PREFACE TO THE FIFTH EDITION ................................... xi
PREFACE TO THE FOURTH EDITION ................................ xiii
PREFACE TO THE THIRD EDITION ................................... xv
ACKNOWLEDGEMENTS ............................................. xvii
LIST OF SYMBOLS ............................................... xix
1. Introduction: Dimensional Analysis: Similitude .............. 1
Definition of a turbomachine ................................ 1
Units and dimensions ........................................ 3
Dimensional analysis and performative laws .................. 5
Incompressible fluid analysis ............................... 6
Performance characteristics ................................. 7
Variable geometry turbomachines ............................. 8
Specific speed ............................................. 10
Cavitation ................................................. 12
Compressible gas flow relations ............................ 15
Compressible fluid analysis ................................ 16
The inherent unsteadiness of the flow within
turbomachines .............................................. 20
References ................................................. 21
Problems ................................................... 22
2. Basic Thermodynamics, Fluid Mechanics: Definitions of
Efficiency ................................................. 24
Introduction ............................................... 24
The equation of continuity ................................. 24
The first law of thermodynamics - internal energy .......... 25
The momentum equation - Newton's second law of motion ...... 26
The second law of thermodynamics - entropy ................. 30
Definitions of efficiency .................................. 31
Small stage or polytropic efficiency ....................... 35
Nozzle efficiency .......................................... 42
Diffusers .................................................. 44
References ................................................. 54
Problems ................................................... 55
3. Two-dimensional Cascades ................................... 56
Introduction ............................................... 56
Cascade nomenclature ....................................... 57
Analysis of cascade forces ................................. 58
Energy losses .............................................. 60
Lift and drag .............................................. 60
Circulation and lift ....................................... 62
Efficiency of a compressor cascade ......................... 63
Performance of two-dimensional cascades .................... 64
The cascade wind tunnel .................................... 64
Cascade test results ....................................... 66
Compressor cascade performance ............................. 69
Turbine cascade performance ................................ 72
Compressor cascade correlations ............................ 72
Fan blade design (McKenzie) ................................ 80
Turbine cascade correlation (Ainley and Mathieson) ......... 83
Comparison of the profile loss in a cascade and in
a turbine stage ............................................ 88
Optimum space-chord ratio of turbine blades (Zweifel) ...... 89
References ................................................. 90
Problems ................................................... 92
4. Axial-flow Turbines: Two-dimensional Theory ................ 94
Introduction ............................................... 94
Velocity diagrams of the axial turbine stage ............... 94
Thermodynamics of the axial turbine stage .................. 95
Stage losses and efficiency ................................ 97
Soderberg's correlation .................................... 98
Types of axial turbine design ............................. 100
Stage reaction ............................................ 102
Diffusion within blade rows ............................... 104
Choice of reaction and effect on efficiency ............... 108
Design point efficiency of a turbine stage ................ 109
Maximum total-to-static efficiency of a reversible
turbine stage ............................................. 113
Stresses in turbine rotor blades .......................... 115
Turbine flow characteristics .............................. 121
Flow characteristics of a multistage turbine .............. 123
The Wells turbine ......................................... 125
Pitch-controlled blades ................................... 132
References ................................................ 139
Problems .................................................. 140
5. Axial-flow Compressors and Fans ........................... 145
Introduction .............................................. 145
Two-dimensional analysis of the compressor stage .......... 146
Velocity diagrams of the compressor stage ................. 148
Thermodynamics of the compressor stage .................... 149
Stage loss relationships and efficiency ................... 150
Reaction ratio ............................................ 151
Choice of reaction ........................................ 151
Stage loading ............................................. 152
Simplified off-design performance ......................... 153
Stage pressure rise ....................................... 155
Pressure ratio of a multistage compressor ................. 156
Estimation of compressor stage efficiency ................. 157
Stall and surge phenomena in compressors .................. 162
Control of flow instabilities ............................. 167
Axial-flow ducted fans .................................... 168
Blade element theory ...................................... 169
Blade element efficiency .................................. 171
Lift coefficient of a fan aerofoil ........................ 173
References ................................................ 173
Problems .................................................. 174
