Turbomachinery Flow Physics and Dynamic Performance Bearbeitet von Meinhard T Schobeiri 1. Auflage 2004. Buch. XXI, 522 S. Hardcover ISBN 978 3 540 22368 9 Format (B x L): 15,5 x 23,5 cm Gewicht: 2070 g Weitere Fachgebiete > Technik > Werkstoffkunde, Mechanische Technologie > Aerodynamik schnell und portofrei erhältlich bei Die Online-Fachbuchhandlung beck-shop.de ist spezialisiert auf Fachbücher, insbesondere Recht, Steuern und Wirtschaft. Im Sortiment finden Sie alle Medien (Bücher, Zeitschriften, CDs, ebooks, etc.) aller Verlage. Ergänzt wird das Programm durch Services wie Neuerscheinungsdienst oder Zusammenstellungen von Büchern zu Sonderpreisen. Der Shop führt mehr als 8 Millionen Produkte.
Contents I Turbomachinery Flow Physics 1 Introduction, Turbomachinery, Applications, Types 1 1.1 Turbine.... 1 1.2 Compressor... 5 1.3 Application of Turbomachines... 7 1.3.1 Power Generation, Steam Turbines.... 7 1.3.2 Power Generation, Gas Turbines... 7 1.3.3 Aircraft Gas Turbines.... 8 1.3.4 Diesel Engine Application... 10 1.4 Classification of Turbomachines... 11 1.4.1 Compressor Types... 11 1.4.2 Turbine Types.... 12 1.5 Working Principle of a Turbomachine.... 12 References, Chapter 1... 12 2 Kinematics of Turbomachinery Fluid Motion 13 2.1 Material and Spatial Description of the Flow Field... 13 2.1.1 Material Description.... 13 2.1.2 Jacobian Transformation Function and its Material Derivative 15 2.1.3 Spatial Description... 18 2.2 Translation, Deformation, Rotation... 19 2.3 Reynolds Transport Theorem.... 23 References, Chapter 2... 25 3 Differential Balances in Turbomchinery 27 3.1 Differential Mass Flow Balance in Stationary Frame of Reference.. 27 3.1.1 Incompressibility Condition... 29 3.2 Differential Momentum Balance in Stationary Frame of Reference.. 30 3.2.1 Relationship Between Stress Tensor and Deformation Tensor 32 3.2.2 Navier-Stokes Equation of Motion.... 34 3.2.3 Special Case: Euler Equation of Motion.... 36 3.3 Some Discussions on Turbomachinery Flow, Navier-Stokes Equations36 3.4 Energy Balance in Stationary Frame of Reference.... 36 3.4.1 Mechanical Energy... 36 3.4.2 Thermal Energy... 39
X Contents 3.4.3 Total Energy...................................... 40 3.4.4 Entropy Balance.................................... 41 3.5 Differential Balances in Rotating Frame of Reference............ 42 3.5.1 Velocity and Acceleration in Rotating Frame............. 42 3.5.2 Continuity Equation in Rotating Frame of Reference....... 44 3.5.3 Equation of Motion in Rotating Frame of Reference........ 45 3.5.4 Energy Equation in Rotating Frame of Reference.......... 47 3.6 Reynolds Averaged Navier Stokes Equations, Intermittency........ 48 3.6.1 Physics of Intermittently Laminar-Turbulent Boundary Layer 49 3.6.2 Identification of Intermittent Behavior of Steady Flows.... 50 3.6.3 Turbulent/Non-Turbulent Decisions.................... 51 3.6.4 Identification of Intermittent Behavior of Unsteady Flows.. 53 3.7 Implementation of Intermittency into Navier Stokes Equations..... 54 3.7.1 Reynolds-Averaged Equations for Fully Turbulent Flow.. 54 3.7.2 Conditioning the RANS for Intermittency Implementation. 59 3.8 Modeling the Unsteady Intermittency for Turbomachinery Flow... 61 References, Chapter 3........................................ 65 4 Integral Balances in Turbomachinery 69 4.1 Mass Flow Balance....................................... 69 4.2 Balance of Linear Momentum.............................. 71 4.3 Balance of Moment of Momentum........................... 7 6 4.4 Balance of Energy....................................... 81 4.4.1 Energy Balance Special Case 1: Steady Flow............. 87 4.4.2 Energy Balance Special Case 2: Steady, Constant Mass Flow 87 4.5 Application of Energy Balance to Turbomachinery Components........................................... 88 4.5.1 Application: pipe, diffuser, nozzle..................... 88 4.5.2 Application: Combustion Chamber..................... 89 4.5.3 Application: Turbine, Compressor..................... 90 4.5.3.1 Uncooled turbine........................... 90 4.5.3.2 Cooled turbine............................. 91 4.5.3.3 Uncooled compressor....................... 92 4.6 Irreversibility and Total Pressure Losses...................... 93 4.6.1 Application of Second Law to Turbomachinery Components. 95 4.7 Flow at High Subsonic and Transonic Mach Numbers............ 97 4.7.1 Density Changes with Mach Number, Critical State........ 98 4.7.2 Effect of Cross-Section Change on Mach Number........ 103 4.7.3 Flow though Channels with Constant Cross Section....... 110 4.7.4 Normal Shock Wave Relations....................... 116 4.7.5 Oblique Shock Wave Relations...................... 123 4.7.6 Detached Shock Wave.............................. 126 4.7.7 Prandtl-Meyer Expansion........................... 127 References, Chapter 4....................................... 130
