Principles of Turbomachinery

To J. M. T.

Principles of Turbomachinery

R. K. Turton Lecturer in Mechanical Engineering Loughborough University of Technology

London New York

E. & F. N. Spon

ISBN 978-94-010-9691-1 ISBN 978-94-010-9689-8 (eBook)

DOI 10.1007/978-94-010-9689-8

First published 1984 by E. & F. N. Spon Ltd

11 New Fetter Lane, London EC4P 4EE Published in the USA by

E. & F. N. Spon 733 Third Avenue, New York NY 10017

© R. K. Turton 1984 Softcover reprint ofthe hardcover 1st edition 1984

J. W. Arrowsmith Ltd, Bristol

This title is available in both hardbound and paperback editions. The paperback edition is sold subject to the condition

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All rights reserved. No part of this book may be reprinted, or reproduced or utilized in any form or by any electronic,

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storage and retrieval system, without permission in writing from the Publisher.

British Library Cataloguing in Publication Data Turton, R. K.

Principles of turbomachinery. 1. Turbomachines-Fluid dynamics 2. Thermodynamics I. Title 621.8'11 TJ267

ISBN 978-94-010-9691-1

Library of Congress Cataloging-in Publication Data Turton, R. K. (Robert Keith)

Principles of turbomachinery.

Bibliography: p. Includes index. 1. Turbomachines. I.Title.

TJ267.T88 1984 621.406 84-5490 ISBN 978-94-010-9691-1

Contents

Preface Symbols used: their meaning and dimensions

1 Fundamental principles 1.1 Introduction 1.2 Euler equation 1.3 Reaction 1.4 Application to a centrifugal machine 1.5 Application to axial pumps and turbines

1.5.1 Axial pump or fan 1.5.2 Axial turbine stage

1.6 Alternative operating modes 1.7 Compressible flow theory

1.7.1 General application to a machine 1.7.2 Compression process 1.7.3 Expansion process

1.8 Shock wave effects 1.9 Cavitation

1.9.1 Phenomenon of cavitation 1.9.2 Suction pressure and NPSH (or NPSE)

1.10 Illustrative examples 1.10.1 Radial outflow machine (pump) 1.10.2 Axial pump and turbine 1.10.3 Compressible flow problem 1.10.4 Example of an NPSE calculation

2 Principles and practice of scaling laws 2.1 Introduction 2.2 Performance laws

Page IX

xi

1 1 2 3 4 8 8

11 13 14 14 15 19 23 24 24 27 29 29 30 31 33

34 34 35

vi Contents

2.3 Concept of specific speed 2.4 Cavitation parameters 2.5 Scale effects in incompressible units

2.5.1 Hydraulic machines 2.5.2 Cavitation problems 2.5.3 Fans and blowers

2.6 Scale effects in compressible machines 2.7 1llustrative examples

2.7.1 Similarity laws applied to a water turbine 2.7.2 Compressor performance prediction problem

3 Principles of axial flow machines 3.1 Introduction 3.2 Wing theory 3.3 Isolated aerofoil data 3.4 Cascade data 3.5 Radial equilibrium theories 3.6 Actuator disc approach 3.7 Stall and surge effects

3.7.1 Introduction 3.7.2 Stalling offans and compressor stages 3.7.3 Surge and stall in compressors

4 Principles of radial and mixed flow machines 4.1 Introduction 4.2 One-dimensional approach 4.3 Two-dimensional approach

4.3.1 Passage shapes 4.3.2 Impeller or rotating cascade

4.4 Three-dimensional problem 4.5 Discussion of theoretical approaches to analysis and

design

5 Centrifugal machines 5.1 Introduction 5.2 Inlet or intake systems 5.3 Impeller

5.3.1 Eye or inducer section 5.3.2 Impeller design

38 39 41 41 44 45 45 46 46 47

49 49 51 56 59 70 73 74 74 74 75

77 77 77 79 79 81 87

88

91 91 95 95 95 97

5.4 Outlet systems 5.4.1 Vaneless diffuser 5.4.2 Volute or spiral casing 5.4.3 Vaned diffuser systems

5.5 Thrust loads due to hydrodynamic effects 5.5.1 Radial thrust forces 5.5.2 Axial thrust loads

6 Axial machines for incompressible ftow 6.1 Introduction 6.2 Axial flow pumps and fans 6.3 Axial water turbines 6.4 Forces on blades and their implications for design

