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  • Centrifugal Compressor Surge

    Modeling and Identification for Control

  • This research was financially supported by TNO Science & Industry and

    Siemens Power Generation and Industrial Applications.

    A catalogue record is available from the Eindhoven University of Technology Library

    Helvoirt, Jan van

    Centrifugal Compressor Surge, Modeling and Identification for Control / by Jan vanHelvoirt. Eindhoven : Technische Universiteit Eindhoven, 2007Proefschrift. ISBN-13: 978-90-386-1095-5NUR 978Trefwoorden: centrifugaal compressor / surge / modelleren /identificatie / regelenSubject headings: centrifugal compressor / surge / modeling /identification / control

    Copyright c2007 by J. van Helvoirt. All rights reserved.

    This thesis was prepared with the LATEX2 documentation system.Reproduction: PrintPartners Ipskamp B.V., Enschede, The Netherlands.

  • Centrifugal Compressor Surge

    Modeling and Identification for Control

    PROEFSCHRIFT

    ter verkrijging van de graad van doctor aan deTechnische Universiteit Eindhoven, op gezag van deRector Magnificus, prof.dr.ir. C.J. van Duijn, voor een

    commissie aangewezen door het College voorPromoties in het openbaar te verdedigen

    op woensdag 12 september 2007 om 16.00 uur

    door

    Jan van Helvoirt

    geboren te Utrecht

  • Dit proefschrift is goedgekeurd door de promotor:

    prof.dr.ir. M. Steinbuch

    Copromotor:dr.ir. A.G. de Jager

  • Contents

    Summary ix

    Nomenclature xi

    1 Introduction 1

    1.1 General introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Centrifugal compression systems . . . . . . . . . . . . . . . . . . . . . . . 2

    1.2.1 Principle of operation . . . . . . . . . . . . . . . . . . . . . . . . . 21.2.2 Industrial centrifugal compressors . . . . . . . . . . . . . . . . . . 4

    1.3 Review of compressor instabilities . . . . . . . . . . . . . . . . . . . . . . 71.3.1 Rotating stall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.3.2 Surge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

    1.4 Surge suppression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.4.1 Surge avoidance and suppression techniques . . . . . . . . . . . . 101.4.2 Technology assessment . . . . . . . . . . . . . . . . . . . . . . . . 121.4.3 Modeling and identification for control . . . . . . . . . . . . . . . 17

    1.5 Research objectives and scope . . . . . . . . . . . . . . . . . . . . . . . . . 19

    2 Theoretical modeling of centrifugal compression systems 23

    2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.1.1 Literature on compression system modeling . . . . . . . . . . . . 24

    2.2 The Greitzer lumped parameter model . . . . . . . . . . . . . . . . . . . . 282.2.1 System boundaries and model assumptions . . . . . . . . . . . . . 282.2.2 Compressor and throttle ducts . . . . . . . . . . . . . . . . . . . . 302.2.3 Plenum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.2.4 Transient compressor response . . . . . . . . . . . . . . . . . . . . 32

    2.3 Model adjustment and scaling . . . . . . . . . . . . . . . . . . . . . . . . . 322.3.1 Variable cross-sectional area . . . . . . . . . . . . . . . . . . . . . 332.3.2 Aerodynamic scaling . . . . . . . . . . . . . . . . . . . . . . . . . 34

    2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

    v

  • vi CONTENTS

    3 Centrifugal compression system model 39

    3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.2 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403.3 Lumped parameter model . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

    3.3.1 Model equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443.3.2 Model parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 463.3.3 Compressor characteristic . . . . . . . . . . . . . . . . . . . . . . . 473.3.4 Throttle characteristic . . . . . . . . . . . . . . . . . . . . . . . . . 49

    3.4 Model identification and validation . . . . . . . . . . . . . . . . . . . . . . 533.4.1 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . 533.4.2 Time varying gas properties . . . . . . . . . . . . . . . . . . . . . . 61

    3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

    4 Dynamic compressor model including piping acoustics 65

    4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654.2 Centrifugal compression system . . . . . . . . . . . . . . . . . . . . . . . 66

    4.2.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . 674.2.2 Compressor model . . . . . . . . . . . . . . . . . . . . . . . . . . 684.2.3 Model identification and validation . . . . . . . . . . . . . . . . . . 70

    4.3 Piping system acoustics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 734.3.1 Dynamic model for piping system . . . . . . . . . . . . . . . . . . 754.3.2 Piping boundary conditions . . . . . . . . . . . . . . . . . . . . . . 78

    4.4 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 804.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

    5 Analysis of compressor dynamics 91

    5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 915.2 Nonlinear compressor dynamics . . . . . . . . . . . . . . . . . . . . . . . 93

    5.2.1 Surge cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 935.2.2 Parameter analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

    5.3 Linear compressor dynamics . . . . . . . . . . . . . . . . . . . . . . . . . 1015.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

    6 Stability parameter identification 107

    6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1076.2 Hydraulic inductance approximation . . . . . . . . . . . . . . . . . . . . . 109

    6.2.1 Compressor duct division . . . . . . . . . . . . . . . . . . . . . . . 1096.2.2 Discussion on hydraulic inductance calculations . . . . . . . . . . 114

    6.3 Model identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1176.3.1 Step response measurements . . . . . . . . . . . . . . . . . . . . . 1186.3.2 Parameter identification with approximate realizations . . . . . . . 121

  • CONTENTS vii

    6.3.3 Results and validation . . . . . . . . . . . . . . . . . . . . . . . . . 1236.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

    7 Surge control design and evaluation 131

    7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1317.2 Surge control design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

    7.2.1 Sensor and actuator selection . . . . . . . . . . . . . . . . . . . . . 1337.2.2 Controller design . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

    7.3 Surge control actuator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1427.3.1 Actuator requirements . . . . . . . . . . . . . . . . . . . . . . . . 1437.3.2 Actuator design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1457.3.3 Design evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

    7.4 Surge control experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . 1487.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

    8 Conclusions and recommendations 155

    8.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1558.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

    A Fluid dynamics 163

    A.1 Conservation laws in integral form . . . . . . . . . . . . . . . . . . . . . . 163A.2 Speed of sound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167A.3 Incompressible flow assumption . . . . . . . . . . . . . . . . . . . . . . . 168

    B Aeroacoustics 169

    B.1 Aeroacoustic wave equation . . . . . . . . . . . . . . . . . . . . . . . . . . 169B.2 Transmission line model . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

    C Approximations for compressor and valve characteristics 175

    C.1 Approximation of compressor characteristics . . . . . . . . . . . . . . . . 175C.1.1 Compressor characteristics for test rig A . . . . . . . . . . . . . . . 175C.1.2 Compressor characteristics for test rig B . . . . . . . . . . . . . . . 179

    C.2 Throttle characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179C.2.1 Valve data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181

    Bibliography 191

    Samenvatting 193

    Acknowledgements 195

    Curriculum Vitae 197

  • viii CONTENTS

    Stellingen 199

  • SUMMARY

    Centrifugal Compressor SurgeModeling and Identification for Control

    Surge is an unstable operating mode of a compression system that occurs at mass flowsbelow the so-called surge line. The instability is characterized by large limit cycle oscil-lations in compressor flow and pressure rise that reduce compressor performance. Thelarge thermal and mechanical loads involved can also endanger safe operation of thecompression system.

    The concept of stabilizing a compression system to the left of the surge line by modify-ing its dynamics through the use of appropriate feedback has lead to many promisingresults. However, a real breakthrough in the practical application of this approach hasnot been made yet. Therefore, the goals of t