559–575.

14. Heshmat, H., and O. Pinkus, ‘‘Performance of Starved Journal Bearings with Oil RingLubrication,’’ Journal of Tribology, Trans. ASME 107, no. 1 (1985): 23–32.

15. Heshmat, H., and O. Pinkus, ‘‘Experimental Study of Stable High-Speed Oil Rings,’’Journal of Tribology, ASME 107, no. 1 (1985): 14–22.

16. Heshmat, H., and O. Pinkus, ‘‘Performance of Oil Ring Bearing,’’ International ScienceConf. on Friction, Wear, Lubr., Tashkent, U.S.S.R., May 1985.

17. Hustek, J. F., and O. J. Peer, ‘‘Design Considerations for Compressors with MagneticBearings,’’ Proc. 3rd Int. Symposium on Magnetic Bearings, July 1993, Alexandria, VA.

18. Jones, G. J., and F. A. Martin, ‘‘Geometry Effects in Tilting-Pad Journal Bearings,’’ASLE Paper No. 78-AM-@A-2, 1978.

19.152 CHAPTER NINETEEN

19. Ku, C.-P. R., and H. Heshmat, ‘‘Compliant Foil Bearing Structural Stiffness Analysis:Part I—Theoretical Model Including Strip and Variable Bump Foil Geometry,’’ Journalof Tribology, Trans. ASME, vol. 114, no. 2 (1992): 394–400.

20. Pinckney, F. D., and J. M. Keesee, ‘‘Magnetic Bearing Design and Control Optimizationfor a Four-Stage Centrifugal Compressor,’’ Proceedings of Mag. ’92, pp. 218–227.

21. Pinkus, O., and B. Sternlicht, ‘‘Theory of Hydrodynamic Lubrication’’ (New York:McGraw-Hill, 1961).

22. Pinkus, O., and D. F. Wilco*ck, ‘‘Low Power Loss Bearings for Electric Utilities: VolumeII: Conceptual Design and Optimization of High Stability Journal Bearings; Volume III:Performance Tables and Design Guidelines for Thrust and Journal Bearings,’’ MTI Re-port Nos. 82TR42, 82TR43, April 1982.

23. Pinkus, O., ‘‘Analysis of Elliptical Bearings,’’ Trans. ASME, vol. 78, 1956, pp. 965–973.

24. Pinkus, O., ‘‘Analysis and Characteristics of the Three-Lobe Bearing,’’ Trans. ASME,Ser.D., vol. 81, March 1959.

25. Pinkus, O., ‘‘Solution of the Tapered-Land Sector Thrust Bearing,’’ Trans. ASME, vol.80, Oct. 1958.

26. Pinkus, O., ‘‘Analysis of Non-circular Gas Journal Bearings,’’ Journal of Lubr. Technol-ogy, Trans. ASME, Oct. 1975.

27. Pinkus, O., ‘‘Solution of Reynolds Equation for Arbitrarily Loaded Journal Bearings,’’Trans. ASME, Series D, vol. 83, no. 2, June 1961.

28. Pinkus, O., ‘‘Misalignment in Thrust Bearings Including Temperature and CavitationEffects,’’ Journal of Tribology, Oct. 1986.

29. Pinkus, O., ‘‘Optimization of Tilting Pad Journal Bearings Including Turbulence andThermal Effects,’’ Israel Journal of Technology, vol. 22, nos. 2–3, 1984/85.

30. Pinkus, O., ‘‘Manual of Bearing Failure and Repair in Power Plant Rotating Equipment,’’EPRI, July 1991.

31. Raimondi, A. A., and J. Boyd, ‘‘A Solution for the Finite Journal Bearing and Its Ap-plication to Analysis and Design—III,’’ Trans. ASLE, vol. l, no. l, 1959.

32. Reddickoff, J. M., and J. H. Vohr, ‘‘Hydrostatic Bearings for Cryogenic Rocket EngineTurbopumps,’’ Journal Lubr. Technology, July 1969.

33. Schmied, J. L. and J. C. Predetto, ‘‘Rotor Dynamic Behaviour of a High-Speed Oil-FreeMotor Compressor with a Rigid Coupling Supported on Four Radial Magnetic Bear-ings,’’ Proceedings of 4th International Symposium on Magnetic Bearings, August 23–26, 1994, ETH Zurich, Switzerland, pp. 441–447.

34. Vohr, J. H., ‘‘The Design of Hydrostatic Bearings,’’ Columbia University, NY.

35. Walton, J. F., and H. Heshmat, ‘‘Compliant Foil Bearings for Use in Cryogenic Turbo-pumps,’’ Proceedings of Advanced Earth-to-Orbit Propulsion Technology ConferenceHeld at NASA/MSFC May 17–19, 1994, NASA CP3282, vol. 1, Sept. 19, 1994, pp.372–381.

36. Wilco*ck, D. F., and Booser, E. R., ‘‘Bearing Design and Application’’ (New York:McGraw Hill, 1957).

20.1

CHAPTER 20COMPRESSOR VALVES

Walter J. Tuymerho*rbiger Corporation of America, Inc.

Dr. Erich H. MachuConsulting Mechanical Engineerho*rbiger Corporation of America, Inc.

20.1 PURPOSE

Compressor valves are check valves that control the flow into and out of a com-pressor cylinder. There has to be at least one suction valve and one discharge valvein every compression chamber.

20.2 HISTORY

The modern era of compressor valves started in 1897 when the Austrian engineer,Hanns ho*rbiger, designed and patented a steel plate valve intended for a lowpressure air blower in a steel mill application. Interestingly, this design employeda frictionless guided valve plate useful for non-lubricated compressors, a feature,which until the introduction of non metallic materials to compressor valves waspoorly achieved by most other valve designs.

In 1910, Hans Mayer patented a different valve design that became known asthe ‘‘Feather valve.’’ This design uses several flexible steel strips as sealing ele-ments and became the standard for the Worthington Company for many years.

In 1931, Ingersoll Rand patented yet another valve design that became knownas the ‘‘Channel valve.’’ The channel valve employed several strips with a crosssection like a ‘‘U’’ (therefore the name ‘‘channel’’), each supported by a leaf spring.It was the standard valve for the Ingersoll Rand Company and was probably pro-duced in higher numbers than any other compressor valve.

A valve design older than all the others was rediscovered in the late 1950’s withthe event of pipeline compressor applications and the availability of high strengthplastics, in this case nylon. Thompson Industries developed this poppet valve for

20.2 CHAPTER TWENTY

the Clark Brothers, a compressor manufacturer in Olean, New York. This valveproved to be extremely efficient in low compression ratio applications.

20.3 SURVEY OF VALVE DESIGN

All automatic compressor valves have several basic components in common:

• Valve seat

• Sealing element(s)

• Lift constraint (guard)

• Spring(s)

The flow passages in a valve can be arranged in various different ways:

• Circular rows of ports

• Parallel series of ports

• Irregular arranged number of holes

20.3.1 Valve Designs Used in Air and Gas Compressors

Ring Valve. Ring valves are probably the most commonly used valves in air aswell as gas compressors. A properly manufactured valve ring is a very simpleelement with a perfectly uniform stress distribution. It therefore has a high tolerancefor impacts. From a valve designer’s point of view, rings can easily be guided andthe utilization of the available area is good (for manufacturing reasons most valvesare round). The disadvantage of individual rings is the need for each ring to beseparately spring loaded. Since the specific spring load for each ring cannot beperfectly identical and because the flow distribution across a valve is not uniform,it is difficult if not impossible to make all rings move uniformly. On the other hand,due to the possibility of individual motion of each ring, this design is more tolerantto liquids than other designs.

Several ring valve designs which are used are discussed below.Simple Ring Valve. This design uses plain rings guided in the valve guard. The

valve springs can either be small individual coil springs, separate for each ring, orslightly larger springs supporting two rings. Some older valve designs use one largecoil per ring. Wafer or lentoid springs are used in smaller valves. The advantageof these springs is their low space requirement, allowing for extremely thin valveguards and therefore low clearance volume. The disadvantage of these springs isthe limited possibility of adaptation to different operating conditions. For this rea-son, they are mostly used in air compressors.

Damped Ring Valve. The only damping system used in ring valves is gas damp-ing. This design uses very thick valve rings guided on the full diameter in a closelyfit groove in the valve guard. In theory, when the valve opens, the gas beneath the

COMPRESSOR VALVES 20.3

FIGURE 20.1 Ring and spring set for ringvalve with one spring covering 2 rings.

FIGURE 20.2 Ring valve with wafer springs.

valve ring is trapped in the guard groove and has to be squeezed out through thenarrow passages on either side of the valve ring. The effect of damping largelydepends on production tolerances, state of wear, and/or presence of liquid or solidcontamination in the gas. On valves with non-metallic valve rings and steel guards,the different coefficient of thermal expansion makes this an almost impossible taskfor the designer. It follows that the application for this damping system is limitedto metallic sealing elements.

Contoured Ring Valves. Some valve designs utilize a contoured valve ring to-gether with a heavily chamfered or contoured valve seat groove. This is done toachieve a lower flow resistance in the lift area where, with conventional designs,the gas has to make two 90� turns. On the other hand, for given valve lift and giventotal length of seat lands, the geometric valve port area is reduced in the proportionof sine of the angle of flow deviation.

All these valves use non-metallic valve ring materials. Since these materials havea different thermal expansion coefficient than the valve seat material, there may bea leakage problem either in the cold or hot condition of the valve. This problem isreduced by a certain flexibility of the valve ring which allows it to ‘‘roll into’’ thevalve seat groove.

20.4 CHAPTER TWENTY

DAMPENING BY

TRAPPED GAS

VALVE SEAT

VALVE GUARD

VALVE PLATECONTROLLED

GAP

FIGURE 20.3 Gas dampened ring valve.

FIGURE 20.4 Contoured ringvalve (courtesy Cook Manly).

Ported Plate Valve. There are basically two types of ported plate valves in exist-ance:

Simple Plate Valve. Plate valves, for the most part, are ring valves with theirindividual rings connected by bridges. The advantage of a plate valve over anindividual ring valve is that there is only one sealing element to be controlled. Thesimultaneous opening or closing of all ports is automatically given. This advantagehowever comes at a price. From a stress point of view, the simple, very uniformvalve ring has been transformed into a much more complicated element. When avalve plate impacts at one point it starts to bend, causing a rather complex, nonuniform stress distribution.

Double or Mass Damped Plate Valve. The designation double damped valvesis actually a misnomer, since there is only one real damping feature used. Thevalve springs themselves are not to be considered a damping feature.

Plate valves allow for a very effective, mechanical damping system. So calleddamping plates are positioned between the valve plate and the valve guard andsometimes are spring loaded separately. During the valve opening event, the valve

COMPRESSOR VALVES 20.5

FIGURE 20.5 Double damped valve.

FIGURE 20.6 Velocity diagram of mass dampedvalve.

plate travels the first portion of the lift alone and then collides with the dampingplates. During this impact, linear momentum is conserved, but kinetic energy isdestroyed. In other words, the energy required to accelerate the mass of the damp-ing plates results in a reduction of the velocity of the valve plate itself and con-sequently reduces the final impact velocity against the valve guard. As an extrabonus, the valve plate tends to be leveled when contacting the damping plates.

Channel Valve. By numbers, this valve design is by far the most widely usedcompressor valve in the Western hemisphere. It uses a number of straight sealingelements with the U shaped cross section, therefore the name channel valve. Eachindividual channel is spring loaded by a leaf spring and guided on both ends of

20.6 CHAPTER TWENTY

FIGURE 20.7 Channel valve (courtesy ofDresser Rand ).

FIGURE 20.8 Feather valve(courtesy of Dresser Rand ).

the channel by a comb like guide. This valve design is very efficient in low tomedium pressure, low to medium speed compressors.

Feather Valve. This valve design is intriguing for its apparent simplicity. It usesa leaf type sealing element which is allowed to bow into a machined recess in theguard. The leaf is therefore also its own spring. Feather valves are no longer usedin new compressors and their application was limited to low and medium pressurecompressors with clean gas service.

Poppet Valve. Poppet valves use rather large (approx. 7/8 inch diameter) holesin the valve seat and for each of these holes there is a mushroom shaped sealingelement, called a poppet. Each poppet has its own valve spring. The original pop-pets were made of bronze, which due to its high mass, was practically useless. Theadvent of Nylon made this design the valve of choice for low compression ratio,low speed compressors. Valve lifts of up to 3/8 inch were commonly used and inpipeline service this valve’s efficiency was unequaled.

COMPRESSOR VALVES 20.7

FIGURE 20.9 Poppet valve (courtesyof Dresser Rand ).

When PEEK (Polyetheretherketone,1 a polymer) became available, poppet valveswere also successfully used in higher compression ratios. With reduced valve liftsnecessary for these applications, the efficiency of the standard poppet valve shouldbe checked against other valve designs.

For high speed compressors, a variation of the common poppet valve was de-veloped. This design utilizes a much smaller poppet—called Minipoppet—andtherefore a smaller valve seat hole. Lower valve lifts without reducing flow areaare possible with this design.

Double Deck Valve. In conventional cylinder designs, there is limited space avail-able for compressor valves. If the valve area achieved is insufficient and addedclearance volume can be tolerated, double deck valves can be used. Double deckvalves can be of different basic valve designs such as ring-, plate-, poppet- orfeather valves. In all but the feather valve design, a second valve is positionedupside down above the first valve. The two valves are separated by a spacer andheld together by means of a sleeve. The gas flow to the bottom deck is straightfrom the cylinder; the flow to the top deck is through the sleeve and then reversedby means of a cover. The combined valve area of a double deck valve is approx-imately 40% larger than that of the same size single deck valve.

Deck-and-One-Half Valve. Deck-and-one-half valves are valves where a full deckvalve is positioned above a ring type bottom valve and the flow through both valvesis in the same direction. These valves provide an even larger valve area than doubledeck valves, but require a very deep valve pocket since the cylinder porting has tobe above the top deck valve. A cone type spacer is normally used to separate thetwo valve decks and provides flow access to the top deck. The total valve area ofa deck-and-one-half valve can be 60 to 65% larger then the same size single deckvalve.

1See e.g. Purdue proceedings 1990, page 701.

20.8 CHAPTER TWENTY

FIGURE 20.10 Double deck poppetvalve.

Concentric Valves. Concentric valves are valves where a suction and a dischargevalve are arranged concentrically either within one body, or as two individualvalves. Either the suction or the discharge valve can be arranged in the center, theother valve is then positioned around it. These valves are normally used on singleacting cylinders and are positioned on the face of the cylinder. The original objec-tive was to make maximum use of available cover area with minimum clearancevolume. This is needed in compressors with very high compression ratios as seenin refrigeration compressors and small air compressors. Small displacement highpressure cylinders also use this valve design.

Reed Valve. The domain of the reed valve encompasses small refrigeration andair compressors. A reed valve normally consists of a single seat plate with valvereeds positioned on both sides of the seat plate. The reeds themselves are made ofthin strip steel and can have almost any shape. The reed is held on one end andcovers a port with the other end. The valve opens when the differential pressurestarts to bend the reed away from the seat plate. This elastic deformation of thereed also acts as the valve spring and no other springs are used.

There are reed valve designs using two seat plates with a spacer (normally agasket) and the valve reeds positioned between the seat plates. The advantage ofthis design is a positive stop for the valve reed when the valve is open; the dis-advantage is its high clearance volume and a higher cost compared to a single seatplate design. Due to the low mass of the moving element—the valve reed—thisdesign can be used at very high compressor speeds. Reed valves are commonlyused in compressors up to 3600 rpm and have been successfully tested at speedsup to 7000 rpm.

COMPRESSOR VALVES 20.9

20.4 THEORY

20.4.1 Principle of operation

The essential part of every compressor valve is the sealing element. It is usuallyspring loaded and allowed to move between two stops, the valve seat and the valveguard. When resting against the valve seat the valve is closed, when against thevalve guard, it is considered to be fully opened. The distance the sealing elementcan travel between these two stops is called the valve lift.

The sealing element is made to move by the action of a gas force and a springforce rather than mechanically. The forces of gravity or inertia forces due to ma-chine vibration are usually small and can be neglected. Other forces are undesiredlike the viscous sticking force due to the presence of liquids, but sometimes haveto be taken into account9.

When the valve is opened, the flowing gas will exert a dynamic gas drag forceon the valve plate which is of the order of magnitude of the pressure drop of thegas flow across the valve multiplied by valve plate area. When closed, the valvehas to be able to support the full static pressure difference between suction anddischarge pressures, which can be very high. The flexural strength required to resistthis pressure difference is supplied by the valve seat.

Special attention has to be given to the motion of the sealing element during theopening and closing events. In fact, in most cases, it is the impact of the sealingelement against one of its stops that causes the valve to fail. Small impact velocitiesare a condition necessary to assure long valve life. Other reasons for prematurevalve failure may be wear, erosion and clogging due to solid or liquid contaminants,poor maintenance or simply mechanical overload.

20.4.2 Relationship between Valve Design and Compressor

Efficiencies and Work

The compressor efficiencies of interest are

• The energy efficiency or isentropic efficiency �is, comparing work requirementsof the real machine and ideal machine operating under identical conditions ofnominal suction pressure and temperature, nominal discharge pressure and gascomposition

• The volumetric efficiency �vol or better efficiency of delivery �, comparing strokevolume with the volume of gas at nominal suction conditions delivered per cycle.

The amount of work required by a compression cycle is the amount of energyrequired by one working chamber (called head end or crank end depending on thelocation with respect to the crankshaft) to take a mass of gas M from the suctionline, compressing it inside the cylinder from suction to discharge pressure, thendelivering M to the discharge line, and re-expanding the gas remaining in thecylinder to suction pressure.

20.10 CHAPTER TWENTY

• The isentropic part Wis which is theoretically required by the ideal machine ofsame size working without losses under the same external conditions, i.e. withidentical gas composition, suction and discharge pressures, suction temperature.In the real machine however, the gas inside the cylinder at the beginning of thecompression stroke will be at a temperature T1,s generally higher (for reasonsexplained below and given in more detail in12) than T1 , consequently already theisentropic work Wis to be expended per unit mass of gas will be increased in theproportion of T1,s /T1.

