《Turbomachinery Flow Physics and Dynamic Performance》第二版和增强版

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《Turbomachinery Flow Physics and Dynamic Performance》第二版和增强版
叶轮机械流动物理和动态性能
作者：
Prof. Dr.-Ing. Meinhard T. Schobeiri
Department of Mechanical Engineering
Texas A&M University
出版社：Springer
出版时间：2012年

《Turbomachinery Flow Physics and Dynamic Performance》第二版和增强版

《Turbomachinery Flow Physics and Dynamic Performance》第二版和增强版

《Turbomachinery Flow Physics and Dynamic Performance》第二版和增强版

《Turbomachinery Flow Physics and Dynamic Performance》第二版和增强版

目录
I Turbomachinery Flow Physics
1 Introduction, Turbomachinery, Applications, Types . . . . . . . 3
1.1 Turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Compressor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3 Application of Turbomachines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.1 Power Generation, Steam Turbines . . . . . . . . . . . . . . . . . . . . . . 9
1.3.2 Power Generation, Gas Turbines . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.3 Aircraft Gas Turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3.4 Diesel Engine Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.4 Classification of Turbomachines . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.4.1 Compressor Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.4.2 Turbine Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.5 Working Principle of a Turbomachine . . . . . . . . . . . . . . . . . . . . . . . . 14
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2 Kinematics of Turbomachinery Fluid Motion . . . . . . . . . . . 15
2.1 Material and Spatial Description of the Flow Field . . . . . . . . . . . . . . 15
2.1.1 Material Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.2 Jacobian Transformation Function and Its Material Derivative 17
2.1.3 Spatial Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2 Translation, Deformation, Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3 Reynolds Transport Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3 Differential Balances in Turbomachinery . . . . . . . . . . . . . . . . 29
3.1 Mass Flow Balance in Stationary Frame of Reference . . . . . . . . . . . . 29
3.1.1 Incompressibility Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2 Differential Momentum Balance in Stationary Frame of Reference . 32
3.2.1 Relationship between Stress Tensor and Deformation Tensor 34
3.2.2 Navier-Stokes Equation of Motion . . . . . . . . . . . . . . . . . . . . . . 36
3.2.3 Special Case: Euler Equation of Motion . . . . . . . . . . . . . . . . . 38
3.3 Some Discussions on Navier-Stokes Equations . . . . . . . . . . . . . . . . . 41
3.4 Energy Balance in Stationary Frame of Reference . . . . . . . . . . . . . . . 42
3.4.1 Mechanical Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.4.2 Thermal Energy Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.4.3 Total Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.4.4 Entropy Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.5 Differential Balances in Rotating Frame of Reference . . . . . . . . . . . . 50
3.5.1 Velocity and Acceleration in Rotating Frame . . . . . . . . . . . . . 50
3.5.2 Continuity Equation in Rotating Frame of Reference . . . . . . . 52
3.5.3 Equation of Motion in Rotating Frame of Reference . . . . . . . . 53
3.5.4 Energy Equation in Rotating Frame of Reference . . . . . . . . . . 55
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4 Integral Balances in Turbomachinery . . . . . . . . . . . . . . . . . . . . . 59
4.1 Mass Flow Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.2 Balance of Linear Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.3 Balance of Moment of Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.4 Balance of Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.4.1 Energy Balance Special Case 1: Steady Flow . . . . . . . . . . . . . 77
4.4.2 Energy Balance Special Case 2: Steady Flow,
