1 Working Principles ??????????????????????????????????????????????????????????????????????????????????? 1
1.1 Definition of a Turbomachine ???????????????????????????????????????????????????????????? 1
1.2 Examples of Axial Turbomachines ???????????????????????????????????????????????????? 2
1.2.1 Axial Hydraulic Turbine ????????????????????????????????????????????????????????? 2
1.2.2 Axial Pump ????????????????????????????????????????????????????????????????????????????? 4
1.3 Mean Line Analysis ???????????????????????????????????????????????????????????????????????????? 5
1.4 Basic Laws for Stationary Duct Parts ???????????????????????????????????????????????? 7
1.4.1 Conservation of Mass ????????????????????????????????????????????????????????????? 7
1.4.2 Conservation of Momentum ?????????????????????????????????????????????????? 7
1.4.3 Conservation of Energy ?????????????????????????????????????????????????????????? 9
1.4.4 Forms of Energy: Mechanical Energy and Head ??????????????????? 10
1.4.5 Energy Dissipation: Head Loss ?????????????????????????????????????????????? 12
1.5 Basic Laws for Rotating Duct Parts ??????????????????????????????????????????????????? 14
1.5.1 Work and Energy Equations in a Rotating Frame
with Constant Angular Velocity ????????????????????????????????????????????? 14
1.5.2 Moment of Momentum in the Absolute Frame: Rotor Work ??? 16
1.5.3 Moment of Momentum in the Relative Frame:
Forces Intervening in the Rotor Work ???????????????????????????????????? 21
1.5.4 Energy Component Changes Caused By the Rotor Work ?????? 23
1.5.5 Rotor Work in the Mean Line Representation of the Flow ???? 24
1.6 Energy Analysis of Turbomachines ??????????????????????????????????????????????????? 25
1.6.1 Mechanical Efficiency and Internal Efficiency ?????????????????????? 25
1.6.2 Energy Analysis of an Axial Hydraulic Turbine ???????????????????? 26
1.6.3 Energy Analysis of an Axial Pump ???????????????????????????????????????? 30
1.7 Examples of Radial Turbomachines ??????????????????????????????????????????????????? 33
1.8 Performance Characteristics ??????????????????????????????????????????????????????????????? 36
1.9 Exercises ???????????????????????????????????????????????????????????????????????????????????????????? 40
References ??????????????????????????????????????????????????????????????????????????????????????????????????? 46
2 Basic Components ????????????????????????????????????????????????????????????????????????????????????? 47
2.1 Aerofoils ????????????????????????????????????????????????????????????????????????????????????????????? 47
2.1.1 Force Generation ???????????????????????????????????????????????????????????????????? 47
2.1.2 Performance Parameters ???????????????????????????????????????????????????????? 49
xviii Contents
2.1.3 Pressure Distribution ?????????????????????????????????????????????????????????????? 51
2.1.4 Boundary Layer Separation ??????????????????????????????????????????????????? 52
2.1.5 Loss Mechanism Associated to Friction: Energy Dissipation 55
2.1.6 Profile Shapes ???????????????????????????????????????????????????????????????????????? 58
2.1.7 Blade Rows with Low Solidity ?????????????????????????????????????????????? 59
2.2 Linear Cascades ????????????????????????????????????????????????????????????????????????????????? 60
2.2.1 Relation with the Real Machine ????????????????????????????????????????????? 60
2.2.2 Cascade Geometry ????????????????????????????????????????????????????????????????? 61
2.2.3 Flow in Lossless Cascades: Force Components ???????????????????? 62
2.2.4 Significance of Circulation ???????????????????????????????????????????????????? 65
2.2.5 Flow in Lossless Cascades: Work ?????????????????????????????????????????? 67
2.2.6 Flow in Cascades with Loss: Force Components ?????????????????? 68
2.2.7 Flow in Cascades with Loss: Energy Dissipation
and Work by Drag Force ???????????????????????????????????????????????????????? 70
2.2.8 The Zweifel Tangential Force Coefficient ????????????????????????????? 72
2.2.9 The Lieblein Diffusion Factor ???????????????????????????????????????????????? 74
2.2.10 Performance Parameters of Axial Cascades ????????????????????????? 75
2.3 Channels ????????????????????????????????????????????????????????????????????????????????????????????? 75
2.3.1 Straight Channels ??????????????????????????????????????????????????????????????????? 75
2.3.2 Bends ?????????????????????????????????????????????????????????????????????????????????????? 77
2.4 Diffusers ????????????????????????????????????????????????????????????????????????????????????????????? 79
2.4.1 Dump Diffusers ?????????????????????????????????????????????????????????????????????? 79
2.4.2 Inlet Flow Distortion ?????????????????????????????????????????????????????????????? 79
2.4.3 Flow Separation ????????????????????????????????????????????????????????????????????? 81
2.4.4 Flow Improvement ????????????????????????????????????????????????????????????????? 81
2.4.5 Representation of Diffuser Performance ???????????????????????????????? 82
2.4.6 Equivalent Opening Angle ????????????????????????????????????????????????????? 84
2.4.7 Diffusion in a Bend ???????????????????????????????????????????????????????????????? 85
2.5 Exercises ???????????????????????????????????????????????????????????????????????????????????????????? 87
