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 |  موضوع: كتاب Fluid Mechanics and Thermodynamics of Turbomachinery الخميس 17 مارس 2022, 12:32 am | |
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Fluid Mechanics and Thermodynamics of Turbomachinery
Sixth Edition
S. L. Dixon, B. Eng., Ph.D.
Honorary Senior Fellow, Department of Engineering,
University of Liverpool, UK
C. A. Hall, Ph.D.
University Lecturer in Turbomachinery,
University of Cambridge, UK
و المحتوى كما يلي :
Contents
Preface to the Sixth Edition xi
Acknowledgments . xiii
List of Symbols . xv
CHAPTER 1 Introduction: Basic Principles . 1
1.1 Definition of a Turbomachine 1
1.2 Coordinate System . 2
1.3 The Fundamental Laws . 4
1.4 The Equation of Continuity . 5
1.5 The First Law of Thermodynamics . 5
1.6 The Momentum Equation 7
1.7 The Second Law of Thermodynamics—Entropy . 9
1.8 Bernoulli’s Equation . 11
1.9 Compressible Flow Relations . 12
1.10 Definitions of Efficiency . 15
1.11 Small Stage or Polytropic Efficiency . 18
1.12 The Inherent Unsteadiness of the Flow within Turbomachines . 24
References 26
Problems 26
CHAPTER 2 Dimensional Analysis: Similitude . 29
2.1 Dimensional Analysis and Performance Laws . 29
2.2 Incompressible Fluid Analysis 30
2.3 Performance Characteristics for Low Speed Machines 32
2.4 Compressible Fluid Analysis 33
2.5 Performance Characteristics for High Speed Machines . 37
2.6 Specific Speed and Specific Diameter 40
2.7 Cavitation . 47
References 49
Problems 50
CHAPTER 3 Two-Dimensional Cascades 53
3.1 Introduction 53
3.2 Cascade Geometry . 56
3.3 Cascade Flow Characteristics . 59
3.4 Analysis of Cascade Forces . 64
3.5 Compressor Cascade Performance . 68
v3.6 Turbine Cascades . 78
References 92
Problems 94
CHAPTER 4 Axial-Flow Turbines: Mean-Line Analysis and Design 97
4.1 Introduction 97
4.2 Velocity Diagrams of the Axial-Turbine Stage 99
4.3 Turbine Stage Design Parameters 100
4.4 Thermodynamics of the Axial-Turbine Stage 101
4.5 Repeating Stage Turbines 103
4.6 Stage Losses and Efficiency . 105
4.7 Preliminary Axial Turbine Design . 107
4.8 Styles of Turbine 109
4.9 Effect of Reaction on Efficiency . 113
4.10 Diffusion within Blade Rows . 115
4.11 The Efficiency Correlation of Smith (1965) 118
4.12 Design Point Efficiency of a Turbine Stage 121
4.13 Stresses in Turbine Rotor Blades 125
4.14 Turbine Blade Cooling 131
4.15 Turbine Flow Characteristics 133
References 136
Problems . 137
CHAPTER 5 Axial-Flow Compressors and Ducted Fans . 143
5.1 Introduction . 143
5.2 Mean-Line Analysis of the Compressor Stage . 144
5.3 Velocity Diagrams of the Compressor Stage . 146
5.4 Thermodynamics of the Compressor Stage . 147
5.5 Stage Loss Relationships and Efficiency . 148
5.6 Mean-Line Calculation Through a Compressor Rotor . 149
5.7 Preliminary Compressor Stage Design . 153
5.8 Simplified Off-Design Performance . 157
5.9 Multi-Stage Compressor Performance 159
5.10 High Mach Number Compressor Stages . 165
5.11 Stall and Surge Phenomena in Compressors 166
5.12 Low Speed Ducted Fans 172
5.13 Blade Element Theory . 174
5.14 Blade Element Efficiency 176
5.15 Lift Coefficient of a Fan Aerofoil . 176
References 177
Problems . 179
vi ContentsCHAPTER 6 Three-Dimensional Flows in Axial Turbomachines 183
6.1 Introduction . 183
6.2 Theory of Radial Equilibrium . 183
6.3 The Indirect Problem 185
6.4 The Direct Problem 193
6.5 Compressible Flow Through a Fixed Blade Row . 194
6.6 Constant Specific Mass Flow . 195
6.7 Off-Design Performance of a Stage . 197
