《Fundamentals of Turbomachines》
《Fundamentals of Turbomachines》涡轮机原理
作者：Erik Dick
Department of Flow, Heat and Combustion
Mechanics
Ghent University
出版社：Springer
出版时间：2015年
目录
1 Working Principles1
1.1 Definition of a Turbomachine1
1.2 Examples of Axial Turbomachines2
1.2.1 Axial Hydraulic Turbine2
1.2.2 Axial Pump4
1.3 Mean Line Analysis5
1.4 Basic Laws for Stationary Duct Parts7
1.4.1 Conservation of Mass7
1.4.2 Conservation of Momentum7
1.4.3 Conservation of Energy9
1.4.4 Forms of Energy: Mechanical Energy and Head10
1.4.5 Energy Dissipation: Head Loss12
1.5 Basic Laws for Rotating Duct Parts14
1.5.1 Work and Energy Equations in a Rotating Frame
with Constant Angular Velocity14
1.5.2 Moment of Momentum in the Absolute Frame: Rotor Work16
1.5.3 Moment of Momentum in the Relative Frame:
Forces Intervening in the Rotor Work21
1.5.4 Energy Component Changes Caused By the Rotor Work23
1.5.5 Rotor Work in the Mean Line Representation of the Flow24
1.6 Energy Analysis of Turbomachines25
1.6.1 Mechanical Efficiency and Internal Efficiency25
1.6.2 Energy Analysis of an Axial Hydraulic Turbine26
1.6.3 Energy Analysis of an Axial Pump30
1.7 Examples of Radial Turbomachines33
1.8 Performance Characteristics36
1.9 Exercises40
References46
2 Basic Components47
2.1 Aerofoils47
2.1.1 Force Generation47
2.1.2 Performance Parameters49
xviii Contents
2.1.3 Pressure Distribution51
2.1.4 Boundary Layer Separation52
2.1.5 Loss Mechanism Associated to Friction: Energy Dissipation 55
2.1.6 Profile Shapes58
2.1.7 Blade Rows with Low Solidity59
2.2 Linear Cascades60
2.2.1 Relation with the Real Machine60
2.2.2 Cascade Geometry61
2.2.3 Flow in Lossless Cascades: Force Components62
2.2.4 Significance of Circulation65
2.2.5 Flow in Lossless Cascades: Work67
2.2.6 Flow in Cascades with Loss: Force Components68
2.2.7 Flow in Cascades with Loss: Energy Dissipation
and Work by Drag Force70
2.2.8 The Zweifel Tangential Force Coefficient72
2.2.9 The Lieblein Diffusion Factor74
2.2.10 Performance Parameters of Axial Cascades75
2.3 Channels75
2.3.1 Straight Channels75
2.3.2 Bends77
2.4 Diffusers79
2.4.1 Dump Diffusers79
2.4.2 Inlet Flow Distortion79
2.4.3 Flow Separation81
2.4.4 Flow Improvement81
2.4.5 Representation of Diffuser Performance82
2.4.6 Equivalent Opening Angle84
2.4.7 Diffusion in a Bend85
2.5 Exercises87
References95
3 Fans97
3.1 Fan Aplications and Fan Types97
3.1.1 Fan Applications97
3.1.2 Large Radial Fans98
3.1.3 Small Radial Fans99
3.1.4 Large Axial Fans99
3.1.5 Small Axial Fans100
3.1.6 Cross-Flow Fans100
3.2 Idealised Mean Line Analysis of a Radial Fan101
3.2.1 Idealised Flow Concept: Infinite Number of Blades101
3.2.2 Degree of Reaction102
3.2.3 Relation Between Rotor Blade Shape and Performance
Parameters103
3.2.4 Performance Characteristics with Idealised Flow105
Contents xix
3.3 Radial Fan Analysis for Lossless Two-Dimensional Flow
with Finite Number of Rotor Blades106
3.3.1 Relative Vortex in Blade Channels106
3.3.2 Velocity Difference over a Rotating Blade107
3.3.3 Slip: Reduction of Rotor Work112
3.3.4 Number of Blades and Solidity: Pfleiderer Moment
Coefficient115
3.3.5 Number of Blades: Examples118
3.4 Internal Losses with Radial Fans120
3.4.1 Turning Loss at Rotor Entrance120
3.4.2 Incidence Loss at Rotor Entrance120
3.4.3 Displacement by Blade Thickness122
3.4.4 Rotor Friction Loss and Rotor Diffusion Loss123
3.4.5 Dump Diffusion Loss at Volute Entrance123
3.4.6 Incidence Loss at Volute Entrance125
