Fluid Mechanics and Thermodynamics of Turbomachinery, Fourth Edition

Turbomachines are those in which energy is transferred to or from a continuously moving fluid by the motion of a rotating element. Some of the most common and important machines used in engineering and industry fall into this category, including those which absorb power (and thereby increase fluid pressure), such as fans, compressors and pumps. Also included are equally vital varieties of machines which generate power from the expansion of fluids to lower pressures such as hydraulic, steam and gas turbines. This general definition embraces a number of devices that are classified as 'open', such as propellers, windmills and unshrouded fans. The machines examined here are those defined as 'closed', where a finite quantity of fluid can be considered to pass through the machine in unit time, for it is these which are of the most interest to students and professionals in the fields of mechanical, chemical, and plant engineering. It is in these areas that the devices that form the subject matter of this book find their most important applications, making this treatment of vital importance to anyone working in or studying them. Example questions and answers throughout Includes more new material on axial flow compressors and pumps Contents......Page 6 Preface to the Fourth Edition......Page 10 Preface to Third Edition......Page 12 Acknowledgements......Page 14 Superscript......Page 18 Definition of a turbomachine......Page 20 Units and dimensions......Page 22 Dimensional analysis and performance laws......Page 23 Incompressible fluid analysis......Page 25 Performance characteristics......Page 26 Variable geometry turbomachines......Page 28 Specific speed......Page 29 Cavitation......Page 31 Compressible gas flow relations......Page 34 Compressible fluid analysis......Page 35 The inherent unsteadiness of the flow within turbomachines......Page 39 The equation of continuity......Page 42 The first law of thermodynamics internal energy......Page 43 Soderberg’s correlation......Page 0 The second law of thermodynamics entropy......Page 48 Definitions of efficiency......Page 49 Small stage or polytropic efficiency......Page 54 Nozzle efficiency......Page 60 Diffusers......Page 62 3 Two- dimensional Cascades......Page 74 Cascade nomenclature......Page 75 Analysis of cascade forces......Page 76 Lift and drag......Page 78 Circulation and lift......Page 80 Efficiency of a compressor cascade......Page 81 The cascade wind tunnel......Page 82 Cascade test results......Page 84 Compressor cascade performance......Page 87 Turbine cascade performance......Page 89 Compressor cascade correlations......Page 90 Fan blade design (McKenzie)......Page 99 Turbine cascade correlation (Ainley)......Page 100 Comparison of the profile loss in a cascade and in a turbine stage......Page 105 Optimum space chord ratio of turbine blades (Zweifel)......Page 106 Velocity diagrams of the axial turbine stage......Page 112 Thermodynamics of the axial turbine stage......Page 113 Stage losses and efficiency......Page 115 Types of axial turbine design......Page 118 Stage reaction......Page 120 Diffusion within blade rows......Page 122 Choice of reaction and effect on efficiency......Page 126 Design point efficiency of a turbine stage......Page 127 Maximum total-to-static efficiency of a reversible turbine stage......Page 131 Stresses in turbine rotor blades......Page 133 Turbine flow characteristics......Page 139 Flow characteristics of a multistage turbine......Page 141 The Wells turbine......Page 143 5 Axial- flow Compressors and Fans......Page 156 Two-dimensional analysis of the compressor stage......Page 157 Velocity diagrams of the compressor stage......Page 159 Thermodynamics of the compressor stage......Page 160 Stage loss relationships and efficiency......Page 161 Choice of reaction......Page 162 Stage loading......Page 163 Simplified off-design performance......Page 164 Stage pressure rise......Page 166 Pressure ratio of a multistage compressor......Page 167 Estimation of compressor stage efficiency......Page 168 Stall and surge phenomena in compressors......Page 173 Control of flow instabilities......Page 178 Axial-flow ducted fans......Page 179 Blade element theory......Page 181 Blade element efficiency......Page 182 Lift coefficient of a fan aerofoil......Page 183 Theory of radial equilibrium......Page 188 The indirect problem......Page 190 The direct problem......Page 198 Compressible flow through a fixed blade row......Page 199 Constant specific mass flow......Page 200 Off-design performance of a stage......Page 202 Free-vortex turbine stage......Page 203 Actuator disc approach......Page 205 Blade row interaction effects......Page 209 Computer-aided methods of solving the through-flow problem......Page 210 Secondary flows......Page 212 7 Centrifugal Pumps, Fans and Compressors......Page 218 Some definitions......Page 219 Theoretical analysis of a centrifugal compressor......Page 221 Impeller......Page 222 Conservation of rothalpy......Page 223 Inlet velocity limitations......Page 224 Optimum design of a pump inlet......Page 225 Optimum design of a centrifugal compressor inlet......Page 227 Slip factor......Page 232 Head increase of a centrifugal pump......Page 237 Performance of centrifugal compressors......Page 238 The diffuser system......Page 246 Choking in a compressor stage......Page 249 8 Radial Flow Gas Turbines......Page 255 Types of inward flow radial turbine......Page 256 Thermodynamics of the 90 deg IFR turbine......Page 258 Basic design of the rotor......Page 260 Nominal design point