6.8 Free-Vortex Turbine Stage . 198
6.9 Actuator Disc Approach 200
6.10 Computer-Aided Methods of Solving the Through-Flow Problem . 206
6.11 Application of Computational Fluid Dynamics to the Design of
Axial Turbomachines 209
6.12 Secondary Flows 210
References 212
Problems . 213
CHAPTER 7 Centrifugal Pumps, Fans, and Compressors . 217
7.1 Introduction . 217
7.2 Some Definitions 220
7.3 Thermodynamic Analysis of a Centrifugal Compressor . 221
7.4 Diffuser Performance Parameters 225
7.5 Inlet Velocity Limitations at the Eye . 229
7.6 Optimum Design of a Pump Inlet . 230
7.7 Optimum Design of a Centrifugal Compressor Inlet . 232
7.8 Slip Factor 236
7.9 Head Increase of a Centrifugal Pump . 242
7.10 Performance of Centrifugal Compressors 244
7.11 The Diffuser System . 251
7.12 Choking In a Compressor Stage 256
References 258
Problems . 259
CHAPTER 8 Radial Flow Gas Turbines . 265
8.1 Introduction . 265
8.2 Types of Inward-Flow Radial Turbine . 266
8.3 Thermodynamics of the 90° IFR Turbine . 268
8.4 Basic Design of the Rotor 270
8.5 Nominal Design Point Efficiency 272
8.6 Mach Number Relations 276
8.7 Loss Coefficients in 90° IFR Turbines . 276
Contents vii8.8 Optimum Efficiency Considerations . 278
8.9 Criterion for Minimum Number of Blades 283
8.10 Design Considerations for Rotor Exit 286
8.11 Significance and Application of Specific Speed . 291
8.12 Optimum Design Selection of 90° IFR Turbines 294
8.13 Clearance and Windage Losses . 296
8.14 Cooled 90° IFR Turbines . 297
References 298
Problems . 299
CHAPTER 9 Hydraulic Turbines . 303
9.1 Introduction . 303
9.2 Hydraulic Turbines . 305
9.3 The Pelton Turbine . 308
9.4 Reaction Turbines 317
9.5 The Francis Turbine . 317
9.6 The Kaplan Turbine 324
9.7 Effect of Size on Turbomachine Efficiency . 328
9.8 Cavitation . 330
9.9 Application of CFD to the Design of Hydraulic Turbines 334
9.10 The Wells Turbine 334
9.11 Tidal Power 346
References 349
Problems . 350
CHAPTER 10 Wind Turbines . 357
10.1 Introduction . 357
10.2 Types of Wind Turbine . 360
10.3 Outline of the Theory . 364
10.4 Actuator Disc Approach 364
10.5 Estimating the Power Output 372
10.6 Power Output Range . 372
10.7 Blade Element Theory . 373
10.8 The Blade Element Momentum Method . 381
10.9 Rotor Configurations . 389
10.10 The Power Output at Optimum Conditions . 397
10.11 HAWT Blade Section Criteria 398
10.12 Developments in Blade Manufacture . 399
10.13 Control Methods (Starting, Modulating, and Stopping) . 400
10.14 Blade Tip Shapes . 405
10.15 Performance Testing . 406
viii Contents10.16 Performance Prediction Codes 406
10.17 Environmental Considerations 408
References 411
Problems . 413
Appendix A: Preliminary Design of an Axial Flow Turbine for a Large Turbocharger . 415
Appendix B: Preliminary Design of a Centrifugal Compressor for a Turbocharger 425
Appendix C: Tables for the Compressible Flow of a Perfect Gas . 433
Appendix D: Conversion of British and American Units to SI Units 445
Appendix E: Answers to Problems . 447
Index
Index
A
Actuator disc, 364–365
alternative proof of betz’s result, 366–367
approach, 200–206
axial flow induction factor for, 367, 370–371
axial force coefficient, 368–370
blade row interaction effects, 204–206
and boundary stream tube model, 365
concept, 201–203
estimating power output, 372
mean-value rule, 203
power coefficient, 367
and radial equilibrium, 203
settling-rate rule, 203–204
theory for compressible flow, 206
theory of, 365–366, 378–379
Aerofoils, 57–58, 59, 109
theory, 172
vortex system of, 373–374
