Fluid Mechanics and Thermodynamics of Turbomachinery, Seventh Edition [7th Ed] (Instructor's Edu Resource 1 of 2, Solution Manual) (Solutions)

Fluid Mechanics and Thermodynamics of Turbomachinery is the leading turbomachinery book due to its balanced coverage of theory and application. Starting with background principles in fluid mechanics and thermodynamics, the authors go on to discuss axial flow turbines and compressors, centrifugal pumps, fans, and compressors, and radial flow gas turbines, hydraulic turbines, and wind turbines. In this new edition,more coverage is devoted to modern approaches to analysis and design, including CFD and FEA techniques. Used as a core text in senior undergraduate and graduate level courses this book will also appeal to professional engineers in the aerospace, global power, oil & gas and other industries who are involved in the design and operation of turbomachines. More coverage of a variety of types of turbomachinery, including centrifugal pumps and gas turbines Addition of numerical and computational tools, including more discussion of CFD and FEA techniques to reflect modern practice in the area More end of chapter exercises and in-chapter worked examples Fluid Mechanics and Thermodynamics of Turbomachinery 2 Copyright 3 Dedication 4 Preface to the Seventh Edition 5 Acknowledgments 7 List of Symbols 9 Subscripts 11 Superscripts 12 1 Introduction: Basic Principles 13 1.1 Definition of a turbomachine 13 1.2 Coordinate system 14 Relative velocities 16 Sign convention 16 Velocity diagrams for an axial flow compressor stage 17 1.3 The fundamental laws 18 1.4 The equation of continuity 18 1.5 The first law of thermodynamics 19 The steady flow energy equation 20 1.6 The momentum equation 21 Moment of momentum 21 The Euler work equation 22 Rothalpy and relative velocities 23 1.7 The second law of thermodynamics—entropy 23 1.8 Bernoulli’s equation 25 1.9 The thermodynamic properties of fluids 26 Ideal gases 26 Perfect gases 28 Steam 29 Commonly used thermodynamic terms relevant to steam tables 29 1.10 Compressible flow relations for perfect gases 30 Choked flow 33 1.11 Definitions of efficiency 34 Efficiency of turbines 34 Steam and gas turbines 35 Hydraulic turbines 37 Efficiency of compressors and pumps 38 1.12 Small stage or polytropic efficiency 39 Compression process 39 Small stage efficiency for a perfect gas 41 Turbine polytropic efficiency 43 Reheat factor 43 1.13 The inherent unsteadiness of the flow within turbomachines 45 References 48 2 Dimensional Analysis: Similitude 50 2.1 Dimensional analysis and performance laws 50 2.2 Incompressible fluid analysis 51 2.3 Performance characteristics for low-speed machines 53 2.4 Compressible flow analysis 55 Flow coefficient and stage loading 58 2.5 Performance characteristics for high-speed machines 59 Compressors 59 Turbines 60 2.6 Specific speed and specific diameter 64 The Cordier diagram 67 Compressible specific speed 71 2.7 Cavitation 72 Cavitation limits 73 References 77 3 Two-Dimensional Cascades 79 3.1 Introduction 79 3.2 Cascade geometry 82 Compressor blade profiles 83 Turbine blade profiles 84 3.3 Cascade flow characteristics 85 Streamtube thickness variation 86 Cascade performance parameters 87 Blade surface velocity distributions 90 3.4 Analysis of cascade forces 90 Lift and drag forces 91 Lift and drag coefficients 92 Circulation and lift 93 3.5 Compressor cascade performance 94 Compressor loss and blade loading 94 Fluid deviation 96 Incidence effects 97 Incompressible cascade analysis 99 Effects of Mach number 102 3.6 Turbine cascades 105 Turbine loss correlations 105 Correlation of Ainley and Mathieson 106 Reynolds number correction 109 Soderberg’s correlation 109 Mach number effects on loss 111 The Zweifel criterion 112 Flow exit angle 115 Turbine limit load 116 3.7 Cascade computational analysis 118 Calculation geometry 118 Method types 119 Boundary conditions 120 Transonic effects 121 Viscous effects 122 References 125 4 Axial-Flow Turbines: Mean-Line Analysis and Design 128 4.1 Introduction 128 4.2 Velocity diagrams of the axial turbine stage 130 4.3 Turbine stage design parameters 131 Design flow