Contents XI 5 Theory of Turbomachinery Stages 131 5.1 Energy Transfer in Turbomachinery Stages................... 131 5.2 Energy Transfer in Relative Systems........................ 132 5.3 General Treatment of Turbine and Compressor Stage........... 133 5.4 Dimensionless Stage Parameters........................... 137 5.5 Relation Between Degree of Reaction and Blade Height........ 139 5.6 Effect of Degree of Reaction on the Stage Configuration......... 143 5.7 Effect of Stage Load Coefficient on Stage Power.............. 144 5.8 Unified Description of a Turbomachinery Stage............... 145 5.8.1 Unified Description of Stage with Constant Mean Diameter.. 145 5.8.2 Generalized Dimensionless Stage Parameters............. 146 5.9 Special Cases.......................................... 149 5.9.1 Case 1, Constant Mean Diameter..................... 149 5.9.2 Case 2, Constant Meridional Velocity Ratio............. 149 5.10 Increase of Stage Load Coefficient, Discussion................ 150 References, Chapter 5....................................... 152 6 Turbine and Compressor Cascade Flow Forces 153 6.1 Blade Force in an Inviscid Flow Field....................... 153 6.2 Blade Forces in a Viscous Flow Field....................... 158 6.3 The Effect of Solidity on Blade Profile Losses................ 164 6.4 Relationship Between Profile Loss Coefficient and Drag........ 164 6.5 Optimum Solidity....................................... 166 6.6 Generalized Lift-Solidity Coefficient........................ 167 6.6.1 Turbine Stator..................................... 169 6.6.2 Turbine Rotor..................................... 172 References, Chapter 6....................................... 176 II Turbomachinery Losses, Efficiencies, Blades 7 Losses in Turbine and Compressor Cascades 177 7.1 Profile Losses.......................................... 178 7.2 Viscous Flow in Compressor Cascade....................... 178 7.2.1 Calculation of Viscous Flows........................ 179 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 Calculation of Secondary Flow Losses for Unshrouded Blades192 7.4.2 Secondary Flow Losses in Shrouded Blading............ 195 7.4.3 Losses Due to Leakage Flow in Shrouds................ 197
XII Contents 7.5 Exit Loss.............................................. 203 7.6 Trailing Edge Ejection Mixing Losses of Gas Turbine Blades..... 204 7.6.1 Calculation of Mixing Losses........................ 205 7.6.2 Trailing Edge Ejection Mixing Losses.................. 209 7.6.3 Effect of Injection Velocity Ratio on Mixing Loss........ 209 7.6.4 Optimum Trailing Edge Mixing Losses................. 211 7.7 Stage Total Loss Coefficient.............................. 212 References, Chapter 7....................................... 213 8 Efficiency of Multi-stage Turbomachines 215 8.1 Polytropic Efficiency.................................... 215 8.2 Isentropic Turbine Efficiency, Recovery Factor............... 218 8.3 Compressor Efficiency, Reheat Factor....................... 222 8.4 Polytropic vs. Isentropic Efficiency......................... 223 References, Chapter 8....................................... 225 9 Incidence and Deviation 227 9.1 Cascade with Low Flow Deflection......................... 227 9.1.1 Conformal Transformation.......................... 227 9.1.2 Flow Through an Infinitely Thin Circular Arc Cascade..... 236 9.1.3 Thickness Correction............................... 242 9.1.4 Optimum Incidence................................ 242 9.1.5 Effect of Compressibility............................ 244 9.2 Deviation for High Flow Deflection......................... 245 9.2.1 Calculation of Exit Flow Angle....................... 247 References, Chapter 9....................................... 249 10 Simple Blade Design 251 10.1 Compressor Blade Design................................ 251 10.1.1 Low Subsonic Compressor Blade Design............... 25 1 10.1.2 Intermediate Subsonic Compressor Blades............. 258 10.1.3 Transonic, Supersonic Compressor Blades............. 258 10.2 Simple Turbine Blade Design............................. 259 References, Chapter 10...................................... 261 11 Radial Equilibrium 263 11.1 Derivation of Equilibrium Equations........................ 264 11.2 Application of Streamline Curvature Method to Turbomachinery. 272 11.2.1 Step-by-Step Solution Procedure..................... 274 11.2.2 Examples....................................... 279 11.3 Special Cases......................................... 282 11.3.1 Free Vortex Flow................................. 282 11.3.2 Forced vortex flow................................ 283 11.3.3 Flow with Constant Flow Angle..................... 284 References, Chapter 11...................................... 285