zero lift line, 176–177
Aileron control system, 402–405
Ainley and Mathieson correlation, 81–83
Annulus wall boundary layers, 161–164
Axial flow induction factor for actuator
disc, 367, 370–371
Axial flow turbomachine, 1, 2
Axial velocity density ratio (AVDR), 60
Axial-flow compressors, 143–144
blade aspect ratio, 156–157
and blading arrays, 145
casing treatment, 169–171
control of flow instabilities, 171–172
design of, 144
flow coefficient, 154–155
flow within, 144
mean-line analysis, 144–146
Mollier diagram for stage, 147
multi-stage, 159–165
off-design performance, 157–159
reaction, 155–156
stage loading, 153–154
stage loss relationships and efficiency,
148–149
stall and surge in, 166–172
thermodynamics, 147
three-dimensional flow effects,
160–161
velocity diagrams for stage, 146
Axial-flow turbines, 97–98, 415
blade and flow angle, 422
blade aspect ratio, 420
design of, 100–101, 107–109, 415
efficiency, determining, 417–418
ellipse law, 133, 134
estimating pitch/chord ratio, 421–422
fifty percent reaction stage, 110–113
flow characteristics, 133–136
flow coefficient, 100–101, 104, 121
mean line analysis, 97–98
mean radius design, 417–418
mean radius velocity triangles, determining,
417–418
mechanical arrangement, 416
Mollier diagram of, 103, 110, 111
with multiple stages, 103, 134–136
normal stage, 103
number of stages, 107–108
pitchline analysis, 97–98
reaction effect on efficiency, 114
repeating stage, 103–105
root and tip radii, determining, 418–419
stage loading coefficient, 101,
104, 121
stage losses and efficiency, 105–107
stage reaction, 101, 104
thermal efficiency vs. inlet gas
temperature, 133
thermodynamics of stage, 101–102
turbofan jet engine, 99
variation of reaction at hub, 419–420
451Axial-flow turbines (Cont.)
velocity diagrams of stage, 99–100, 110,
111, 125, 135
zero reaction stage, 109–110, 123, 124
B
Bernoulli’s equation, 11–12
Blade element momentum (BEM) method, 364,
381
parameter variation, 381–383
torque and axial force, evaluating, 383–385
Blade element theory, 174–175, 373–381, 406–
407
and actuator disc theory, 378–379
forces acting on, 376–377
tangential flow induction factor, 374–376
Blade row method, 106
Blade tip correction
performance calculations with, 388–389
Prandtl’s method, 385–387
Blades
aspect ratio, 156–157
cavitation coefficient, 230
centrifugal stresses in rotor, 126–131
cooling systems, 131–132
criterion for minimum number of, 283–285
developments in manufacture, 399–400
diffusion in, 115–118
element efficiency, 176
height and mean radius, 108–109
inlet Mach number, 74–78
loading of, 68–72
pitch control, 400–401
planform, 389–390
row interaction effects, 204–206
section criteria, 398–399
surface velocity distributions, 63–64
tip shapes, 405–406
turbine, 58
C
Camber line, 56–58
Cantilever IFR turbine, 266–267
Cascades, two-dimensional, 53
camber angle, 57
circulation and lift, 67
contraction coefficient, 54
drag coefficient, 66–67
drag forces, 65–66
energy loss coefficient, 62
flow characteristics, 59–64
forces, analysis, 64–67
geometry, 56–58
hub–tip radius ratios, 55–56
incidence effects, 74, 75
lift coefficient, 66–67
lift forces, 65–66
performance parameters, 61–63
pressure rise coefficient, 62
profile loss coefficient, 81
profile thickness distribution, 56–57
space–chord ratio, 55–56, 72
stagger angle, 57
stagnation pressure loss coefficient, 61
streamtube thickness variation, 59–60
total pressure loss coefficient, 61
turbine loss correlations, 80
wind tunnels, 53, 54
Cavitation, 47–49
avoiding, 334