3.4.7 Friction Loss Within the Volute126
3.4.8 Diffusion at the Rotor Inlet126
3.4.9 Flow separation at Rotor Inlet and Rotor Outlet127
3.4.10 Applicability of the Loss Models129
3.4.11 Optimisation of the Rotor Inlet of a Centrifugal Fan129
3.4.12 Characteristics Taking Losses into Account131
3.5 Overall Performance Evaluation134
3.5.1 Mechanical Loss134
3.5.2 Leakage Loss135
3.5.3 Overall Efficiency with Power Receiving Machines135
3.5.4 Overall Efficiency with Power Delivering Machines136
3.6 Rotor Shape Choices with Radial Fans136
3.7 Axial and Mixed-Flow Fans140
3.7.1 Degree of Reaction with Axial Fans140
3.7.2 Free Vortex and Non-Free Vortex Types141
3.7.3 Axial Fan Characteristics; Adjustable Rotor Blades143
3.7.4 Mixed-Flow Fans144
3.8 Exercises146
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 Fan147
3.8.4 Volute of a Centrifugal Fan147
3.8.5 Leakage Flow Rate with Centrifugal Fan147
3.8.6 Centrifugal Pump (Finite Number of Blades and
Internal Losses)148
3.8.7 Axial Fan (Idealised Flow): Analysis on Average
Diameter148
3.8.8 Axial Fan (Idealised Flow): Free Vortex and Non-
Free Vortex149
xx Contents
3.8.9 Inlet Guide Vane with a Centrifugal Fan149
3.8.10 Change of Rotational Speed with Centrifugal and
Axial Fans149
3.8.11 Two-Stage Axial Fan150
3.8.12 Axial Turbine151
References151
4 Compressible Fluids153
4.1 Basic Laws153
4.2 Compressibility and Velocity of Sound156
4.3 Compressibility Effect on the Velocity-Pressure Relation158
4.4 Shape of a Nozzle160
4.5 Nozzle with Initial Velocity162
4.6 Nozzle with Losses: Infinitesimal Efficiency163
4.7 Isentropic and Polytropic Efficiencies167
4.8 Exercises171
References174
5 Performance Measurement175
5.1 Pressure Measurement175
5.1.1 The Metal Manometer175
5.1.2 The Pressure Transducer175
5.1.3 The Digital Manometer176
5.1.4 Calibration of Pressure Meters177
5.2 Temperature Measurement177
5.2.1 The Glass Thermometer177
5.2.2 The Temperature Transducer177
5.2.3 The Digital Thermometer178
5.3 Flow Rate Measurement178
5.3.1 Reservoir178
5.3.2 Flow Over a Weir178
5.3.3 Pressure Drop Devices179
5.3.4 Industrial Mass Flow Rate Meters180
5.3.5 Positioning of Flow Rate Meters in Ducts180
5.4 Torque Measurement181
5.4.1 Swinging Suspended Motor or Brake181
5.4.2 Calibrated Motor181
5.4.3 The Torque Transducer181
5.5 Rotational Speed Measurement182
5.5.1 Pulse Counters182
5.5.2 The Speed Transducer182
5.5.3 Electric Tachometer182
5.6 Laboratory Test of a Pelton Turbine182
5.6.1 Test Rig182
5.6.2 Measurements183
Contents xxi
5.6.3 Measurement Procedure183
5.6.4 Calculations184
5.6.5 Measurement Example184
5.7 Laboratory Test of a Centrifugal Fan184
5.7.1 Test Rig184
5.7.2 Measurements187
5.7.3 Measurement Procedure187
5.7.4 Calculations188
5.7.5 Measurement Example188
5.8 Laboratory Test of a Centrifugal Pump189
5.8.1 Test Rig189
5.8.2 Measurements190
5.8.3 Measurement Procedure190
5.8.4 Calculations191
5.8.5 Measurement Example192
6 Steam Turbines193
6.1 Applications of Steam Turbines193
6.2 Working Principles of Steam Turbines195
6.3 The Steam Cycle199
6.4 The Single Impulse Stage or Laval Stage200
6.4.1 Velocity Triangles200
6.4.2 Work and Energy Relations201
6.4.3 Stage Efficiency Definitions204
6.4.4 Blade Profile Shape205
6.4.5 Loss Representation208
6.4.6 Optimisation of Total-to-Static Efficiency209
6.5 The Pressure-Compounded Impulse Turbine
or Rateau Turbine212
6.5.1 Principle212
6.5.2 Efficiency213
6.6 The Velocity-Compounded Impulse Turbine or Curtis Turbine214