Constant Mass Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.5 Application of Energy Balance to Turbomachinery Components . . . 78
4.5.1 Application: Accelerated, Decelerated Flows . . . . . . . . . . . . . 79
4.5.2 Application: Combustion Chamber . . . . . . . . . . . . . . . . . . . . . 80
4.5.3 Application: Turbine, Compressor . . . . . . . . . . . . . . . . . . . . . 81
4.5.3.1 Uncooled Turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.5.3.2 Cooled Turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.5.3.3 Uncooled Compressor . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.6 Irreversibility and Total Pressure Losses . . . . . . . . . . . . . . . . . . . . . . 84
4.6.1 Application of Second Law to Turbomachinery Components . . 85
4.7 Flow at High Subsonic and Transonic Mach Numbers . . . . . . . . . . . 87
4.7.1 Density Changes with Mach Number, Critical State . . . . . . . . . 88
4.7.2 Effect of Cross-Section Change on Mach Number . . . . . . . . . 93
4.7.3 Compressible Flow through Channels with
Constant Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.7.4 The Normal Shock Wave Relations . . . . . . . . . . . . . . . . . . . . 109
4.7.5 The Oblique Shock Wave Relations . . . . . . . . . . . . . . . . . . . . 115
4.7.6 The Detached Shock Wave . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.7.7 Prandtl-Meyer Expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
5 Theory of Turbomachinery Stages . . . . . . . . . . . . . . . . . . . . . . . 123
5.1 Energy Transfer in Turbomachinery Stages . . . . . . . . . . . . . . . . . . . 123
5.2 Energy Transfer in Relative Systems . . . . . . . . . . . . . . . . . . . . . . . . 124
5.3 General Treatment of Turbine and Compressor Stages . . . . . . . . . . 125
5.4 Dimensionless Stage Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
5.5 Relation between Degree of Reaction and Blade Height . . . . . . . . 131
5.6 Effect of Degree of Reaction on the Stage Configuration . . . . . . . . 134
5.7 Effect of Stage Load Coefficient on Stage Power . . . . . . . . . . . . . . 136
5.8 Unified Description of a Turbomachinery Stage . . . . . . . . . . . . . . . 137
5.8.1 Unified Description of Stage with Constant Mean Diameter . 137
5.8.2 Generalized Dimensionless Stage Parameters . . . . . . . . . . . . 138
5.9 Special Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
5.9.1 Case 1, Constant Mean Diameter . . . . . . . . . . . . . . . . . . . . . . 141
5.9.2 Case 2, Constant Mean Diameter and
Meridional Velocity Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
5.10 Increase of Stage Load Coefficient, Discussion . . . . . . . . . . . . . . . . 140
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
6 Turbine and Compressor Cascade Flow Forces . . . . . . . . . . 145
6.1 Blade Force in an Inviscid Flow Field . . . . . . . . . . . . . . . . . . . . . . . 145
6.2 Blade Forces in a Viscous Flow Field . . . . . . . . . . . . . . . . . . . . . . . 150
6.3 The Effect of Solidity on Blade Profile Losses . . . . . . . . . . . . . . . . 156
6.4 Relationship Between Profile Loss Coefficient and Drag . . . . . . . . 156
6.5 Optimum Solidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
6.5.1 Optimum Solidity, by Pfeil . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
6.5.2 Optimum Solidity, by Zweifel . . . . . . . . . . . . . . . . . . . . . . . . 158
6.6 Generalized Lift-Solidity Coefficient . . . . . . . . . . . . . . . . . . . . . . . . 162
6.6.1 Lift-Solidity Coefficient for Turbine Stator . . . . . . . . . . . . . . 164
6.6.2 Turbine Rotor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
II Turbomachinery Losses, Efficiencies, Blades
7 Losses in Turbine and Compressor Cascades . . . . . . . . . . . . 175
7.1 Turbine Profile Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
7.2 Viscous Flow in Compressor Cascade . . . . . . . . . . . . . . . . . . . . . . . 178
7.2.1 Calculation of Viscous Flows . . . . . . . . . . . . . . . . . . . . . . . . . 178
7.2.2. Boundary Layer Thicknesses . . . . . . . . . . . . . . . . . . . . . . . . . 179