in hydraulic turbines, 330–334
inception, 47–48
limits, 48–49
net positive suction head, 49
tensile stress in liquids, 48–49
vapour formation, 48
vapour pressure, 48–49
Centrifugal compressor, 2, 217, 218, 219
air mass flow, 425
applications of, 217
with backswept impeller vanes, 217–218,
246–249
blade Mach number of, 246, 248
choking of stage, 256–258
design requirements, 425
diffuser, 220, 223–225, 257
effect of prewhirl vanes, 235–236, 237
efficiency of impeller in, 427
452 Indexexit stagnation pressure, 431–432
impeller, 220, 222, 249–250, 257
impeller exit, design of, 427–428
impeller exit Mach number of, 248, 247
impeller inlet, design of, 425–427
impeller radius and blade speed, 425
inlet, 257
inlet, optimum design of, 232–236
inlet velocity limitations at eye, 229–230
kinetic energy at impeller, 249–250
mechanical arrangement, 416
Mollier diagram for, 223
overall efficiency, 431–432
performance of, 244–251
pressure ratio, 244–246
stage and velocity diagrams, 220
thermodynamic analysis of, 221–225
volute, 220, 251–252
Centrifugal pump
head increase of, 242–244
hydraulic efficiency of, 242
impellers, 240, 242
volute, 251–252
Centripetal turbine. See 90° Inward-flow radial
turbines
CFD. See Computational fluid dynamics
Coefficient
contraction, 54
drag, 66–67, 173–174, 377–378
energy loss, 62
enthalpy loss, 277
flow, 36, 100–101, 104, 121,
154–155, 340
lift, 66–67, 173–174, 176–177, 377–378
nozzle loss, 277
power, 367, 392
pressure rise, 62
profile loss, 81, 82
rotor loss, 277
stagnation pressure loss, 61, 63
total pressure loss, 61
Compressible flow
actuator disc theory for, 206
diffuser performance in, 225–226
equation, 430
through fixed blade row, 194–195
Compressible fluid analysis, 33–36
Compressible gas flow relations, 12–14
Compressible specific speed, 45–47
Compression process, 19–20
Compressor, 220. See also Centrifugal
compressor
blade profiles, 57–58
high speed, 37–38
Compressor cascade, 68–78
and blade notation, 56
choking of, 78
equivalent diffusion ratio, 70–71
Howell’s correlation, 72, 73
Lieblein’s correlation, 68, 69, 70–71
Mach number effect, 76, 77–78
Mollier diagrams for, 62
performance characteristics, 68–78
pitch–chord ratio, 69
velocity distribution, 69
wake momentum thickness ratio,
69–70, 71
wind tunnels, 54
Compressor stage, 186
high Mach number, 165–166
mean-line analysis, 144–146
off-design performance, 157–159,
197–198
reaction, 155–156
stage loading, 153–154
stage loss relationships and efficiency,
148–149
thermodynamics of, 147
velocity diagrams of, 146
Computational fluid dynamics (CFD), 107
application in axial turbomachines, 209–210
application in hydraulic turbines
design, 334
methods, 53
Conical diffuser, 224, 254–255, 256
Constant specific mass flow, 195–197
Contraction coefficient, 54
Cordier diagram, 44–45
Index 453Correlation
Ainley and Mathieson, 81–83
Howell, 72, 73
Lieblein, 68, 69, 70–71
Soderberg, 83–85, 113
D
Darcy’s equation, 313
Darrieus turbine, 361
Deflection of fluid, 72–74
nominal, 72
Design problem. See Indirect problem
Deviation of fluid, 72–74
Diffuser, 220, 223–225, 251–256
conical, 224, 254–255, 256
design calculation, 254–256
efficiency, 225, 226, 229
performance parameters, 225–229
radial, 253, 254, 255
two-dimensional, 224, 225
vaned, 253–254
vaneless, 252–253
Diffusion factor (DF), 69
local, 68
Diffusion in turbine blades, 115–118
Dimensional analysis, 29–30
Direct problem, radial equilibrium
equation for, 193–194
Drag coefficient, 66–67, 173–174,
377–378
Drag forces, 65–66
