Principles of. Turbomachinery. Seppo A. Korpela. The Ohio State University WILEY A JOHN WILEY & SONS, INC., PUBLICATION

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1 Principles of Turbomachinery Seppo A. Korpela The Ohio State University WILEY A JOHN WILEY & SONS, INC., PUBLICATION

2 CONTENTS Foreword xiii Acknowledgments xv 1 Introduction Energy and fluid machines Energy conversion of fossil fuels Steam turbines Gas turbines Hydraulic turbines Wind turbines Compressors Pumps and blowers Other uses and issues Historical survey Water power Wind turbines Steam turbines Jet propulsion Industrial turbines Note on units 12 vii

3 Viii CONTENTS 2 Principles of Thermodynamics and Fluid Flow Mass conservation principle First law of thermodynamics Second law of thermodynamics Tds equations Equations of state Properties of steam Ideal gases Air tables and isentropic relations Ideal gas mixtures Incompressibility Stagnation state Efficiency Efficiency measures Thermodynamic losses Incompressible fluid Compressible flows Momentum balance 47 Exercises 54 3 Compressible Flow through Nozzles Mach number and the speed of sound Mach number relations Isentropic flow with area change Converging nozzle Converging-diverging nozzle Normal shocks Rankine Hugoniot relations Influence of friction in flow through straight nozzles Polytropic efficiency Loss coefficients Nozzle efficiency Combined Fanno flow and area change Supersaturation Prandtl-Meyer expansion Mach waves Prandtl-Meyer theory Flow leaving a turbine nozzle 100 Exercises Principles of Turbomachine Analysis 105

4 CONTENTS ix 4.1 Velocity triangles Moment of momentum balance Energy transfer in turbomachines Trothalpy and specific work in terms of velocities Degree of reaction Utilization Scaling and similitude Similitude Incompressible flow Shape parameter or specific speed Compressible flow analysis Performance characteristics Compressor performance map Turbine performance map 131 Exercises Steam Turbines Introduction Impulse turbines Single-stage impulse turbine Pressure compounding Blade shapes Velocity compounding Stage with zero reaction Loss coefficients 160 Exercises Axial Turbines Introduction Turbine stage analysis Flow and loading coefficients and reaction ratio Fifty percent (50%) stage Zero percent (0%) reaction stage Off-design operation Three-dimensional flow Radial equilibrium Free vortex flow Fixed blade angle Constant mass flux Turbine efficiency and losses Soderberg loss coefficients 190

5 X CONTENTS Stage efficiency Stagnation pressure losses Performance charts Zweifel correlation Further discussion of losses Ainley-Mathieson correlation Secondary loss Multistage turbine Reheat factor in a multistage turbine Polytropic or small-stage efficiency 216 Exercises Axial Compressors Compressor stage analysis Stage temperature and pressure rise Analysis of a repeating stage Design deflection Compressor performance map Radial equilibrium Modified free vortex velocity distribution Velocity distribution with zero-power exponent Velocity distribution with first-power exponent Diffusion factor Momentum thickness of a boundary layer Efficiency and losses Efficiency Parametric calculations Cascade aerodynamics Blade shapes and terms Blade forces Other losses Diffuser performance Flow deviation and incidence Multistage compressor Compressibility effects 261 Exercises Centrifugal Compressors and Pumps Compressor analysis Slip factor Pressure ratio

6 CONTENTS XI 8.2 Inlet design Choking of the inducer Exit design Performance characteristics Diffusion ratio Blade height Vaneless diffuser Centrifugal pumps Specific speed and specific diameter Fans Cavitation Diffuser and volute design Vaneless diffuser Volute design 306 Exercises Radial Inflow Turbines Turbine analysis Efficiency Specific speed and specific diameter Stator flow Loss coefficients for stator flow Design of the inlet of a radial inflow turbine Minimum inlet Mach number Blade stagnation Mach number Inlet relative Mach number Design of the Exit Minimum exit Mach number Radius ratio rzslr Blade height-to-radius ratio 62/^ Optimum incidence angle and the number of blades 351 Exercises Hydraulic Turbines Hydroelectric Power Plants Hydraulic turbines and their specific speed Pelton wheel Francis turbine Kaplan turbine Cavitation 380 Exercises 382

7 Xii CONTENTS 11 Hydraulic Transmission of Power Fluid couplings Fundamental relations Flow rate and hydrodynamic losses Partially filled coupling Torque converters Fundamental relations Performance 394 Exercises Wind turbines Horizontal-axis wind turbine Momentum and blade element theory of wind turbines Momentum Theory Ducted wind turbine Blade element theory and wake rotation Irrotational wake Blade Forces Nonrotating wake Wake with rotation Ideal wind turbine Prandtl's tip correction Turbomachinery and future prospects for energy 429 Exercises 430 Appendix A: Streamline curvature and radial equilibrium 431 A.l Streamline curvature method 431 A.1.1 Fundamental equations 431 A. 1.2 Formal solution 435 Appendix B: Thermodynamic Tables 437 References 449 Index 453

Principles of Turbomachinery

Principles of Turbomachinery Principles of Turbomachinery Seppo A. Korpela The Ohio State University WILEY A JOHN WILEY & SONS, INC., PUBLICATION Copyright 2011 by John Wiley & Sons, Inc. All rights reserved.