6.7 The Reaction Turbine217
6.7.1 Degree of Reaction217
6.7.2 Efficiency218
6.7.3 Axial Inlet and Outlet222
6.8 Steam Turbine Construction Forms224
6.8.1 Large Steam Turbines for Power Stations224
6.8.2 Industrial Steam Turbines229
6.9 Blade Shaping231
6.9.1 HP and IP Blades231
6.9.2 LP Blades233
6.10 Exercises236
References246
xxii Contents
7 Dynamic Similitude247
7.1 Principles of Dynamic Similitude247
7.1.1 Definition of Dynamic Similitude247
7.1.2 Dimensionless Parameter Groups248
7.1.3 Similitude Conditions248
7.1.4 Purpose of Similitude Analysis250
7.1.5 Dimensional Analysis251
7.1.6 Independent and Dependent Parameter Groups252
7.1.7 Dimensionless Parameter Groups in Turbomachines
with a Constant Density Fluid252
7.1.8 Strong and Weak Similitude Conditions254
7.2 Characteristic Numbers of Turbomachines254
7.2.1 Definition of a Characteristic Number254
7.2.2 Specific Speed and Specific Diameter255
7.2.3 Relation Between Characteristic Numbers
and Machine Shape257
7.2.4 Design Diagrams259
7.2.5 Shape of Characteristic Curves261
7.2.6 Power Specific Speed262
7.3 Application Example of Similitude: Variable Rotational
Speed with a Pump263
7.4 Imperfect Similitude266
7.4.1 Effect of Reynolds Number with the Same Fluid266
7.4.2 Effect of Relative Roughness267
7.4.3 Effect of Viscosity268
7.4.4 Rotor Diameter Reduction: Impeller Trimming270
7.4.5 Reduced Scale Models271
7.5 Series and Parallel Connection272
7.5.1 Parallel Connection of Fans272
7.5.2 Parallel Connection of Pumps273
7.5.3 Series Connection of Fans274
7.6 Turbomachine Design Example: Centrifugal Fan276
7.7 Exercises279
References282
8 Pumpsalic283
8.1 Cavitation283
8.1.1 Cavitation Phenomenon and Cavitation Consequences283
8.1.2 Types of Cavitation284
8.1.3 Cavitation Assessment: Cavitation Number and
Required Net Positive Suction Height286
8.1.4 Optimisation of the Inlet of a Centrifugal Pump Rotor289
8.1.5 Net Positive Suction Head of the Installation291
8.1.6 Increasing the Acceptable Suction Height292
Contents xxiii
8.2 Priming of Pumps: Self-Priming Types293
8.2.1 Side Channel Pump293
8.2.2 Peripheral Pump (regenerative pump)295
8.2.3 Self-Priming Centrifugal Pump296
8.2.4 Jet Pump297
8.3 Unstable Operation297
8.4 Component Shaping299
8.4.1 Simply and Doubly Curved Blades in Radial Rotors299
8.4.2 Mixed-Flow and Axial Pumps300
8.4.3 Pump Inlet300
8.4.4 Pump Outlet301
8.4.5 Vaneless Diffuser Rings301
8.4.6 Vaned Diffuser Rings302
8.4.7 Volute303
8.4.8 Return Channels305
8.5 Internal Parallel and Series Connection Of Rotors305
8.5.1 Reason for Internal Parallel or Series Connection305
8.5.2 Internal Parallel Connection of Rotors306
8.5.3 Internal Series Connection of Rotors: Multistage Pumps306
8.6 Constructional Aspects307
8.6.1 Rotor307
8.6.2 Stator307
8.6.3 Shaft Sealing307
8.6.4 Bearings309
8.6.5 Axial Force Balancing with Single-Stage Pumps309
8.6.6 Axial Force Balancing with Multistage Pumps310
8.6.7 Wear Rings311
8.7 Special Pumps311
8.7.1 Borehole Pumps312
8.7.2 High-Pressure Pumps312
8.7.3 Sealless Pumps: Circulation Pumps, Chemical Pumps312
8.7.4 Slurry Pumps313
8.7.5 Pumping of Solid Materials314
8.7.6 Vertical Submerged Pumps314
8.7.7 Partial Emission Pumps315
8.7.8 Pumps for Viscous Fluids315
8.8 Exercises316
8.8.1 Looking up Pump Characteristics316
8.8.2 Verification of an NPSH-Value316
References317
9 Hydraulic Turbines319
9.1 Hydraulic Energy319
9.2 Hydraulic Turbine Types320
9.2.1 Large Turbines (> 10 MW)320