Ducted fans, 172–174
E
Efficiency
compressors and pumps, 18
correlation, 118–121
design point, 121–124
diffuser, 225, 226, 229
hydraulic turbines, 17, 305–307, 321
isentropic, 15
mechanical, 15
nominal design point, 272–275
optimum, IFR turbine, 278–283
overall, 15
reaction effect on, 113–115
size effect on turbomachine, 328–330
small stage/polytropic, 18–24
steam and gas turbines, 16–17
turbine, 15, 105–107
turbine polytropic, 22–23
Energy loss coefficient, 62
Enthalpy loss coefficient, 277
Entropy, 9–11
Environmental considerations for
wind turbine, 408–411
acoustic emissions, 410
visual intrusion, 409–410
Equation of continuity, 5
Euler’s equation
pump, 8
turbine, 8, 321–322
work, 8–9
Exhaust energy factor, 292
F
Fans, 217, 220, 221
axial-flow, 172, 174
ducted, 172–174
lift coefficient of, 176–177
First law of thermodynamics, 5–7
Flow angle, 196
Flow coefficient, 36, 100–101, 104, 121,
154–155, 340
Flow velocities, 3–4
Fluid deviation, 72–74
Forced vortex design, 189–190
Forces
drag, 65–66
lift, 65–66
Francis turbine, 2, 265, 317–324
basic equations, 321–324
capacity of, 307–308
cavitation in, 330, 332
design point efficiency of, 306
hydraulic efficiency of, 321
runner of, 318–319
velocity triangles for, 320, 321
454 Indexvertical shaft, 318, 322
volute, 317–318
Free-vortex flow, 185–186, 194,
324–325, 325–326
Free-vortex turbine stage, 198–200
G
Gas properties, variation with temperature, 14
Gas turbines, cooling system for, 131
H
Horizontal axis wind turbine (HAWT),
361, 362–363
aerofoils for, 399, 400
blade section criteria, 398–399
energy storage, 364
tower height, 363–364
Howell’s correlation, 72, 73
HP turbine
nozzle guide vane cooling system, 132
rotor blade cooling system, 132
Hydraulic turbines, 265, 303. See also Francis
turbine; Kaplan turbine; Pelton turbine
application ranges of, 307
cavitation in, 330–334
design of, CFD application to, 334
flow regimes for maximum efficiency of,
305–307
history of, 305
operating ranges of, 306
radial-inflow, 305
Hydropower, 303
harnessed and harnessable potential of,
distribution of, 304
Hydropower plants, features of, 304, 305
I
IFR turbines. See Inward-flow radial turbines
Impellers
centrifugal compressor, 220, 222,
249–250, 257
centrifugal pump, 240, 242
efficiency, 427
exit, design of, 427–428
head correction factors for, 241
inlet, design of, 425–427
Mach number at exit, 247, 248
prewhirl vanes at, 235–236
stresses in, 246
total-to-total efficiency of, 249–250
Impulse blading, 81, 82
Impulse turbine stage, 111
Incompressible flow
diffuser performance in, 228–229
parallel-walled radial diffuser in, 253, 255
Incompressible fluid analysis, 30–32
Indirect problem, radial equilibrium equation
for, 185–193
compressor stage, 186
first power stage design, 190–193
forced vortex, 189–190
free-vortex flow, 185–186
whirl distribution, 190
Inequality of Clausius, 10
Inward-flow radial (IFR) turbines, 265, 415
90 degree type. See 90° Inward-flow radial
turbines
cantilever, 266–267
efficiency levels of, 287
optimum efficiency, 278–283
types of, 266–268
90° Inward-flow radial (IFR) turbines, 267–268
cooling of, 297
loss coefficients in, 276–277
Mollier diagram, 269
optimum design selection of, 294–296
optimum efficiency, 278–283
specific speed, significance and application,
291–293
specific speed function, 292
thermodynamics of, 268–270
Isentropic temperature ratio, 416
K
Kaplan turbine, 2, 305, 324–327
basic equations, 325–327
cavitation in, 332
design point efficiencies of, 306
Index 455Kaplan turbine (Cont.)