• And an additional �W covering the losses occurring in the real machine, corre-sponding to the work losses due to pressure drops in valves and valve pockets,repeated expenditure of work for recompressing gas that has leaked back duringa previous cycle, heat exchange ‘‘in the wrong moment’’ causing the process tobe polytropic, mechanical friction between moving parts like piston rings andpackings, etc. The term work loss is in fact a misnomer and in apparent conflictwith the principle of conservation of energy or the first law of thermodynamics.What really happens is that energy of a high value (mechanical or electricalenergy coming from the driver) is converted into useless energy, useless in thesense of the second law of thermodynamics, i.e. heat energy at a low temperaturelevel whose presence is even a nuisance.

Since the days of James Watt some 200 years ago, it is common practice tomeasure total work exchange between a piston and the gas inside a cylinder as thearea of the PV-diagram or indicator diagram. The ratio between the work requiredby the ideal machine and the work required by the real machine is called energyefficiency or isentropic efficiency

100 � Wis� � [%]is T1,sW � �Wis T1

Volumetric efficiency �vol is defined geometrically and can be taken from an in-dicator diagram.

1 / �Z P1 2� � 100 � s � 1 [%]� � � �vol Z P2 1

where

s total cylinder clearance [%]Z1, Z2 real gas compressibility at nominal suction and discharge conditionsP1, P2 nominal suction and discharge pressures

� exponent of an isentropic temperature change in the range between P1 andP2, with an ideal gas, � Cp /Cv

The efficiency of delivery � is equal to volumetric efficiency �vol minus a sum ofvolume losses

COMPRESSOR VALVES 20.11

� � � � (volume losses) [%]vol

While the influence of the valve on �vol is limited to its contribution to clearancevolume s, the volume losses responsible for the difference between �vol and theefficiency of delivery � depend to a great part on design and state of wear of thevalves, in particular:

• Temperature corrections to account for the fact that the gas inside the cylinderat the beginning of the compression stroke will be at a higher temperature thanT1 and hence lighter. This heating results from the conversion of the part of �Wcorresponding to the work loss in suction valves and pockets into heat dissipatedin the gas during the intake cycle. In addition, there can be heat exchange betweenthe gas and the walls of the suction plenum, of the suction valve and of thecylinder.

• Volume losses due to leakage in valves, piston rings and packings. With theexception of packings, the impact of leakage is twofold: it reduces the amountof gas and increases the temperature.

• Volume losses due to excessive valve throttling

• Volume losses due to late valve closure

• Pulsations can cause compression to start from a lower pressure than p1 thusproducing a volume loss.

An analytical treatment of this problem area based on differential equations isgiven in Ref. 11, based on simple algebraic equations in Refs. 12 and 14. It followsthat both, isentropic efficiency volume losses due to leakage in valves, piston ringsand packings. Except for leaking packings, the impact of leakage and efficiency ofdelivery are affected by valve losses, which therefore have to be minimized. Onthe other hand, valve life should be as long as possible.

Unfortunately, both postulates are contradictory: For a given valve design, goodefficiencies mean small �W and therefore small pressure drops in the valves, hencelarge flow areas and a high valve lift. On the other hand, a long lasting valve meanssmall impact velocities and hence a small lift. It is up to the skill and the experienceof the valve engineer to find the best possible compromise by properly selectingvalve design, lift, springs and materials.

20.4.3 Motion of Sealing Element

Under ideal conditions the opening motion of the valve sealing element is initiatedby the pressure differential across the valve overcoming the pre-load of the valvesprings. The acceleration of the element is a function of the gas drag force and anelastic force provided by the valve springs.

During the opening period of the valve its instantaneously available valve areastarts at zero and gradually increases to its full flow area. At this time however thepiston moves with a certain velocity. Depending on which changes faster, the vol-

20.12 CHAPTER TWENTY

Mean pist ty

Piston speed

p - v DiagramDischarge pressure

Suction pressure

Max piston speed

on veloci

FIGURE 20.11 P-V diagram with piston veloc-ity.

ume displaced by the piston or the gas flow rate through the valve, the differentialpressure across the valve increases or decreases. This condition causes the ‘‘openinghump’’ seen on most pv-diagrams (Fig. 20.11). Once the valve is open, the volumeflow through the valve should more or less equal the piston displacement, such thatthe pressure changes inside the cylinder are small. During this phase, the instan-taneous gas velocity in the valve lift area is approximately equal to the instanta-neous piston velocity multiplied by the ratio of the piston area and the valve liftarea. As the piston approaches the dead center position, its velocity approacheszero and the gas drag force decreases. The valve springs should be sized to over-come this diminishing gas drag force and start the closing motion of the sealingelement in order to make sure that the valve is closed at the moment the pistonreaches dead center.

If the media to be compressed contains foreign elements which have an adhesiveeffect (water, oil, etc.), the valve motion is adversely affected. Depending on thecontact area between the sealing element and the valve seat or valve guard, theadhesive force (commonly called valve ‘‘sticktion’’) can be sizable. The differentialpressure required to open the valve is equal to the pre-load of the valve springsplus the adhesive force. The valve plate motion will be delayed while the pressuredifferential continues to increase and to reach high values. Once the valve platehas left the seat, the sticking force suddenly drops to zero, the higher gas dragforce is left without any counteracting force, thus producing a much higher accel-eration than would normally be the case. Consequently, the opening impact of thesealing element against the valve guard is very high. In addition, the ‘‘opening

COMPRESSOR VALVES 20.13

-20

100

0 20 40 60 80 100 120 140 160 180

100

120

0 20 40 60 80 100 120 140 160 180

100

120

0 20 40 60 80 100 120 140 160 180

100

0 20 40 60 80 100 120 140 160 180

CYLINDER PRESSURE

VALVE LIFT

EQUIVALENT VALVE AREA

VALVE PLATE VELOCITY

CRANKANGLE DEGREE

FIGURE 20.12 Discharge valve opening event.

hump’’ on the pv-diagram is larger than normal. When closing the valve, the springforce has to overcome the gas drag force and in addition the adhesive force of thesealing element against the guard. This can cause the valve to close well after thepiston reaches dead center, resulting in gas flowing back through the valve againcausing a high impact of the sealing element against the valve seat.

20.4.4 Valve lift

There are only two technical items of interest to a valve user: the valve losses orefficiency, and the valve life. Valves presently used are pressure activated whichimplies a pressure differential and therefore losses. However a minimum loss isrequired in order to control the valve motion properly. The valve life is normallya function of the valve lift. Assuming clean gas and no liquids in the gas-stream,valves fail due to fatigue caused by impacts. A valve sealing element normallyincreases its velocity throughout the whole lift, which means the higher the valve

20.14 CHAPTER TWENTY

200 300 400 500 600 700 800 1000 1500

0.039

0.078

0.028

0.118

0.157

0.2360 PSIG

100 PSIG

1000 PSIG

5000 PSIG

COMPRESSOR RPM

LVE

LIF

T [

IN]

FIGURE 20.13 Allowable valve lifts for steel.

lift, the higher the impact velocity and the shorter the valve life. Impact velocitiesof valve sealing elements can only be calculated approximately when performinga complete valve motion study. There are however guidelines for maximum rec-ommended valve lifts depending on the speed of the compressor and the operatingpressure. One guideline that has been used for decades and which closely reflectscurves published by a major valve manufacturer is given by the following empiricalformula for steel valve plates

13h �steel 2 / 3 1 / 6RPM p

where

h allowable lift [in]p line pressure [psia]

RPM speed [rpm]

For non metallic plates, add .040 in to hsteel, for poppets simply double this value.

20.4.5 Valve Areas

As the gas flows through a compressor valve, it passes through areas which aredefined more or less arbitrarily, but physically meaningful, in the following way.

Seat Area. The seat area is normally defined as the area of the seat grooves minusthe area of all radial webs in the vertical projection, in other words the area inwhich, if a valve seat is held against a light source, light becomes visible. Asalready stated, the valve seat has to provide flexural strength against the high pres-sure load when the valve is closed. This is achieved by giving it a certain heightand providing enough radial webs thus reducing flow area. The best solution can

COMPRESSOR VALVES 20.15

only be found by sophisticated calculations of mechanical strength, usually by usingfinite element methods.

Lift Area. Lift area equals the total length of seat lands multiplied by the valvelift. The seat lands area is where the sealing element seals against the valve seat.With increasing total length of the seat lands, the risk of valve leakage also in-creases.

Guard Area. Its definition is analogous to seat area.

Required Geometric Valve Lift Area. In the past, valves have been sized for anapplication primarily by using the valve velocity as the main criterion. Guidelinesfor acceptable velocities have been established by a number of companies. Thevalve velocity certainly has an influence in sizing a valve, but in itself is notsufficient. In terms of losses the important criteria are the pressure drop across thevalve and the assurance of full pressure recovery inside the cylinder at piston deadcenter, i.e. allow the cylinder pressure to recover fully to the line pressure at theend of the stroke. An indicator—the q—value was introduced11 representing theadequacy of a valve.

2bore � �� 2 � stroke � RPM

4v �m n � f � 12e

where

vm valve velocity ft /minbore cylinder bore inches

stroke piston stroke inchesn number of suction (discharge) valves per cylinder endfe lift area for one suction (discharge) valve in sq. inches� 3.14159

22� � f 100s eq � � � v � �� SV m8 p 144 � 3600 � gs

where

�s suction gas density lb/cu.ftps suction pressure psia equivalent area sq.inches

qSV relative pressure drop % of suction line pressureg acceleration due to gravity � 32 ft/s2

qSV is a dimensionless parameter used in the differential equations describing pres-sure and temperature evolution inside the cylinder.11 For normal flow through a

20.16 CHAPTER TWENTY

V E A ctual

VE Theore tical

Pressure

S troke

FIGURE 20.14 P-V diagram for cylinder with insuffi-cient suction valve area (q-value � 16).

suction valve and small pressure drops, qSV can be interpreted as the maximumpressure drop in % of line pressure. Discharge valves, providing they do not leakand close in time, have almost no influence on compressor capacity, but high qDV

signify excessive pressure drops and work losses. With a good valve design,q-values should be within the limits 2% and 12% for both, suction and dischargevalves. Too small q-values mean too small pressure drops, hence too small gasdrag forces and too small spring forces since these have to be sized to matchpressure drop. The valve cannot be actuated properly; it will flutter and total workloss will be higher than necessary. Too high q-values mean high pressure dropsand losses of work and capacity. In the suction valve, a qSV value in excess ofapproximately 16% indicates no pressure recovery in the cylinder at dead center.This will cause a late closing of the valve and capacity losses.

Equivalent Area. The equivalent area is the effective orifice area of a valve whenthe valve is completely open. It is the geometric valve area affected by its coeffi-cient of flow contraction and is therefore the area which should be used to calculatevalve losses accurately. Most reputable valve manufacturers flow test their valvesin order to establish this value. The equivalent area is influenced by the basic valvedesign, the valve lift and also by the manufacturing quality. It is for the last itemthat the exact value of the equivalent area can vary from one valve to another ofthe same design.

Given that the valve is designed using acceptable industry standards, the equiv-alent area can be estimated for plate or ring valves by formula developed by HuntDavis.2

11 1 1

� � � �2 2 2 2 2 2k � A k � A k � Al l be be s s

COMPRESSOR VALVES 20.17

where

A lift area1

A area between elementsbe

A seat areas

k � .851

k � .66be

k � 1s

From the suction flange of a cylinder to the compression chamber, the gas passesnot only through the valve but also through internal cylinder passages, the valvecage and from the valve through the valve port. Every one of these passages po-tentially contributes to the total losses incurred which are normally called totalventilation losses. The ratio of total ventilation losses over valve losses can bequantified using a pocket loss factor.8

20.4.6 Valve Springs

The function of valve springs is to close the valve in time. The objective is thatall valves should be closed when the compressor piston reaches dead center. Sincethe valve sealing element has to travel the whole valve lift from the fully openedto the fully closed position, the closing motion has to start before dead center andtherefore against the gas flow. If the valve springs are too weak, the valve willclose late (after the piston passes the dead center position) and gas is allowed toflow back through the valve causing the valve sealing element to slam closed. Onthe other hand if the valve springs are too heavy, the valve will close early. Sincethe piston continues to travel toward dead center, the pressure differential betweencylinder and line will increase and the valve will reopen. An extreme case of tooheavy springs leads to valve flutter. Tendency to valve flutter increases if the springload considerably exceeds the values given in the two formulas below. Small pres-sure drops together with high valve lifts require springs with low spring rates andthin wires lacking sturdiness. In addition, these springs have to be long and havea tendency to buckle.

p � .4 � q � pf SV s

for a suction valve and

�pdp � .4 � q � p � � �f DV s ps

for a discharge valve, provided qDV is calculated as if it was a suction valve, i.e.using vm, ƒe and of the discharge valve, but �s and ps.

Both above formulas are approximate and valid for pressures up to about 500[psia]. For other applications, it is indicated to verify spring selection by means ofmotion study. Properly selected valve springs have practically no effect on the valveopening.

20.18 CHAPTER TWENTY

20.4.7 Theoretical Valve Motion

All the formulas shown above have been found empirically and are valid only fora typical range of parameters. They can be used to conventionally size valves, liftsand springs for one and only one given operating condition. However if parametersare outside typical ranges or if operating conditions are variable, these methodsfail. They cannot tell us whether a valve sized and tuned for one condition cansafely be used for another condition as well. To answer such a question, the inter-action between valve and compressor has to be modeled. The result is a system ofat least three ordinary differential equations: one for the changes of valve lift; onefor cylinder pressure; and one for cylinder temperature. These equations are toocomplex to be integrated analytically and have to be solved numerically in stepsby one of the well known algorithms (Runge-Kutta, predictor-corrector and simi-lar), necessitating a considerable amount of computation.

In its simplest form, this approach was published almost half a century ago.1

Since then, particularly since the availability of powerful computers, the modelshave been extended. For lack of space only some typical improvements shall bementioned here, for example including gas pressure pulsations,5 considering gasinertia in the valve ports,4,7,10 the so called gas spring effect,10 gas leakages,11 heatexchange,6,11,12 higher modes of a valve reed,3 more degrees of freedom of thevalve plate’s motion to predict the higher impact velocities resulting from co*ckingof the valve plate,13 etc. All this is to show that the problem is in fact rathercomplex.

When interpreting computed valve motions one should therefore always bear inmind that

• The models currently in use are far from being physically comprehensive, andreal motions may look more or less different.

• The coefficients of flow resistance and drag force and their variation with valvelift as used in the model may be different from those in the real valve.

• External data like pressures, temperatures, gas analysis, pulsation patterns mayvary.

• The gas may be contaminated, liquid may be present.

• Numerical algorithms are always subject to local loss of precision, particularlyin the vicinity of piston dead center positions and when valve pressure drops aresmall (usually with q-values � 2%).

The results of these motion studies depend therefore to a large degree on theirinterpretation. As general rules the following can be used:

• A perfect looking valve motion is usually not as good as it looks, since theabsence of rebounds on the seat is often due to late closure and therefore dan-gerous.

• A normal valve opening with no or little rebound on the guard is desirable.Although computed rebounds do not necessarily represent reality, they largely

COMPRESSOR VALVES 20.19

depend on the way the impact is modeled and the arbitrary choice of coefficientsof restitution. Usually they are inoffensive.

• The valve should stay open without flutter during most of the piston stroke.

• An early valve closing (before dead center) is preferred.

• Ignore rebounds which start shortly before the piston reaches dead center at theend of valve closure.

• The model computes impact velocities. A sealing element fails due to excessivelocal stresses in the material. One of the problems, therefore, is to convert impactvelocities into stresses, and set allowable limits for them. These limits depend onthe valve design, material choice, quality of production and also on the compu-tational model used and the experience gained with it so far.

Some hints may be taken from the theory of one-dimensional wave propagationin an elastic medium. With this assumption, the pressure amplitude �p (� changein pressure � stress ) is related to �u (� velocity amplitude � impact velocity)by �p � � � c � �u, where � is the density and c the velocity of sound in thesealing element material, given by Thus, knowledge of very basic ma-c � �E /�.terial properties such as density �, modulus of elasticity E and allowable stress �is sufficient to estimate allowable impact velocities �u. This method finds about1100 ft/min for valve plate steel, and 2200 to 3900 ft/min for PEEK dependingon temperature. With all the imperfections of theoretical valve motion studies ex-plained above and doubts as to the applicability of linear wave propagation theory,it seems indicated not to exceed one-third of these values (‘‘factor of safety �factor of ignorance’’). A more sophisticated approach, still using the theory of wavepropagation in elastic media, but considering the properties of the seat as well, canbe found in Ref. 16, laboratory results in Ref. 17.

The proper interpretation of a theoretical valve motion study is a matter ofexperience. People with little or no experience should consult with an expert beforedrawing wrong conclusions.

20.5 VALVE MATERIALS

For most applications, normal carbon or alloy steels are used for the valve body.The determining factor is the necessary valve seat strength to withstand the differ-ential pressure the valve is subjected to. For corrosive gases, martensitic or austen-itic stainless steels are used and some highly corrosive applications require Monel,Hastelloy or similar materials. For aggressive gases such as hydrogen sulfide, sep-arate specifications18 have been established and should be followed.

20.5.1 Valve Sealing Elements

In the past, most valve sealing elements have been manufactured from heat treatedmartensitic stainless steel like AISI 410 or 420. For more corrosive gases, precip-

20.20 CHAPTER TWENTY

itation hardening steels (17-7 PH) or Inconel X750 were used. These materials arestill in use for high temperature and high pressure applications or when fingerunloaders are used and the valve plate deflection in unloaded condition is high.

Today’s materials of choice are injection molded composite materials with Nylon6/6 (30% glass-filled) being the best choice providing the operating temperatureis within the limit of this material. The maximum allowable operating temperaturefor Nylon 6/6 varies from manufacturer to manufacturer, but should be approxi-mately 250�F or less, depending on the operating pressure. For higher temperature,PEEK (Polyetheretherketone) is used. The temperature limit for this material againvaries depending on the manufacturer and is approximately 450�F. Constantly, newmaterials are developed especially by the aerospace industry, which are then usedfor compressor valve parts.

20.5.2 Valve Springs

The most widely used compressor valve spring material is a precipitation hardeningstainless steel of type 17-7 PH. For highly corrosive application nickel alloys suchas Inconel X750 or Nimonic 90 are used, with some special applications using amultiphase material type MP 35 N or Elgiloy.