7.2.3 Boundary Layer Integral Equation . . . . . . . . . . . . . . . . . . . . . 181
7.2.4 Application of Boundary Layer Theory to Compressor Blades 182
7.2.5 Effect of Reynolds Number . . . . . . . . . . . . . . . . . . . . . . . . . . 186
7.2.6 Stage Profile Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
7.3 Trailing Edge Thickness Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
7.4 Losses Due to Secondary Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
7.4.1 Vortex Induced Velocity Field, Law of Bio-Savart . . . . . . . . 194
7.4.2 Calculation of Tip Clearance Secondary Flow Losses . . . . . . 197
7.4.3 Calculation of Endwall Secondary Flow Losses . . . . . . . . . . 200
7.5 Flow Losses in Shrouded Blades . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
7.5.1 Losses Due to Leakage Flow in Shrouds . . . . . . . . . . . . . . . . 204
7.6 Exit Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
7.7 Trailing Edge Ejection Mixing Losses of Gas Turbine Blades . . . . 212
7.7.1 Calculation of Mixing Losses . . . . . . . . . . . . . . . . . . . . . . . . 212
7.7.2 Trailing Edge Ejection Mixing Losses . . . . . . . . . . . . . . . . . . 217
7.7.3 Effect of Ejection Velocity Ratio on Mixing Loss . . . . . . . . . 217
7.7.4 Optimum Mixing Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
7.8 Stage Total Loss Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
7.9 Diffusers, Configurations, Pressure Recovery, Losses . . . . . . . . . . . 220
7.9.1 Diffuser Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
7.9.2 Diffuser Pressure Recovery . . . . . . . . . . . . . . . . . . . . . . . . . . 222
7.9.3 Design of Short Diffusers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
7.9.4 Some Guidelines for Designing High Efficiency Diffusers . . 228
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
8 Efficiency of Multi-stage Turbomachines . . . . . . . . . . . . . . . . 231
8.1 Polytropic Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
8.2 Isentropic Turbine Efficiency, Recovery Factor . . . . . . . . . . . . . . . 234
8.3 Compressor Efficiency, Reheat Factor . . . . . . . . . . . . . . . . . . . . . . . 237
8.4 Polytropic versus Isentropic Efficiency . . . . . . . . . . . . . . . . . . . . . . 239
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
9 Incidence and Deviation . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
9.1 Cascade with Low Flow Deflection . . . . . . . . . . . . . . . . . . . . . . . . . 241
9.1.1 Conformal Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
9.1.2 Flow Through an Infinitely Thin Circular Arc Cascade . . . . . 250
9.1.3 Thickness Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
9.1.4 Optimum Incidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
9.1.5 Effect of Compressibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258
9.2 Deviation for High Flow Deflection . . . . . . . . . . . . . . . . . . . . . . . . . 259
9.2.1 Calculation of Exit Flow Angle . . . . . . . . . . . . . . . . . . . . . . . 261
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
10 Simple Blade Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
10.1 Conformal Transformation, Basics . . . . . . . . . . . . . . . . . . . . . . . . . . 265
10.1.1 Joukowsky Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . 267
10.1.2 Circle-Flat Plate Transformation . . . . . . . . . . . . . . . . . . . . . . 267
10.1.3 Circle-Ellipse Transformation . . . . . . . . . . . . . . . . . . . . . . . . 268
10.1.4 Circle-Symmetric Airfoil Transformation . . . . . . . . . . . . . . . 269
10.1.5 Circle-Cambered Airfoil Transformation . . . . . . . . . . . . . . . . 271
10.2 Compressor Blade Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
10.2.1 Low Subsonic Compressor Blade Design . . . . . . . . . . . . . . . 273
10.2.2 Compressors Blades for High Subsonic Mach Number . . . . 279
10.2.3 Transonic, Supersonic Compressor Blades . . . . . . . . . . . . . . 280
