Gas Turbine Design, Components and System Design Integration (eBook)

Preface to the First Edition 5
Table of Content 8
Nomenclature 15
1 Introduction, Gas Turbines, Applications, Types 20
1.1 Power Generation Gas Turbines 20
1.2 Compressed Air Energy Storage Gas Turbines, CAES 25
1.3 Power Generation Gas Turbine Process 27
1.4 Significant Efficiency Improvement of Gas Turbines 29
1.5 Ultra High Efficiency Gas Turbine With Stator Internal Combustion 33
1.6 Aircraft Gas Turbines 36
1.7 Aircraft-Derivative Gas Turbines 38
1.8 Gas Turbines Turbocharging Diesel Engines 41
1.9 Gas Turbine Components, Functions 43
1.9.1 Group 1: Inlet, Exhaust, Pipe 44
1.9.2 Group 2: Heat Exchangers, Combustion Chamber, After- Burners 45
1.9.3 Group 3: Compressor, Turbine Components 48
References 49
2 Gas Turbine Thermodynamic Process 50
2.1 Gas Turbine Cycles, Processes 50
2.1.1 Gas Turbine Process 51
2.2 Improvement of Gas Turbine Thermal Efficiency 58
2.2.1 Minor Improvement of Gas Turbine Thermal Efficiency 59
2.2.2 Major Improvement of Gas Turbine Thermal Efficiency 60
2.1.3 Compressed Air Energy Storage Gas Turbine 64
References 66
3 Thermo-Fluid Essentials for Gas Turbine Design 67
3.1 Mass Flow Balance 67
3.2 Balance of Linear Momentum 69
3.3 Balance of Moment of Momentum 71
3.4 Balance of Energy 74
3.4.1 Energy Balance Special Case 1: Steady Flow 75
3.4.2 Energy Balance Special Case 2: Steady Flow, Constant Mass Flow 76
3.5 Application of Energy Balance to Gas Turbines Components 76
3.5.1 Application: Accelerated, Decelerated Flows 77
3.5.2 Application: Combustion Chamber, Heat Exchanger 78
3.5.3 Application: Turbine, Compressor 81
3.5.3.1 Uncooled turbine. 81
3.5.3.2 Cooled turbine: 82
3.5.3.3 Uncooled compressor. 83
3.5.3.4 Cooled Compressor. 84
3.6 Irreversibility and Total Pressure Losses 85
3.6.1 Application of Second Law to Turbomachinery Components 87
3.7 Flow at High Subsonic and Transonic Mach Numbers 89
3.7.1 Density Changes with Mach Number, Critical State 90
3.7.2 Effect of Cross-Section Change on Mach Number 95
3.7.3 Compressible Flow through Channels with Constant Cross Section 102
3.7.4 The Normal Shock Wave Relations 110
3.7.5 The Oblique Shock Wave Relations 116
3.7.6 Detached Shock Wave 120
3.7.7 Prandtl-Meyer Expansion 120
References 123
4 Theory of Turbomachinery Stages 124
4.1 Energy Transfer in Turbomachinery Stages 124
4.2 Energy Transfer in Relative Systems 125
4.3 General Treatment of Turbine and Compressor Stages 126
4.4 Dimensionless Stage Parameters 130
4.5 Relation Between Degree of Reaction and Blade Height for a Normal Stage Using Simple Radial Equilibrium 132
4.6 Effect of Degree of Reaction on the Stage Configuration 135
4.7 Effect of Stage Load Coefficient on Stage Power 137
4.8 Unified Description of a Turbomachinery Stage 138
4.8.1 Unified Description of Stage with Constant Mean Diameter 138
4.8.2 Generalized Dimensionless Stage Parameters 139
4.9 Special Cases 141
4.9.1 Case 1, Constant Mean Diameter 142
4.9.2 Case 2, Constant Mean Diameter and Meridional Velocity Ratio 142
4.10 Increase of Stage Load Coefficient, Discussion 143
References 145
5 Turbine and Compressor Cascade Flow Forces 146
5.1 Blade Force in an Inviscid Flow Field 146