20.6 VALVE LIFE

In ideal conditions, a properly designed valve has almost infinite life. Unfortunately,this condition is never found. Contamination in the gas in the form of foreignparticles or liquids, including oil, corrosion as well as poorly designed or appliedvalves with inferior dynamic behavior result in finite life of compressor valves.

• Foreign Particles: Depending on the materials used for the valve components andthe size and substance of these particles, they do more or less damage. Theimportant thing to recognize is that they do damage. Very small particles normallypass through any valve design, but they cause abrasion on the valve seat and thesealing element, eventually leading to valve failure.

Somewhat larger but still small particles can cause breakage of the sealingelement when metallic sealing elements are used but are normally embedded intothe material on non-metallic sealing elements.

No valve will survive if large, hard parts are passed through it.

• Liquid in the gas is also detrimental to valve life. Valve designs with individualsealing elements possibly made of non-metallic materials tolerate liquids betterthan valves with one solid sealing element. Liquids drops impact on the sealingelement causing a deformation on a single element valve which can result ininstant breakage. In single element valves, the one element struck by the liquiddrop can move independently not resulting in any damage.

The effect of ‘‘oil sticktion’’ was explained above in ‘‘Motion of Sealing El-ement.’’

COMPRESSOR VALVES 20.21

• Poor valve design or application almost always results in valve flutter or latevalve closing. In either case, there are either multiple impacts per compressioncycle or too high impacts resulting in premature valve failure.

20.7 METHODS TO VARY THE CAPACITY OF A

COMPRESSOR

A compressor running at constant speed, with constant suction pressure and tem-perature, discharge pressure and gas composition will always deliver the sameamount of gas per unit time. If capacity is to be varied, special methods have tobe applied. Some of these are mentioned hereafter.

20.7.1 Clearance Volume Regulation

The disadvantage of this type of control is its initial cost and problems of spacewhen applied to the crank end of a cylinder.

Varying the effective clearance volume in a compressor cylinder affects the in-take volume of a compression chamber (see the definition of �vol). The amount ofcompressed gas remaining in the clearance volume has to expand to the intakepressure before new gas can be drawn into the cylinder through the suction valve.Depending on the size of the clearance volume, the minimum capacity of a com-pression chamber can be as low as 0%. This method recovers all of the energyused to compress the gas with the exception of mechanical and fluid dynamicfriction and heat losses. Several different methods are known to accomplish this.

Fixed Clearance Volume. A fixed volume is attached to the compressor cylinderand connected to it by means of some shutoff mechanisms. This shutoff device canbe a normal compressor valve equipped with an unloading device or a plug un-loader activated by a mechanical or pneumatic actuator. Fixed clearance volumescan be attached to a valve port if either single or double deck valves with a centerhole are used. On the head end of a cylinder clearance volume, bottles can easilybe added. Compressor capacity can be varied in steps only: Opening the pocketvalve means minimum capacity, and closing it gives full load.

Variable Clearance Volume. Variable clearance volumes are added almost exclu-sively to the head end of a compressor cylinder. They consist of a volume bottlewith a movable piston and normally a manually operated spindle to move thepiston. Since the position of the clearance volume piston can be varied continu-ously, the same holds true for compressor capacity. The problems with these de-signs are leakage through the packing of the clearance volume piston as well asthe high actuating force required when adjusting the volume size while the com-pressor is in operation. When the gas is not very clean and the clearance volumepiston has not been moved for some time, it may stick and cause problems whentrying to change its position.

20.22 CHAPTER TWENTY

FIGURE 20.15 P-V diagram at various loads.

20.7.2 Fixed Volume, Variable Pressure Clearance Volume

The amount of gas stored in a fixed volume can be varied if the pressure in thatspace is varied. This can be achieved when the clearance volume is separated fromthe compression chamber by means of an additional valve equipped with an un-loader and actuator, opening and closing once per crankshaft revolution at instantsof crank angle that can be selected by varying the unloader force. To do this, it issufficient to vary the unloader force: Zero force gives full load, maximum forcegives minimum load. Intermediate values allow for a stepless adjustment of com-pressor capacity.15

20.7.3 Reverse Flow Capacity Control

The reverse flow capacity control uses an unloader and an actuator on the suctionvalves in order to hold the suction valves open during a portion of the dischargestroke.15 The delayed closing of the suction valves causes the gas in the compres-sion chamber to be pushed back into the suction line rather then being compressedfor as long as the suction valves are kept open. As soon as the suction valves areclosed, or allowed to be closed, the remaining gas in the compression chamber iscompressed and discharged.

Air pressure is applied to the diaphragm of the actuator that causes the controlspring to be compressed and the spring pushes the unloader against the valve plate,opening the valve. During the compression stroke, the gas is pushed back throughthe suction valve into the suction line with a velocity approximately proportionalto the piston speed. The gas velocity therefore increases steadily over the first halfof the piston stroke* and the drag force on the valve plate increases with the gasvelocity. As soon as the drag force on the valve plate overcomes the force thecontrol spring exerts on the unloader, the valve will close. By varying the air

*This is an approximation and technically incorrect. On the head end of a compressor cylinder, themaximum piston speed is always reached after mid-stroke, on the crank end before mid-stroke. Theexact position depends on the ratio of crank throw to connecting rod length.

COMPRESSOR VALVES 20.23

FIGURE 20.16 Suction valve with unloader and actuatorfor reverse flow capacity control.

FIGURE 20.17 Theoretical P-V diagram and valve mo-tion at partial load.

20.24 CHAPTER TWENTY

FIGURE 20.18 Actual P-V diagram at various loads.

pressure on the actuator, the control spring force is changed and therefore the timewhen the suction valves start to close.

The range of the capacity variation is limited to approximately 60% (i.e. from100% or full load down to approximately 40%). Once the maximum of reverseflow pressure drop in the suction valve has been reached without having overcomethe control spring force, the suction valves will not close at all and the compressoris then fully unloaded.

20.7.4 Variable Speed Regulation

This method of capacity control is normally used on compressors with enginedrives. Compressors driven by electric motors normally have fixed speeds for costreasons. The speed range where this system is economically effective dependsprimarily on the driver, but limits are set on the compressor side as well.

When lowering speed, the fluctuations of rotational speed will increase with thesquare of speed reduction. For example, if at full speed the coefficient of fluctuationequals 1%, it will go up to 4% at half speed. The resulting vibrations may bedetrimental to foundations, buildings and the compressor itself. In addition, lowerspeeds may cause malfunction of main bearing lubrication and rod load reversal(API 618, point 2.4.4) which is necessary for lubricating the cross-head pin bearing.Finally, valve layout may also have to be revised if speed is to be variable. Practicalexperience shows that for all these reasons speed reduction is rarely lower than40% of nominal.

20.7.5 Bypass Control

Of all available capacity control methods, this is the one with the worst energyefficiency. The basic principle is to spill back any excess gas from the dischargeside of a compressor to the suction side via an intercooler and a control valve. Theenergy used to compress this excess gas is completely wasted. This method isnormally used when for some reason other more energy efficient methods cannotbe applied.

COMPRESSOR VALVES 20.25

FIGURE 20.19 Plug unloader(courtesy of Dresser Rand ).

20.7.6 Plug Unloaders

Plug unloaders are used in place of finger unloaders to unload the cylinder endwhere they are positioned. Though mechanically reliable, the application of plugunloaders has to be governed by the resulting losses in loaded as well as unloadedcondition.

The plug unloader is basically an opening in the center of the suction valve ora separate port, which connects the compressor cylinder with the suction line whenthe port is open. A ‘‘plug’’ is used to close this port during loaded operation, hencethe name Plug Unloader. When the plug is positioned in the suction valve or in aseparate valve port, it occupies area otherwise used for valve ports and thereforereduces the total valve area. This may be meaningless in some applications—especially when light gases are compressed—but may result in high valve lossesin other applications. The effective plug area also has to be checked for its adequacyin order to insure total unloading of the cylinder side. When a cylinder is unloadedusing plug unloaders, the suction valve is operating normally which means the plugarea and the valve area are effective during the intake stroke, but only the plugarea is available during the discharge stroke.

A thorough loss calculation is recommended before deciding on the applicationof this type of unloading.

20.7.7 Valve Lifters

Valve lifters were used in the past to lift the whole suction valve from its valvepocket thereby unloading a cylinder end. From an efficiency point of view, this isa very effective method to unload a cylinder since not only the valve area but the

20.26 CHAPTER TWENTY

whole valve pocket area is available for flow. API 618 does not recommend thismethod due to seating problems of the valve and therefore it is not used very often.

20.7.8 Valve Depressors (Unloaders)

Valve depressors, also called finger unloaders, are mechanical devices to hold thevalve sealing element open during the intake and the compression stroke. The gastaken into the cylinder during the intake stroke is therefore pushed back into thesuction line during the discharge stroke. No productive compression work is per-formed when the unloaders are depressed. There is some compression workperformed—and transferred into heat—due to the throttling when the gas passesthrough the valve. The equivalent area of a suction valve with unloader is somewhataffected by the unloader since the unloader is positioned directly in front of thevalve. On reasonable designs, this should not result in more than 5 to 10% differ-ence and is for all practical purposes the same for the flow in either direction.

On multiple valve cylinders, all suction valves should be unloaded in order toassure proper unloading and low heat build up.

Unloading Force. When unloading suction valves, it is necessary that the valvesealing elements are depressed rapidly and also that the unloading actuator is ventedadequately so there are no unnecessary impacts between the unloader and the seal-ing element(s). More important however is a proper unloading force which has tobe high enough to keep the suction valve open during the compression strokewithout being so high that the unloader, or suction valve can be destroyed.

COMPRESSOR VALVES 20.27

F � �p � A � C � Fu r 0 w cs

qSV,r�p � 1.2 � � pr s100

where

Fu required force to unload the valve [lbs]�pr pressure build up inside the cylinder on reverse flow through the suction

valves [psi]Ao valve plate areaCw pressure drag coefficient [�], where 0.6 � Cw � 0.9 with usual valve designsfes force of closing springs when valve is open [lbs]

qSV,r q-value for reverse flow through suction valve(s) [%]ps suction pressure [psia]

As can be seen from the above diagram, the approximate formula �pr � 1.2 �qSV,r/100 � ps given above is valid for qSV,r—values up to about 20% and allclearance volumes. For example, with qSV,r � 20[%], the above diagram gives �pr/ps � 0.25 even for clearance volumes as small as 5%. For higher values of qSV,r

and smaller clearance volumes, �pr /ps will be higher: With qSV,r � 50 [%] andclearance volume 5%, the above diagram gives �pr /ps � 0.9. Care should thereforebe taken not to underestimate the unloading forces when q-values are high (willbe the case when not all suction valves are equipped with unloaders) and clearancevolumes are small.

20.7.9 Active Valves

With the advancement of electronics, valves can be controlled in their opening aswell as closing through mechanical devices. This means the differential pressureacross the valve is no longer the factor when a valve opens and when it closes.Some external mechanisms are determining the timing and the differential pressuremay assist in the actual motion. In very simple terms, this consists of a normalsuction valve with an unloader and a special electro-hydraulic actuator. A solenoidvalve—electronically activated—allows very high hydraulic pressure to act on asmall cylinder, depressing the unloader and opening the suction valve. When thehydraulic pressure on the cylinder is vented, the gas pressure in the cylinder actingon the suction valve plate closes the valve. For this system to function, it is ex-tremely important that the solenoid valve has a response time of less then onemillisecond and also that the amount of hydraulic fluid moved is extremely small.Opening impacts can be controlled by properly selecting the instant of valve open-ing. Closing impacts are moderate and controlled by a simple patented hydraulicdamping system. The opening time of the suction valve is not extremely important,but it should be slightly before the cylinder pressure reaches the line pressure. Theclosing time can be any time during the compression stroke, thereby allowing a

20.28 CHAPTER TWENTY

FIGURE 20.20 Suction valve with un-loader and actuator for active valve con-trol.

capacity variation from 100 to 0%. At this time this system is only available onsuction valves. Discharge valves require even higher unloading forces and alsoprovide a safety problem in case of malfunctioning of the unloading system.

The advantage of such a system is the perfect valve action even in varyingoperating conditions, larger valve areas due to higher allowable valve lifts comparedto conventional values, and infinite capacity regulation. The disadvantages are highinitial cost (this may change in due time) and a relatively complex electronic-hydraulic system as well as the limited unloading force available.

20.8 REFERENCES

1. Costagliola, M., Dynamics of a Reed Type Valve, PhD thesis, Massachusetts Institute ofTechnology, 1949.

2. Davis, Hunt, Gas Compressor Valve, Air and Gas Engineering, January 1968.

3. Soedel, W., Introduction to Computer Simulation of Positive Displacement Type Com-pressors, Ray W. Herrick Laboratories, Purdue University, 1972.

COMPRESSOR VALVES 20.29

4. Trella, T. J. and W. Soedel, Effect of Valve Port Gas Inertia on Valve Dynamics, Part I:Simulation of a Poppet Valve, Part II: Flow Retardation on Valve Opening Purdue Com-pressor Technology Conference 1974, proceedings.

5. Soedel, W., Gas Pulsations in Compressor and Engine Manifolds, Ray W. Herrick Lab-oratories, Purdue University, 1978.

6. Brok, S. W., S. Touber, J. S. van der Meer, Modeling of Cylinder Heat Transfer, LargeEffort, Little Effect?, Purdue Compressor Technology Conference 1980, proceedings.

7. Boeswirth, L., A Model for Valve Flow Taking Non Steady Flow into Account, 1984International Compressor Engineering Conference at Purdue, proceedings.

8. Bauer, Dr. F., Valve Losses in Reciprocating Compressors, 1988 Compressor EngineeringConference At Purdue, proceedings and ho*rbiger Engineering Report 52.

9. Bauer, Dr. F., The Influence of Liquids on Compressor Valves, 1990 Compressor Engi-neering Conference At Purdue, proceedings, and ho*rbiger Engineering Report 53.

10. Boeswirth, L., Non Steady Flow in Valves, 1990 International Compressor EngineeringConference at Purdue, proceedings.

11. Machu, Dr. E. H., How Leakages in Valves Can Influence the Volumetric and IsentropicEfficiencies of Reciprocating Compressors, 1990 Compressor Engineering ConferenceAt Purdue, proceedings, and ho*rbiger Engineering Report 54.

12. Machu, E. H., Valve Throttling, its Influence on Compressor Efficiency and Gas Tem-peratures, Part I: Full Load Operation, Part II: Zero Load and Half Load Operation,1992 International Compressor Engineering Conference at Purdue, proceedings.

13. Machu, E. H., The Two-Dimensional Motion of the Valve Plate of a Reciprocating Com-pressor Valve, 1994 International Compressor Engineering Conference at Purdue, pro-ceedings.

14. Machu, E. H., Reciprocating Compressor Valve Selection, Some Points to be Consideredfor Optimizing Life Time and Compressor Efficiency, European Conference on Devel-opments in Industrial Compressors and their Systems, London, proceedings C477/020IMechE 1994.

15. Machu, E. H., New Developments in the Stepless Reverse Flow Capacity Control Systemfor Reciprocating Compressors, European Conference on Developments in IndustrialCompressors and their Systems, London, proceedings C477/019 IMechE 1994.

16. Soedel, W., On Dynamic Stresses in Compressor Valve Reeds or Plates During ColinearImpact in Seats, Purdue Compressor Technology Conference 1974, proceedings.

17. Svenzon, M., Impact Fatigue of Valve Steel, Purdue Compressor Technology Conference1976, proceedings.

18. NACE International, NACE Standard MRO175-95, Item No. 21302, Standard MaterialRequirements Sulfide Stress Cracking Resistant Metallic Materials for Oilfield Equip-ment.

21.1

CHAPTER 21COMPRESSOR CONTROL SYSTEMS

Robert J. LoweT. F. Hudgins, Inc.

21.1 CONTROLS—DEFINITIONS

‘‘Compressor controls’’ have different definitions among users, designers, and sup-pliers. These can be, but are not limited to:

1. Machinery protection

a. Simple alarm system for several parametersb. Simple shutdown system for several parameters

2. Safety shutdown system monitoring multiple parameters for machinery protec-tion and safety of personnel

3. Same as 2, with loading/capacity control

4. Same as 3 with communications and remote monitoring. Computer monitoringprovides enhanced automation and energy management in addition to the ca-pability to store and manipulate data for maintenance and diagnostic purposes.

5. Environmental regulations have made the addition of emissions controls on com-pressors and engine drivers necessary for certain geographical areas.

21.2 RECIPROCATING COMPRESSOR MONITORING

Monitoring systems have progressed to measuring many parameters beyond thoserequired for basic safety. These include capacity, pressure, volume, time, vibration,calculations of gas polytropic exponents, rod load, power, fuel consumption andefficiency.

The industry is also rapidly moving to a ‘‘predictive maintenance’’ mode ascompared to ‘‘preventive maintenance.’’ Monitoring systems must be more complexto accomplish predictive maintenance.

21.2 CHAPTER TWENTY-ONE

Modern technology provides the means to track progressive machine conditionswhich, when compared to machine history, can provide the user with sufficient datato predict when a repair or maintenance must be completed as compared to routinescheduled maintenance.

21.2.1 Centrifugal/Axial Compressor Monitoring

Centrifugal and axial compressors are less forgiving than slower speed reciprocat-ing machines because of the operating speeds.

The controls for centrifugal machines must have very quick response times inorder to prevent catastrophic failures and are much more complex than the systemsrequired for reciprocating compressors.

Real time on-line performance monitoring and trending is now commonplacebecause of available high speed computer systems.

Surge control on axial and centrifugal machines is essential to prevent damagein the event of rapidly changing flow conditions. Bearing vibration monitoring inthree planes and axial trip sensors, along with bearing trip monitors, are commonpractice on centrifugal machinery.

Refer to API Standard 670.

21.3 SYSTEM CONSIDERATIONS

The control system must be selected to suit the machine, the operator, and theapplication. These considerations include, but are not limited to:

1. Is this machine part of a critical process?

2. What is the cost/benefit ratio to be provided by controls?

3. What are the personnel hazards?

4. Is this machine in a hazardous area?

5. What codes such as NEC, API, NFPA, OSHA, EPA or other regulatory agenciesapply?

6. What degree of complexity is required for safety shutdown, capacity control,loading control, remote start-stop capability, and communications?