flow angles for, 328
hydraulic efficiency of, 321
runner of, 325
velocity diagrams of, 326
Kutta–Joukowski theorem, 67
L
Lieblein’s correlation, 68, 69, 70–71
Lift coefficient, 66–67, 173–174, 377–378
of fan aerofoil, 176–177
Lift forces, 65–66
Lifting surface, prescribed wake theory
(LSWT), 407
Ljungström steam turbine, 265, 266
Local diffusion factor, 68
Loss coefficients in 90° IFR turbines,
276–277
M
Mach number, 12, 196, 428, 429
blade, 244, 246
blade inlet, 74–78
compressor stage, 165–166
at impeller exit, 247, 248
radial flow gas turbines, 276
Manometric head, 242
Matrix through-flow method, 208
Mean radius velocity triangles, 417–418
Mean-value rule, 203
Mixed flow turbomachines, 1, 2
Mollier diagram
90° IFR turbine, 269
for axial compressor stage, 147
for axial turbine stage, 103
for centrifugal compressor stage, 223
compression process, 19–20
compressor blade cascade, 62
compressors and pumps, 18
for diffuser flow, 226
for fifty percent reaction turbine stage, 111
for impulse turbine stage, 111
reheat factor, 23, 24
steam and gas turbines, 16
turbine blade cascade, 62
for zero reaction turbine stage, 110
Momentum
equation, 7–9
moment of, 7–8
Multi-stage compressor, 159–165
annulus wall boundary layers, 161–164
off-design operation, 164–165
pressure ratio of, 159–160
Multi-stage turbines, 103
flow characteristics, 134–136
N
National Advisory Committee for Aeronautics
(NACA), 57–58
Net positive suction head (NPSH), 49, 230, 331
Newton’s second law of motion, 7
Nominal fluid deflection, 72
Nozzle loss coefficients, 277
NPSH. See Net positive suction head
O
Off-design performance of compressor,
157–159
Optimum design
of 90° IFR turbines, 280, 294–296
of centrifugal compressor inlet, 232–236
of pump inlet, 230–232
Optimum efficiency, IFR turbine, 278–283
Optimum space–chord ratio, 85
P
Peak and post-peak power predictions, 408
Pelton turbine, 2, 47, 305, 308–317
design point efficiencies of, 306
energy losses in, 314–316
hydraulic efficiency of, 321
hydroelectric scheme, 311, 312
jet impinging on bucket, 310
overall efficiency of, 315, 316
runner of, 309
six-jet vertical shaft, 310
sizing the penstock, 313
speed control of, 311–313
456 Indexsurge tank, 311
water hammer, 313
Performance prediction codes, wind turbine,
406–408
Power coefficient, 367, 392
at optimum conditions, 397
Prandtl’s tip correction factor, 385–387
Prescribed velocity distribution (PVD)
method, 57
Pressure loss coefficient
stagnation, 61, 63
total, 61
Pressure ratio of multi-stage compressor,
159–160
Pressure rise coefficient, 62, 229
Profile loss coefficient, 81
Pump, 220, 221. See also Centrifugal pump
inlet, optimum design of, 230–232
radial-flow, 221
R
Radial diffuser, 253, 254, 255
Radial equilibrium
direct problem, 193–194
equation, 183–185, 193
fluid element in, 184
indirect problem, 185–193
theory of, 183–185
Radial flow gas turbines, 265
basic design of rotor, 270–271
cantilever type, 266–267
clearance and windage losses, 296–297
cooling of, 297
criterion for number of vanes, 285, 286
Francis type, 265
IFR type. See Inward-flow radial turbines
incidence loss, 276–277
Ljungström steam type, 265, 266
mach number relations, 276
nominal design point efficiency, 272–275
nozzle loss coefficients, 277
optimum design selection, 294–296
optimum efficiency considerations, 278–283
rotor loss coefficients, 277
spouting velocity, 271
velocity triangles, 267, 268
Radial flow turbomachine, 1
Reaction, turbine stage, 101, 104
fifty percent, 110–113
zero value, 109–110, 123, 124
Reaction turbine, 317
Reheat factor, 23–24
Relative eddy, 238
Relative maximum power coefficient, 367
Relative velocity, 4, 9
Reynolds number correction, 83
Rotating stall in compressor, 167
Rothalpy, 9, 102
Rotor, 149–153
compressible case, 149–150
incompressible case, 150–153
Rotor blade configurations, 389–396
blade variation effect, 390
optimum design criteria, 393–396
planform, 389–390
tip–speed ratio effect, 390–393
Rotor design, 270–271, 286–290
nominal, 270–271
Whitfield, 280–283
Rotor loss coefficients, 277
S
Scroll. See Volute
SeaGen tidal turbine, 304, 348–349
Second law of thermodynamics, 9–11
Secondary flows, 210–211
vorticity, 210
Settling-rate rule, 203–204
Slip factor, 236–242