6.4.1 Static blades 6.4.2 Rotating blades

6.5 Concluding remarks

7 Axial turbines and compressors for compressible ftow 7.1 Introduction 7.2 Approach to axial compressor principles 7.3 Axial turbine principles

7.3.1 General principles 7.3.2 Partial admission problem

7.4 Other problems

8 Radial flow turbines 8.1 Introduction 8.2 Water turbines 8.3 Radial inflow gas turbine

8.3.1 Nozzle systems 8.3.2 Rotor geometry 8.3.3 Worked example

8.4 Ljungstrom or radial outflow turbine

9 Cavitation and other matters 9.1 Introduction 9.2 Effects of cavitation on machines

9.2.1 Surface damage and erosion effects 9.2.2 Hydrodynamic effects

Contents vii

108 109 111 116 120 120 121

125 125 125 129 138 138 140 140

142 142 143 151 151 157 158

159 159 161 163 163 165 168 169

172 172 172 172 174

viii Contents

9.2.3 Thermodynamic effects on pump cavitation 175 9.2.4 Inducer 178

9.3 Problems involved in special pumping applications 179 9.3.1 Gas suspension problems 179 9.3.2 Solids pumping 180 9.3.3 Pumping viscous fluids 182

9.4 Pumped storage systems 182 9.5 Some comments on output control of rotating machines 185

References 188 Additional bibliography 195 Index 196

Preface

This text outlines the fluid and thermodynamic principles that apply to all classes of turbomachines, and the material has been presented in a unified way. The approach has been used with successive groups of final year mechanical engineering students, who have helped with the development of the ideas outlined. As with these students, the reader is assumed to have a basic understanding of fluid mechanics and thermodynamics. However, the early chapters combine the relevant material with some new concepts, and provide basic reading references.

Two related objectives have defined the scope of the treatment. The first is to provide a general treatment of the common forms of turbo machine, covering basic fluid dynamics and thermodynamics of flow through passages and over surfaces, with a brief derivation of the fundamental governing equations. The second objective is to apply this material to the various machines in enough detail to allow the major design and performance factors to be appreciated. Both objectives have been met by grouping the machines by flow path rather than by application, thus allowing an appreciation of points of similarity or difference in approach. No attempt has been made to cover detailed points of design or stressing, though the cited references and the body of information from which they have been taken give this sort of information.

The first four chapters introduce the fundamental relations, and the suc­ceeding chapters deal with applications to the various flow paths. The last chapter covers the effects of cavitation, solids suspensions, gas content and pumped storage systems, and includes a short discussion of the control of output. These topics have been included to highlight the difficulties encoun­tered when the machine is not dealing with a clean Newtonian fluid, or in systems where problems are posed that can only be solved by compromise. Chapter 5 discusses all the conventional centrifugal machines, covering in a uniform manner the problems faced with liquids and gases: since high pressure rise machines have a number of stages, the ways in which fluid is

x Preface

guided from stage to stage are introduced. Thrust load problems are described and the common solutions adopted are outlined. The discussion of axial machines has been divided between two chapters, as the technologies of pumps, fans and water turbines are similar but differ from those used in compressible machines. Radial flow turbines form the subject matter of Chapter 8, and the common designs in use in industry and in turbochargers are discussed.

Worked examples have been included in all chapters but the last. They are intended to provide illustration of the main points of the text, and to give a feel for both the shape of the velocity triangles and the sizes of the velocity vectors that normally apply. They are of necessity simplified, and must not be regarded as representing current practice in all respects. No problems for student solution have been provided. Teachers normally prefer to devise their own material, and may obtain copies of examination qu~stions set by other institutions if they wish.