References ??????????????????????????????????????????????????????????????????????????????????????????????????? 95
3 Fans ???????????????????????????????????????????????????????????????????????????????????????????????????????????? 97
3.1 Fan Aplications and Fan Types ?????????????????????????????????????????????????????????? 97
3.1.1 Fan Applications ???????????????????????????????????????????????????????????????????? 97
3.1.2 Large Radial Fans ?????????????????????????????????????????????????????????????????? 98
3.1.3 Small Radial Fans ?????????????????????????????????????????????????????????????????? 99
3.1.4 Large Axial Fans ???????????????????????????????????????????????????????????????????? 99
3.1.5 Small Axial Fans ???????????????????????????????????????????????????????????????????? 100
3.1.6 Cross-Flow Fans ???????????????????????????????????????????????????????????????????? 100
3.2 Idealised Mean Line Analysis of a Radial Fan ??????????????????????????????????? 101
3.2.1 Idealised Flow Concept: Infinite Number of Blades ????????????? 101
3.2.2 Degree of Reaction ????????????????????????????????????????????????????????????????? 102
3.2.3 Relation Between Rotor Blade Shape and Performance
Parameters ?????????????????????????????????????????????????????????????????? 103
3.2.4 Performance Characteristics with Idealised Flow ?????????????????? 105
Contents xix
3.3 Radial Fan Analysis for Lossless Two-Dimensional Flow
with Finite Number of Rotor Blades ???????????????????????????????????????????????? 106
3.3.1 Relative Vortex in Blade Channels ??????????????????????????????????????? 106
3.3.2 Velocity Difference over a Rotating Blade ?????????????????????????? 107
3.3.3 Slip: Reduction of Rotor Work ????????????????????????????????????????????? 112
3.3.4 Number of Blades and Solidity: Pfleiderer Moment
Coefficient ???????????????????????????????????????????????????????????????????????????? 115
3.3.5 Number of Blades: Examples ?????????????????????????????????????????????? 118
3.4 Internal Losses with Radial Fans ????????????????????????????????????????????????????? 120
3.4.1 Turning Loss at Rotor Entrance ??????????????????????????????????????????? 120
3.4.2 Incidence Loss at Rotor Entrance ???????????????????????????????????????? 120
3.4.3 Displacement by Blade Thickness ??????????????????????????????????????? 122
3.4.4 Rotor Friction Loss and Rotor Diffusion Loss ????????????????????? 123
3.4.5 Dump Diffusion Loss at Volute Entrance ???????????????????????????? 123
3.4.6 Incidence Loss at Volute Entrance ??????????????????????????????????????? 125
3.4.7 Friction Loss Within the Volute ??????????????????????????????????????????? 126
3.4.8 Diffusion at the Rotor Inlet ?????????????????????????????????????????????????? 126
3.4.9 Flow separation at Rotor Inlet and Rotor Outlet ?????????????????? 127
3.4.10 Applicability of the Loss Models ??????????????????????????????????????? 129
3.4.11 Optimisation of the Rotor Inlet of a Centrifugal Fan ????????? 129
3.4.12 Characteristics Taking Losses into Account ??????????????????????? 131
3.5 Overall Performance Evaluation ?????????????????????????????????????????????????????? 134
3.5.1 Mechanical Loss ?????????????????????????????????????????????????????????????????? 134
3.5.2 Leakage Loss ???????????????????????????????????????????????????????????????????????? 135
3.5.3 Overall Efficiency with Power Receiving Machines ??????????? 135
3.5.4 Overall Efficiency with Power Delivering Machines ?????????? 136
3.6 Rotor Shape Choices with Radial Fans ???????????????????????????????????????????? 136
3.7 Axial and Mixed-Flow Fans ????????????????????????????????????????????????????????????? 140
3.7.1 Degree of Reaction with Axial Fans ???????????????????????????????????? 140
3.7.2 Free Vortex and Non-Free Vortex Types ?????????????????????????????? 141
3.7.3 Axial Fan Characteristics; Adjustable Rotor Blades ???????????? 143
3.7.4 Mixed-Flow Fans ????????????????????????????????????????????????????????????????? 144
3.8 Exercises ?????????????????????????????????????????????????????????????????????????????????????????? 146
3.8.1 Centrifugal Pump (Idealised Flow) ?????????????????????????????????????? 146
3.8.2 Rotor of a Centrifugal Fan (Finite Number of Blades
and Internal Losses) ????????????????????????????????????????????????????????????? 146
3.8.3 Number of Blades of a Rotor of a Centrifugal Fan ?????????????? 147
3.8.4 Volute of a Centrifugal Fan ?????????????????????????????????????????????????? 147
3.8.5 Leakage Flow Rate with Centrifugal Fan ???????????????????????????? 147
3.8.6 Centrifugal Pump (Finite Number of Blades and
Internal Losses) ???????????????????????????????????????????????????????????????????? 148
3.8.7 Axial Fan (Idealised Flow): Analysis on Average
Diameter ??????????????????????????????????????????????????????????????????????????????? 148
3.8.8 Axial Fan (Idealised Flow): Free Vortex and Non-
Free Vortex ??????????????????????????????????????????????????????????????????????????? 149
xx Contents
3.8.9 Inlet Guide Vane with a Centrifugal Fan ?????????????????????????????? 149
3.8.10 Change of Rotational Speed with Centrifugal and
Axial Fans ???????????????????????????????????????????????????????????????????????????? 149
3.8.11 Two-Stage Axial Fan ???????????????????????????????????????????????????????????? 150
3.8.12 Axial Turbine ???????????????????????????????????????????????????????????????????????? 151