7. Should the safety devices be monitored by the information/operations/capacitycontrols system or should safety monitoring be in a separate stand alone system?

8. Will the system be maintained by:

a. Mechanics and/or operatorsb. Instrument techniciansc. Electronics techniciansd. Communications technicianse. Users or contract personnel

9. Will the system require expansion at a later date?

COMPRESSOR CONTROL SYSTEMS 21.3

21.4 SYSTEM SELECTION—DEFINE THE SCOPE

Answers to the preceding questions will generate additional questions and providedirection for selection of the proper system.

The systems available at present, range from simple pneumatic and electric sys-tems to highly complex electronic systems that operate, not only as safety systems,but provide control and operation of compressors while storing and trending data.These systems are also capable of predictive maintenance and repair managementwhen properly structured.

Instrumentation and control technology developments have provided many im-provements, allowing expansion of monitoring and control systems. Fiber optics,Ethernet, and modern technology provide massive information flow over great dis-tances and allow centralized control of multiple machine locations.

Prior to computer systems, machinery managers did manual calculations to de-termine fuel efficiency and gas measurement. The calculations are so complex thatresults were obtainable once per hour, at best.

There are over 100 parameters to be considered in the American Gas Association(AGA3) and NX19 Fuel Flow Calculations and Super Compressibility Calculations.

Computers can provide these results every 60 to 90 seconds, enabling operatorsto manage fuel efficiency, engine emissions, while monitoring torque, compressorrod load, horsepower, capacity, and other conditions.

The goal is to improve efficiency and increase run time by managing operatingcosts and maintenance.

It should be noted that specialties have developed in certain applications suchas speed control, vibration monitoring, emissions monitoring, and centrifugal com-pressor surge control. These can be separate ‘‘stand alone’’ systems interfaced withthe overall controls system. Each requires careful analysis and system selectionusing the compression manufacturer’s specific data.

21.5 HUMAN FACTORS

Selection of controls must take into consideration the equipment and the personneloperating and maintaining the system. The control system designer must be thor-oughly familiar with the operational and mechanical aspects of the machines to bemonitored. The designer must make a careful evaluation of material compatibilityin the environment and all parts of the process. The mechanics and operators mustbe involved early in the design discussions is essential to the system success. Train-ing requirements and the ‘‘user friendly’’ features of the system are necessary forreliability and acceptance by the operators.

The system goals, sequencing, interlocks, peripherals, transient conditions, timedelays, response times, accuracy, reset differentials, passwords, and security keysmust be defined early in the process of system design.

Component access for calibration and maintenance is necessary on all systemsand a major factor determining system layout and assembly. Inspections of similar

21.4 CHAPTER TWENTY-ONE

FIGURE 21.1 Nitrogen compres-sor control panel (Class 1, Group C& D, Division II Area) front panelview. (Courtesy of Autocator Prod-ucts Division T. F. Hudgins, Incor-porated ).

installations and interviews with existing users will save time and expense, mini-mizing errors.

Documentation, detailed drawings, schematics, component instructions, andparts list are as necessary as the hardware. Instructions for calibration, testing, andmaintenance must be provided with the system in order to have satisfactory oper-ation.

21.6 ELECTRICAL AND ELECTRONIC CONTROLS

21.6.1 Applicable Codes

Specific codes govern the use of electrical equipment in hazardous as well as non-hazardous areas. Some guidelines on these ratings are as follows.

Hazardous area electrical classifications for USA and Canada—Class, Divisionsand Groups.

Class I Combustible gasses and vapor.Class II Combustible dustClass III Fibers and lintDivision 1 Combustible present or probably present in normal operation.Division 2 Combustible not present in normal operation.Group A: AcetyleneGroup B: Hydrogen

COMPRESSOR CONTROL SYSTEMS 21.5

FIGURE 21.2 Nitrogen Compressor ControlPanel (Class 1, Group C & D, Division II Area)inside panel view. (Courtesy of Autocator Prod-ucts Division T. F. Hudgins, Incorporated ).

FIGURE 21.3 Pipeline compressorpanel (programmable logic controllerpanel) front view.

21.6 CHAPTER TWENTY-ONE

FIGURE 21.4 Pipeline compressorpanel (separate electrical compart-ment). (Courtesy of Advanced ControlEngineering Services ).

FIGURE 21.5 Pipeline compressorpanel (separate pneumatic compart-ment). (Courtesy of Advanced ControlEngineering Services).

COMPRESSOR CONTROL SYSTEMS 21.7

FIGURE 21.6 Pipeline compressorpanel (programmable logic controllerand temperature scanner) front panelview. (Courtesy of Advanced ControlEngineering Services).

FIGURE 21.7 Pipeline compressorpanel (programmable logic controllerand temperature scanner) inside panelview. (Courtesy of Advanced ControlEngineering Services).

Group C: Acetaldehyde, Ethylene, Methyl EtherGroup D: Acetone, Gasoline, Methanol, PropaneGroup E: Metal DustGroup F: Carbon DustGroup G: Grain Dust

21.8 CHAPTER TWENTY-ONE

FIGURE 21.8 Control schematic.

Refer to NFPA 325M, 497M, CSA22.1, FM3610, UL913, NFPA70 and CSAC22.2,No. 157 ANSI/ISARP12.6. Also see National Elec. Code articles 500 to 504.

Intrinsically safe equipment is safe by nature of its operation and design. Thefollowing description is from the Instrument Society of America, Standard ISA-RP12.6:

‘‘Intrinsically safe equipment and wiring is equipment which is incapable of releasingsufficient electrical or thermal energy under normal or abnormal conditions, to causeignition of a specific hazardous atmosphere mixture in its most ignitable concentration.

COMPRESSOR CONTROL SYSTEMS 21.9

Intrinsically safe electrical equipment and wiring may be installed in any hazardouslocation of any Group classification for which it is accepted without requiring explo-sion proof housings or other means of protection.’’

21.6.2 Electrical Controls

Electrical controls for compressors include:

1. Switch gage systems employing pressure and temperature gages with the gagepointer as an electrical contact for alarm or shutdown by activating a mastercontrol circuit. Annunciation is a pop-out or digital annunciator. Improvementsin recent years provide micro-switch contacts on gage systems for Division IIhazardous areas.

2. Digital annunciator systems using switch sensors. These annunicators displaya number which is compared on a printed legend on the panel listing the alarmand shutdown sensors which are monitored. These can be certified for use inClass 1, Group C and D, Division I and II hazardous areas.

3. Relay logic systems require pilot lights or annunciators for indication. Theseare generally used on applications in non-hazardous areas and use standardswitch sensors. Relays are also available for Class 1, Group C and D, DivisionII areas.

4. Electronic systems which are factory programmed with logic sequences anddisplays are available for general purpose and hazardous areas. The number ofinput and output relays are fixed by the manufacturer.

5. Electronic systems which are pre-programmed micro processor based, and fieldconfigurable with compressor logic sequences were introduced in the mid1980’s. These are applied in hazardous areas and are generally intrinsicallysafe for Class 1, Group C and D, Division I or II areas. Displays are alpha-numeric. These systems use both discrete switch and analog sensors. The an-alog systems are scanners for monitoring multiple inputs and have configurableset points.

The quantities of inputs and outputs are not infinitely expandable but canbe field selected within limits. (Communications capability allows this systemto operate as a ‘‘stand alone’’ system communicating to a host or processcomputer.)

6. Process controllers and distributed controls systems (DCS) can be used whenavailable in lieu of a stand alone control system at the machine. This is im-portant when capacity control from a central control system is essential for theprocess. There must be an evaluation as to the inclusion of the safety controlswithin the central control system or to have the safety system as a separatesystem.

Note: Most electrical compressor control systems interface with pneumatic actua-tors for valve actuation power.

21.10 CHAPTER TWENTY-ONE

7. Programmable Logic Controllers Programmable Logic Controllers are mi-croprocessor based electronic systems which are modular and expandable tohundreds of inputs and outputs. Modules are available to accept all standardsensors. Input and output modules can receive and send the commonly usedsignals. These include variable 4 to 20 mA, 1 to 5 Volt DC, switch and com-munication signals. Trained programmers using hand held or other computersset up ladder logic, Proportionate-Integer-Derivative (PID) loops, timers andother control functions. PID controllers provide compensation to control orlimit lead, lag and oscillation in the system response. Graphic and alphanu-meric displays are readily available. First introduced in the 1960’s, these con-trols have been industrially hardened and are now available for Class 1, GroupC and D, Division II hazardous areas.

7a. Logic controllers built specifically for compressors have been designed withthe programmability and flexibility of a small Programmable Logic Controllers(PLC) and using similar logic systems and programming. The alphanumericdisplay is incorporated into the single unit with logic module, along with inputand output cards and communications. These small systems are modular, butdo have limited input/output quantities.

Note 1: Electronic analog controls provide the distinct advantage of multiple alarmset points for a single sensor. Alarm can occur prior to reaching a dangerous shut-down condition.Note 2: Electrical or electronic panel can be made explosion proof for Division Iareas when used with a monitored air or inert gas purge system designed specifi-cally for this purpose to purge the control cabinet with air. The purge systemincludes a pressure sensor to alarm or shutdown when purge pressure is low.

The Z and X purge air systems are used in hazardous areas. Type X purge airsystems usually alarm but not shutdown in the event of pressure loss. Type Z purgeair systems cause a shutdown in the event purge air pressure is lost.

21.7 PNEUMATIC CONTROLS

Pneumatic controls were developed for hazardous area safety control and operationof compressors early in the natural gas and process industries. They are inherentlyexplosion proof and can be interfaced with electric or electronic systems usingpressure switches and transmitters. Air or gas provides the power for valve actu-ation on all compressor systems, especially process or pipeline gas compressors.These valves include:

Fuel valve on engine driver

Starting air control valve

Suction valve

Discharge valve

COMPRESSOR CONTROL SYSTEMS 21.11

FIGURE 21.9 Marine seismic compressor (pneumaticcontrol panel). (Courtesy of Eureka Energy Systems,Inc.).

Bypass valve

Purge valve

Blowdown valve

Capacity control valves

Capacity control actuators

21.7.1 Indication

The systems include differential pressure operated three-way valves with a windowin the side of the valve body and red/green stripes on the spool. This device actsas an indicating relay or ‘‘pneumatic pilot light’’ and sequencing valve.

Pneumatic sensors for temperature, pressure, level vibration, and speed moni-toring are connected by pneumatic tubing to a pneumatic indicating relay valve.These can be tubed in parallel or series circuits, depending on the manufacturer’sdesign to provide a shutdown or alarm indication.

Pneumatic indicating relays have been operating since the early 1950’s andproven reliable under severe operating condition.

System circuitry can be designed to provide many complex sequences.

21.8 MANUAL CONTROLS

Manual start-stop and loading sequences are used but for safety reasons, usuallyin conjunction with a control/monitoring system. Loading-unloading and capacitycontrol can be manually regulated but this procedure is labor intensive and moreprecisely handled automatically.

21.12 CHAPTER TWENTY-ONE

21.9 PRELUBE-POST LUBE SYSTEM

Prior to start:Prelube the machine to distribute oil to metal wear parts for a time determined

by the manufacturer, usually 90 to 300 seconds. This is accomplished using anelectric or air motor driven auxiliary pump controlled by the control system.

A pressure switch or valve can initiate the start sequence upon completion ofprelube or cause a ‘‘READY TO START’’ indication, once the prelube pressureand/or time is adequate.Post lube:

Operation of the auxiliary oil pump for a timed period at the time shutdownprovides cooling to remove residual heat from the compressor and lubricate themachine.

21.10 LOADING-UNLOADING

Automatic loading and unloading of a small air compressor is common. The com-pressor discharge is automatically opened to atmosphere as the compressor reachesthe selected discharge pressure.

Loading and unloading of process or pipeline compressors pertains to operationof valves in the suction and discharge piping permitting or stopping flow throughthe machine. The sequence of operation will be clearly defined in the manufac-turer’s instruction manual.

21.11 CAPACITY CONTROL

Loading and unloading should not be confused with capacity control. Capacitycontrol is used for the following reasons:

1. Process flow control

2. Fuel/power efficiency

3. Rod load regulation

4. Pressure regulation

Capacity can be changed in several ways.

1. Speed regulation

2. Control of supply gas to the machine

3. Bypassing the discharge flow back to the suction side of the machine

4. Finger unloaders—(manual or pneumatic) finger unloaders are rods projectingfrom an actuated hub located in the suction valve chamber. The rods press the

COMPRESSOR CONTROL SYSTEMS 21.13

suction valve disc to the open position to unload the cylinder. These can beoperated on multiple valves on a cylinder to step-unload or load the machineincreasing or decreasing capacity according to the number of active valves.

5. Plug unloaders serve the same purpose of the finger unloaders but are con-structed with an actuated plug positioned to open or close a hole in the centerof the valve. Gas flows in and out of the center hole when the valve is deacti-vated by opening the plug. These unloaders can be manual or air cylinder op-erated.

6. Clearance pockets—cylinder volume can be changed by the addition of clear-ance (volume) pockets to valve ports or the head end of a compressor cylinder.Control of flow in and out of these clearance pockets can be by automatic air,hydraulic, or manual valve actuation.

Note: Operating and discharge temperatures must be monitored while using capac-ity control methods 3 through 6 listed above. Gas surging in and out of the cylindercan result in heat build up if improperly controlled.

21.12 LOADING AND UNLOADING

Gas compressors, depending on the service, will use either a three valve sequence,four valve sequence, or five valve sequence.

3 Valve Sequence

Suction

Discharge

Blowdown

4 Valve Sequence

Suction

Discharge

Blowdown

Bypass

5 Valve Sequence

Suction

Discharge

Blowdown

Bypass

Purge

21.14 CHAPTER TWENTY-ONE

21.12.1 Three Valve Loading Sequence

Start the driver with the compressor ‘‘unloaded.’’

Discharge valve closed

Suction valve closed

Blowdown valve open

To load—

1. Open discharge valve.

2. Open suction valve.

3. Close blowdown valve after a delay which is long enough to allow all air to bepurged from the machine, by the gas, vented through the blowdown valve.

To unload—

1. Open blowdown valve.

2. Close suction valve.

3. Close discharge valve.

21.12.2 Four Valve Loading Sequence

Start the driver with the compressor ‘‘unloaded’’

Discharge valve closed

Suction valve closed

*Blowdown valve open (or closed)

Bypass valve open

To load—

1. Open discharge valve.

2. Open suction valve.

3. Close blowdown valve if open.

4. Close bypass valve.

To unload—

1. Open blowdown valve.

2. Open bypass valve.

3. Close suction valve.

4. Close discharge valve.

COMPRESSOR CONTROL SYSTEMS 21.15

21.12.3 Five Valve Loading Sequence Machine Not Running

Blowdown valve open

Bypass valve open

Suction valve closed

Discharge valve closed

Purge valve closed

Prior to start—

1. Close bypass valve.

2. Open purge valve.

3. After time delay for pressurized purge, open bypass.

Start machine—

1. After warm-up or appropriate time, initiate load sequence.

2. Open purge valve (pressurize compressor and confirm pressure).

3. Close purge valve.

4. Open discharge valve.

5. Open suction valve.

6. Close bypass valve to begin flow through the compressor. (Bypass valve can beused to control flow through the machine.)

Five Valve Unloading Sequence

1. Open bybass valve.

2. Open blowdown valve (optional)

3. Close suction valve.

4. Close discharge valve.

Emergency shutdown should cause blowdown valve to immediately open.

*Note: Starting with the blowdown valve closed allows the compressor to remaincharged with gas when stopped. Special packing seals are necessary to retain thegas when the machine is in the stopped position. These seals grip the rod at thepacking case when the compressor stops and are interlocked with the control systemto release seals prior to starting and to grip the rod only after the machine stops.

The compressor loading sequences can be completely automated and shouldalways include valve position sensors to confirm valve positions. Appropriate timedelays between steps must be included. In addition, if valve positions are not con-firmed within 30 to 45 seconds (adjust as necessary), the system should shut downfor safety reasons.

21.16 CHAPTER TWENTY-ONE

Certain systems use either the suction valve or the bypass valve for capacitycontrol.

Caution: All sequences should be in accordance with the manufacturer’s instruc-tions. Careful attention must be given to the gas dynamics when using clearancepockets and valve unloaders to avoid temperature build-up within the cylinders.

21.13 SENSOR CLASSIFICATION—(ALARM CLASSES)

Sensors can be classed as one of the three main groups for purposes of monitoringon reciprocating machines. There are subgroups, but the three main classes are:

Class A SensorsClass A sensors are monitored continuously and must be healthy at all times.Typical would be liquid levels and discharge temperature.

Class B SensorsClass B Sensors—Certain conditions which are not present when the machineis not running are not monitored during the start sequence and are locked outby use of a timer. Low oil pressure and water pressure are examples. Vibrationcan be time-latched out during the start sequence.

Class C SensorsClass C Sensors—Process conditions, low suction, low discharge pressure andother sensors do not become healthy until the machine is running and loaded.Class C sensors become armed and monitored after the sensor becomes healthyand resets.

Recap:In order to start, all Class A sensors must be healthy; Class B sensors are armedat the expiration of a Class B timer or as the sensor becomes healthy. Class Csensors become armed as the sensor or the complete group of C sensors resetin healthy condition. This is dependent upon the system logic.

21.14 SENSORS

Operating conditions on and around compressors include high temperatures, grease,oil, vibration and pulsation. Rugged sensors are necessary to operate reliably underthese conditions.

Sensors are available as:

1. 4–20mA transmitters

2. 1–5 volt transmitter

3. Switches

4. Pneumatic valves

COMPRESSOR CONTROL SYSTEMS 21.17

5. Thermocouples—the common alloys are (K) Chrome-Alumel and (J) Iron-Constantan.

6. (RTD) Resistance temperature detectors

7. Mechanical trip valves

8. Proximity sensors

Starting: (Sensors)Starting can begin automatically by control system or manually upon completion

of prelube time.Engine drivers rotate on start command driven by the starting system—the au-

tomated system measures the speed and applies ignition and fuel according tomanufacturer’s instructions. The engine should complete warm-up cycle determinedby a timer or a temperature sensor prior to being loaded.

