Mecanica De Fluidos

Fluid Mechanics, Thermodynamics of Turbomachinery
S.L. Dixon, B.Eng., PH.D.
Senior Fellow at the University of Liverpool

FOURTH EDITION in SI/METRIC UNITS

Fluid Mechanics, Thermodynamics of Turbomachinery

FOURTH EDITION in SI/METRIC UNITS

In memory of Avril and baby Paul

Fluid Mechanics, Thermodynamics of Turbomachinery
S. L. Dixon, B.Eng., Ph.D.
Senior Fellow at theUniversity of Liverpool

FOURTH EDITION in SI/METRIC UNITS

Butterworth-Heinemann Linacre House, Jordan Hill, Oxford OX2 8DP 225 Wildwood Avenue, Woburn, MA 01801-2041 A division of Reed Educational and Professional Publishing Ltd A member of the Reed Elsevier plc group First published by Pergamon Press Ltd 1966 Second edition 1975 Third edition 1978 Reprinted 1979, 1982 (twice), 1984, 1986, 1989,1992, 1995 Fourth edition 1998

© S.L. Dixon 1978, 1998
All rights reserved. No part of this publication may be reproduced in any material form (including photocopying or storing in any medium by electronic means and whether or not transiently or incidentally to some other use of this publication) without the written permission of the copyright holder except in accordance with the provisions ofthe Copyright, Designs and Patents Act 1988 or under the terms of a license issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London, England W1P 9HE. Applications for the copyright holder’s written permission to reproduce any part of this publication should be addressed to the publishers British Library Cataloguing in Publication Data A catalogue record for this book isavailable from the British Library ISBN 0 7506 7059 2 Library of Congress Cataloguing in Publication Data A catalogue record for this book is available from the Library of Congress

Typeset by Laser Words, Madras, India Printed and bound in

Contents
PREFACE TO FOURTH EDITION PREFACE TO THIRD EDITION ACKNOWLEDGEMENTS LIST OF SYMBOLS xv
1

ix xi

xiii

1. Introduction: Dimensional Analysis:Similitude
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 References 21 Problems 22

20

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 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

25

viContents

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 71Fan blade design (McKenzie) 80 Turbine cascade correlation (Ainley) 81 Comparison of the profile loss in a cascade and in a turbine stage Optimum space-chord ratio of turbine blades (Zweifel) 87 References 88 Problems 90

86

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 lossesand 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 Stresses in turbine rotor blades 114 Turbine flow characteristics 120 Flow characteristics of a multistage turbine...