References ????????????????????????????????????????????????????????????????????????????????????????????????? 151
4 Compressible Fluids ???????????????????????????????????????????????????????????????????????????????? 153
4.1 Basic Laws ??????????????????????????????????????????????????????????????????????????????????????? 153
4.2 Compressibility and Velocity of Sound ???????????????????????????????????????????? 156
4.3 Compressibility Effect on the Velocity-Pressure Relation ??????????????? 158
4.4 Shape of a Nozzle ????????????????????????????????????????????????????????????????????????????? 160
4.5 Nozzle with Initial Velocity ????????????????????????????????????????????????????????????? 162
4.6 Nozzle with Losses: Infinitesimal Efficiency ?????????????????????????????????? 163
4.7 Isentropic and Polytropic Efficiencies ????????????????????????????????????????????? 167
4.8 Exercises ?????????????????????????????????????????????????????????????????????????????????????????? 171
References ????????????????????????????????????????????????????????????????????????????????????????????????? 174
5 Performance Measurement ???????????????????????????????????????????????????????????????????? 175
5.1 Pressure Measurement ????????????????????????????????????????????????????????????????????? 175
5.1.1 The Metal Manometer ?????????????????????????????????????????????????????????? 175
5.1.2 The Pressure Transducer ?????????????????????????????????????????????????????? 175
5.1.3 The Digital Manometer ???????????????????????????????????????????????????????? 176
5.1.4 Calibration of Pressure Meters ????????????????????????????????????????????? 177
5.2 Temperature Measurement ??????????????????????????????????????????????????????????????? 177
5.2.1 The Glass Thermometer ??????????????????????????????????????????????????????? 177
5.2.2 The Temperature Transducer ???????????????????????????????????????????????? 177
5.2.3 The Digital Thermometer ????????????????????????????????????????????????????? 178
5.3 Flow Rate Measurement ?????????????????????????????????????????????????????????????????? 178
5.3.1 Reservoir ?????????????????????????????????????????????????????????????????????????????? 178
5.3.2 Flow Over a Weir ????????????????????????????????????????????????????????????????? 178
5.3.3 Pressure Drop Devices ????????????????????????????????????????????????????????? 179
5.3.4 Industrial Mass Flow Rate Meters ??????????????????????????????????????? 180
5.3.5 Positioning of Flow Rate Meters in Ducts ??????????????????????????? 180
5.4 Torque Measurement ???????????????????????????????????????????????????????????????????????? 181
5.4.1 Swinging Suspended Motor or Brake ?????????????????????????????????? 181
5.4.2 Calibrated Motor ?????????????????????????????????????????????????????????????????? 181
5.4.3 The Torque Transducer ????????????????????????????????????????????????????????? 181
5.5 Rotational Speed Measurement ???????????????????????????????????????????????????????? 182
5.5.1 Pulse Counters ?????????????????????????????????????????????????????????????????????? 182
5.5.2 The Speed Transducer ?????????????????????????????????????????????????????????? 182
5.5.3 Electric Tachometer ?????????????????????????????????????????????????????????????? 182
5.6 Laboratory Test of a Pelton Turbine ????????????????????????????????????????????????? 182
5.6.1 Test Rig ???????????????????????????????????????????????????????????????????????????????? 182
5.6.2 Measurements ?????????????????????????????????????????????????????????????????????? 183
Contents xxi
5.6.3 Measurement Procedure ??????????????????????????????????????????????????????? 183
5.6.4 Calculations ?????????????????????????????????????????????????????????????????????????? 184
5.6.5 Measurement Example ????????????????????????????????????????????????????????? 184
5.7 Laboratory Test of a Centrifugal Fan ??????????????????????????????????????????????? 184
5.7.1 Test Rig ???????????????????????????????????????????????????????????????????????????????? 184
5.7.2 Measurements ?????????????????????????????????????????????????????????????????????? 187
5.7.3 Measurement Procedure ??????????????????????????????????????????????????????? 187
5.7.4 Calculations ?????????????????????????????????????????????????????????????????????????? 188
5.7.5 Measurement Example ????????????????????????????????????????????????????????? 188
5.8 Laboratory Test of a Centrifugal Pump ???????????????????????????????????????????? 189
5.8.1 Test Rig ???????????????????????????????????????????????????????????????????????????????? 189
5.8.2 Measurements ?????????????????????????????????????????????????????????????????????? 190
5.8.3 Measurement Procedure ??????????????????????????????????????????????????????? 190
5.8.4 Calculations ?????????????????????????????????????????????????????????????????????????? 191
5.8.5 Measurement Example ????????????????????????????????????????????????????????? 192
6 Steam Turbines ???????????????????????????????????????????????????????????????????????????????????????? 193
6.1 Applications of Steam Turbines ??????????????????????????????????????????????????????? 193
6.2 Working Principles of Steam Turbines ????????????????????????????????????????????? 195
6.3 The Steam Cycle ?????????????????????????????????????????????????????????????????????????????? 199
6.4 The Single Impulse Stage or Laval Stage ???????????????????????????????????????? 200