6. Three-dimensional Flows in Axial Turbomachines ............ 177
Introduction .............................................. 177
Theory of radial equilibrium .............................. 177
The indirect problem ...................................... 179
The direct problem ........................................ 187
Compressible flow through a fixed blade row ............... 188
Constant specific mass flow ............................... 189
Off-design performance of a stage ......................... 191
Free-vortex turbine stage ................................. 192
Actuator disc approach .................................... 194
Blade row interaction effects ............................. 198
Computer-aided methods of solving the through-flow
problem ................................................... 199
Application of Computational Fluid Dynamics (CFD) to
the design of axial turbomachines ......................... 201
Secondary flows ........................................... 202
References ................................................ 205
Problems .................................................. 205
7. Centrifugal Pumps, Fans and Compressors ................... 208
Introduction .............................................. 208
Some definitions .......................................... 209
Theoretical analysis of a centrifugal compressor .......... 211
Inlet casing .............................................. 212
Impeller .................................................. 212
Conservation of rothalpy .................................. 213
Diffuser .................................................. 214
Inlet velocity limitations ................................ 214
Optimum design of a pump inlet ............................ 215
Optimum design of a centrifugal compressor inlet .......... 217
Slip factor ............................................... 222
Head increase of a centrifugal pump ....................... 227
Performance of centrifugal compressors .................... 229
The diffuser system ....................................... 237
Choking in a compressor stage ............................. 240
References ................................................ 242
Problems .................................................. 243
8. Radial Flow Gas Turbines .................................. 246
Introduction .............................................. 246
Types of inward-flow radial turbine ....................... 247
Thermodynamics of the 90 deg IFR turbine .................. 249
Basic design of the rotor ................................. 251
Nominal design point efficiency ........................... 252
Much number relations ..................................... 256
Loss coefficients in 90 deg IFR turbines .................. 257
Optimum efficiency considerations ......................... 258
Criterion for minimum number of blades .................... 263
Design considerations for rotor exit ...................... 266
Incidence losses .......................................... 270
Significance and application of specific speed ............ 273
Optimum design selection of 90 deg IFR turbines ........... 276
Clearance and windage losses .............................. 278
Pressure ratio limits of the 90 deg IFR turbine ........... 279
Cooled 90 deg IFR turbines ................................ 280
A radial turbine for wave energy conversion ............... 282
References ................................................ 285
Problems .................................................. 287
9. Hydraulic Turbines ........................................ 290
Introduction .............................................. 290
Hydraulic turbines ........................................ 291
The Pelton turbine ........................................ 294
Reaction turbines ......................................... 303
The Francis turbine ....................................... 304
The Kaplan turbine ........................................ 310
Effect of size on turbomachine efficiency ................. 313
Cavitation ................................................ 315
Application of CFD to the design of hydraulic turbines .... 319
References ................................................ 320
Problems .................................................. 320
10. Wind Turbines ............................................. 323
Introduction .............................................. 323
Types of wind turbine ..................................... 325
Growth of wind power capacity and cost .................... 329
Outline of the theory ..................................... 330
Actuator disc approach .................................... 330
Estimating the power output ............................... 337
Power output range ........................................ 337
Blade element theory ...................................... 338
The blade element momentum method ......................... 346
Rotor configurations ...................................... 353
The power output at optimum conditions .................... 360
HAWT blade selection criteria ............................. 361
Developments in blade manufacture ......................... 363
Control methods (starting, modulating and stopping) ....... 364
Blade tip shapes .......................................... 369
Performance testing ....................................... 370
Performance prediction codes .............................. 370
Comparison of theory with experimental data ............... 371
Peak and post-peak power predictions ...................... 371
Environmental considerations .............................. 373
References ................................................ 374
Bibliography .................................................. 377
Appendix 1. Conversion of British and US Units to SI Units .... 378
Appendix 2. Answers to Problems ............................... 379
Index ......................................................... 383
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