coefficient 131 Stage loading coefficient 132 Stage reaction 132 4.4 Thermodynamics of the axial turbine stage 132 4.5 Repeating stage turbines 133 4.6 Stage losses and efficiency 136 Turbine loss sources 138 Steam turbines 140 4.7 Preliminary axial turbine design 142 Number of stages 143 Blade height and mean radius 143 Number of aerofoils and axial chord 144 4.8 Styles of turbine 144 Zero reaction stage 145 50% Reaction stage 145 4.9 Effect of reaction on efficiency 149 4.10 Diffusion within blade rows 150 4.11 The efficiency correlation of 152 4.12 Design point efficiency of a turbine stage 155 Total-to-total efficiency of 50% reaction stage 155 Total-to-total efficiency of a zero reaction stage 157 Total-to-static efficiency of stage with axial velocity at exit 157 4.13 Stresses in turbine rotor blades 159 Centrifugal stresses 160 4.14 Turbine blade cooling 164 4.15 Turbine flow characteristics 168 Flow characteristics of a multistage turbine 169 References 175 5 Axial-Flow Compressors and Ducted Fans 177 5.1 Introduction 177 5.2 Mean-line analysis of the compressor stage 178 5.3 Velocity diagrams of the compressor stage 179 5.4 Thermodynamics of the compressor stage 180 5.5 Stage loss relationships and efficiency 181 Compressor loss sources 183 5.6 Mean-line calculation through a compressor rotor 184 Compressible case 184 Incompressible case 186 5.7 Preliminary compressor stage design 188 Stage loading 189 Flow coefficient 190 Reaction 190 Interstage swirl 191 Blade aspect ratio 191 5.8 Off-design performance 195 5.9 Multistage compressor performance 196 Overall pressure ratio and efficiency 196 Off-design operation and stage matching 198 Stage stacking 201 Annulus wall boundary layers 202 5.10 High Mach number compressor stages 203 5.11 Stall and surge phenomena in compressors 206 Casing treatment 208 Control of flow instabilities 211 5.12 Low speed ducted fans 212 Lift and drag coefficients 213 Blade element theory 214 Blade element efficiency 215 Lift coefficient of a fan aerofoil 216 References 221 6 Three-Dimensional Flows in Axial Turbomachines 223 6.1 Introduction 223 6.2 Theory of radial equilibrium 223 6.3 The indirect problem 226 Free-vortex flow 226 Compressor stage 226 Forced vortex 230 Variable vortex design 230 Mixed vortex design 231 First power stage vortex design 231 6.4 The direct problem 235 Some special cases 235 The general solution of the radial equilibrium equation 236 A special case 236 6.5 Compressible flow through a fixed blade row 237 6.6 Constant specific mass flow 238 6.7 Off-design performance of a stage 240 6.8 Free-vortex turbine stage 241 6.9 Actuator disc approach 243 Blade row interaction effects 247 Application to compressible flow 248 6.10 Computational through-flow methods 250 6.11 3D flow features 253 Secondary flow 253 Leakage flows 256 6.12 3D design 258 Sweep 258 Lean 259 Endwall profiling 259 Leakage paths, seals, and gaps 260 6.13 The application of 3D computational fluid dynamics 260 Single-passage steady computations 262 Multiple blade row steady computations 262 Unsteady computations 263 Current and future application of CFD to turbomachinery 263 References 270 7 Centrifugal Pumps, Fans, and Compressors 272 7.1 Introduction 272 7.2 Some definitions 274 7.3 Thermodynamic analysis of a centrifugal compressor 276 The impeller 276 The diffuser 278 7.4 Inlet velocity limitations at the compressor eye 279 7.5 Design of a pump inlet 280 7.6 Design of a centrifugal compressor inlet 282 Case A 넀㄀㴀 뀀 282 Case B 넀㄀─アパート攀 뀀 283 Some remarks on the use of prewhirl vanes at entry to the impeller 286 7.7 The slip factor 288 Introduction 288 The relative eddy concept 289 Slip factor correlations 289 7.8 A unified correlation for slip factor 293 Comparison of the new slip factor theory with experimental results 295 Method of Calculating the Shape Factor F 295 Illustrative exercise 296 Results 296 7.9 Head increase of a centrifugal pump 297 7.10 Performance of centrifugal compressors 299 Determining the pressure ratio 299 Effect of backswept vanes 301 Illustrative exercise 304 Kinetic energy leaving the impeller 305 Illustrative exercise 306 7.11 The diffuser