Electric motor starting should also incorporate the compressor prelube cycle ifnecessary, and in certain applications, require a fan driven air purge prior to starting.The control system should incorporate a timer or a pressure switch to acknowledgecompletion of the prelube and/or air purge cycle. This occurs in a manner similarto compressor prelube and should be according to manufacturer’s instructions.

21.14.1 Monitoring Compressor Parameters

The following list includes points to monitor on a typical large compressor system.

Ambient temperature

Compressor crosshead guide temperature

Compressor packing case temperature (high)

Compressor packing case vent (leak detection) (high)

Compressor rod bearing temperature

Compressor rod drop (rider band wear)

Compressor valve temperature

Coolant flow rates

Coolant pressure

Crankcase pressure (high)

Differential pressure—oil filter

Emergency shutdown

Engine fuel flow rates

Engine fuel temperature

Engine manifold pressure (low)

Engine power cylinder exhaust temperature

Engine turbocharger bearing coolant in and out

Engine turbocharger bearing temperature

21.18 CHAPTER TWENTY-ONE

Engine turbocharger lubricating oil pressureEngine turbocharger lubricating oil temperatureEngine/compressor main bearing temperatureFire detection system shutdownFuel level (low)Lube oil pressure (low)Lubrication flow (low)Lubrication oil consumptionLubricator flow (low)Metal (in oil) particle detectionMotor bearing temperatureMotor bearing vibrationMotor overloadMotor power failureMotor purge fan failureMotor vibrationMotor winding failureMotor winding temperatureOil cooler temperature in and out (high)Oil filter Differential (high)Oil level–compressor (low)Oil level—driver (low)Oil level—lubricator (low)Scrubber level (high)Scrubber level (low)Suction, discharge, interstage pressure (high)Suction, discharge, interstage pressure (low)Suction, discharge, interstage temperatureVibration—compressor (high)Vibration—cooler (high)Vibration—driver (high)Water cooler temperature in and out (high)Water pump differential pressure (low)

21.15 SPECIAL COMPRESSOR CONTROLS

The compressor industry has created a demand for special control systems andsensors for problems unique to compressors. Among these are:

COMPRESSOR CONTROL SYSTEMS 21.19

FIGURE 21.10 Pneu-matic compressor packingcase purge control panel tocontrol packing leakage.(Courtesy of AutocatorProducts Division, T. F.Hudgins, Incorporated ).

Packing case purge controlRod drop measurement and alarmsVibration monitoringVibration sensorsMounting vibration sensorsMetal particle detection in lubrication oilLubrication flow sensorsSensors for pulsating compression pressuresEutectic temperature sensorsEnergy managementCylinder pressure measurement

21.15.1 Packing Case Purge Controls

Control systems used to maintain purge gas on packing cases designed to preventleakage of process gas along the rod to atmosphere have proven effective. Mea-surement of vent gases is used as a diagnostic tool to determine the rod packingwear and replacement schedule.

21.15.2 Surge Control

Centrifugal and axial compressor surge control is a specialty area of compressorcapacity control and safety. These systems are necessary to provide stable operationon high speed centrifugal compressors.

21.20 CHAPTER TWENTY-ONE

FIGURE 21.11 Flow meter connection for measuring purge andpacking leakage flow.

21.15.3 Compressor Rod Drop

Measuring rod drop is an effective tool in determining when rider rings should bereplaced and can minimize cylinder wear. Rod drop occurs in a horizontal com-pressor cylinder as piston or rider rings wear, allowing the piston to descend. Theintent of a compressor rod drop measuring system is to alarm this event prior tothe piston contacting the cylinder.

Three measurement systems are in use today. These are:

1. Pneumatic eutectic sensor is a bracket mounted sensor located beneath the rod.As the rod rubs on the sensor, the friction causes the eutectic solder to melt,allowing the pneumatic control system to vent and alarm or shut down themachine.

2. Proximity rod drop measurement without the crank angle monitoring system isan electronic equivalent of the pneumatic system alarming when the rod reachesa set point. The operator can also observe a read-out and trends from the systemdisplay.

3. Proximity rod drop sensor in conjunction with a crank angle detection systemwhich measures rod position at exactly the same point within the rod stroke.The proximity probe is an eddy current sensor. The output varies in responseto rod position. Measuring a specific crank angle allows the operator to beassured of the piston position at the time of measurement.

COMPRESSOR CONTROL SYSTEMS 21.21

FIGURE 21.12 Metal particle detector.

21.15.4 Vibration Monitoring

Vibration monitoring systems are necessary for determining the health of a ma-chine. An experienced analyst can determine the exact cause of a noise or conditionby analyzing the vibration patterns. The system complexity can vary with speedand critical nature of the machine.

If a machine is equipped with vibration alarms, these signals can alert the op-erator to call for an extensive vibration analysis by a specialist using portablediagnostic equipment to determine the exact cause of the vibration. The other op-tion is to provide the extensive analysis diagnostic system as part of the installationand machine controls.

21.15.5 Vibration Sensors

1. Inertia sensors are available as pneumatic valves and electric switches. Theseare intended to respond to vibration on low speed equipment and in ranges from0 to 3000 cpm to 0 to 12000 cpm, at vibration sensing ranges 0 to 5g’s and 0to 10 g’s. These devices are sensitive to vibration parallel to the axis of thesensor mechanism.

2. Eddy current sensors measure machinery motion and are frequently used tomonitor moving shafts because direct contact is not necessary. Position, dynamicmotion, and wear are now measurable using these sensors.

3. Accelerometer based sensors sense impact events and are available with andwithout conditioning. Conditioning, either in the sensor or in the control system,converts the accelerometer signal to velocity or displacement signals propor-tional to vibration. The conditioned accelerometers convert the low poweredsignal from the sensor into a 4 to 20mA or 1 to 5 volt DC signal, and can beconnected to electronic monitors that are not especially designed for monitoringvibration. Unconditioned sensors have low output signal and are intended to beconnected to an electronic monitor that includes the conditioning and vibrationmonitoring system.

4. There is a wide selection of read-out devices and systems that provide indica-tions and alarms, computerized systems data storage, and trending of the fol-lowing data. This is a very specialized technology and there are manufacturers

21.2

FIGURE 21.13 Metal particle detection diagram.

COMPRESSOR CONTROL SYSTEMS 21.23

providing this service worldwide. Typical displays, either in velocity or displace-ment, would be:

Running speed vibration

Crank case deflection

Compressor crosshead vibration

Compressor cylinder head vibration

5. Compressor valve covers can be monitored temporarily by accelerometers aspart of a portable compressor analysis diagnostic system to determine valvecondition and operation.

Selection of vibration sensors requires careful analysis of machine speed, sensorlocation, and vibration amplitude based on experience or manufacturer’s data. Vi-bration on low speed machines (120 to 1,500 rpm) is commonly measured in milsor mm displacement. High speed machine (360 to 90,000 rpm) vibration is mea-sured in inches per second or mm/s velocity.

21.15.6 Mounting Vibration Sensor

‘‘Bearings take the load during vibration’’ and are the desired vibration monitoringpoints. The restraint provided by the base can limit vertical movement, therefore,the sensor must be mounted where the most movement is predicted.

21.15.7 Metal Particle Detectors

Metal particles in oil are an indication of:

A. Contamination

B. Machinery wear

Metal particles from bearings, pump wear, cylinder wear, and other failures havebeen detected by these sensors prior to the build up of temperature or vibration.These systems provide a constant monitoring for metal particles in the lubricatingfluid.

The application requires a small oil side stream from the dirty side of the filterto flow through a perforated printed circuit card within a suitable housing. As theparticles complete the circuit, the alarm circuit is energized. These detectors re-spond to all conductive particles.

Sensors for ferrous only particles are also available.

21.15.8 Lubrication Low Flow Sensors

Compressor lubrication system failure can be detected by monitoring switches orvalves which remain in a ‘‘healthy’’ condition with flow. As lubrication system flowdiminishes, or stops, the sensor trips.

21.24 CHAPTER TWENTY-ONE

More sophisticated electronic systems actually measure the flow and transmitthe data to computers. The alarm set point can be in the flow monitor or in thecomputer.

21.15.9 Pressure Sensors

The need to measure engine firing pressures and compression pressures has causedseveral very rugged sensor types to be developed to withstand the pulsation andhigh temperatures. The rugged construction is necessary because these sensors aremounted on the cylinder for measuring internal pulsating cylinder pressures.

The sensors have piezo-electric and strain gage elements and are proving valu-able for controlling operating conditions by computer and evaluating the machineperformance. These are available with and without the requirement for water cool-ing.

21.15.10 Cautions

Sensors must be installed in accordance with the ISA recommendations andASME codes and Regulations Agency codes.

Sensors must be protected from corrosive fluids and excessively high pressuresand temperatures.

Temperature sensors can be protected by suitable thermowells.

Static pressure sensors can be protected by suitable gage isolators where nec-essary. These are sealed diaphragm devices especially designed for this purpose.

21.16 TEMPERATURE CONTROL (OIL AND WATER)

Controlling oil and water temperatures is essential in order to maintain properrunning clearances. In addition, proper temperatures minimize wear, maintain clear-ances and proper lubricant viscosity, and prevent condensation in the crankcase.Temperatures are controlled by either self-contained thermostatic valves or tem-perature control valves with controllers.

21.16.1 Self Contained Thermostatic Valves

Special self contained three way valves using internal copper impregnated expand-ing wax elements were developed for the compressor and engine industries. Thesevalves are located in the oil and water piping.

During a cold start-up, the fluid is recirculated back to the heat source (bypassposition). As the machine warms up, and approaches the element set point, within

COMPRESSOR CONTROL SYSTEMS 21.25

5�F to 7�F, the element begins to close the bypass port and send fluid to the cooler.The valve will modulate flow to bypass and cooler in order to maintain the settemperature maintaining a constant flow volume through the machine.

Sizes are selected for a pressure drop of 2 to 7 psi in order to be certain ofproper velocities and to maintain heat transfer to the element for proper response.

These valves are available with a variety of body materials, trim, and seals.Material compatibility and codes must be considered. As an example, API rec-ommends that piping systems containing hydrocarbons be of steel construction.

Certain lubricants are not compatible with standard o-rings and the thermostaticvalves must be specified accordingly. Commercially available sizes range from1/2 inch to 8 inch flanges. Available materials are cast iron, steel, ductile iron,bronze, and stainless steel.

21.16.2 Cooling Water and Lube Oil

FIGURE 21.14 Cooling water and lube oil systems.

21.26 CHAPTER TWENTY-ONE

21.17 ELECTRIC MOTOR AND PNEUMATICALLY OPERATED

TEMPERATURE CONTROL VALVES

Three way temperature control valves have been designed for use with pneumaticcylinder and electric motor operators. The need to provide very low pressure dif-ferential, yet maintain control, were considerations. External actuators allow theuse of remote sensing elements and controller to suit the application.

Pneumatic and electronic industrial controllers can be used with these valvesand operators to regulate temperatures. Another option is to use the central plantprocess control system. The pneumatic controller allows the valve to be placed ina hazardous area such as a gas pipeline compressor station.

Proportional controls which vary the output according to the input, proportional,integral, derivative (PID) controls provide a more precise control regulation byeliminating the offset between the desired and actual temperatures. The derivativeaction attempts to anticipate temperature changes based on the cyclic rates ofchange experienced by the system. I to P converters are used to interface an elec-tronic controller to a pneumatic operator. Commercially available in sizes rangefrom 2 inch to 16 inch flanges. Industrial control valves can be used in this service,but do operate at higher differential pressures.

21.18 ENERGY MANAGEMENT SYSTEMS

Energy management systems provide dramatic cost savings where multiple ma-chines are used in industries such as foundries, automotive or process plants, aswell as pipeline and process industries.

Careful analysis and control of machine run time, along with capacity control,will optimize power consumption. An added benefit is reduced machine wear andmaintenance.

21.19 SPECIFICATIONS, CODES, AND STANDARDS

Refer to the following publication for suggested specifications, codes, and stan-dards.

Instrument Society of America—ISA

S5.1 Instrumentation Symbols and Identification

S5.4 Instrument Loop Diagrams

S5.5 Graphic Symbols for Process Displays

RP12.6 Installation of Intrinsically Safe Systems for Hazardous (Classified) Lo-cations

COMPRESSOR CONTROL SYSTEMS 21.27

Standards and Practices for Instrumentation

National Electrical Manufacturers Association—NEMA

ICS 3–1978 Industrial Systems

ICS 6–1978 Enclosures for Industrial Controls and Systems

American Petroleum Institute—API

API 670–Vibration, Axial-Position, and Bearing-Temperature Monitoring Sys-tems

API 618–Recommended Practice for Compressor Emissions Monitoring

API RP–550 Manual on Installation of Refinery Instruments and Controls

API RP–520 Design and Installation of Refinery Instruments and Controls

API RP–521 Guide for Pressure Relief and Depressuring Systems

API RP–14F Recommended Practice for Design and Installation of ElectricalSystems for Offshore Production Platforms

Underwriter’s Laboratories, Inc.—UL

Standards for Safety

Factory Mutual System—FM

Approved Standards and Data Sheets

National Fire Protection Association—NFPA

National Fire Codes Volumes 1 through 16

22.1

CHAPTER 22COMPRESSOR FOUNDATIONS

Robert L. Rowan, Jr.Robert L. Rowan & Associates, Inc.

22.1 FOUNDATIONS

The key to rotating and reciprocating machinery reliability is the foundation. Oneof the main functions of foundations is to support the machines at a precise ele-vation, thus allowing the original precision alignment to be maintained over thelife of the machine.

Besides the critical task of maintaining the alignment of the machine, the foun-dation must supply enough mass to absorb the unbalanced forces that the operatingmachine produces. Good engineering input from the manufacturer of the machineis essential to the designer of the foundation, but equally as important is a geo-technical analysis of the soil on which the foundation will rest.

22.1.1 Types of Foundations

Reciprocating and centrifugal compressors can be packaged or unitized on a fab-ricated skid (Fig. 22.1), block mounted (Fig. 22.2), or set on a pile cap foundation(Fig. 22.3). Large centrifugal machines are also sometimes set on ‘‘table top’’foundations, which are shaped much like a kitchen table with multiple legs (Fig.22.4). This style is popular for larger machines and allows the space underneathto be used for long radius, large diameter piping and auxiliary equipment.

The above types represent practices in the United States. No review, though,would be complete without mentioning a new option that is starting to be seen inthe United States because of successful installations in Europe. This option in thetype of compressor foundations, is the use of spring supports. The advantages ofthis option include good isolation of the dynamic forces, good definition of supportproperties and additional possibilities for future modifications or corrections. Springsupport systems for compressor applications will typically have vertical naturalfrequencies in the range of 3 to 5 Hz. Horizontal frequencies usually are slightlyless than the vertical frequency. As these values are less than comparable frequen-

22.2 CHAPTER TWENTY-TWO

FIGURE 22.1 Skid mounted /packaged compressor. (Illustration courtesy of Robt. L. Rowan &Assoc., Inc.)

FIGURE 22.2 Block mounted compressor. (Illustration courtesy of Robt. L. Rowan & Assoc.,Inc.)

COMPRESSOR FOUNDATIONS 22.3

FIGURE 22.3 Pile cap foundation. (Illustration courtesy of Robt. L. Rowan & Assoc., Inc.)

22.4 CHAPTER TWENTY-TWO

FIGURE 22.4 Table top foundation. (Illustration courtesy of Robt. L. Rowan & Assoc., Inc.)

cies for soil or pile supported systems, the spring system typically provides betterisolation of the dynamic forces of the compressor. The springs themselves, usuallysteel coil designs, provide well defined stiffnesses both horizontally and vertically.This advantage simplifies the dynamic analysis of the foundation eliminating theneed to incorporate a range of soil properties in this analysis. By including viscousdampers in the design, the complete dynamic system can be put together with greatconfidence. Finally, the discrete nature of the spring support system permits easyreplacement of the elements if a change to the stiffness or damping characteristicsbecomes necessary. Similarly, misalignment from settlement and similar sourcescan be corrected at the spring support level.

22.1.2 Design

The detailed design of any of the above foundations is beyond the scope of thischapter. Unfortunately, there are no established building codes at this time (1996),but under the auspices of the American Concrete Institute, a committee is workingto develop a report that could eventually become a foundation design guide doc-ument. Major engineering firms, operating companies, and equipment manufactur-

COMPRESSOR FOUNDATIONS 22.5

ers that have their own in-house guidelines are represented on the committee. Ad-ditionally, under the sponsorship of the Pipeline Compressor Research Counsel,Southwest Research Institute, along with interested industry users of compressors,much needed data on both dynamic and thermal stresses in foundations is beingdeveloped. With such input data, along with the work of ACI, the design of foun-dations in the future can be more precise.

22.1.3 Soil Frequency and Vibration

While there have been many technical articles written on theories of foundationdesign and vibration, a very comprehensive reference is the work of Prakash andPuri, Foundations for Machines: Analysis and Design.1 With a good backgroundin geotechnical engineering, the authors tie together very well the interaction be-tween the cyclic vibrations caused by the machine with the natural frequency ofthe soil-foundation system. Foundations must be designed to avoid the dreadfulconsequences of harmonic resonance, which occurs when the frequency of thevibrating machine matches the natural frequency of the foundation (block and soil).Prakash and Puri teach that by applying the principles of soil engineering and soildynamics with theories of vibration, low tuned or high tuned foundations can bedesigned so as to avoid resonance. Their work leads the way to designing foun-dations for dynamic machines which will have acceptable levels of vibration. Goodengineering at this stage will pay off with a smoother running machine, bettermaintenance of alignment, and lower maintenance costs for the replacement of wearparts (bearing, seals, etc.).

22.1.4 Collection of Data for the Design Step*

While readers of this handbook may not ever be called on to design a foundation,they may very well be asked to supply data to an engineering design firm workingunder its direction.