5.2 Blade Forces in a Viscous Flow Field 151
5.3 The Effect of Solidity on Blade Profile Losses 157
5.4 Relationship Between Profile Loss Coefficient and Drag 157
5.5 Optimum Solidity 159
5.5.1 Optimum Solidity, by Pfeil 160
5.5.2 Optimum Solidity by Zweifel 161
5.6 Generalized Lift-Solidity Coefficient 163
5.6.1 Lift-Solidity Coefficient for Turbine Stator 165
5.6.2 Turbine Rotor 169
References 172
6 Losses in Turbine and Compressor Cascades 174
6.1 Turbine Profile Loss 175
6.2 Viscous Flow in Compressor Cascade 177
6.2.1 Calculation of Viscous Flows 177
6.2.2. Boundary Layer Thicknesses 178
6.2.3 Boundary Layer Integral Equation 179
6.2.4 Application of Boundary Layer Theory to Compressor Blades 181
6.2.5 Effect of Reynolds Number 185
6.2.6 Stage Profile Losses 185
6.3 Trailing Edge Thickness Losses 185
6.4 Losses Due to Secondary Flows 191
6.4.1 Vortex Induced Velocity Field, Law of Bio -Savart, Preparatory 193
6.4.2 Calculation of Tip Clearance Secondary Flow Losses 196
6.4.3 Calculation of Endwall Secondary Flow Losses 199
6.5 Flow Losses in Shrouded Blades 203
6.5.1 Losses Due to Leakage Flow in Shrouds 203
6.6 Exit Loss 209
6.7 Trailing Edge Ejection Mixing Losses of Gas Turbine Blades 211
6.7.1 Calculation of Mixing Losses 211
6.7.2 Trailing Edge Ejection Mixing Losses 216
6.7.3 Effect of Ejection Velocity Ratio on Mixing Loss 216
6.7.4 Optimum Mixing Losses 218
6.8 Stage Total Loss Coefficient 218
6.9 Diffusers, Configurations, Pressure Recovery, Losses 219
6.9.1 Diffuser Configurations 220
6.9.2 Diffuser Pressure Recovery 221
6.9.3 Design of Short Diffusers 224
6.9.4 Some Guidelines for Designing High Efficiency Diffusers 227
References 228
7 Efficiency of Multi-Stage Turbomachines 230
7.1 Polytropic Efficiency 230
7.2 Isentropic Turbine Efficiency, Recovery Factor 233
7.3 Compressor Efficiency, Reheat Factor 236
7.4 Polytropic versus Isentropic Efficiency 238
References 240
8 Incidence and Deviation 241
8.1 Cascade with Low Flow Deflection 241
8.1.1 Conformal Transformation 241
8.1.2 Flow Through an Infinitely Thin Circular Arc Cascade 250
8.1.3 Thickness Correction 256
8.1.4 Optimum Incidence 256
8.1.5 Effect of Compressibility 258
8.2 Deviation for High Flow Deflection 259
8.2.1 Calculation of Exit Flow Angle 261
References 263
9 Blade Design 265
9.1 Conformal Transformation, Basics 265
9.1.1 Joukowsky Transformation 267
9.1.2 Circle-Flat Plate Transformation 267
9.1.3 Circle-Ellipse Transformation 268
9.1.4 Circle-Symmetric Airfoil Transformation 269
9.1.5 Circle-Cambered Airfoil Transformation 271
9.2 Compressor Blade Design 272
9.2.1 Low Subsonic Compressor Blade Design 273
9.2.2 Compressors Blades for High Subsonic Mach Number 279
9.2.3 Transonic, Supersonic Compressor Blades 280
9.3 Turbine Blade Design 281
9.3.1 Steps for Designing the Camberline 282
9.3.2 Camberline Coordinates Using Bèzier Function 285
9.3.3 Alternative Calculation Method 287
9.4 Assessment of Blades Aerodynamic Quality 288
References 291
10 Radial Equilibrium 293
10.1 Derivation of Equilibrium Equation 294
10.2 Application of Streamline Curvature Method 302
10.2.1 Step-by-step solution procedure 304
10.3 Compressor Examples 308
10.4 Turbine Example, Compound Lean Design 311