Content XIII III Turbomachinery Dynamic Performance 12 Nonlinear Dynamic Simulation of Turbomachinery Components and Systems 287 12.1 Theoretical Background.................................. 288 12.2 Preparation for Numerical Treatment....................... 294 12.3 One-Dimensional Approximation.......................... 295 12.3.1Time Dependent Equation of Continuity............... 295 12.3.2 Time Dependent Equation of Motion................. 296 12.3.3 Time Dependent Equation of Total Energy............. 298 12.4 Numerical Treatment................................... 303 References, Chapter 12...................................... 304 13 Generic Modeling of Turbomachinery Components and Systems 305 13.1 Generic Component Configuration......................... 307 13.1.1 Group 1: Modular Configuration of Inlet, Exhaust, Pipe.... 307 13.1.2 Group 2: Heat Exchangers, Combustion Chamber........ 307 13.1.3 Group 3: Adiabatic Compressor and Turbine Components 309 13.1.4 Group 4: Diabatic Turbine and Compressor Components... 311 13.1.5 Group 5: Control System, Valves, Shaft, Sensors......... 313 13.1.6 Coupling Module Plenum........................... 313 13.2 Modular System Configuration Concept..................... 314 13.3 Configuration of Systems of Partial Differential Equations...... 318 References, Chapter 13...................................... 318 14 Modeling of Inlet, Exhaust, and Pipe Systems 319 14.1 Unified Modular Treatment.............................. 319 14.2 Physical and Mathematical Modeling of Modules.............. 319 14.3 Modeling of a Shock Tube............................... 322 14.3.1 Shock Tube Dynamic Behavior...................... 323 References, Chapter 14...................................... 327 15 Modeling of Heat Exchangers, Combustion Chambers, Afterburners 329 15.1 Modeling the Recuperators............................... 330 1 5.1.1 Recuperator Hot Side Transients..................... 331 15.1.2 Recuperator Cold Side Transients.................... 331 15.1.3 Coupling Condition Hot, Cold Side.................... 332 15.1.4 Recuperator Heat Transfer Coefficient................. 332 15.2 Modeling Combustion Chamber........................... 333 15.2.1. Mass Flow Transients............................. 335 15.2.2. Temperature Transients............................ 336 15.2.3 Combustion Chamber Heat Transfer.................. 338
XIV Contents 15.3 Example: Startup, Shutdown of a Combustor-Preheater System.. 340 15.4 Modeling of Afterburners................................ 344 References, Chapter 15...................................... 344 16 Modeling Compressor Component, Design, Off-Design. 345 16.1 Compressor Losses..................................... 346 16.1.1 Profile Losses.................................... 347 16.1.2 Diffusion Factor.................................. 349 16.1.3 Generalized Maximum Velocity Ratio for Cascade, Stage.. 353 16.1.4 Compressibility Effect............................. 355 16.1.5 Shock Losses.................................... 359 16.1.6 Correlations for Boundary Layer Momentum Thickness... 369 16.1.7 Influence of Different Parameters on Profile Losses...... 370 16.1.7.1 Mach Number Effect....................... 370 16.1.7.2 Reynolds number effect..................... 371 16.1.7.3 Blade thickness effect....................... 371 16.2 Compressor Aerodynamic Design and Off-Design Performance... 371 16.2.1 Stage-by-stage and Row-by-Row Adiabatic Compression.. 372 16.2.1.1 Stage-by-stage calculation of compression process. 373 16.2.1.2 Row-by-row adiabatic compression............. 374 16.2.1.3 Off-design efficiency calculation............... 378 16.2.3 Generation of Steady State Performance Map............ 381 16.3. Modeling the Compressor Module for Dynamic Performance... 385 16.3.1 Module Level 1: Using Performance Maps.............. 385 16.3.1.1 Quasi dynamic modeling using performance maps.. 388 16.3.1.2 Simulation example.......................... 389 16.3.2 Module Level 2: Row-by-Row Adiabatic Calculation..... 391 16.3.2.1 Active surge prevention...................... 392 16.3.2.2 Simulation example......................... 393 16.3.3 Module Level 3: Row-by-Row Diabatic Compression..... 398 16.3.3.1 Description of diabatic compressor module........ 