Compressor Surge and Rotating Stall

1 Compressor Surge and Stall: An Introduction.- 1.1 Introduction.- 1.2 Compressors.- 1.2.1 Types of compressors.- 1.2.2 The axial compressor, principles of operation.- 1.2.3 The centrifugal compressor, principles of operation.- 1.3 Application of compressors.- 1.3.1 Gas turbines and jet engines for propulsion and power generation.- 1.3.2 Compression in the process industry.- 1.3.3 Transportation of gases and fluids in pipelines.- 1.3.4 Supercharging of internal combustion engines.- 1.4 Stability of Compression Systems.- 1.4.1 Surge.- 1.4.2 Rotating Stall.- 1.4.3 Other instabilities.- 1.5 Previous work on modeling of axial compression systems.- 1.5.1 Why model compression systems?.- 1.5.2 The model of Greitzer (1976).- 1.5.3 The model of Moore and Greitzer (1986).- 1.5.4 Other models.- 1.6 Previous work on modeling of centrifugal compr. systems.- 1.6.1 Greitzer-type models for centrifugal compressors.- 1.6.2 Other models.- 1.7 Jet engine and gas turbine models.- 1.8 Previous work on surge/stall avoidance.- 1.8.1 Background and motivation.- 1.8.2 Industrial solutions to surge avoidance.- 1.9 Active Control of Surge and Rotating Stall.- 1.9.1 Background and motivation.- 1.9.2 Control of surge in centrifugal and axial compressors.- 1.9.3 Control of surge and rotating stall in axial compressors.- 1.10 Sensor/actuator selection in surge/stall control.- 1.10.1 Motivation.- 1.10.2 Selection of sensors and actuators for surge control.- 1.10.3 Selection of sensors and actuators for rotating stall control.- 1.10.4 Actuator requirements.- 2 CCV Control of Surge and Rotating Stall for the MG Model.- 2.1 Introduction.- 2.1.1 Motivation and main idea.- 2.1.2 Previous work.- 2.2 Preliminaries.- 2.2.1 The Model of Moore and Greitzer.- 2.2.2 Close Coupled Valve.- 2.2.3 Equilibria.- 2.2.4 Change of Variables.- 2.2.5 Disturbances.- 2.3 Surge Control.- 2.3.1 Undisturbed Case.- 2.3.2 Determination of ?0.- 2.3.3 Time Varying Disturbances.- 2.3.4 Adaption of Constant Disturbances.- 2.4 Control of Rotating Stall.- 2.4.1 Undisturbed Case.- 2.4.2 Disturbed Case.- 2.5 Simulations.- 2.5.1 Surge Control.- 2.5.2 Rotating Stall Control.- 2.6 Conclusion.- 3 Passivity Based Surge Control.- 3.1 Introduction.- 3.1.1 Motivation.- 3.1.2 Notation.- 3.2 Model.- 3.3 Passivity.- 3.3.1 Passivity of Flow Dynamics.- 3.3.2 Passivity of Pressure Dynamics.- 3.3.3 Control Law.- 3.4 Disturbances.- 3.5 Simulations.- 3.6 Concluding Remarks.- 4 A MG Model for Axial Compr. with Non-constant Speed.- 4.1 Introduction.- 4.2 Preliminaries.- 4.3 Modeling.- 4.3.1 Spool Dynamics.- 4.3.2 Compressor.- 4.3.3 Entrance Duct and Guide Vanes.- 4.3.4 Exit Duct and Guide Vanes.- 4.3.5 Overall Pressure Balance.- 4.3.6 Plenum Mass Balance.- 4.3.7 Galerkin Procedure.- 4.3.8 Final Model.- 4.4 Simulations.- 4.4.1 Unstable Equilibrium, ? = 0.5.- 4.4.2 Stable Equilibrium ? = 0.65.- 4.5 Concluding Remarks.- 5 Modelling and Control of Surge for a Centrifugal Compressor with Non-constant Speed.- 5.1 Introduction.- 5.2 Model.- 5.2.1 Impeller.- 5.2.2 Diffuser.- 5.3 Energy Transfer.- 5.3.1 Ideal Energy Transfer.- 5.3.2 Slip.- 5.3.3 Compressor Torque.- 5.3.4 Incidence Losses.- 5.3.5 Frictional Losses.- 5.3.6 Efficiency.- 5.4 Energy Transfer and Pressure Rise.- 5.5 Choking.- 5.6 Dynamic Model.- 5.7 Surge Control Idea.- 5.8 Controller Design and Stability Analysis.- 5.9 Simulations.- 5.10 Conclusion.- 6 Concluding remarks and further research.- 6.1 Conclusions.- 6.2 Further research.- 6.2.1 Mass flow measurements.- A Stability of the Greitzer model.- B Nomenclature.- C Some Thermodynamic and Fluid Mechanical Relations.- C.1 Flow and Pressure Coefficients.- C.2 Isentropic Processes.- C.3 Mass Balance of the Plenum.- C.4 Flow through a Nozzle.- C.5 Compressor Pressure Rise.- D Including a CCV in the Moore-Greitzer Model.- E Numerical Values Used in Simulations.- F Bounds on the Controller Parameters of Theorem 2.5.