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Contents PREFACE TO FOURTH EDITION ix PREFACE TO THIRD EDITION xi ACKNOWLEDGEMENTS xiii LIST OF SYMBOLS xv 1. Introduction: Dimensional Analysis: Similitude 1 Definition of a turbomachine 1 Units and dimensions 3 Dimensional analysis and performance laws 4 Incompressible fluid analysis 6 Performance characteristics 7 Variable geometry turbomachines 9 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 23 Introduction 23 The equation of continuity 23 The first law of thermodynamics internal energy 24 The momentum equation Newton's second law of motion 25 The second law of thermodynamics entropy 29 Definitions of efficiency 30 Small stage or polytropic efficiency 35 Nozzle efficiency 41 Diffusers 43 References 53 Problems 53 vi Contents 3. Two-dimensional Cascades 55 Introduction 55 Cascade nomenclature 56 Analysis of cascade forces 57 Energy losses 59 Lift and drag 59 Circulation and lift 61 Efficiency of a compressor cascade 62 Performance of two-dimensional cascades 63 The cascade wind tunnel 63 Cascade test results 65 Compressor cascade performance 68 Turbine cascade performance 70 Compressor cascade correlations 71 Fan blade design (McKenzie) 80 Turbine cascade correlation (Ainley) 81 Comparison of the profile loss in a cascade and in a turbine stage 86 Optimum space-chord ratio of turbine blades (Zweifel) 87 References 88 Problems 90 4. Axial-flow Turbines: Two-dimensional Theory 93 Introduction 93 Velocity diagrams of the axial turbine stage 93 Thermodynamics of the axial turbine stage 94 Stage losses and efficiency 96 Soderberg's correlation 97 Types of axial turbine design 99 Stage reaction 101 Diffusion within blade rows 103 Choice of reaction and effect on efficiency 107 Design point efficiency of a turbine stage 108 Maximum total-to-static efficiency of a reversible turbine stage 112 Stresses in turbine rotor blades 114 Turbine flow characteristics 120 Flow characteristics of a multistage turbine 122 The Wells turbine 124 References 132 Problems 133 5. Axial-flow Compressors and Fans 137 Introduction 137 Two-dimensional analysis of the compressor stage 138 Velocity diagrams of the compressor stage 140 Thermodynamics of the compressor stage 141 Contents vii Stage loss relationships and efficiency 142 Reaction ratio 143 Choice of reaction 143 Stage loading 144 Simplified off-design performance 145 Stage pressure rise 147 Pressure ratio of a multistage compressor 148 Estimation of compressor stage efficiency 149 Stall and surge phenomena in compressors 154 Control of flow instabilities 159 Axial-flow ducted fans 160 Blade element theory 162 Blade element efficiency 163 Lift coefficient of a fan aerofoil 164 References 165 Problems 166 6. Three-dimensional Flows in Axial Turbomachines 169 Introduction 169 Theory of radial equilibrium 169 The indirect problem 171 The direct problem 179 Compressible flow through a fixed blade row 180 Constant specific mass flow 181 Off-design performance of a stage 183 Free-vortex turbine stage 184 Actuator disc approach 186 Blade row interaction effects 190 Computer-aided methods of solving the through-flow problem 191 Secondary flows 193 References 195 Problems 196 7. Centrifugal Pumps, Fans and Compressors 199 Introduction 199 Some definitions 200 Theoretical analysis of a centrifugal compressor 202 Inlet casing 203 Impeller 203 Conservation of rothalpy 204 Diffuser 205 Inlet velocity limitations 205 Optimum design of a pump inlet 206 Optimum design of a centrifugal compressor inlet 208 Slip factor 213 Head increase of a centrifugal pump 218 viii Contents Performance of centrifugal compressors 219 The diffuser system 227 Choking in a compressor stage 230 References 232 Problems 233 8. Radial Flow Gas Turbines 236 Introduction 236 Types of inward flow radial turbine 237 Thermodynamics of the 90 deg IFR turbine 239 Basic design of the rotor 241 Nominal design point efficiency 242 Mach number relations 246 Loss coefficients in 90 deg IFR turbines 247 Optimum efficiency considerations 248 Criterion for minimum number of blades 253 Design considerations for rotor exit 256 Incidence losses 260 Significance and application of specific speed 263 Optimum design selection of 90 deg IFR turbines 266 Clearance and windage losses 269 Pressure ratio limits of the 90 deg IFR turbine 269 Cooled 90 deg IFR turbines 271 References 272 Problems 273 9. Hydraulic Turbines 277 Introduction 277 Hydraulic turbines 278 The Pelton turbine 281 Reaction turbines 290 The Francis turbine 290 The Kaplan turbine 296 Effect of size on turbomachine efficiency 299 Cavitation 301 References 305 Problems 306
Library of Congress Subject Headings for this publication:
Turbomachines -- Fluid dynamics.