10.3 Turbine Blade Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
10.3.1 Graphic Design of Camberline . . . . . . . . . . . . . . . . . . . . . . . . 282
10.3.2 Camberline Coordinates Using Bèzier Curve . . . . . . . . . . . . . 283
10.3.3 Alternative Calculation Method . . . . . . . . . . . . . . . . . . . . . . . 285
10.4 Assessment of Blades Aerodynamic Quality . . . . . . . . . . . . . . . . . . 287
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290
11 Radial Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
11.1 Derivation of Equilibrium Equation . . . . . . . . . . . . . . . . . . . . . . . . . 292
11.2 Application of Streamline Curvature Method . . . . . . . . . . . . . . . . . 300
11.2.1 Step-by-step solution procedure . . . . . . . . . . . . . . . . . . . . . . . 302
11.2 Compressor Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306
11.3 Turbine Example, Compound Lean Design . . . . . . . . . . . . . . . . . . . 309
11.3.1 Blade Lean Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310
11.3.2 Calculation of Compound Lean Angle Distribution . . . . . . . . 311
11.3.3 Example: Three-Stage Turbine Design . . . . . . . . . . . . . . . . . 313
11.4 Special Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316
11.4.1 Free Vortex Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316
11.4.2 Forced vortex flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317
11.4.3 Flow with constant flow angle . . . . . . . . . . . . . . . . . . . . . . . . 318
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319
III Turbomachinery Dynamic Performance
12 Dynamic Simulation of Turbomachinery Components . . . 323
12.1 Theoretical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324
12.2 Preparation for Numerical Treatment . . . . . . . . . . . . . . . . . . . . . . . . 330
12.3 One-Dimensional Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . 331
12.3.1 Time Dependent Equation of Continuity . . . . . . . . . . . . . . . . 331
12.3.2 Time Dependent Equation of Motion . . . . . . . . . . . . . . . . . . . 333
12.3.3 Time Dependent Equation of Total Energy . . . . . . . . . . . . . . 334
12.4 Numerical Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340
13 Generic Modeling of Turbomachinery Components . . . . . 341
13.1 Generic Component, Modular Configuration . . . . . . . . . . . . . . . . . . 342
13.1.1 Plenum as Coupling Module . . . . . . . . . . . . . . . . . . . . . . . . . 343
13.1.2 Group 1: Modules: Inlet, Exhaust, Pipe . . . . . . . . . . . . . . . . . 345
13.1.3 Group 2: Recuperators, Combustion Chambers, Afterburners 346
13.1.4 Group 3: Adiabatic Compressor and Turbine Components . . 348
13.1.5 Group 4: Diabatic Turbine and Compressor Components . . . 350
13.1.6 Group 5: Control System, Valves, Shaft, Sensors . . . . . . . . . 352
13.2 System Configuration, Nonlinear Dynamic Simulation . . . . . . . . . 352
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356
14 Modeling of Inlet, Exhaust, and Pipe Systems . . . . . . . . . . . . 357
14.1 Unified Modular Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357
14.2 Physical and Mathematical Modeling of Modules . . . . . . . . . . . . . . 357
14.3 Example: Dynamic behavior of a Shock Tube . . . . . . . . . . . . . . . . 360
14.3.1 Shock Tube Dynamic Behavior . . . . . . . . . . . . . . . . . . . . . . . 361
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365
15 Modeling of Recuperators, Combustors, Afterburners . . . 367
15.1 Modeling Recuperators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368
15.1.1 Recuperator Hot Side Transients . . . . . . . . . . . . . . . . . . . . . . 369
15.1.2 Recuperator Cold Side Transients . . . . . . . . . . . . . . . . . . . . . 369
15.1.3 Coupling Condition Hot, Cold Side . . . . . . . . . . . . . . . . . . . . 370
15.1.4 Recuperator Heat Transfer Coefficient . . . . . . . . . . . . . . . . . . 371
15.2 Modeling Combustion Chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . 372