399 16.3.3.2 Heat transfer closure equations................ 401 References, Chapter 16...................................... 403 17 Turbine Aerodynamic Design and Off-design Performance 409 17.1 Stage-by-Stage and Row-by-Row Adiabatic Design, Off-Design.. 411 17.1.1 Stage-by-Stage Calculation of Expansion Process........ 412 17.1.2 Row-by-Row Adiabatic Expansion.................... 413 17.1.3 Off-Design Efficiency Calculation.................... 418 17.1.4 Behavior Under Extreme Low Mass Flows............. 420 17.1.5 Example: Steady Design and Off-Design Behavior of a Multi-Stage Turbine........................... 423 17.2 Off-Design Calculation Using Global Turbine Characteristics.... 425 17.3 Modeling Turbine Module for Dynamic Performance Simulation. 427 17.3.1 Module Level 1: Using Performance Characteristics.... 427
Contents XV 17.3.2 Module Level 2: Row-by-Row Adiabatic Expansion...... 428 17.3.3 Module Level 3: Row-by-Row Diabatic Expansion....... 429 17.3.3.1 Diabatic turbine module, description method 1.... 431 17.3.3.2 Diabatic turbine module, description method 2.... 433 17.3.3.3 Heat transfer closure equations................ 435 References, Chapter 17...................................... 436 18 Gas Turbine Engines Design and Off-design Dynamic Performance............................................ 439 18.1 Gas Turbine Processes, Steady Design Operation............. 441 18.1.1 Gas Turbine Process.............................. 443 18.1.2 Improvement of Gas Turbine Thermal Efficiency....... 449 18.2 Non-Linear Gas Turbine Dynamic Simulation................ 451 18.2.1 State of Dynamic Simulation, Background.............. 452 18.3 Engine Components, Modular Concept, ModuleIdentification.... 453 18.4 Levels of Gas Turbine Engine Simulations, Cross Coupling..... 459 18.5 Non-Linear Dynamic Simulation Case Studies................ 460 18.5.1 Case Study 1: Compressed Air Energy Storage Gas Turbine 461 18.5.1.1 Simulation of emergency shutdown........... 463 18.5.1.2 Simulation of a cold startup.................. 465 18.5.2 Case Study 2: Power Generation Gas Turbine Engine..... 470 18.5.3 Case Study 3: Simulation of a Multi-Spool Gas Turbines.. 475 18.6 A Byproduct of Dynamic Simulation: Detailed Efficiency Calculation............................................ 478 18.7 Summary Part 3, Further Development...................... 480 References, Chapter 18...................................... 482 A Vector and Tensor Analysis 485 A. 1 Tensors in Three-Dimensional Euclidean Space............... 485 A.1.1 Index Notation.................................... 486 A.2 Vector Operations: Scalar, Vector and Tensor products.......... 487 A.2.1 Scalar product..................................... 487 A.2.2 Vector or cross product.............................. 487 A.2.3 Tensor product.................................... 488 A.3 Contraction of Tensors................................... 489 A.4 Differential Operators in Fluid Mechanics.................... 489 A.4.1 Substantial derivatives.............................. 490 A.4.2 Differential operator L.............................. 490 A5 Operator L Applied to Different Functions.................... 493 A5.1 Scalar Product of L and V............................ 493 A5.2 Vector product of L and V............................ 494 A5.3 Tensor Product of L and V............................ 495 A5.4 Scalar Product of L and a Second Order Tensor........... 495 References, Appendix A... 499
XVI Contents B Tensor Operations in Orthogonal Curvilinear Coordinate Systems 501 B.1 Change of Coordinate System.............................. 501 B.2 Co- and Contravariant Base Vectors, Metric Coefficients........ 501 B.3 Physical Components of a Vector.......................... 504 B.4 Derivatives of the Base Vectors, Christoffel Symbols.......... 504 B.5 Spatial Derivatives in Curvilinear Coordinate System........... 505 B.5.1 Application of L to Tensor Functions.................. 505 B.6 Application Example 1: Inviscid Flow Motion................ 507 B.6.1 Equation of Motion in Curvilinear Coordinate Systems.... 507 B.6.2 Special Case: Cylindrical Coordinate System............ 508 B.6.3 Base Vectors, Metric Coefficients..................... 508 B.6.4 Christoffel Symbols................................ 509 B.6.5 Introduction of Physical Components................... 510 B.7. Application Example 2: Viscous Flow Motion................ 511 B.7.1 Equation of Motion in Curvilinear Coordinate Systems..... 511 B.7.2 Special Case: Cylindrical Coordinate System............. 512 References, Appendix B..................................... 512 Index 515