Busemann, 240–241
correlations, 238–242
Stanitz, 241
Stodola, 239
Wiesner, 241–242
Soderberg’s correlation, 83–85, 113
Solid-body rotation. See Forced vortex design
Space-chord ratio, 422
Specific diameter, 40–47
Index 457Specific speed, 40–47, 333
compressible, 45–47
efficiency for turbines, 293
significance and application of, 291–293
Spouting velocity, 271
Stage loading, 36, 101, 104, 121, 153–154
Stagger angle, 57
Stagnation enthalpy, 6, 12
Stagnation pressure loss coefficient, 61, 63
Stall and surge in compressor, 166–172
Steady flow
energy equation, 6–7
moment of momentum, 7–8
momentum equation, 7–9
Steam turbines, 97
low pressure, 98
Streamline curvature method, 207–208
Stresses in turbine rotor blades, 125–131
centrifugal, 126–131
Suction specific speed, 333
T
Tangential flow induction factor, 374–376
Tangential velocity distribution, 190
Thoma coefficient, 331, 333
Three-dimensional flows in axial turbomachines,
183–215
Through-flow problem
computer-aided methods of solving,
206–208
techniques for solving, 207–208
Tidal power, 304, 346–349. See also
SeaGen tidal turbine
categories of, 347
Tidal stream generators, 347–348
Tides
neap, 346, 347
spring, 346, 347
Time-marching method, 208
Tip–speed ratio, 379, 390–393
Total-to-static efficiency, 17, 272, 294–295
effect of reaction on, 113–115
of stage with axial velocity at exit,
123–124, 125
Total-to-total efficiency, 16
of fifty percent reaction turbine stage,
121–122
of impeller, 249–250
of turbine stage, 105
of zero reaction turbine stage, 123, 124
Turbine cascade (two-dimensional), 78–92
Ainley and Mathieson correlation, 81–83
Dunham and Came improvements, 81
flow exit angle, 88–91
flow outlet angles, 81, 82
limit load, 91–92
optimum space to chord ratio, 85, 86
Reynolds number correction, 83
Soderberg’s correlation, 83–85
turbine limit load, 91–92
turbine loss correlations, 80
Zweifel criterion, 85–88
Turbines
axial-flow. See Axial-flow turbines
Francis. See Francis turbine
free-vortex stage, 198–200
high speed, 38–40
hydraulic. See Hydraulic turbines
Kaplan. See Kaplan turbine
off-design performance of stage, 197–198
Pelton. See Pelton turbine
radial flow gas. See Radial flow gas turbines
reaction, 317
Wells. See Wells turbine
wind. See Wind turbine
Turbochargers, 415
advantages, 415
types, 415
Turbomachines
categories of, 1
as control volume, 7–8, 30
coordinate system, 2–4
definition of, 1–2
efficiency, size effect on, 328–330
flow unsteadiness, 24–25
performance characteristics of, 32–33
Turbomachines, axial
blade rows in, 204
458 Indexdesign of, 209–210
solving through-flow problem in, 206–208
Two-dimensional cascades. See Cascades,
two-dimensional
U
Unsteadiness paradox, 25
V
Vaned diffuser, 253–254, 430–431
Vaneless diffuser, 252–253
space, flow in, 428–430
Vapour pressure, 48–49
Velocity, spouting, 271
Velocity triangles for root, mean and tip radii,
421, 422
Vertical axis wind turbine (VAWT), 361
Volute, 431
centrifugal compressor, 220, 251–252
centrifugal pump, 251–252
Vorticity, secondary, 210
W
Wave power, 304. See also Wells turbine
Wells turbine, 304, 334–335, 336
blade of, velocity and force vectors acting
on, 337
blade solidity effect on, 340
characteristics under steady flow
conditions, 344
design and performance variables, 338–341
flow coefficient, effect on, 340
hub–tip ratio, effect on, 340
operating principles, 335–336
and oscillating water column, 334–335
self pitch-controlled blades, 341, 342–346
starting behaviour of, 341, 342
two-dimensional flow analysis, 336–338
Whirl distribution, 190
White noise, 48
Whitfield’s design of rotor, 280–283
Wind energy, availability, 357–359
Wind shear, 363–364
Wind turbine, 357, 410–411
blade section criteria, 398–399
control methods, 400–405
environmental considerations, 408–411
historical viewpoint, 359
performance testing, 406
power coefficient of, 367
power output, 372–373
Prandtl’s blade tip correction for, 385–387
rotor blade configuration, 389–396
solidity, 379–380
stall control, 401
types of, 360–364
Windmills, 359
Z
Zero lift line of aerofoil, 176–177
Zero reaction turbine stage, 109–110
Mollier diagram for, 110
total-to-total efficiency of, 123, 124
Zweifel criterion,
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