15.2.1 Mass Flow Transients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373
15.2.2 Temperature Transients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374
15.2.3 Combustion Chamber Heat Transfer . . . . . . . . . . . . . . . . . . . 376
15.3 Example: Startup and Shutdown of a Combustion Chamber . . . . . . 378
15.4 Modeling of Afterburners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382
16 Modeling of Compressor Component, Design, Off-Design 383
16.1 Compressor Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384
16.1.1 Profile Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385
16.1.2 Diffusion Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387
16.1.3 Generalized Maximum Velocity Ratio for Cascade, Stage . . 391
16.1.4 Compressibility Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393
16.1.5 Shock Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397
16.1.6 Correlations for Boundary Layer Momentum Thickness . . . . 406
16.1.7 Influence of Different Parameters on Profile Losses . . . . . . . 407
16.1.7.1 Mach Number Effect . . . . . . . . . . . . . . . . . . . . . . . . 407
16.1.7.2 Reynolds Number Effect . . . . . . . . . . . . . . . . . . . . . 408
16.2 Compressor Design and Off-Design Performance . . . . . . . . . . . . . . 409
16.2.1 Stage-by-Stage and Row-by-Row Compression Process . . . 409
16.2.1.1 Stage-by-Stage Calculation of Compression Process 409
16.2.1.2 Row-by-Row Adiabatic Compression . . . . . . . . . . . 411
16.2.1.3 Off-Design Efficiency Calculation . . . . . . . . . . . . . 415
16.3 Generation of Steady State Performance Map . . . . . . . . . . . . . . . . . 418
16.3.1 Inception of Rotating Stall . . . . . . . . . . . . . . . . . . . . . . . . . . . 420
16.3.2 Degeneration of Rotating Stall into Surge . . . . . . . . . . . . . . . 422
16.4 Compressor Modeling Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423
16.4.1 Module Level 1: Using Performance Maps . . . . . . . . . . . . . . 424
16.4.1.1 Quasi-dynamic Modeling Using Performance Maps 426
16.4.1.2 Simulation Example: . . . . . . . . . . . . . . . . . . . . . . . . 427
16.4.2 Module Level 2: Row-by-Row Adiabatic Compression . . . . 429
16.4.2.1 Active Surge Prevention by Adjusting the
Stator Blades . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430
16.4.2.2 Simulation Example: Surge and Its Prevention . . . . 431
16.4.3 Module Level 3: Row-by-Row Diabatic Compression . . . . . 436
16.4.3.1 Description of Diabatic Compressor Module . . . . . 437
16.4.3.2 Heat Transfer Closure Equations: . . . . . . . . . . . . . . 439
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442
17 Turbine Aerodynamic Design, Performance . . . . . . . . . . . . . 445
17.1 Stage-by-Stage and Row-by-Row Design . . . . . . . . . . . . . . . . . . . . . 447
17.1.1 Stage-by-Stage Calculation of Expansion Process . . . . . . . . 448
17.1.2 Row-by-Row Adiabatic Expansion . . . . . . . . . . . . . . . . . . . . 449
17.1.3 Off-Design Efficiency Calculation . . . . . . . . . . . . . . . . . . . . . 454
17.1.4 Behavior under Extreme Low Mass Flows . . . . . . . . . . . . . . 456
17.1.5 Example: Steady Design and Off-Design Behavior . . . . . . . 459
17.2 Off-Design Calculation Using Global Turbine Characteristics . . . . 461
17.3 Modeling of Turbine Module for Dynamic Performance Simulation 462
17.3.1 Module Level 1: Using Turbine Performance Characteristics 463
17.3.2 Module Level 2: Row-by-Row Expansion Calculation . . . . . 464
17.3.3 Module Level 3: Row-by-Row Diabatic Expansion . . . . . . . . 465
17.3.3.1 Description of Diabatic Turbine Module,
First Method: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467
17.3.3.2 Description of Module, Second Method . . . . . . . . . 469
17.3.3.3 Heat Transfer Closure Equations . . . . . . . . . . . . . . . 471
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 472
18 Gas Turbine Engines, Design and Dynamic Performance 473
18.1 Gas Turbine Steady Design Operation, Process . . . . . . . . . . . . . . . 475