6.4.1 Velocity Triangles ????????????????????????????????????????????????????????????????? 200
6.4.2 Work and Energy Relations ?????????????????????????????????????????????????? 201
6.4.3 Stage Efficiency Definitions ???????????????????????????????????????????????? 204
6.4.4 Blade Profile Shape ?????????????????????????????????????????????????????????????? 205
6.4.5 Loss Representation ????????????????????????????????????????????????????????????? 208
6.4.6 Optimisation of Total-to-Static Efficiency ??????????????????????????? 209
6.5 The Pressure-Compounded Impulse Turbine
or Rateau Turbine ????????????????????????????????????????????????????????????????????????????? 212
6.5.1 Principle ??????????????????????????????????????????????????????????????????????????????? 212
6.5.2 Efficiency ????????????????????????????????????????????????????????????????????????????? 213
6.6 The Velocity-Compounded Impulse Turbine or Curtis Turbine ??????? 214
6.7 The Reaction Turbine ??????????????????????????????????????????????????????????????????????? 217
6.7.1 Degree of Reaction ??????????????????????????????????????????????????????????????? 217
6.7.2 Efficiency ????????????????????????????????????????????????????????????????????????????? 218
6.7.3 Axial Inlet and Outlet ??????????????????????????????????????????????????????????? 222
6.8 Steam Turbine Construction Forms ????????????????????????????????????????????????? 224
6.8.1 Large Steam Turbines for Power Stations ???????????????????????????? 224
6.8.2 Industrial Steam Turbines ???????????????????????????????????????????????????? 229
6.9 Blade Shaping ?????????????????????????????????????????????????????????????????????????????????? 231
6.9.1 HP and IP Blades ?????????????????????????????????????????????????????????????????? 231
6.9.2 LP Blades ????????????????????????????????????????????????????????????????????????????? 233
6.10 Exercises ???????????????????????????????????????????????????????????????????????????????????????? 236
References ????????????????????????????????????????????????????????????????????????????????????????????????? 246
xxii Contents
7 Dynamic Similitude ????????????????????????????????????????????????????????????????????????????????? 247
7.1 Principles of Dynamic Similitude ???????????????????????????????????????????????????? 247
7.1.1 Definition of Dynamic Similitude ???????????????????????????????????????? 247
7.1.2 Dimensionless Parameter Groups ???????????????????????????????????????? 248
7.1.3 Similitude Conditions ?????????????????????????????????????????????????????????? 248
7.1.4 Purpose of Similitude Analysis ???????????????????????????????????????????? 250
7.1.5 Dimensional Analysis ?????????????????????????????????????????????????????????? 251
7.1.6 Independent and Dependent Parameter Groups ??????????????????? 252
7.1.7 Dimensionless Parameter Groups in Turbomachines
with a Constant Density Fluid ?????????????????????????????????????????????? 252
7.1.8 Strong and Weak Similitude Conditions ?????????????????????????????? 254
7.2 Characteristic Numbers of Turbomachines ?????????????????????????????????????? 254
7.2.1 Definition of a Characteristic Number ????????????????????????????????? 254
7.2.2 Specific Speed and Specific Diameter ????????????????????????????????? 255
7.2.3 Relation Between Characteristic Numbers
and Machine Shape ?????????????????????????????????????????????????????????????? 257
7.2.4 Design Diagrams ?????????????????????????????????????????????????????????????????? 259
7.2.5 Shape of Characteristic Curves ???????????????????????????????????????????? 261
7.2.6 Power Specific Speed ??????????????????????????????????????????????????????????? 262
7.3 Application Example of Similitude: Variable Rotational
Speed with a Pump ??????????????????????????????????????????????????????????????????????????? 263
7.4 Imperfect Similitude ????????????????????????????????????????????????????????????????????????? 266
7.4.1 Effect of Reynolds Number with the Same Fluid ???????????????? 266
7.4.2 Effect of Relative Roughness ??????????????????????????????????????????????? 267
7.4.3 Effect of Viscosity ???????????????????????????????????????????????????????????????? 268
7.4.4 Rotor Diameter Reduction: Impeller Trimming ??????????????????? 270
7.4.5 Reduced Scale Models ????????????????????????????????????????????????????????? 271
7.5 Series and Parallel Connection ????????????????????????????????????????????????????????? 272
7.5.1 Parallel Connection of Fans ????????????????????????????????????????????????? 272
7.5.2 Parallel Connection of Pumps ?????????????????????????????????????????????? 273
7.5.3 Series Connection of Fans ???????????????????????????????????????????????????? 274
7.6 Turbomachine Design Example: Centrifugal Fan ???????????????????????????? 276
7.7 Exercises ?????????????????????????????????????????????????????????????????????????????????????????? 279
References ????????????????????????????????????????????????????????????????????????????????????????????????? 282
8 Pumps ??????????????????????????????????????????????????????????????????????????????????????????????????????? 283
8.1 Cavitation ????????????????????????????????????????????????????????????????????????????????????????? 283
8.1.1 Cavitation Phenomenon and Cavitation Consequences ??????? 283
8.1.2 Types of Cavitation ?????????????????????????????????????????????????????????????? 284