While the work of ACI committee is incomplete at this stage, probable recom-mended data collection steps will be as follows:

1. Data gathering

a) Design goalb) Site factorsc) Sub-soil datad) Machine data

2. Design criteria

a) Static loads

*Based on preliminary draft of ACI 351-2 Sub-Committee

22.6 CHAPTER TWENTY-TWO

b) Dynamic loads

3. Concrete strength/stresses

a) Compressiveb) Flexuralc) Tensiond) Bearinge) Fatigue

4. Concrete deflection/deformation

5. Soil strength/stresses

6. Soil deformation/settlement

7. Vibration limits

8. Psychological factors

22.1.5 Materials of Construction

Portland Cement Concrete: Reinforced portland cement concrete is the usualmaterial of construction for either the foundation proper, or for the mat under afabricated steel skid. A mix design, based on locally available ingredients, can bedeveloped that yields a compressive strength of 4,000 psi in 28 days. The amountof steel will depend on the tensile and bending loads, as well as thermal stresses.Many foundations designed over the past 30 years have been under-reinforced, asevidenced by cracking. Cracking can lead to deterioration of the alignment con-dition and even catastrophic failure. Extra steel, to increase flexural and tensilestrength is very prudent. Steel, put in initially, does not cost very much, but afoundation repair later, because of an under-reinforced foundation, is very costly.Figures 22.5 and 22.6 show a modern design with extra rebar vs. a design donetwenty years ago.

Polymer Modified Concrete: While reinforced portland cement concrete is al-most universally used today, many older foundations have been repaired using amore technologically advanced material called ‘‘Polymer Modified Concrete.’’ Sub-stituting a polymer for the usual water in portland cement concrete, produces animproved concrete. The polymer, along with fiber reinforcing, produces a verydense product with low heat of hydration, stronger physical properties in tensileand flexure, and cures in 24 hours2.

22.1.6 Anchor Bolts

Anchor bolts are a vital link between the compressor and the foundation. Unfor-tunately, designers often overlook important points concerning anchor bolts, suchas how long and strong they should be and the amount of preload. Anchor bolts,as well as other parts of the support system, such as sole plates and chocks (to be

COMPRESSOR FOUNDATIONS 22.7

FIGURE 22.5 Typical perimeter steel reinforcing—era 1960s.

FIGURE 22.6 Dense steel reinforcing based on currentdesign practices.

discussed in section 22.1.7), can be one of the principle points of failure on newconstruction projects. Failure usually occurs during the first year of operation.

While the number and size of the anchor bolts are set by the equipment man-ufacturer, their length, configuration, and material of construction are in the handsof the foundation designer. Figure 22.7 shows good and bad designs.

22.8 CHAPTER TWENTY-TWO

FIGURE 22.7 Evolution of anchorbolt designs. (Illustration courtesy of Robt. L. Rowan& Assoc., Inc.)

Length: Short anchor bolts have historically caused problems in compressorfoundations. Horizontal cracks in the foundation often result. The best practicetoday is to make them as long as possible, terminating them in the concrete matunder the concrete foundation. In this manner, they do not contribute to horizontalcracking and have the added benefit of adding a post-tensioning effect.

Material: Anchor bolts for any dynamic machine cannot be too strong. Today,anchor bolts made from steel, conforming to ASTM A-193 with a yield strengthof 105,000 psi, are not much more expensive than steel half as strong. As the needfor high clamping forces for compressors is being recognized, alloy steel bolts toASTM A-193 provide the necessary capacity without going to a larger anchor bolt.

Preload: While some compressor manufacturers will specify an initial torquevalue for the initial installation, often field experience will show a much higher(maybe two to three times) clamping force will be required to lower framemovement/vibration. Unless the anchor bolts put into the foundation to start withhave extra capacity, the machine will not perform as it should, or a costly retrofitwill have to be done.

22.1.7 Support Systems

Figure 22.8 shows a range of options on how to support a gas compressor fromthe older method of full bed grouting, to the latest technology of adjustable support

COMPRESSOR FOUNDATIONS 22.9

FIGURE 22.8 Types of compressor frame support systems. (Illustrationscourtesy of Robt. L. Rowan & Assoc., Inc.)

systems. Adjustable supports are the system of choice today, because they eliminatea potential problem of poor initial alignment which happens from time to time withfull bed grouting. Adjustable systems also allow the optimum hot running conditionto be achieved as the frame can be re-aligned to correct for the alignment changesthat occur as the machine heats up during its first 100 hours of operation.

22.1.8 Grout

Since the introduction of epoxy grouts for gas compressor grouting in 1957, theuse of cementitious grouts mixed with water has virtually stopped. Epoxy groutsare stronger, resist oil and many chemicals, and perform well in dynamically loadedsituations.

While grout need not be stronger in compressive strength than the concreteunderneath, a good grout will be tough enough to take impact and cyclical loadsfrom the dynamic machine it supports. For that reason, compressive strengths above5,000 psi and tensile strength above 1,000 psi are all that are required. Highercompressive strengths are not necessarily better if the product is brittle and cracksexcessively in service. Almost all good machinery grouts can crack, so expansionjoints are required. The expansion joints should be strategically placed so crackswill not develop in the prime load transfer area adjacent to the anchor bolts.

22.10 CHAPTER TWENTY-TWO

FIGURE 22.9 Section view, looking from the flywheel end towards the oil pump end. (Illustra-tion courtesy of Robt. L. Rowan & Assoc., Inc.)

22.1.9 Repair of Foundations

Almost every foundation 20 twenty years old and designed with only minimal steelreinforcing is a candidate for replacement or repair. Common repair techniquesinclude removing the top 24 inches to 30 inches of grout and concrete, cutting offand up-grading the anchor bolts, adding a heavy rebar layout in the excavated areaand post-tensioning the repair to old remaining concrete.

What to use for the post-tensioned repair described above is extremely important.If the job schedule will allow 21 to 28 days, portland cement concrete is the bestchoice. If a 24-hour curing product is needed, then a polymer modified concreteshould be used. Either product will have a modulus of elasticity of at least4,000,000 psi, and will have negligible creep at typical compressor foundationtemperatures. What should not be used as a deep pour repair material to replacethe removed concrete is the epoxy grout material that is used as the final cap ontop of the foundation. Epoxy grouts are just that—a grout designed to be used in2 to 4 inch thicknesses. Epoxy grouts, as a class of material, have a modulus ofelasticity ranging from under 1,000,000 psi up to 2,500,000 psi, with the lowerrange being the most prevalent. This means epoxy grout will compress under load,two to five times more than concrete. Additionally, some epoxy grouts creep enoughat typical foundation temperatures to cause equipment misalignment. There have

COMPRESSOR FOUNDATIONS 22.11

been catastrophic machine failures as a result of deep pours of epoxy grout. A newcompressor foundation should not be designed with a 14-inch thick upper pour ofepoxy grout nor should an older concrete foundation be repaired that way.

Besides up-grading the anchor bolts, an adjustable support system is also addedto allow easier realignment. Figure 22.9 shows a typical foundation repair design.

22.2 REFERENCES

1. Prakask, Shamsher, and Vijay K. Puri, Foundations for Machines: Analysis & Design,Wiley Series in Geotechnical Engineering.

2. Rowan, Robert L. & Associates, Inc., Re-Grouting Reciprocating Gas Compressors, 5Year Repairs vs. 20 Year Reliability Criteria, 1:12 Grouting Technology Newsletter.

23.1

CHAPTER 23PACKAGING COMPRESSORS

Judith E. VeraProject EngineerEnergy Industries, Inc.

Compressor packages can be used for a variety of applications including gas boost-ing, gas gathering, gas lifting, gas injection, gas turbine compression, vapor recov-ery, landfill, and digester gas compression, or propane/butane refrigeration com-pression. Two basic types of positive displacement compressor packages will bediscussed in this section: reciprocating gas compressors, and rotary screw gas com-pressors.

Reciprocating gas compressors can handle from 60 horsepower to 7,200 horse-power (using a 6-throw compressor frame and an electric motor driver). Althoughreciprocating units are the most common due to their ability to handle large horse-power requirements, high pressure, and varying conditions, rotary screw units areadvantageous when limited space or limited package weight specifications apply.Rotary screw units are ideal for large volume/low suction pressure applicationsand have fewer maintenance and vibration problems.

23.1 COMPRESSOR SIZING

Most packagers have a compressor sizing program available to choose a compressorframe and driver to compress the gas under the desired conditions. To properly sizea compressor, the following must be provided: suction pressure, discharge pressure,gas analysis or gas specific gravity, elevation, ambient temperature, suction tem-perature, and desired capacity.

The driver can be a gas engine, gas turbine, or electric motor depending on theend user’s specific requirements. Although the primary components of the packagedgas compressor unit are the compressor frame and its driver, numerous other partsare essential to the efficient operation of the unit.

23.2 CHAPTER TWENTY-THREE

23.2 BASE DESIGN

Gas compressor package bases are designed of sufficient mass to support the weightof the entire package. Bases can be designed as structural steel only when thepackage must be kept within certain weight limitations. However, the preferredbase design is a steel frame filled with reinforced concrete. This design is portableand eliminates the need for field-poured foundations.

The base can be designed with or without the drain and vent piping inside theskid frame. An ecology rail should be designed to keep any oil or water leakageonto the skid contained into a drain system. This rail is usually made of 2 � 2 or3 � 3 angle around the perimeter of the base and skid drains located at four ormore locations at the skid edge.

Lifting eyes, designed with a 4:1 safety factor that can be added to the skid, ordraw bars are located at the edge of the skid to aid in pulling the package up ontoa truck.

Scrubber plates are preferred and are usually made of 1/2 inch steel plate andare located on the skid for scrubber placement.

The engine and compressor set on a pedestal which is preferably filled withconcrete. It is important that this pedestal is one solid piece on reciprocating com-pressor packages. The natural vibrating forces in a reciprocating package on apedestal that is two separate pieces can cause skid failure or misalignment of theengine and compressor during normal operation. A typical skid design prior to theconcrete fill is shown in Fig. 23.1. The skid is then filled with concrete, as shownin Fig. 23.2.

23.3 SCRUBBER DESIGN

Scrubbers are designed to remove solids and liquids from the gas before they reachthe compressor cylinder. This is necessary because the tolerances in a compressorare such that any foreign matter can damage the internal parts of the compressor.Scrubbers should be placed before each stage of compression. On a multi-stageunit, the interstage scrubbers are required to remove any liquids formed by con-densation during the cooling process.

Mist pad scrubbers are the most common scrubber design. They are verticalvessels which have a wire mesh mist pad, typically 4 to 6 inches thick with 9 to12 lb/cft bulk density. (Gas Processors Suppliers Association’s Engineering DataBook, Volume I, 10th Edition1 contains a method for sizing mist pad scrubbers.)Scrubbers are sized based on the critical or terminal gas velocity required forparticles to drop or settle out of gas. Equation 23.1 defines the maximum gasvelocity entering the mist pad scrubber as a function of the gas density and theliquid density.

0.5pl � pgVt � K (23.1)� �pg

PACKAGING COMPRESSORS 23.3

FIGURE 23.1 Typical skid design prior to concrete fill.

where Vt � terminal gas velocity (ft /sec)K � empirical constant for mist pad scrubber sizing (ft /sec), (Fig. 23.3)1

pl � liquid phase density, droplet or particle (lb/cft). This is assumed tobe water and is equal to 62.4 lb/cft.

pg � gas phase density (lb/cft).

Equation (23.1) is an empirical equation based on Stoke’s Law. The inside area, A(sq ft ) of the mist pad scrubber can then be found by:

QaA � (23.2)

where: Qa � actual gas flow rate (cft /sec).

From the inside area of the mist pad scrubber, we can then determine the minimumrequired inside diameter of the mist pad scrubber to ensure all liquids are removedfrom the gas of a maximum specified flow rate.

Figure 23.4 shows a typical design of a mist pad scrubber and the instrumen-tation normally used on scrubbers. The gas enters the scrubber and is directeddownward toward an impingement or baffle plate. The liquids and solids collectedon this plate are forced through holes that allow the liquids and solids to drain into

23.4 CHAPTER TWENTY-THREE

FIGURE 23.2 Typical skid design with concrete fill.

an accumulation chamber. The change in direction, decrease in velocity and grav-itational force further help the dropout of the liquids and solids. The gas then passesthrough a mist extractor which allows the fine droplets of liquid to be collecteduntil they grow heavy enough to fall to the impingement plate. Liquid collected inthe accumulation chamber rises to a level sensed by a liquid level controller andthen is dumped from the scrubber through a diaphragm-operated dump valve. Ifthe liquid flow is greater than the dump valve can handle, a high liquid levelshutdown switch is added to prevent liquid overflow into the cylinders. A liquidlevel sight gauge allows visual monitoring of the scrubber liquid level. A manualdrain is supplied to completely drain the scrubber.

Vane scrubbers are much more efficient than mist pad scrubbers and thereforeit is possible to use a smaller diameter vessel with a vane scrubber than is requiredby a mist pad scrubber. Vane scrubbers use a vane pack made up of several cor-rugated plates with liquid drainage traps. Manufacturers of vane scrubbers shouldbe contacted on the details of the design of their vessels since vane sizing designsare proprietary.

PACKAGING COMPRESSORS 23.5

FIGURE 23.3 Typical K & C factors for sizing woven wire demisters. (Reprintedwith permission from Gas Processor Suppliers Association Engineering Data Book,Volume I, Section 7, Fig. 7-9, p. 7-7, GPSA, 1987).

23.4 LINE SIZING

The gas lines on a compressor package are typically sized for a gas velocity ofless than or equal to 3500 ft/min. One method used to determine the gas flow rateis the Weymouth equation2:

0.52 2Q � 433.5 T E P � Pb 1 2 2.667(d) (23.3)� �P SL T Zb m avg avg

where: Q � gas flow rate at base conditions (cft /day).d � pipe inside diameter (in)

Lm � length of pipe (mi)Tb � temperature at base conditions (�R), (ANSI 2530 specification: Tb �

520�R)Tavg � average temperature (�R), [Tavg � 1/2 (Tin � Tout)]

23.6 CHAPTER TWENTY-THREE

FIGURE 23.4 Typical scrubber dump instrumentation.

PACKAGING COMPRESSORS 23.7

Pb � base absolute pressure (psia) (ANSI 2530 specification: Pb � 14.73psia)

E � pipeline efficiency factor, (usually assumed to be 1.00)P1 � inlet pressure (psia)P2 � outlet pressure (psia)

Zavg � average compressibility factorS � specific gravity of the gas with respect to air (where S � 1)

Then velocity can be confirmed by using V � Q /A, where A � line flow area,making sure to keep the units uniform.

Gas piping on a compressor package includes, but is not limited to, process gaspiping, a valved bypass line from the aftercooler outlet to the first stage scrubberfor unloaded starting, a vent line or valve for purging the machine, scrubber dumppiping, compressor cylinder packing and distance piece vents and drains, and en-gine gas start and fuel system piping. All lines should be hydrotested to the max-imum allowable working pressure of the flange class. Flange ratings should be inaccordance with ANSI B16.53. Piping should also be x-rayed in accordance withANSI B31.34.

23.5 PULSATION BOTTLE DESIGN

On reciprocating gas compressors, some form of vibration control is required. With-out the pulsation bottle or some other device to change the frequency of gas pul-sations caused by the movement of the piston, the harmonic rhythm of their fre-quency would cause a progressive increase in vibration and eventual damage to theunit.

On small horsepower units (less than 350 horsepower), pulsation bottles are notrequired to eliminate vibration. However, orifice plates are required in the suctionand discharge lines on each stage of compression. These plates can be welded intothe lines or placed between flanges to allow flexibility when pressure and flowconditions change.

On units greater than 350 horsepower, pulsation bottles are required. There aretwo different approaches to pulsation bottle design. One approach, adequate formany compressor applications, is to design a volume bottle only. This approach,however, does not guarantee elimination of harmful vibration. To design a volumebottle, the following empirical relation can be used.

Bottle volume � 10 � swept volume of cylinder(Swept volume � cylinder area � stroke)

This gives the volume required to determine the diameter and seam-to-seam di-mension of the bottle. Bottles should be mounted as close as possible to the cylinderand the nozzles should be located in the center of the bottle to reduce unbalancedforces. Nozzle flanges should be designed to meet the required pressure and tem-perature operating conditions (refer to ANSI 16.53 for flange ratings).

23.8 CHAPTER TWENTY-THREE

Another approach that does offer the guarantee of no harmful vibration is thevolume-choke-volume method that involves choking the flow prior to the volumebottle or choking the flow inside the volume bottle. Analog and/or digital studiescan be performed on a particular machine to further verify the guarantee of noharmful pulsations. Design of these pulsation bottles takes into account the rota-tional speed of the compressor, the gas composition, and the operating conditions.Chokes should be designed for about .5% pressure drop, but not more than 1%.See API Standard 618, Reciprocating Compressors for General Refinery Services5,for a more detailed discussion on recommended design approaches for pulsationbottles. All pressure vessels, bottles and scrubbers, should be designed to meetSection VIII of ASME Code6 and be of sufficient pressure rating to cover alloperating conditions.

23.6 PRESSURE RELIEF VALVE SIZING

Pressure relief valves or pressure safety valves are required on the discharge bottlesor lines of the compressor. These valves are designed to open when the operatingpressure exceeds the set pressure of the relief valve. The set pressure of these valvesshould be determined by the lowest working pressure of the compressor packageof the system the valve is designed to protect. Figure 23.5 is a typical Piping andInstrumentation Diagram. This diagram is a schematic that follows the flow of thecompressor package. The table on the top of the diagram shows the maximumallowable working pressure (MAWP) of all of the vessels and coolers. This diagramalso shows all the valves and instrumentation on the compressor package. By usingthis diagram, the relief valve set pressure can be determined.

There are two types of relief valves: spring-operated, and pilot-operated. Pilot-operated relief valves are useful when the operating pressure is closer than 15% ofthe relief valve set pressure. The spring-operated relief valves tend to pop frequentlywhen the operating pressure is close to the set pressure. Pilot-operated valves areless sensitive and will not relieve the pressure until the exact set pressure is reached.The orifice sizes required in the relief valves can be sized by the manufacturer orby formulas found in the ASME Boiler and Pressure Vessel Code, Appendix 11,Section VIII, Division 16.

.5W � CKAP (M /T) (23.4)

where: W � weight flow of gas that valve is relieving (lb/hr)K � flow coefficient for gas [see UG-131(d) and (e)]6

A � actual discharge flow area of the safety valve or orifice (sq in)P � (set pressure � 1.1 plus atmospheric pressure*) (psia)

(* Relief valves are typically rated at 10% over set pressure.)M � molecular weightT � absolute temperature at inlet (�F � 460)C � constant for gas or vapor which is a function of ratio of specific heat,

Cp /Cv

23.9

FIGURE 23.5 Typical piping and instrumentation diagram.