18.1.1 Gas Turbine Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477
18.1.2 Improvement of Gas Turbine Thermal Efficiency . . . . . . . . . 483
18.2 Non-Linear Gas Turbine Dynamic Simulation . . . . . . . . . . . . . . . . . 485
18.2.1 State of Dynamic Simulation, Background . . . . . . . . . . . . . . 486
18.3 Engine Components, Modular Concept, Module Identification . . . . 487
18.4 Levels of Gas Turbine Engine Simulations, Cross Coupling . . . . . . 493
18.5 Non-Linear Dynamic Simulation Case Studies . . . . . . . . . . . . . . . . 494
18.5.1 Case Study 1: Compressed Air Energy Storage Gas Turbine . 495
18.5.1.1 Simulation of Emergency Shutdown . . . . . . . . . . . . 497
18.5.2 Case Study 2: Power Generation Gas Turbine Engine . . . . . . 499
18.5.3 Case Study 3: Simulation of a Multi-Spool Gas Turbine . . . 504
18.6 A Byproduct of Dynamic Simulation: Detailed Calculation . . . . . . 507
18.7 Summary Part III, Further Development . . . . . . . . . . . . . . . . . . . . . 510
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511
IV Turbomachinery CFD-Essentials
19 Basic Physics of Laminar-Turbulent Transition . . . . . . . . . . 515
19.1 Transition Basics: Stability of Laminar Flow . . . . . . . . . . . . . . . . . 515
19.2 Laminar-Turbulent Transition, Fundamentals . . . . . . . . . . . . . . . . . 515
19.3 Physics of an Intermittent Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 518
19.3.1 Intermittent Behavior of Statistically Steady Flows . . . . . . . 519
19.3.2 Turbulent/Non-turbulent Decisions . . . . . . . . . . . . . . . . . . . . 520
19.3.3 Intermittency Modeling for Flat Plate Boundary Layer . . . . 524
19.4 Physics of Unsteady Boundary Layer Transition . . . . . . . . . . . . . . . 525
19.4.1 Experimental Simulation of the Unsteady Boundary Layer . 527
19.4.2 Ensemble Averaging High Frequency Data . . . . . . . . . . . . . 530
19.4.3 Intermittency Modeling for Periodic Unsteady Flow . . . . . . . 533
19.5 Implementation of Intermittency into Navier Stokes Equations . . . . 536
19.5.1 Reynolds-Averaged Navier-Stokes Equations (RANS) . . . . . 536
19.5.2 Conditioning RANS for Intermittency Implementation . . . . . 540
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 542
20 Turbulent Flow and Modeling in Turbomachinery . . . . . . . 545
20.1 Fundamentals of Turbulent Flows . . . . . . . . . . . . . . . . . . . . . . . . . . 545
20.1.1 Type of Turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 547
20.1.2 Correlations, Length and Time Scales . . . . . . . . . . . . . . . . . . 548
20.1.3 Spectral Representation of Turbulent Flows . . . . . . . . . . . . . 555
20.1.4 Spectral Tensor, Energy Spectral Function . . . . . . . . . . . . . . 558
20.2 Averaging Fundamental Equations of Turbulent Flow . . . . . . . . . . 560
20.2.1 Averaging Conservation Equations . . . . . . . . . . . . . . . . . . . . 561
20.2.1.1Averaging the Continuity Equation . . . . . . . . . . . . . 561
20.2.1.2 Averaging the Navier-Stokes Equation . . . . . . . . . . 561
20.2.1.3 Averaging the Mechanical Energy Equation . . . . . . 562
20.2.1.4 Averaging the Thermal Energy Equation . . . . . . . . 563
20.2.1.5 Averaging the Total Enthalpy Equation . . . . . . . . . 565
20.2.1.6 Quantities Resulting from Averaging to Be Modeled 568
20.2.2 Equation of Turbulence Kinetic Energy . . . . . . . . . . . . . . . . . 570
20.2.3 Equation of Dissipation of Kinetic Energy . . . . . . . . . . . . . . . 576
20.3 Turbulence Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 577
20.3.1 Algebraic Model: Prandtl Mixing Length Hypothesis . . . . . . 578
20.3.2 Algebraic Model: Cebeci-Smith Model . . . . . . . . . . . . . . . . . 584
20.3.3 Baldwin-Lomax Algebraic Model . . . . . . . . . . . . . . . . . . . . . 585
20.3.4 One- Equation Model by Prandtl . . . . . . . . . . . . . . . . . . . . . . 586
20.3.5 Two-Equation Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587
20.3.5.1 Two-Equation k-

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