9.2.2 Small Turbines (< 10 MW)322
xxiv Contents
9.3 Pelton Turbines: Impulse Turbines324
9.3.1 Performance Characteristics324
9.3.2 Specific Speed326
9.3.3 Determination of the Main Dimensions328
9.3.4 Flow Rate Control and Over-Speed Protection328
9.4 Francis and Kaplan Turbines: Reaction Turbines329
9.4.1 Shape of the Velocity Triangles: Kinematic Parameters329
9.4.2 Optimisation of the Velocity Triangles330
9.4.3 Degree of Reaction and Speed Ratio331
9.4.4 Velocity Triangles with Varying Degree of Reaction332
9.4.5 Specific Speed and Meridional Shape of Francis Turbines333
9.4.6 Flow Rate Control with Reaction Turbines335
9.4.7 Examples (Figs. 9.16, 9.17)337
9.5 Bulb and Tube Turbines338
9.6 Reversible Pump-Turbines340
9.7 Exercises342
References345
10 Wind Turbines347
10.1 Wind Energy347
10.2 Types of Wind Energy Conversion Systems348
10.2.1 Drag Machines348
10.2.2 High-Speed Horizontal-Axis Turbines349
10.2.3 Technical Aspects of Horizontal-Axis Wind
Turbines for Electricity Generation351
10.2.4 Low-Speed Horizontal-Axis Wind Turbines355
10.2.5 Vertical-Axis Wind Turbines356
10.3 Wind Turbine Performance Analysis358
10.3.1 Momentum Analysis (Single Streamtube Analysis)358
10.3.2 Multiple Streamtube Analysis361
10.3.3 Blade Element Analysis363
10.4 Adaptation to a Wind Regime365
References368
11 Power Gas Turbines369
11.1 General Concept and Components369
11.1.1 Definition of a Gas Turbine369
11.1.2 Comparison with Other Thermal Engines371
11.1.3 Example of a Power Gas Turbine372
11.1.4 Compressor Part374
11.1.5 Turbine Part377
11.1.6 Combustion Chamber381
11.2 Thermodynamic Modelling384
11.2.1 Isentropic Efficiency with Adiabatic Compression
or Expansion384
11.2.2 Reheat Effect387
Contents xxv
11.2.3 Infinitesimal Efficiency; Polytropic Efficiency389
11.2.4 Thermodynamic Properties of Air and Combustion Gas392
11.2.5 Heat Capacity Representation396
11.2.6 Cooled Expansion396
11.2.7 Compression with Extraction401
11.3 Performance of Simple-Cycle Power Gas Turbines402
11.3.1 Idealised Simple Cycle402
11.3.2 Simple Cycle with Component Efficiencies and
Different Heat Capacities of Air and Combustion Gas403
11.3.3 Simple Cycle with Component Efficiencies, Cooling
and Variable Gas Properties405
11.4 Performance of Power Gas Turbines with Enhanced Cycles409
11.4.1 Compression with Intercooling409
11.4.2 Expansion with Reheat411
11.4.3 Recuperator412
11.4.4 Combined Gas and Steam Cycles413
11.4.5 Steam Injection416
References417
12 Thrust Gas Turbines419
12.1 Thrust Generation419
12.1.1 Screw or Propeller419
12.1.2 Reactor or Jet Engine423
12.1.3 Rocket426
12.2 Overview of Aircraft Gas Turbine Engines427
12.2.1 Turbojet427
12.2.2 Turboprop and Turbo-Shaft427
12.2.3 Bypass Turbojet428
12.2.4 Turbofan428
12.2.5 Prop-fan and Unducted Fan429
12.2.6 Geared Turbofan432
12.3 Performance Parameters of Aircraft Propulsion Systems432
12.3.1 Specific Thrust432
12.3.2 Dynamic Power433
12.3.3 Gas Power and Dynamic Efficiency433
12.3.4 Thermal Power, Thermodynamic Efficiency and
Thermal Efficiency433
12.3.5 Propulsive Power and Propulsive Efficiency434
12.3.6 Overall Efficiency434
12.3.7 Rocket435
12.3.8 Generalisation for Double-Flow Engines435
12.3.9 Specific Fuel Consumption437
12.4 Performance of the Gas Generator
and the Single-Jet Engine438
12.4.1 Analysis with Loss-Free Components439
12.4.2 Analysis with Component Losses441
xxvi Contents
12.5 Performance of Double-Flow Engines444
12.5.1 Unmixed Flows (Double-Jet Engine: Turbofan,