10.4.1 Blade Lean Geometry 312
10.4.2 Calculation of Compound Lean Angle Distribution 313
10.4.3 Example: Three-Stage Turbine Design 315
10.5 Special Cases 318
10.5.1 Free Vortex Flow 318
10.5.2 Forced vortex flow 319
10.6.3 Flow with constant flow angle 320
References 321
11 Nonlinear Dynamic Simulation of Turbomachinery Components and Systems 323
11.1 Theoretical Background 324
11.2 Preparation for Numerical Treatment 331
11.3 One-Dimensional Approximation 331
11.3.1 Time Dependent Equation of Continuity 331
11.3.2 Time Dependent Equation of Motion 333
11.3.3 Time Dependent Equation of Total Energy 334
11.4 Numerical Treatment 339
References 340
12 Generic Modeling of Turbomachinery Components and Systems 341
12.1 Generic Component, Modular Configuration 343
12.1.1 Plenum the Coupling Module 343
12.1.2 Group1 Modules: Inlet, Exhaust, Pipe 345
12.1.3 Group 2: Heat Exchangers, Combustion Chamber, After- Burners 346
12.1.4 Group 3: Adiabatic Compressor and Turbine Components 348
12.1.5 Group 4: Diabatic Turbine and Compressor Components 350
12.1.6 Group 5: Control System, Valves, Shaft, Sensors 352
12.2 System Configuration, Nonlinear Dynamic Simulation 352
12.3 Configuration of Systems of Non-linear Partial Differential Equations 356
References 356
13 Modeling of Inlet, Exhaust, and Pipe Systems 358
13.1 Unified Modular Treatment 358
13.2 Physical and Mathematical Modeling of Modules 358
13.3 Example: Dynamic behavior of a Shock Tube 360
13.3.1 Shock Tube Dynamic Behavior 362
References 366
14 Modeling of Recuperators, Combustion Chambers, Afterburners 367
14.1 Modeling Recuperators 368
14.1.1 Recuperator Hot Side Transients 369
14.1.2 Recuperator Cold Side Transients 369
14.1.3 Coupling Condition Hot, Cold Side 370
14.1.4 Recuperator Heat Transfer Coefficient 371
14.2 Modeling Combustion Chambers 372
14.2.1. Mass Flow Transients 373
14.2.2. Temperature Transients 374
14.2.3 Combustion Chamber Heat Transfer 376
14.3 Example: Startup and Shutdown of a Combustion Chamber- Preheater System 378
14.4 Modeling of Afterburners 381
References 382
15 Modeling the Compressor Component, Design and Off-Design 383
15.1 Compressor Losses 384
15.1.1 Profile Losses 386
15.1.2 Diffusion Factor 387
15.1.3 Generalized Maximum Velocity Ratio for Stator and Rotor 391
15.1.4 Compressibility Effect 393
15.1.5 Shock Losses 397
15.1.6 Correlations for Boundary Layer Momentum Thickness 406
15.1.7 Influence of Different Parameters on Profile Losses 407
15.1.7.1 Mach Number Effect: 407
15.1.7.2 Reynolds number effect: 408
15.1.7.3 Blade thickness effect: 408
15.2 Compressor Design and Off-Design Performance 409
15.2.1 Stage-by-stage and Row-by-Row Adiabatic Compression Process 409
15.2.1.1 Stage-by-stage calculation of compression process: 409
15.2.1.2 Row-by-row adiabatic compression: 411
15.2.1.3 Off-design efficiency calculation: 415
15.3 Generation of Steady State Performance Map 418
15.3.1 Inception of Rotating Stall 420
15.3.2 Degeneration of Rotating Stall into Surge 422
15.4 Compressor Modeling Levels 423
15.4.1 Module Level 1: Using Performance Maps 424
15.4.1.1 Quasi dynamic modeling using performance maps: 426
15.4.1.2 Simulation Example: 427
15.4.2 Module Level 2: Row-by-Row Adiabatic Calculation Procedure 429