system 307 Vaneless diffusers or volutes 308 Vaned diffusers 310 7.12 Diffuser performance parameters 312 Diffuser design calculation 315 7.13 Choking in a compressor stage 316 Inlet 316 Impeller 317 Diffuser 317 References 323 8 Radial-Flow Gas Turbines 325 8.1 Introduction 325 8.2 Types of IFR turbine 326 Cantilever turbine 326 The 90° IFR turbine 327 8.3 Thermodynamics of the 90° IFR turbine 328 8.4 Basic design of the rotor 330 Nominal design 330 Spouting velocity 331 8.5 Nominal design point efficiency 332 8.6 Some Mach number relations 336 8.7 The scroll and stator blades 337 Stator loss models 338 Effects of varying the vaneless space and the vane solidity 339 Loss coefficients used in 90° IFR turbines 339 Nozzle 339 Rotor loss coefficients 340 8.8 Optimum efficiency considerations 340 Design for optimum efficiency 343 Solution of Whitfield’s design problem 343 8.9 Criterion for minimum number of blades 346 8.10 Design considerations for rotor exit 349 8.11 Significance and application of specific speed 354 8.12 Optimum design selection of 90° IFR turbines 357 8.13 Clearance and windage losses 358 8.14 Cooled 90° IFR turbines 360 References 365 9 Hydraulic Turbines 367 9.1 Introduction 367 Tidal power 368 Wave power 368 Features of hydropower plants 368 9.2 Hydraulic turbines 369 Early history of hydraulic turbines 369 Flow regimes for maximum efficiency 369 Capacity of large Francis turbines 371 9.3 The Pelton turbine 372 A simple hydroelectric scheme 375 Controlling the speed of the Pelton turbine 375 Sizing the penstock diameter 377 Energy losses in the Pelton turbine 377 Optimum jet diameter 378 Exercise 381 9.4 Reaction turbines 383 9.5 The Francis turbine 383 Basic equations 387 The pump turbine 390 9.6 The Kaplan turbine 391 Basic equations 392 9.7 Effect of size on turbomachine efficiency 395 9.8 Cavitation in hydraulic turbines 397 Connection between Thoma’s coefficient, suction specific speed, and specific speed 400 Exercise 401 Avoiding Cavitation 401 Peripheral velocity factor 401 Selecting the right turbine 402 9.9 Application of CFD to the design of hydraulic turbines 404 9.10 The Wells turbine 404 Introduction 404 Operating principles 406 Two-dimensional flow analysis 406 Design and performance variables 408 Effect of flow coefficient 409 Effect of blade solidity 409 Effect of hub–tip ratio 410 The starting behavior of the Wells turbine 411 Pitch-controlled blades 411 A turbine with self-pitch-controlled blades 411 Further work 415 9.11 Tidal power 415 Categories of tidal power 416 Tidal stream generators 416 The SeaGen tidal turbine 417 References 423 10 Wind Turbines 425 10.1 Introduction 425 Wind characteristics and resource estimation 426 Historical viewpoint 428 10.2 Types of wind turbine 428 Large HAWTs 431 Small HAWTs 432 Effect of tower height 432 10.3 Performance measurement of wind turbines 433 Wind speed probability density function 433 Storing energy 435 Calculating the maximum possible power production of a wind turbine 435 10.4 Annual energy output 437 10.5 Statistical analysis of wind data 437 Basic equations 437 Wind speed probability distributions 438 10.6 Actuator disc approach 439 Introduction 439 Theory of the actuator disc 440 An alternative proof of Betz’s result 441 The power coefficient 442 The axial force coefficient 443 Correcting for high values of a ̄ 446 Estimating the power output 447 10.7 Blade element theory 447 Introduction 447 The vortex system of an aerofoil 448 Wake rotation 448 Forces acting on a blade element 450 Lift and drag coefficients 451 Connecting actuator disc theory and blade element theory 452 Tip–speed ratio 454 Turbine solidity 454 Solving the equations 454 10.8 The BEM method 455 Spanwise variation of parameters 455 Evaluating the torque and axial force 456 Correcting for a finite number of blades 459 Prandtl’s correction factor 459 Performance calculations with tip correction included 462 10.9 Rotor configurations 464 Blade planform 464 Effect of varying the number of blades 464 Effect of varying tip–speed ratio 465 Rotor optimum design criteria 466 10.10 The power output at optimum conditions 471 10.11 HAWT blade section