Turboprop)444
12.5.2 Mixed Flows (Bypass Engine)448
12.5.3 Intercooling and Recuperation450
12.6 Technological Aspects of the Turbofan Engine451
12.6.1 Discs and Shafts451
12.6.2 Vanes and Blades451
12.6.3 Combustion Chamber452
12.6.4 Mixer and Thrust Reverser454
12.7 Exercises454
12.7.1 Single-Flow Jet Engine454
12.7.2 Single-Flow Jet Engine with Post-Combustion455
12.7.3 Turbofan with Separate Flows456
12.7.4 Turbofan with Mixed Flows456
12.7.5 Optimisation of Turbine Inlet Temperature with a
Turbofan Engine456
12.7.6 Helicopter Rotor456
12.7.7 Ramjet457
References457
13 Axial Compressors459
13.1 Mean Line Analysis459
13.1.1 Velocity Triangles460
13.1.2 Fundamental Equations461
13.1.3 Loss Representation462
13.1.4 Loss Coefficients465
13.1.5 Force Components465
13.1.6 Diffusion Factor and Loss Correlations466
13.1.7 Kinematic Parameters470
13.1.8 Secondary Flow: Principle471
13.1.9 Radial Variation of Flow: Principle473
13.1.10 Optimisation of a Stage474
13.1.11 Blade Shape476
13.1.12 Attainable Pressure Ratio478
13.2 Secondary Flow478
13.2.1 Definition of Secondary Flow478
13.2.2 Passage Vortex and Trailing Vortices479
13.2.3 Corner Vortices480
13.2.4 Horseshoe Vortex480
13.2.5 Leakage Vortex and Scraping Vortex480
13.2.6 Loss Assessment481
13.3 Radial Flow Variation481
13.3.1 S1-S2 Decomposition481
13.3.2 Radial Equilibrium482
13.3.3 Free Vortex Blades483
Contents xxvii
13.3.4 Forcing of the Vortex Distribution485
13.3.5 Effect of End Wall Boundary Layers487
13.3.6 Three-dimensional Blade Design488
13.4 Compressor Blade Profiles491
13.4.1 Subsonic and Supercritical Cascades491
13.4.2 Transonic Cascades494
13.4.3 Supersonic Cascades and Transonic Cascades with
High Inlet Mach Number496
13.5 Performance Characteristics and Operating Range497
13.5.1 General Shape of a Characteristic Curve497
13.5.2 Rotating Stall498
13.5.3 Choking499
13.5.4 Surge501
13.5.5 Operating Range502
13.6 Exercises505
References506
14 Radial Compressors509
14.1 Construction Forms and Applications509
14.1.1 Rotor Types509
14.1.2 General Shape of a Radial Compressor511
14.1.3 Comparison Between Radial and Axial Compressors512
14.1.4 Examples of Radial Compressors513
14.2 Kinematic Parameters516
14.3 Pressure Ratio519
14.4 Rotor Shape521
14.4.1 Number of Blades521
14.4.2 Inducer523
14.5 Diffusers525
14.5.1 Flow Non-homogeneity at Rotor Outlet525
14.5.2 Mixing Zone526
14.5.3 Vaneless Diffusers527
14.5.4 Vaned Diffusers527
14.6 Performance Characteristics528
14.6.1 Flow Instability528
14.6.2 Choking528
14.6.3 Operating Characteristics and Operating Range529
14.7 Exercises531
14.7.1 Velocity Variation at Constant Radius in a Rotor531
14.7.2 Variable Geometry533
References533
15 Axial and Radial Turbines for Gases535
15.1 Axial Turbines535
15.1.1 Kinematic Parameters535
15.1.2 Radial Variation of Flow Parameters541
xxviii Contents
15.1.3 Blade Profiles542
15.1.4 Three-dimensional Blade Design545
15.1.5 Vane and Blade Clocking546
15.1.6 Operating Characteristic of Axial Turbines546
15.2 Radial Turbines549
15.2.1 Shape and Functioning549
15.2.2 Kinematic Parameters551
15.2.3 Operating Characteristic of Radial Turbines553
15.2.4 Radial Turbine Applications554
15.3 Dimensional Analysis with Compressible Fluids554
15.3.1 Independent and Dependent Π-groups554
15.3.2 Dimensionless Compressor and Turbine Characteristics556
15.3.3 Corrected Quantities556
15.4 Exercises557
References558
Index561
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