8.1.3 Cavitation Assessment: Cavitation Number and
Required Net Positive Suction Height ????????????????????????????????? 286
8.1.4 Optimisation of the Inlet of a Centrifugal Pump Rotor ??????? 289
8.1.5 Net Positive Suction Head of the Installation ?????????????????????? 291
8.1.6 Increasing the Acceptable Suction Height ??????????????????????????? 292
Contents xxiii
8.2 Priming of Pumps: Self-Priming Types ??????????????????????????????????????????? 293
8.2.1 Side Channel Pump ?????????????????????????????????????????????????????????????? 293
8.2.2 Peripheral Pump (regenerative pump) ????????????????????????????????? 295
8.2.3 Self-Priming Centrifugal Pump ??????????????????????????????????????????? 296
8.2.4 Jet Pump ??????????????????????????????????????????????????????????????????????????????? 297
8.3 Unstable Operation ??????????????????????????????????????????????????????????????????????????? 297
8.4 Component Shaping ????????????????????????????????????????????????????????????????????????? 299
8.4.1 Simply and Doubly Curved Blades in Radial Rotors ?????????? 299
8.4.2 Mixed-Flow and Axial Pumps ????????????????????????????????????????????? 300
8.4.3 Pump Inlet ???????????????????????????????????????????????????????????????????????????? 300
8.4.4 Pump Outlet ????????????????????????????????????????????????????????????????????????? 301
8.4.5 Vaneless Diffuser Rings ??????????????????????????????????????????????????????? 301
8.4.6 Vaned Diffuser Rings ??????????????????????????????????????????????????????????? 302
8.4.7 Volute ??????????????????????????????????????????????????????????????????????????????????? 303
8.4.8 Return Channels ??????????????????????????????????????????????????????????????????? 305
8.5 Internal Parallel and Series Connection Of Rotors ?????????????????????????? 305
8.5.1 Reason for Internal Parallel or Series Connection ??????????????? 305
8.5.2 Internal Parallel Connection of Rotors ????????????????????????????????? 306
8.5.3 Internal Series Connection of Rotors: Multistage Pumps ???? 306
8.6 Constructional Aspects ????????????????????????????????????????????????????????????????????? 307
8.6.1 Rotor ????????????????????????????????????????????????????????????????????????????????????? 307
8.6.2 Stator ???????????????????????????????????????????????????????????????????????????????????? 307
8.6.3 Shaft Sealing ???????????????????????????????????????????????????????????????????????? 307
8.6.4 Bearings ??????????????????????????????????????????????????????????????????????????????? 309
8.6.5 Axial Force Balancing with Single-Stage Pumps ???????????????? 309
8.6.6 Axial Force Balancing with Multistage Pumps ???????????????????? 310
8.6.7 Wear Rings ??????????????????????????????????????????????????????????????????????????? 311
8.7 Special Pumps ?????????????????????????????????????????????????????????????????????????????????? 311
8.7.1 Borehole Pumps ??????????????????????????????????????????????????????????????????? 312
8.7.2 High-Pressure Pumps ??????????????????????????????????????????????????????????? 312
8.7.3 Sealless Pumps: Circulation Pumps, Chemical Pumps ???????? 312
8.7.4 Slurry Pumps ???????????????????????????????????????????????????????????????????????? 313
8.7.5 Pumping of Solid Materials ????????????????????????????????????????????????? 314
8.7.6 Vertical Submerged Pumps ?????????????????????????????????????????????????? 314
8.7.7 Partial Emission Pumps ??????????????????????????????????????????????????????? 315
8.7.8 Pumps for Viscous Fluids ????????????????????????????????????????????????????? 315
8.8 Exercises ?????????????????????????????????????????????????????????????????????????????????????????? 316
8.8.1 Looking up Pump Characteristics ???????????????????????????????????????? 316
8.8.2 Verification of an NPSH-Value ???????????????????????????????????????????? 316
References ????????????????????????????????????????????????????????????????????????????????????????????????? 317
9 Hydraulic Turbines ????????????????????????????????????????????????????????????????????????????????? 319
9.1 Hydraulic Energy ????????????????????????????????????????????????????????????????????????????? 319
9.2 Hydraulic Turbine Types ?????????????????????????????????????????????????????????????????? 320
9.2.1 Large Turbines (> 10 MW) ??????????????????????????????????????????????????? 320
9.2.2 Small Turbines (< 10 MW) ??????????????????????????????????????????????????? 322
xxiv Contents
9.3 Pelton Turbines: Impulse Turbines ?????????????????????????????????????????????????? 324
9.3.1 Performance Characteristics ???????????????????????????????????????????????? 324
9.3.2 Specific Speed ?????????????????????????????????????????????????????????????????????? 326
9.3.3 Determination of the Main Dimensions ??????????????????????????????? 328
9.3.4 Flow Rate Control and Over-Speed Protection ???????????????????? 328
9.4 Francis and Kaplan Turbines: Reaction Turbines ???????????????????????????? 329
9.4.1 Shape of the Velocity Triangles: Kinematic Parameters ?????? 329
9.4.2 Optimisation of the Velocity Triangles ???????????????????????????????? 330
9.4.3 Degree of Reaction and Speed Ratio ??????????????????????????????????? 331
9.4.4 Velocity Triangles with Varying Degree of Reaction ??????????? 332
9.4.5 Specific Speed and Meridional Shape of Francis Turbines ? 333
9.4.6 Flow Rate Control with Reaction Turbines ?????????????????????????? 335