23.10 CHAPTER TWENTY-THREE

The K value is determined by a series of tests conducted at the National Boardof Boiler and Pressure Vessels in Columbus, Ohio in accordance to the ASMESection VIII Code. Equation 23.4 should be used to solve for A, or the orifice sizeof the relief valve, and then pick a relief valve that has a standard orifice size largerthan the A value calculated.

23.7 COOLER DESIGN

Governed by the basic gas law, the gas temperature increases in proportion to theincrease in pressure so that each stage of compression requires cooling prior toentering the next stage of compression. The cooler also acts as a radiator to coolthe engine and compressor frame. The cooler should be fitted with a surge tank tovent the system of all entrained air and also serve as a fill point for the coolingsystem. It is outside the scope of the packager to design the cooler, however, it isthe responsibility of the packager to ensure the cooler manufacturer has the correctrequirements in order to do a proper cooler design. The packager must furnish thecooler manufacturer with the performance run which gives the pressures, temper-atures, flow conditions, elevation and ambient temperature. The packager must alsoprovide any additional information required to correctly design the cooler, such ascustomer specifications. It is important that the packager ensure that the pass ar-rangement designed by the cooler manufacturer provides the most efficient pipingarrangement available.

Packagers normally use air-cooled heat exchangers. These units use ambient airto cool fluids and gases. Typically, the design ambient air used is 100�F for summerconditions. Manual or automatic louvers are used over the gas sections to ensurethe cooler does not overly cool in the winter months.

Heatload information provided by the engine manufacturer is used to determinethe proper sizing of the engine jacket water sections. The gas coil sections aregenerally designed to take the discharge temperature from the cylinders and coolit down to either 120�F or 130�F on the interstage sections and 120�F on theaftercooler section.

The basic formula that cooler manufacturers use to determine the heatload re-quired for the gas sections is7:

Q � mc (T � T ) (23.5)p d c

where: Q � heatload (Btu/hr)m � mass flowrate (lbs/hr)cp � specific heat at average temperature (Btu/lb�F)Td � discharge temperature (�F)Tc � cooled temperature (�F)

PACKAGING COMPRESSORS 23.11

FIGURE 23.6 Typical compressor lubrication system.

23.8 COMPRESSOR LUBRICATION

To keep size and weight down, packages are usually built around high speed com-pressors. This makes lubrication of the cylinders and piston and rod packing crit-ical. The lubrication system is determined by the size of the cylinder and rod. Aseparate force-feed lubricator driven off the crankshaft supplies oil to the com-pressor cylinders and piston rod packing. Figure 23.6 shows a typical compressorlubrication system. Divider valve blocks which contain metering pistons aremounted on a base block which contains passageways and built-in check valves toensure proper oil flow to the cylinders. A cycle indicator is used on one of thedivider valve blocks to provide a positive indication of system operation. The in-dicator pin is an extension of the piston and cycles back and forth as the pistonmoves. The pints of oil per day and a maximum cycle time is determined by thecompressor packager.

23.9 CONTROL PANEL & INSTRUMENTATION

The control panel is the brain of the compressor package. It operates in conjunctionwith numerous safety switches to monitor the compressor package and protect it

23.1

FIGURE 23.7 Typical electric panel display. (Reprinted with permission from Altronic Controls,Inc.)

PACKAGING COMPRESSORS 23.13

FIGURE 23.8 Typical electric panel.

from major failures. The panel may be electric or pneumatic. Although instrumen-tation will vary from package to package, some of the most common safetyswitches on the panel monitor low engine lube oil pressure/level, high enginejacket-water temperature, engine overspeed, low jacket-water level, low compressorcrankcase lube oil pressure/level, lubricator no flow, cooler and compressor vibra-tion, high/low inlet pressure, high/low interstage pressure, high/low discharge

23.14 CHAPTER TWENTY-THREE

FIGURE 23.9 Typical pneumatic panel.

pressure (each stage), high discharge temperature (each cylinder), high liquid level(inlet and interstage scrubbers), and automatic fuel shutoff valve.

An electric control panel uses power generated by the magneto to perform thesafety shutdown functions of the unit. Under normal operating conditions, the elec-tric current flows from the magneto to the ignition system. The magneto is alsowired to the control panel which is wired to the safety switches. When a safetyswitch is tripped and goes to ground, the electric current is diverted from the

PACKAGING COMPRESSORS 23.15

FIGURE 23.10 Trailer-mounted CAT G3304NA/C12 sullair unit.

ignition to the control panel. In the control panel, a switch is tripped causing themagneto to ground and shut off the engine. Figure 23.7 shows what’s typicallymonitered and displayed on a panel. Figure 23.8 is a photograph of the same panel.

A pneumatic control panel uses gas pressure instead of electricity to trigger ashutdown. Tubing is run between the safety switches, control panel relays, and theengine fuel shut-off valve. The safety switches maintain a low pressure signallocked into the control panel relays as long as the unit is within safe operatinglimits. If the limits are exceeded, the safety switch vents gas from the indicatorrelay, thus triggering the shutdown. The vented gas also causes the relay valve tochange positions, allowing additional gas to be vented from the fuel shut-off valveas well as from a pressure switch which causes the magneto to ground and shutoff the engine. The unit will remain down until the problem is corrected and thepanel is reset. The unit can then be restarted. Figure 23.9 shows a typical pneumaticpanel.

23.10 ROTARY SCREW GAS COMPRESSORS

A rotary screw compressor consists of two intermeshing helical rotors inside ahousing. The helical rotor grooves are filled with gas as they pass over the suction

23.16 CHAPTER TWENTY-THREE

FIGURE 23.11 Typical reciprocating unit, CAT G3516LEA/FE665-21, Energy Industries.

port. As the rotors turn, the grooves are closed by the housing, forming a com-pression chamber. Lubricant is injected into the screw to provide sealing, cooling,and lubrication. Because the lubricant is recirculated, the screw compressor usesless lubricant than a reciprocating compressor. The gas/lubricant mixture exits fromthe compressor and passes over the discharge port. As with the reciprocating units,a scrubber is required ahead of the screw compressor to keep solids and liquidsout of the compressor. However, unlike the reciprocating units, the screw unitrequires the use of a separator to separate the lubricant from the gas. The separatoris usually constructed according to ASME code and consists of an upper chamberthat houses a coalescing filter element to separate the lubricant from the gas. Thebottom chamber is the impingement section and reservoir with drain. As with thereciprocating units, the screw package also includes a driver, either electric motoror gas engine, gas piping, control panel and instrumentation, and cooler. Pulsationbottles are not required since there are no cylinders and since there is little or novibration caused by the screw compressor. The units are simple with few compo-nents, and it is possible to design a self-contained, trailer-mounted unit, such asthe CAT G3304NA/Sullair C-12 unit shown in Fig. 23.10. A typical reciprocatingunit is shown in Fig. 23.11.

PACKAGING COMPRESSORS 23.17

23.11 REGULATORY COMPLIANCE & OFFSHORE

CONSIDERATIONS

The regulatory documents most commonly referred to when designing compressorpackages are the American Petroleum Institute (API) API 11P8 and API 6185.

When units are packaged for offshore use, several other factors must be consid-ered. The Minerals Management Service requires that gas compressors used off-shore must adhere to their regulations. Also the API RP14C, Section A89 requiresspecific safety devices.

23.12 TESTING

Units should be tested in the shop prior to shipment to the customer. Although itis usually not possible to test the unit under fully-loaded conditions, the unit canbe run with air, checked for vibration problems, and examined to ensure all safetyshutdowns operate properly.

23.13 REFERENCES

1. Gas Processors Suppliers Association, Engineering Data Book, Volume I, Section 7, Fig.7-9, Typical K & C Factors For Sizing Woven Wire Demisters, p. 7-7. Reprinted withpermission.

2. Gas Processors Suppliers Association, Engineering Data Book, Volume II, Section 17,Eq. 17-22, p. 17-6, 1987.

3. ASME/ANSI B16.5 ‘‘Pipe Flanges and Flanged Fittings.’’ ASME, 1988.

4. ASME/ANSI B31.3 ‘‘Chemical Plant and Petroleum Refinery Piping.’’ ASME, 1990.

5. API STANDARD 618, ‘‘Reciprocating Compressors for General Refinery Services.’’ API,3rd Ed., February 1986.

6. ASME ‘‘Boiler and Pressure Vessel Code.’’ ASME, Section VIII, Division 1, 1995 Ed.

7. Lindberg, Peter, P.E., ‘‘Thermodynamics,’’ Professional Engineering Registration Pro-gram, 6th Ed.

8. API SPECIFICATION 11p, ‘‘Specification for Packaged Reciprocating Compressors forOil and Gas Production Services.’’ API, 2nd Ed., November 1989.

9. API RP 14C, ‘‘API Recommended Practice for Analysis, Design, Installation and Testingof Basic Surface Safety Systems for Offshore Production Platforms.’’ API, 3rd Ed., April15, 1984.

A.1

APPENDIX

A.1 DEFINITIONS OF COMPRESSOR TERMS

A.2 CONVERSION FACTORS

A.3 TEMPERATURE CONVERSION

A.4 AREAS AND CIRCUMFERENCES OF CIRCLES

A.5 PROPERTIES OF SATURATED STEAM

A.6 PARTIAL PRESSURE OF WATER VAPOR IN AIR

A.7 ATMOSPHERIC PRESSURE AND BAROMETRIC READINGS AT DIF-FERENT ALTITUDES

A.8 DISCHARGE OF AIR THROUGH ORIFICE

A.9 LOSS OF AIR PRESSURE DUE TO PIPE FRICTION

A.10 LOSS OF PRESSURE THROUGH SCREW PIPE FITTINGS

A.11 HORSEPOWER TO COMPRESS AIR

A.12 n VALUES AND PROPERTIES OF GASES

A.13 TEMPERATURE RISE VS. COMPRESSION RATIO

A.14 SINGLE-STAGE COMPRESSOR CALCULATIONS

A.15 TWO-STAGE COMPRESSOR CALCULATIONS

A.16 SINGLE-STAGE ADDED CYLINDER CLEARANCE

A.2 APPENDIX

A.1 DEFINITIONS OF GAS COMPRESSOR ENGINEERING

TERMS

Absolute pressure is total pressure measured from absolute zero, i.e., from an ab-solute vacuum. It equals the sum of gauge pressure and atmospheric pressure cor-responding to the barometer (expressed in pounds per square inch).

Absolute temperature equals degrees Fahrenheit plus 459.6 or degrees centigradeplus 273. These values are referred to as degrees Rankine and degrees Kelvin,respectively.

Adiabatic or isentropic compression of a gas is effected when no heat is trans-ferred to or from the gas during the compression process.* The characteristic equa-tion relating pressure and volume during adiabatic compression is

kpv � C

where k is the ratio of the specific heat at constant pressure to the specific heat atconstant volume.

Polytropic compression is effected when heat is transferred to or from gas duringthe compression process at such a precise rate that the relation between pressureand volume can be expressed by the equation

npv � C

in which n is constant.Where the actual compression path for a particular compressor is known, and

where the heat transfer to or from the gas is at the proper rate, the value of n maybe determined from the equation.

Isothermal compression is effected when interchange of heat between air or gasand surrounding bodies occurs at a rate precisely sufficient to maintain the air orgas at constant temperature during compression. It may be considered as a specialcase of polytropic compression.

The characteristic equation for isothermal compression is

pv � C

k value is the value of the exponent defined by the equation under Adiabatic orIsentropic Compression for any particular gas.

n value is the value of the exponent as defined by the equation under PolytropicCompression for any particular gas.

Compressibility factor is a factor expressing the deviation from the perfect-gaslaw.

Pressure ratio or compression ratio is the ratio of the absolute discharge pressureto the absolute inlet pressure.

*In compressor practice, this definition refers only to the reversible adiabatic or isentropic compres-sion process.

APPENDIX A.3

Free air is defined as air at atmospheric conditions at any specific location.Because altitude, barometer, and temperature may vary at different localities andat different times, it follows that this term does not mean air under identical orstandard conditions.

Free air as a measure of volume may be applied either to displacement or ca-pacity, and in no way distinguishes between these two terms.

Standard air is defined as air at a temperature of 68�F, a pressure of 14.70 psia,and a relative humidity of 35% (.0750 density). This agrees with the definitionsadopted by ASME, but in gas industries the temperature of ‘‘standard air’’ is usuallygiven as 60�F.

Displacement of a compressor is the volume displaced per unit of time and isusually expressed in cubic feet per minute. In a reciprocating compressor it equalsthe net area of the compressor piston multiplied by the length of stroke and by thenumber of compression strokes per minute. The displacement rating of a multistagecompressor is the displacement of the low-pressure cylinder only.

Capacity (actual delivery) of an air or gas compressor is the actual quantity ofair or gas compressed and delivered, expressed in cubic feet per minute at condi-tions of total temperature, total pressure, and composition prevailing at the com-pressor inlet. Capacity is always expressed in terms of air or gas at intake conditionsrather than in terms of standard air or gas.

Theoretical horsepower is defined as the horsepower required to compress adi-abatically the air or gas delivered by the compressor through the specified rangeof pressures. For a multistage compressor with intercooling between stages theo-retical horsepower assumes equal work in each stage and perfect cooling betweenstages.

Theoretical power (polytropic) is the mechanical power required to compresspolytropically and to deliver, through the specified range of pressures, the gasdelivered by the compressor.

Air indicated horsepower is the horsepower calculated from compressor-indicator diagrams. The term applies only to displacement-type compressors.

Brake horsepower or shaft horsepower is the measured horsepower input to thecompressor.

It should be noted that horsepower, either indicated or brake, for any displace-ment compressor varies with compression ratio as well as absolute intake anddischarge pressures. Performance guarantees are expressed in terms of horsepowerper cubic foot capacity. In comparing test results with performance guarantees,corrections should be made for any deviation from specified values of absoluteintake pressures and ratio of compression.

Intercooling is the removal of heat from the air or gas between stages or stagegroups.

Degree of intercooling is the difference in air or gas temperatures between theinlet of the compressor and the outlet of the intercooler.

Perfect intercooling prevails when the air temperature leaving the intercoolers isequal to the temperature of the air at the compressor intake.

A.4 APPENDIX

Volumetric efficiency is the ratio of the capacity of the compressor to displace-ment of the compressor. The term does not apply to centrifugal compressors.

Mechanical efficiency is the ratio of the horsepower imparted to the air or gasto brake horsepower. In the case of a displacement-type compressor it is the ratioof air or gas indicated horsepower to indicated horsepower of the power cylindersfor a steam engine or internal-combustion engine-driven compressor or to the brakehorsepower delivered to the shaft in the case of a power-driven compressor.

Compression efficiency (adiabatic) is the ratio of the theoretical horsepower tohorsepower imparted to the air or gas actually delivered by the compressor. Powerimparted to the air or gas is brake horsepower minus mechanical losses.

Efficiency of the compressor is the ratio of the theoretical horsepower to brakehorsepower. It is equal to the product of compression efficiency times mechanicalefficiency.

Compressor efficiency (polytropic), for which alternate terms are ‘‘hydraulic ef-ficiency’’ and stage efficiency,’’ is the ratio of theoretical power (polytropic) to shaftpower.

Temperature-rise ratio is the ratio of computed isentropic temperature rise tomeasured total temperature rise during compression. For a perfect gas, this is equalto the ratio of isentropic enthalpy rise to actual enthalpy rise. Consequently, forgases which do not deviate seriously from the perfect-gas law, the temperature-riseratio is sometimes referred to as ‘‘temperature-rise efficiency.’’

Inlet pressure is the absolute total pressure at the inlet flange of a compressor.Discharge pressure is the absolute total pressure at the discharge flange of a

compressor. It is commonly stated in terms of gauge pressure; unless the associatedbarometric pressure is included, this is an incomplete statement of discharge pres-sure.

Inlet temperature is the total temperature at the intake flange of the compressor.Discharge temperature is the total temperature at the discharge flange of the

compressor.Gas specific weight is the weight of air or gas per unit volume. Unless otherwise

specified, it refers to the weight per unit volume at conditions of total pressure,total temperature, and composition prevailing at the inlet of the compressor.

Specific gravity is the ratio of specific weight of air or gas to that of dry air atthe same pressure and temperature.

Speed refers to the revolutions per minute of the compressor shaft.Electrical input is measured at the motor terminals. For synchronous motors

with separately driven exciters, the excitation input as measured at the slip rings isadded to the input to the stator. For synchronous motors with direct-connectedexciters, the exciter losses are deducted from the measured stator input.

Load factor is the ratio of the average compressor load during a given periodof time to the maximum rated load of the compressor.

APPENDIX A.5

A.2 CONVERSION FACTORS (MULTIPLIERS)

A.6 APPENDIX

A.3 TEMPERATURE CONVERSION CHART

(CENTIGRADE—FAHRENHEIT)

APPENDIX A.7

A.4 AREAS AND CIRCUMFERENCES OF CIRCLES

A.8 APPENDIX

A.5 PROPERTIES OF SATURATED STEAM

APPENDIX A.9

A.6 PARTIAL PRESSURE OF WATER VAPOR IN SATURATED

AIR 32� TO 212�F

In many process applications, it is necessary to determine the compressor ca-pacity required to deliver a given quantity of dry gas, i.e., after all moisture isremoved. Since water vapor carried in incoming gas stream will be eliminated ininterstage coolers, aftercoolers and driers, capacity must be increased to compensatefor vapor which, though it enters the compressor as volume, has no value to theprocess. Thus, if process requires 1000 cfm of dry air at 100�F and intake is 14.7p.s.i.a., 100�F and saturated, required capacity at compressor intake is:

A.10 APPENDIX

14.71000 � � 1068 c.f.m.

14.7 � .949

Thus, capacity has been corrected by multiplying by the suction pressure anddividing by the suction pressure minus the partial pressure of the water vapor atsuction temperature.

If, in the example above, the air was only 70% saturated (70% relative humidity),the partial pressure is multiplied by the percent saturation. Thus:

14.7Capacity at intake � 1000 � � 1047 c.f.m.