efficiency......Page 261 Mach number relations......Page 265 Loss coefficients in 90 deg IFR turbines......Page 266 Optimum efficiency considerations......Page 267 Criterion for minimum number of blades......Page 272 Design considerations for rotor exit......Page 275 Incidence losses......Page 279 Significance and application of specific speed......Page 282 Optimum design selection of 90 deg IFR turbines......Page 285 Pressure ratio limits of the 90 deg IFR turbine......Page 288 Cooled 90 deg IFR turbines......Page 290 9 Hydraulic Turbines......Page 296 Hydraulic turbines......Page 297 The Pelton turbine......Page 300 The Francis turbine......Page 309 The Kaplan turbine......Page 315 Effect of size on turbomachine efficiency......Page 318 Cavitation......Page 320 Bibliography......Page 328 Conversion of British Units to SI Units......Page 329 Answers to Problems......Page 330 Index......Page 333 Contents 6 Preface to the Fourth Edition 10 Preface to Third Edition 12 Acknowledgements 14 Subscripts 18 Superscript 18 1 Introduction: Dimensional Analysis: Similitude 20 Definition of a turbomachine 20 Units and dimensions 22 Dimensional analysis and performance laws 23 Incompressible fluid analysis 25 Performance characteristics 26 Variable geometry turbomachines 28 Specific speed 29 Cavitation 31 Compressible gas flow relations 34 Compressible fluid analysis 35 The inherent unsteadiness of the flow within turbomachines 39 2 Basic Thermodynamics, Fluid Mechanics: Definitions of Efficiency 42 The equation of continuity 42 The first law of thermodynamics internal energy 43 The momentum equation Newton’s second law of motion 0 The second law of thermodynamics entropy 48 Definitions of efficiency 49 Small stage or polytropic efficiency 54 Nozzle efficiency 60 Diffusers 62 3 Two- dimensional Cascades 74 Cascade nomenclature 75 Analysis of cascade forces 76 Energy losses 78 Lift and drag 78 Circulation and lift 80 Efficiency of a compressor cascade 81 Performance of two-dimensional cascades 82 The cascade wind tunnel 82 Cascade test results 84 Compressor cascade performance 87 Turbine cascade performance 89 Compressor cascade correlations 90 Fan blade design (McKenzie) 99 Turbine cascade correlation (Ainley) 100 Comparison of the profile loss in a cascade and in a turbine stage 105 Optimum space chord ratio of turbine blades (Zweifel) 106 4 Axial- flow Turbines: Two- dimensional Theory 112 Velocity diagrams of the axial turbine stage 112 Thermodynamics of the axial turbine stage 113 Stage losses and efficiency 115 Soderberg’s correlation 0 Types of axial turbine design 118 Stage reaction 120 Diffusion within blade rows 122 Choice of reaction and effect on efficiency 126 Design point efficiency of a turbine stage 127 Maximum total-to-static efficiency of a reversible turbine stage 131 Stresses in turbine rotor blades 133 Turbine flow characteristics 139 Flow characteristics of a multistage turbine 141 The Wells turbine 143 5 Axial- flow Compressors and Fans 156 Two-dimensional analysis of the compressor stage 157 Velocity diagrams of the compressor stage 159 Thermodynamics of the compressor stage 160 Stage loss relationships and efficiency 161 Reaction ratio 162 Choice of reaction 162 Stage loading 163 Simplified off-design performance 164 Stage pressure rise 166 Pressure ratio of a multistage compressor 167 Estimation of compressor stage efficiency 168 Stall and surge phenomena in compressors 173 Control of flow instabilities 178 Axial-flow ducted fans 179 Blade element theory 181 Blade element efficiency 182 Lift coefficient of a fan aerofoil 183 6 Three- dimensional Flows in Axial Turbomachines 188 Theory of radial equilibrium 188 The indirect problem 190 The direct problem 198 Compressible flow through a fixed blade row 199 Constant specific mass flow 200 Off-design performance of a stage 202 Free-vortex turbine stage 203 Actuator disc approach 205 Blade row interaction effects 209 Computer-aided methods of solving the through-flow problem 210 Secondary flows 212 7 Centrifugal Pumps, Fans and Compressors 218 Some definitions 219 Theoretical analysis of a centrifugal compressor 221 Inlet casing 222 Impeller 222 Conservation of rothalpy 223 Diffuser 224 Inlet velocity limitations 224 Optimum design of a pump inlet 225 Optimum design of a centrifugal compressor inlet 227 Slip factor 232 Head increase of a centrifugal pump 237 Performance of centrifugal compressors 238 The diffuser system 246 Choking in a compressor stage 249 8 Radial Flow Gas Turbines 255 Types of inward flow radial turbine 256 Thermodynamics of the 90 deg IFR turbine 258 Basic design of the rotor 260 Nominal design point efficiency 261 Mach number relations 265 Loss coefficients in 90 deg IFR turbines 266 Optimum efficiency considerations 267 Criterion for minimum number of blades 272 Design considerations for rotor exit 275 Incidence losses 279 Significance and application of specific speed 282 Optimum design selection of 90 deg IFR turbines 285 Clearance and windage losses 288 Pressure ratio limits of the 90 deg IFR turbine 288 Cooled 90 deg IFR turbines 290 9 Hydraulic Turbines 296 Hydraulic turbines 297 The Pelton turbine 300 Reaction turbines 309 The Francis turbine 309 The Kaplan turbine 315 Effect of size on turbomachine efficiency 318 Cavitation 320 Bibliography 328 Conversion of British Units to SI Units 329 Answers to Problems 330 Index 333 Referex In the intervening 20 years since the 3rd edition of this textbook many advances have been made in the design of turbines and greater understanding of the processes involved have been gained. This 4th edition brings the book up to date