criteria 472 10.12 Developments in blade manufacture 473 10.13 Control methods 475 Blade-pitch control 476 Passive or stall control 477 Aileron control 477 10.14 Blade tip shapes 479 10.15 Performance testing 480 10.16 Performance prediction codes 481 BEM theory 481 Lifting surface, prescribed wake theory 482 Comparison with experimental data 482 Peak and postpeak power predictions 483 Enhanced performance of turbine blades 484 10.17 Environmental matters 484 Visual intrusion 485 Acoustic emissions 486 10.18 The largest wind turbines 486 Appendix A: Preliminary Design of an Axial-Flow Turbine for a Large Turbocharger 492 Design requirements 492 Mean radius design 493 Determining the mean radius velocity triangles and efficiency 494 Determining the root and tip radii 495 Variation of reaction at the hub 496 Choosing a suitable stage geometry 497 Estimating the pitch/chord ratio 498 Blade angles and gas flow angles 499 Additional information concerning the design 500 Postscript 500 References 500 Appendix B: Preliminary Design of a Centrifugal Compressor for a Turbocharge 501 Design requirements and assumptions 501 Determining the blade speed and impeller radius 501 Design of impeller inlet 502 Efficiency considerations for the impeller 503 Design of impeller exit 503 Flow in the vaneless space 504 An iterative procedure 505 The vaned diffuser 507 The volute 507 Determining the exit stagnation pressure, p03, and overall compressor efficiency, ηC 507 References 509 Appendix C: Tables for the Compressible Flow of a Perfect Gas 510 Appendix D: Conversion of British and American Units to SI Units 521 Appendix E: Mollier Chart for Steam 522 Appendix F: Answers to Problems 523 Chapter 1 523 Chapter 2 523 Chapter 3 523 Chapter 4 524 Chapter 5 524 Chapter 6 525 Chapter 7 525 Chapter 8 526 Chapter 9 526 Chapter 10 527 Index 528 Content: Front-matter , Pages i,iii Copyright , Page iv Dedication , Page v Preface to the Seventh Edition , Pages xi-xii Acknowledgments , Pages xiii-xiv List of Symbols , Pages xv-xviii Chapter 1 - Introduction: Basic Principles , Pages 1-37 Chapter 2 - Dimensional Analysis: Similitude , Pages 39-67 Chapter 3 - Two-Dimensional Cascades , Pages 69-117 Chapter 4 - Axial-Flow Turbines: Mean-Line Analysis and Design , Pages 119-167 Chapter 5 - Axial-Flow Compressors and Ducted Fans , Pages 169-214 Chapter 6 - Three-Dimensional Flows in Axial Turbomachines , Pages 215-263 Chapter 7 - Centrifugal Pumps, Fans, and Compressors , Pages 265-317 Chapter 8 - Radial-Flow Gas Turbines , Pages 319-360 Chapter 9 - Hydraulic Turbines , Pages 361-418 Chapter 10 - Wind Turbines , Pages 419-485 Appendix A - Preliminary Design of an Axial-Flow Turbine for a Large Turbocharger , Pages 487-495 Appendix B - Preliminary Design of a Centrifugal Compressor for a Turbocharge , Pages 497-505 Appendix C - Tables for the Compressible Flow of a Perfect Gas , Pages 507-517 Appendix D - Conversion of British and American Units to SI Units , Page 519 Appendix E - Mollier Chart for Steam , Page 521 Appendix F - Answers to Problems , Pages 523-527 Index , Pages 529-537 Fluid Mechanics and Thermodynamics of Turbomachinery is the leading turbomachinery book due to its balanced coverage of theory and application. Starting with background principles in fluid mechanics and thermodynamics, the authors go on to discuss axial flow turbines and compressors, centrifugal pumps, fans, and compressors, and radial flow gas turbines, hydraulic turbines, and wind turbines. In this new edition, more coverage is devoted to modern approaches to analysis and design, including CFD and FEA techniques. Used as a core text in senior undergraduate and graduate level courses this book will also appeal to professional engineers in the aerospace, global power, oil & gas and other industries who are involved in the design and operation of turbomachines. More coverage of a variety of types of turbomachinery, including centrifugal pumps and gas turbines Addition of numerical and computational tools, including more discussion of CFD and FEA techniques to reflect modern practice in the area More end of chapter exercises and in-chapter worked examples