9.4.7 Examples (Figs. 9.16, 9.17) ????????????????????????????????????????????????? 337
9.5 Bulb and Tube Turbines ??????????????????????????????????????????????????????????????????? 338
9.6 Reversible Pump-Turbines ??????????????????????????????????????????????????????????????? 340
9.7 Exercises ?????????????????????????????????????????????????????????????????????????????????????????? 342
References ????????????????????????????????????????????????????????????????????????????????????????????????? 345
10 Wind Turbines ????????????????????????????????????????????????????????????????????????????????????????? 347
10.1 Wind Energy ??????????????????????????????????????????????????????????????????????????????????? 347
10.2 Types of Wind Energy Conversion Systems ?????????????????????????????????? 348
10.2.1 Drag Machines ????????????????????????????????????????????????????????????????? 348
10.2.2 High-Speed Horizontal-Axis Turbines ????????????????????????????? 349
10.2.3 Technical Aspects of Horizontal-Axis Wind
Turbines for Electricity Generation ?????????????????????????????????? 351
10.2.4 Low-Speed Horizontal-Axis Wind Turbines ???????????????????? 355
10.2.5 Vertical-Axis Wind Turbines ???????????????????????????????????????????? 356
10.3 Wind Turbine Performance Analysis ????????????????????????????????????????????? 358
10.3.1 Momentum Analysis (Single Streamtube Analysis) ???????? 358
10.3.2 Multiple Streamtube Analysis ?????????????????????????????????????????? 361
10.3.3 Blade Element Analysis ??????????????????????????????????????????????????? 363
10.4 Adaptation to a Wind Regime ???????????????????????????????????????????????????????? 365
References ????????????????????????????????????????????????????????????????????????????????????????????????? 368
11 Power Gas Turbines ?????????????????????????????????????????????????????????????????????????????? 369
11.1 General Concept and Components ????????????????????????????????????????????????? 369
11.1.1 Definition of a Gas Turbine ?????????????????????????????????????????????? 369
11.1.2 Comparison with Other Thermal Engines ???????????????????????? 371
11.1.3 Example of a Power Gas Turbine ????????????????????????????????????? 372
11.1.4 Compressor Part ??????????????????????????????????????????????????????????????? 374
11.1.5 Turbine Part ?????????????????????????????????????????????????????????????????????? 377
11.1.6 Combustion Chamber ??????????????????????????????????????????????????????? 381
11.2 Thermodynamic Modelling ???????????????????????????????????????????????????????????? 384
11.2.1 Isentropic Efficiency with Adiabatic Compression
or Expansion ????????????????????????????????????????????????????????????????????? 384
11.2.2 Reheat Effect ???????????????????????????????????????????????????????????????????? 387
Contents xxv
11.2.3 Infinitesimal Efficiency; Polytropic Efficiency ????????????????? 389
11.2.4 Thermodynamic Properties of Air and Combustion Gas ??? 392
11.2.5 Heat Capacity Representation ???????????????????????????????????????????? 396
11.2.6 Cooled Expansion ?????????????????????????????????????????????????????????????? 396
11.2.7 Compression with Extraction ????????????????????????????????????????????? 401
11.3 Performance of Simple-Cycle Power Gas Turbines ????????????????????????? 402
11.3.1 Idealised Simple Cycle ??????????????????????????????????????????????????????? 402
11.3.2 Simple Cycle with Component Efficiencies and
Different Heat Capacities of Air and Combustion Gas ?????? 403
11.3.3 Simple Cycle with Component Efficiencies, Cooling
and Variable Gas Properties ??????????????????????????????????????????????? 405
11.4 Performance of Power Gas Turbines with Enhanced Cycles ??????????? 409
11.4.1 Compression with Intercooling ?????????????????????????????????????????? 409
11.4.2 Expansion with Reheat ??????????????????????????????????????????????????????? 411
11.4.3 Recuperator ???????????????????????????????????????????????????????????????????????? 412
11.4.4 Combined Gas and Steam Cycles ?????????????????????????????????????? 413
11.4.5 Steam Injection ??????????????????????????????????????????????????????????????????? 416
References ????????????????????????????????????????????????????????????????????????????????????????????????? 417
12 Thrust Gas Turbines ??????????????????????????????????????????????????????????????????????????????? 419
12.1 Thrust Generation ????????????????????????????????????????????????????????????????????????????? 419
12.1.1 Screw or Propeller ?????????????????????????????????????????????????????????????? 419
12.1.2 Reactor or Jet Engine ????????????????????????????????????????????????????????? 423
12.1.3 Rocket ???????????????????????????????????????????????????????????????????????????????? 426
12.2 Overview of Aircraft Gas Turbine Engines ?????????????????????????????????????? 427
12.2.1 Turbojet ?????????????????????????????????????????????????????????????????????????????? 427
12.2.2 Turboprop and Turbo-Shaft ???????????????????????????????????????????????? 427
12.2.3 Bypass Turbojet ?????????????????????????????????????????????????????????????????? 428
12.2.4 Turbofan ????????????????????????????????????????????????????????????????????????????? 428
12.2.5 Prop-fan and Unducted Fan ??????????????????????????????????????????????? 429
12.2.6 Geared Turbofan ???????????????????????????????????????????????????????????????? 432