14.7 � (.7)(.949)

A.7 ATMOSPHERIC PRESSURE AND BAROMETRIC

READINGS AT DIFFERENT ALTITUDES

APPENDIX A.11

A.8 DISCHARGE OF AIR THROUGH AN ORIFICE

In cu. ft. of Free Air per Min. at Atmospheric Pressure of 14.7 psia,

and 70�F

Based on 100% coefficient of flow. For well-rounded entrance multiply valuesby 0.97. For sharp-edged orifices a multiplier of 0.65 may be used.

This table will give approximate results only. For accurate measurements seeASME Power Test Code, Velocity Volume flow Measurement.

Values for pressures from 1 to 15 psig, calculated by standard adiabatic formula.Values for pressures above 15 psig, calculated by approximate formula proposed

by S. A. Moss:

W � discharge in lb. per sec. P � upstream total pressure0.5303 CP a � area of orifice in sq. in. T � in psia.a 1W �

C � coefficient of flow � upstream temperature�Tin deg. F. abs.

Values used in calculating above table were C � 1.0, P � gauge pressure �14.7 psi., T � 530 F. abs.

Weights (W) were converted to volumes using density factor of 0.07494 lb. percu. ft. This is correct for dry air at 14.7 psia, and 70 F.

Formula cannot be used where P is less than two times the barometric pressure.

A.12 APPENDIX

A.9 LOSS OF AIR PRESSURE DUE TO PIPE FRICTION

To determine the pressure drop in psi, the factor listed in the table for a givencapacity and pipe diameter should be divided by the ratio of compression (fromfree air) at entrance of pipe, multiplied by the actual length of the pipe in feet, anddivided by 1,000.

APPENDIX A.13

A.9 LOSS OF AIR PRESSURE DUE TO PIPE FRICTION

(CONTINUED)

A.14 APPENDIX

A.10 LOSS OF PRESSURE THROUGH SCREW PIPE

FITTINGS

(Given in equivalent lengths (feet) of straight pipe.)

APPENDIX A.15

A.11 HORSEPOWER (THEORETICAL) REQUIRED TO

COMPRESS AIR FROM ATMOSPHERIC PRESSURE TO

VARIOUS PRESSURES—MEAN EFFECTIVE

PRESSURES

*Based on a value for n of 1.3947.

A.16

A.12 n VALUE AND PROPERTIES OF VARIOUS GASES AT

60�F. and 14.7 P.S.I.A.

†To obtain exact characteristics of natural gas and refinery gas, the exact constituents must be known.‡This n value is given at 212�F. All others are at 60�F. Authorities differ slightly; hence all data are average results.

APPENDIX A.17

A.13 TEMPERATURE RISE FACTORS VS. COMPRESSION

RATIO

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Index

Index terms Links

A Absolute pressure A.2

Absolute temperature A.2

Adiabatic compression A.2

Air padding 9.2

Aluminakyle 7.3

Ammonia synthesis 3.73 7.1

Antisurge protection 3.82 4.43

Areas and circumferences of circles A.7

Asphalt production 3.73

Atmospheric pressure and barometric readings at altitudes A.10

Autofrettage 7.11 7.15 7.16 7.19 7.23 7.35 7.37

B Barrel compressor (see Vertically split compressor)

Bearing: circular 19.31 19.63 compliant surface 19.16 19.75 19.94 cryogenic 19.104 damper 3.55 elastohydrodynamic 19.9 elliptical 19.33 19.66 film thickness 19.28 19.78 19.130 flow 19.3 fluid film 19.9

I.2 Index terms Links

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Bearing: (Continued) gas 19.62 hydrostatic 19.15 19.67 19.112 19.140 journal 3.70 19.28 19.74 19.132 liner 4.43 materials 19.122 magnetic 4.43 19.9 19.21 19.93 multipad 19.82 rolling element 19.18 tapered land 19.46 19.139 temperature 19.30 three-lobe 19.37 19.66 thrust 3.70 19.45 19.67 19.85

19.109 19.137 tilt pad 4.43 19.42 19.54 19.133

Benedict-Webb-Rubin-Starling model 3.29

C Capacity 1.10 2.12 5.31 A.3

Capacity control: bypass 2.6 20.24 21.12 clearance pocket 2.7 20.21 A.37 finger unloader 2.7 20.26 21.12 port unloader 2.7 20.25 screw compressor slide 2.6 variable speed 2.6 20.24 21.12

Centrifugal compressor: balance piston 3.2 3.5 3.66 4.11 casing 3.2 3.60 4.1 coupling 3.67 diaphragm 3.2 4.3 diffuser 3.40 4.10 4.23 discharge nozzle 4.10 discharge volute 3.6 4.12

I.3 Index terms Links

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Centrifugal compressor: (Continued) electrical system 8.8 foundations 22.1 guide vane 4.10 impeller 3.2 3.58 3.62 4.3 intercooling 4.4 inlet nozzle 3.3 4.2 inlet volute 3.3 multistage 3.29 19.7 off design operation 4.25 oil system 3.7 performance 3.28 4.16 4.51 4.63 slope 4.16 splitter vane 4.10 thrust bearing 3.3

Choking 3.26 4.16 4.21

Clearance volume 1.9 1.11 2.1

CNG codes and standards 8.19

CNG station 8.8 8.14

CNG pressure vessel 8.12 8.18

CNG compressor: blow down gas recovery 8.5 crankcase 8.4 design 8.1 8.7 lubrication 8.6 sealing 8.3

CNG dispenser 8.10

CNG fill system 8.14

Coatings: fluorocarbon 4.6 nickel 4.6

Compressibility 1.3 1.10

Compressibility factor A.2

I.4 Index terms Links

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Compression ratio 1.7 5.30

Conversion factors A.5

Critical speed 3.47 4.28

Cracking 3.73

Crosshead: auxiliary 7.5 7.6 7.7 connection 7.13 guide 7.6 pin load reversal 2.3 5.15

Cylinder: autofrettage 7.12 construction 7.35 elastic simulation 7.27 fatigue tests 7.19 finish 7.35 heavy walled 7.13 hypercompressor 7.8 materials 7.16 7.35 stress distribution 7.14 tie rods 7.8 7.27

D Damped systems 4.31 4.39

Dewhirl vanes 4.41

Diaphragm compressor: accessories 15.10 applications 15.11 cleaning and testing 15.11 design 15.4 head assembly 15.6 limitations 15.12 materials 15.9 operation 15.1 pressures 15.3

I.5 Index terms Links

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Discharge of air through an orifice A.11

Displacement A.3

Double flow compressor 4.72

E Effective head 3.15

Efficiency: compression (adiabatic) A.4 compressor (polytropic, hydraulic, stage) 3.16 3.19 A.4 delivery 20.10 isentropic 1.7 1.15 3.16 20.10 mechanical A.4 volumetric 1.11 1.14 5.31 6.9

10.11 20.10 A.4 A.30

Emissions control 16.2

Energy equation 1.6

Entering sleeve 17.10

Euler equation 3.17

F Finite element method 7.25 7.32

Fixed clearance 1.9

Flow: coefficient 1.6 3.18 3.22 3.30 subsonic 1.7

Foundations: anchor bolts 22.6 grout 22.9 materials 22.6 pile cap 22.3 reinforcing 22.7 repair 22.10 skid mounted/packaged 22.2 23.2 soil frequency/ vibration 22.5

I.6 Index terms Links

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Foundations: (Continued) table top 22.4 types 22.1

Frame load 2.2

Free air A.3

Friction coefficient 17.33 19.30 19.130

G Gas sampling 4.49

Gas booster: applications 11.1 construction 11.2 cooling 11.6 drive 11.3 flow chart 11.14 pressure ratio 11.9 storage tank 11.15 valves 11.4

Gas laws 1.2

Gas reinjection 3.78

Gas sampling 4.49

Gas transportation 3.79

H Hans ho*rbiger 20.1

Hans Mayer 20.1

Heat transfer 2.17 2.21 2.24 4.55 17.33

Horizontally split compressor 3.7 3.58

Horsepower: air indicated A.3 brake (shaft) A.3 A.26 theoretical (polytropic) 1.9 A.3 A.15

I.7 Index terms Links

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Hypercompressor 7.1

Hyper packing 17.23

I Impeller:

backward leaning 3.23 4.19 discharge section 3.38 forward leaning 3.23 4.11 inlet section 3.37 manufacturing 3.62 overhung 4.3 19.6 radial 3.23 4.19 thrust 3.3 4.14 4.17

Incidence 4.23

Indicator card 1.9

Intercooling A.3

Isentropic compression (see Adiabatic compression)

Isentropic head 3.15

Isentropic temperature exponent 1.4

Isentropic volume exponent 1.4 1.10

Isothermal compression A.2

L Liquids:

effect in cylinders 5.2 in gas stream 4.48 4.66

Liquefaction 3.79

Load factor A.4

Loss of air pressure due to pipe friction A.12

Loss of pressure through pipe fittings A.14

Lubricant production 3.73

Lubrication: additives 18.5 19.126

I.8 Index terms Links

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Lubrication: (Continued) feed rate 18.8 7.37 gas absorption 18.5 hydrocarbon dilution 18.5 low flow sensor 21.23 lubricators 18.11 oil ring 19.57 19.135 19.141 pre-post lube 21.12 removal 18.7 synthetic 18.10 19.123 viscosity 18.3 19.125

M Mach number 3.18

Methanol synthesis 3.76

Modeling (see Simulation)

Mollier chart 1.5 3.14

Myhlestad-Prohl calculation 3.51

N n Value and properties of gases A.16 A.36

Non-lube compressor 17.8 18.8

O Oxygen compression 3.80

P Packaging compressors:

base design 23.2 cooler design 23.10 line sizing 23.5 pressure relief valve 23.6 pulsation bottle design 23.7 scrubber design 23.2

I.9 Index terms Links

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Packing: breaker rings 7.44 17.4 cooling 17.30 cup stress 7.20 distance piece venting 17.18 emissions control 17.20 21.19 friction 17.29 17.33 heat generation 17.32 high pressure 7.43 17.22 leakage 2.19 2.22 17.13 17.18

18.2 lubrication 8.6 17.8 18.8 partition 17.3 purged 17.21 materials 17.7 17.29 18.8 nomenclature 17.2 rod size effects 17.11 seal rings 7.44 17.5 static sealing 17.20 thermal effects 17.10 wiper 17.3 17.22

Partial pressure of water vapor in air A.9

Piping: acoustics 6.4 flow straightener 4.67 velocity profile 4.67

Pipeline compressor 3.11

Piston ring: friction 17.29 leakage 2.20 2.22 5.2 5.7

5.25 17.26 17.28 instantaneous pressure 17.27 materials 17.28 18.9 rider rings 17.25

I.10 Index terms Links

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Polyethylene: compressors 7.4 high density (HDPE) 7.3 low density (LDPE) 7.3 safety aspects 7.12

Polymer buildup 4.5

Polytropic compression A.2

Polytropic head 3.15

Pressure distribution 7.44 17.4 17.27

Pressure drop: contour 3.26 endwall 3.26 friction 3.23 impact 3.26 incidence 3.24 mixing 3.26 overall 3.25

Pressure ratio 3.29 A.2

Pressure/Time (PT) patterns 5.11

Pressure-volume (PV) diagram 2.19 5.3 6.11 20.12

Procedure for determining compressor size A.18

Pulsation 2.16 2.21 2.24 5.9 6.3 13.2 23.7

Purging: nitrogen 7.13

R Redlich-Kwong equation of state 1.3

Reciprocating compressor: capacity control 21.12 cooling 21.24 crankcase lubrication 18.2 cylinder lubrication 18.2 21.9 21.25 23.11 electrical controls 21.4 21.9 23.11

I.11 Index terms Links

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Reciprocating compressor: (Continued) foundations 22.1 loading/unloading 21.12 21.13 manual controls 21.11 monitoring 21.1 21.17 pneumatic controls 21.10 23.14 rod drop 21.20 sensors 21.16 21.21 21.23

Reforming 3.72

Regasification 3.79

Reynolds number 3.19 19.13 19.115 19.148

Rod load 2.2 5.17 5.32

Rotor dynamics 3.50 4.27 19.103

Rotor balancing 3.58 4.28

Rotary screw compressor: adiabatic efficiency 14.8 advantages 14.5 applications 14.6 helical rotors 14.3 lubrication 18.1 packaging 23.15 sizing 14.7

S Screw compressor:

heat transfer 2.24 leakage 2.25 port losses 2.23 pulsation 2.24

Scroll compressor: advantages 12.3 construction 12.4 lubricated 12.5 oilless 12.7

I.12 Index terms Links

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Scroll compressor: (Continued) principal of operation 12.2

Seals: balance piston 4.11 bellows 16.7 bushing 16.4 carbon ring 16.3 circumferential 16.5 double 16.12 honey comb 3.56 4.41 interstage 4.6 labyrinth 3.3 3.56 3.68 4.6

4.40 16.3 leakage 4.55 mechanical 3.69 oil 3.69 performance 16.10 rotary contacting 16.1 rotary non contacting 16.2 sleeve 4.43 sliding 7.36 tandem 16.9 tip 12.5

Simulation: buried piping 6.15 dynamic fluid transient systems 6.3 pulsation 6.3 static systems 6.2 stress 6.3 6.9 thermal flexibility 6.12 vibration 6.3

Sommerfield number 19.29 19.130

Speed triangle (see Velocity vector diagram)

Specific heat ratio 3.19

I.13 Index terms Links

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Spring: valve 5.10 20.17 20.20

Stall 4.24

Standard air A.3

Steam properties A.8

Stonewall (see Choking)

Straight lobe compressor: bearings 13.7 construction 13.3 installation 13.8 noise 13.2 operating principle 13.1 pulsation 13.2 PV diagram 13.4 seals 13.7

Strain gage method 7.32

Stress: axial 7.16 7.24 circumferential 7.16 7.24 factor of safety 7.17 7.19 radial 7.16 7.24 risers 7.17 Von Mises 7.18

Supercompressibility 1.3 21.3

Surge 3.26 4.16 4.22 4.43 21.19

Swirl (see Dewhirl)

T Tank car unloading:

compressor 9.4 pump 9.1 vapor recovery 9.6

Temperature conversion chart A.6

I.14 Index terms Links

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Temperature rise vs compression ratio A.17

Temperature-rise ratio A.4

Testing centrifugal compressors: economizer nozzles 4.55 efficiency 4.60 field data analysis 4.62 instrumentation 4.50 internal temperatures 4.57 iso-cooled compressors 4.54 power 4.59 thermodynamic performance 3.4

Trouble shooting 4.63

Tungsten carbide 7.4 7.15

Turbocompressor 3.13

Turbomachinery 3.12

Turbulence 19.13 19.115 19.148

U Urea production 3.77 7.1

V Vacuum remelted steel 7.17

Valve: active 20.27 area 20.14 axial 7.9 7.30 channel 20.1 20.5 combined suction / discharge 7.12 concentric 20.8 deck-and-one-half 20.7 double deck 20.7 dynamics 2.12 6.10 equivalent area 1.12 20.16 feather 20.1 20.6

I.15 Index terms Links

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Valve: (Continued) leakage 5.4 5.14 5.25 lift 20.11 20.13 losses 1.11 2.15 2.18 5.10

5.30 materials 20.19 motion 20.18 poppet 7.9 7.30 20.1 20.6 ported plate 20.4 radial 7.8 reed 20.8 ring 20.2

Vehicle fueling: appliance 10.1 compressor 10.6 10.13

Vertically-split compressor 3.8 3.59

Velocity vector diagram 3.20 3.38 3.39 4.16

Vibration analysis 3.51 5.19

Viscosity, fluid 19.12 19.30

W Water injection 4.6

Wear: detector 21.20 21.23 distribution 7.46

Compressor handbook - [PDF Document] (2024)

FAQs

What is called a compressor? ›

compressor, device for increasing the pressure of a gas by mechanically decreasing its volume. Air is the most frequently compressed gas but natural gas, oxygen, nitrogen, and other industrially important gases are also compressed.

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How to size a gas compressor? ›

To get a feel for how much air (CFM) you will need, you can figure roughly 4-5 CFM per person in an automotive shop and 12-15 per person in a body shop. Once you determine the CFM you need, take that figure times 1.25 and use that total CFM to choose your compressor.

What is the basic principle of compressor? ›

The working principle of a reciprocating air compressor is to draw gas through an inlet, and then move the gas through a cavity or chamber that decreases in size. This compresses the gas and by doing so the gas within the chamber increases in pressure.

What are the 2 principles of air compressor? ›

There are two generic principles for the compression of air (or gas): Positive displacement compression and dynamic compression. The first one includes, for example, reciprocating (piston) compressors, orbital (scroll) compressors, and different types of rotary compressors (screw, tooth, vane).

What is the simplest compressor design? ›

Vane compressors are simple machines with few moving parts. Like their hydraulic counterparts, vane pumps, the compressors are inexpensive, with low operating cost, and low starting-torque requirement. They are compact and relatively vibration free, with little pulsation in the compressor output.

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How do you master a compressor? ›

Here are some general guidelines if you want to use compression while mastering:

Start your ratio at 1.25:1 or 1.5:1. ...
Set your threshold pretty high so that you're getting 2 dB of gain reduction at most.
Use your ears; if you apply compression and don't like how it affects your master, don't hesitate to take it out.

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Dec 25, 2019

What are the three basic designs of compressors? ›

Breaking Down the 3 Basic Types of Air Compressors

Reciprocating Air Compressors. This air compressor works by positive displacement. ...
Rotary Screw Compressors. Where the piston within a reciprocating compressor is built for stop/start compression, the rotary screw compressor is not. ...
Centrifugal Compressors.

Jan 7, 2019

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What is a compressor in rap? ›

What is compression in music? Compression reduces the overall dynamic range of a piece of audio by detecting when it exceeds a specified level, and then attenuating it by a specified amount. Put simply, it narrows the difference between the loudest and softest parts of a track so that it's more consistent in level.

Is an air conditioner a compressor? ›

Central air conditioning systems are made up of an evaporator, a condenser, and a compressor. The compressor serves as a go-between between the evaporator, located inside your air conditioner, and the condenser, the unit outside your home.

What are the three types of compressors? ›

Rotary screw, vane and reciprocating air compressors are the three most common types of air positive displacement compressors found in small and medium sized industries.

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What is an example of a compressor? ›

For example, a compressor with vertical cylinders, where the cylinders are placed one above the other, always compresses air in a single compression stage. Whereas a V-design compressor has cylinders arranged in a V-shaped pattern which allows for two-stage compression.

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