15.4.3 Active Surge Prevention by Adjusting the Stator Blades 430
15.4.4 Module Level 3: Row-by-Row Diabatic Compression 431
15.4.4.1 Description of diabatic compressor module: 432
15.4.4.2 Heat transfer closure equations: 434
References 436
16 Turbine Aerodynamic Design and Off-design Performance 440
16.1 Stage-by-Stage and Row-by-Row Adiabatic Design and Off- Design Performance 442
16.1.1 Stage-by-Stage Calculation of Expansion Process 443
16.1.2 Row-by-Row Adiabatic Expansion 444
16.1.3 Off-Design Efficiency Calculation 449
16.1.4 Behavior Under Extreme Low Mass Flows 451
16.1.5 Example: Steady Design and Off-Design Behavior of a Multi- Stage Turbine 454
16.2 Off-Design Calculation Using Global Turbine Characteristics Method 456
16.3 Modeling the Turbine Module for Dynamic Performance Simulation 458
16.3.1 Module Level 1: Using Turbine Performance Characteristics 458
16.3.2 Module Level 2: Row-by-Row Adiabatic Expansion Calculation 459
16.3.3 Module Level 3: Row-by-Row Diabatic Expansion 460
16.3.3.1 Description of diabatic turbine module, first method: 462
16.3.3.2 Description of diabatic turbine module, second method: 464
16.3.3.3 Heat transfer closure equations: 466
References 467
17 Gas Turbine Design, Preliminary Considerations 468
17.1 Gas Turbine Preliminary Design Procedure 469
17.2 Gas Turbine Cycle 470
17.3 Compressor Design, Boundary Conditions, Design Process 471
17.3.1 Design Process 471
17.3.2 Compressor Blade Aerodynamics 475
17.3.3 Controlling the Leakage Flow 476
17.3.4 Compressor Exit Diffuser 476
17.3.5 Compressor Efficiency and Performance Maps 476
17.3.6 Stagger Angle Adjustment During Operation 478
17.4 Combustion Chambers 479
17.4.1 Combustion Design Criteria 481
17.4.2 Combustion Types 481
17.5 Turbine Design, Boundary Conditions, Design Process 483
17.5.1 Steps of a Gas Turbine Design Process 483
17.5.2 Mechanical Integrity, Components Vibrational 488
References 488
18 Simulation of Gas Turbine Engines, Design Off-Design and Dynamic Performance 489
18 Gas Turbine Engines, Design, Dynamic Performance 490
18.1 State of Dynamic Simulation, Background 490
18.2 Gas Turbine Configurations 490
18.3 Gas Turbine Components, Modular Concept 493
18.4 Levels of Gas Turbine Engine Simulations 498
18.4.1 Zeroth Simulation Level 498
18.4.2 First Simulation Level 498
18.4.3 Second Simulation Level 498
18.4.4 Third Simulation Level 498
18.5 Non-Linear Dynamic Simulation Case Studies 499
18.5.1 Case Studies: Compressed Air Energy Storage Plant 500
18.5.1.1 Case Study: Emergency Shutdown 503
18.5.1.2 Case Study 1: Grid Fluctuation Response 505
18.5.2 Case Study 2: Dynamic Simulation of a Gas Turbine under Adverse Operation condition 505
18.5.3 Case Studies: Dynamic Simulation of a Split-Shaft Gas Turbine under Adverse Operation condition 510
18.5.1.1 Simulation of Compressor Surge: 511
18.5.3.2 Case 3.2: Surge Prevention by Stator Stagger Angle Adjustment 513
18.5.4 Case Studies: Maximizing the Off-Design Efficiency of a Gas Turbine By Varying the Turbine Stator Stagger Angle 515
18.5.4.1 Dynamic Change of Stagger Angle, when Engine is Running 516
18.5.5 Case Study 3: Simulation of a Multi-Spool Gas Turbine Engine 518
References 521