12.3 Performance Parameters of Aircraft Propulsion Systems ???????????????? 432
12.3.1 Specific Thrust ??????????????????????????????????????????????????????????????????? 432
12.3.2 Dynamic Power ?????????????????????????????????????????????????????????????????? 433
12.3.3 Gas Power and Dynamic Efficiency ?????????????????????????????????? 433
12.3.4 Thermal Power, Thermodynamic Efficiency and
Thermal Efficiency ????????????????????????????????????????????????????????????? 433
12.3.5 Propulsive Power and Propulsive Efficiency ????????????????????? 434
12.3.6 Overall Efficiency ?????????????????????????????????????????????????????????????? 434
12.3.7 Rocket ???????????????????????????????????????????????????????????????????????????????? 435
12.3.8 Generalisation for Double-Flow Engines ?????????????????????????? 435
12.3.9 Specific Fuel Consumption ???????????????????????????????????????????????? 437
12.4 Performance of the Gas Generator
and the Single-Jet Engine ????????????????????????????????????????????????????????????????? 438
12.4.1 Analysis with Loss-Free Components ???????????????????????????????? 439
12.4.2 Analysis with Component Losses ?????????????????????????????????????? 441
xxvi Contents
12.5 Performance of Double-Flow Engines ????????????????????????????????????????????? 444
12.5.1 Unmixed Flows (Double-Jet Engine: Turbofan,
Turboprop) ????????????????????????????????????????????????????????????????????????? 444
12.5.2 Mixed Flows (Bypass Engine) ??????????????????????????????????????????? 448
12.5.3 Intercooling and Recuperation ??????????????????????????????????????????? 450
12.6 Technological Aspects of the Turbofan Engine ???????????????????????????????? 451
12.6.1 Discs and Shafts ????????????????????????????????????????????????????????????????? 451
12.6.2 Vanes and Blades ???????????????????????????????????????????????????????????????? 451
12.6.3 Combustion Chamber ???????????????????????????????????????????????????????? 452
12.6.4 Mixer and Thrust Reverser ????????????????????????????????????????????????? 454
12.7 Exercises ?????????????????????????????????????????????????????????????????????????????????????????? 454
12.7.1 Single-Flow Jet Engine ?????????????????????????????????????????????????????? 454
12.7.2 Single-Flow Jet Engine with Post-Combustion ????????????????? 455
12.7.3 Turbofan with Separate Flows ??????????????????????????????????????????? 456
12.7.4 Turbofan with Mixed Flows ??????????????????????????????????????????????? 456
12.7.5 Optimisation of Turbine Inlet Temperature with a
Turbofan Engine ????????????????????????????????????????????????????????????????? 456
12.7.6 Helicopter Rotor ????????????????????????????????????????????????????????????????? 456
12.7.7 Ramjet ???????????????????????????????????????????????????????????????????????????????? 457
References ????????????????????????????????????????????????????????????????????????????????????????????????? 457
13 Axial Compressors ?????????????????????????????????????????????????????????????????????????????????? 459
13.1 Mean Line Analysis ?????????????????????????????????????????????????????????????????????????? 459
13.1.1 Velocity Triangles ??????????????????????????????????????????????????????????????? 460
13.1.2 Fundamental Equations ?????????????????????????????????????????????????????? 461
13.1.3 Loss Representation ??????????????????????????????????????????????????????????? 462
13.1.4 Loss Coefficients ???????????????????????????????????????????????????????????????? 465
13.1.5 Force Components ????????????????????????????????????????????????????????????? 465
13.1.6 Diffusion Factor and Loss Correlations ????????????????????????????? 466
13.1.7 Kinematic Parameters ???????????????????????????????????????????????????????? 470
13.1.8 Secondary Flow: Principle ????????????????????????????????????????????????? 471
13.1.9 Radial Variation of Flow: Principle ???????????????????????????????????? 473
13.1.10 Optimisation of a Stage ???????????????????????????????????????????????????? 474
13.1.11 Blade Shape ?????????????????????????????????????????????????????????????????????? 476
13.1.12 Attainable Pressure Ratio ????????????????????????????????????????????????? 478
13.2 Secondary Flow ???????????????????????????????????????????????????????????????????????????????? 478
13.2.1 Definition of Secondary Flow ???????????????????????????????????????????? 478
13.2.2 Passage Vortex and Trailing Vortices ????????????????????????????????? 479
13.2.3 Corner Vortices ??????????????????????????????????????????????????????????????????? 480
13.2.4 Horseshoe Vortex ??????????????????????????????????????????????????????????????? 480
13.2.5 Leakage Vortex and Scraping Vortex ????????????????????????????????? 480
13.2.6 Loss Assessment ???????????????????????????????????????????????????????????????? 481
13.3 Radial Flow Variation ?????????????????????????????????????????????????????????????????????? 481
13.3.1 S1-S2 Decomposition ?????????????????????????????????????????????????????????? 481
13.3.2 Radial Equilibrium ????????????????????????????????????????????????????????????? 482
13.3.3 Free Vortex Blades ????????????????????????????????????????????????????????????? 483
Contents xxvii
13.3.4 Forcing of the Vortex Distribution ????????????????????????????????????? 485
13.3.5 Effect of End Wall Boundary Layers ????????????????????????????????? 487