As a matter of course the SI system of units has been used throughout, except in some diagrams. To assist the reader, a list of symbols used in the early chapters, together with a statement of the conventional dimensions used, follows the Preface. As far as possible the British Standard on symbols has been followed but, where current and hallowed practice dictates the use of certain symbols, these have been used; it is hoped that where the same symbol appears to have different meanings the context makes the usage clear.

The material presented forms the core of a lecture course of about 46 hours, and the author hopes that in the inevitable distillation no ambiguities have occurred. He will be grateful for comments and suggestions, as he is still an earnest 'seeker after truth'.

Finally, it is necessary to offer some words of thanks, especially to Mrs Redman, who ensured that the diagrams were clear, to Mrs Smith and Mrs McKnight, who helped with the typing, and finally to my dear wife, who was so patient and who ensured that the proof-reading was done properly.

Symbols used: their meaning and dimensions

a acoustic velocity b passage height CL lift coefficient (Table 3.1)

CD drag coefficient (Table 3.1) Cp pressure rise coefficient (Equation 3.15) Cp specific heat at constant pressure Cy specific heat at constant volume D diameter D drag force on an aerofoil

Fa for~ acting in the axial direction on a foil or blade

FI force acting in the tangential direction on a foil or blade

9 acceleration due to gravity gH specific energy h specific enthalpy H head K lattice coefficient (Equation 3.11) k an alternative to '}' ( = CJCy )

k. dimensionless specific speed L lift force on an aerofoil M pitching moment acting on a foil Mn Mach number (= V fa) m mass flow rate N rotational speed

ms- 1

m

kJkg- 1 K- 1

kJkg- 1 K- 1

m N N

N

ms- 2

Jkg- 1

Jkg- 1

m of liquid

N Nm

kgs- 1

rev min- 1

xii Symbols used: their meaning and dimensions

NPSE net positive suction energy kJkg- 1

NPSEa net positive suction energy available kJkg- 1

NPSER net positive suction energy required kJkg- 1

NPSH net positive suction head m ofliquid Ns specific speed 0 opening or throat in a turbine cascade m

P pressure Nm- 2

Po stagnation pressure Nm- 2

Pv vapour pressure Nm- 2

p power Js- 1 = W

Q volumetric flow rate m3 s- 1

R reaction (Section 1.3) R specific gas constant kJkg- 1 K- 1

Re Reynolds number

Rem model Reynolds number S suction specific speed t blade thickness m t blade passage minimum width or throat m T temperature (absolute) K

To stagnation temperature (absolute) K T torque Nm u Peripheral velocity ms- 1

V absolute velocity ms- 1

v.. axial component of absolute velocity ms- 1

v.. normal component of absolute velocity ms- 1

"is or ("isen) isentropic velocity (Equation 1.34) ms- 1

VR radial component of absolute velocity ms- 1

v.. peripheral component of absolute velocity ms- 1

W relative velocity ms- 1

w.. peripheral component of relative velocity ms- 1

YN,YR loss coefficients (Equation 3.27)

(X angle made by absolute velocity degrees p angle made by relative velocity degrees y ratio of specific heats y stagger angle degrees () deviation angle degrees B fluid deflection degrees , loss coefficient (Equation 3.13)

Symbols used: their meaning and dimensions xiii

11 efficiency

I1ss static to static efficiency

I1TS total to static efficiency

I1rr total to total efficiency () camber angle degrees K elastic modulus kgm- 1 S-2

J.1 absolute viscosity kgm- 1 S-l

v kinematic viscosity m2 S-l

e Markov's loss coefficient (Equation 3.26) p density kgm- 3

(J Thoma's cavitation parameter (J velocity ratio (Equation 3.29) ¢ flow coefficient (V./u)

'" specific energy coefficient

'" I1rr/2cxf. (Equation 3.30)

n Howell's work done factor w angular velocity rads- 1

Subscripts 1, 2 etc indicate the point of reference. For a complete definition of blade terminology please refer also to Fig. 3.2 and Table 3.1.