13.3.6 Three-dimensional Blade Design ??????????????????????????????????????? 488
13.4 Compressor Blade Profiles ??????????????????????????????????????????????????????????????? 491
13.4.1 Subsonic and Supercritical Cascades ????????????????????????????????? 491
13.4.2 Transonic Cascades ???????????????????????????????????????????????????????????? 494
13.4.3 Supersonic Cascades and Transonic Cascades with
High Inlet Mach Number ??????????????????????????????????????????????????? 496
13.5 Performance Characteristics and Operating Range ?????????????????????????? 497
13.5.1 General Shape of a Characteristic Curve ??????????????????????????? 497
13.5.2 Rotating Stall ?????????????????????????????????????????????????????????????????????? 498
13.5.3 Choking ?????????????????????????????????????????????????????????????????????????????? 499
13.5.4 Surge ?????????????????????????????????????????????????????????????????????????????????? 501
13.5.5 Operating Range ???????????????????????????????????????????????????????????????? 502
13.6 Exercises ?????????????????????????????????????????????????????????????????????????????????????????? 505
References ????????????????????????????????????????????????????????????????????????????????????????????????? 506
14 Radial Compressors ???????????????????????????????????????????????????????????????????????????????? 509
14.1 Construction Forms and Applications ?????????????????????????????????????????????? 509
14.1.1 Rotor Types ???????????????????????????????????????????????????????????????????????? 509
14.1.2 General Shape of a Radial Compressor ????????????????????????????? 511
14.1.3 Comparison Between Radial and Axial Compressors ??????? 512
14.1.4 Examples of Radial Compressors ?????????????????????????????????????? 513
14.2 Kinematic Parameters ?????????????????????????????????????????????????????????????????????? 516
14.3 Pressure Ratio ??????????????????????????????????????????????????????????????????????????????????? 519
14.4 Rotor Shape ?????????????????????????????????????????????????????????????????????????????????????? 521
14.4.1 Number of Blades ?????????????????????????????????????????????????????????????? 521
14.4.2 Inducer ??????????????????????????????????????????????????????????????????????????????? 523
14.5 Diffusers ??????????????????????????????????????????????????????????????????????????????????????????? 525
14.5.1 Flow Non-homogeneity at Rotor Outlet ???????????????????????????? 525
14.5.2 Mixing Zone ??????????????????????????????????????????????????????????????????????? 526
14.5.3 Vaneless Diffusers ?????????????????????????????????????????????????????????????? 527
14.5.4 Vaned Diffusers ?????????????????????????????????????????????????????????????????? 527
14.6 Performance Characteristics ????????????????????????????????????????????????????????????? 528
14.6.1 Flow Instability ?????????????????????????????????????????????????????????????????? 528
14.6.2 Choking ?????????????????????????????????????????????????????????????????????????????? 528
14.6.3 Operating Characteristics and Operating Range ???????????????? 529
14.7 Exercises ?????????????????????????????????????????????????????????????????????????????????????????? 531
14.7.1 Velocity Variation at Constant Radius in a Rotor ??????????????? 531
14.7.2 Variable Geometry ????????????????????????????????????????????????????????????? 533
References ????????????????????????????????????????????????????????????????????????????????????????????????? 533
15 Axial and Radial Turbines for Gases ????????????????????????????????????????????????????? 535
15.1 Axial Turbines ?????????????????????????????????????????????????????????????????????????????????? 535
15.1.1 Kinematic Parameters ???????????????????????????????????????????????????????? 535
15.1.2 Radial Variation of Flow Parameters ????????????????????????????????? 541
xxviii Contents
15.1.3 Blade Profiles ????????????????????????????????????????????????????????????????????? 542
15.1.4 Three-dimensional Blade Design ??????????????????????????????????????? 545
15.1.5 Vane and Blade Clocking ??????????????????????????????????????????????????? 546
15.1.6 Operating Characteristic of Axial Turbines ??????????????????????? 546
15.2 Radial Turbines ???????????????????????????????????????????????????????????????????????????????? 549
15.2.1 Shape and Functioning ??????????????????????????????????????????????????????? 549
15.2.2 Kinematic Parameters ???????????????????????????????????????????????????????? 551
15.2.3 Operating Characteristic of Radial Turbines ?????????????????????? 553
15.2.4 Radial Turbine Applications ??????????????????????????????????????????????? 554
15.3 Dimensional Analysis with Compressible Fluids ???????????????????????????? 554
15.3.1 Independent and Dependent Π-groups ??????????????????????????????? 554
15.3.2 Dimensionless Compressor and Turbine Characteristics ??? 556
15.3.3 Corrected Quantities ?????????????????????????????????????????????????????????? 556
15.4 Exercises ?????????????????????????????????????????????????????????????????????????????????????????? 557
References ????????????????????????????????????????????????????????????????????????????????????????????????? 558
Index ??????????????????????????????????????????????????????????????????????????????????????????????????????????????? 561

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