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Fluid Mechanics, Thermodynamics of Turbomachinery

Fluid Mechanics, Thermodynamics Dixon, , Fellow at the University of LiverpoolFOURTH EDITION in SI/METRIC UNITSF luid Mechanics, Thermodynamics ofTurbomachineryFOURTH EDITION in SI/METRIC UNITSIn memory ofAvril and baby PaulFluid Mechanics, Thermodynamics ofTurbomachineryS. L. Dixon, , Fellow at the University of LiverpoolFOURTH EDITION in SI/METRIC UNITSB utterworth-HeinemannLinacre House, Jordan Hill, Oxford OX2 8DP225 Wildwood Avenue, Woburn, MA 01801-2041A division of Reed Educational and Professional Publishing LtdA member of the Reed Elsevier plc groupFirst published by Pergamon Press Ltd 1966 Second edition 1975 Third edition 1978 Reprinted 1979, 1982 (twice), 1984, 1986, 1989, 1992, 1995 Fourth edition 1998 Dixon 1978, 1998 All rights reserved.

Basic Thermodynamics, Fluid Mechanics: Definitions of Efficiency 23 Introduction 23 ... Actuator disc approach 186 Blade row interaction effects 190 ... is a subject that is usually included in many mechanical engineering courses. This

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Transcription of Fluid Mechanics, Thermodynamics of Turbomachinery

1 Fluid Mechanics, Thermodynamics Dixon, , Fellow at the University of LiverpoolFOURTH EDITION in SI/METRIC UNITSF luid Mechanics, Thermodynamics ofTurbomachineryFOURTH EDITION in SI/METRIC UNITSIn memory ofAvril and baby PaulFluid Mechanics, Thermodynamics ofTurbomachineryS. L. Dixon, , Fellow at the University of LiverpoolFOURTH EDITION in SI/METRIC UNITSB utterworth-HeinemannLinacre House, Jordan Hill, Oxford OX2 8DP225 Wildwood Avenue, Woburn, MA 01801-2041A division of Reed Educational and Professional Publishing LtdA member of the Reed Elsevier plc groupFirst published by Pergamon Press Ltd 1966 Second edition 1975 Third edition 1978 Reprinted 1979, 1982 (twice), 1984, 1986, 1989, 1992, 1995 Fourth edition 1998 Dixon 1978, 1998 All rights reserved.

2 No part of this publicationmay be reproduced in any material form (includingphotocopying or storing in any medium by electronicmeans and whether or not transiently or incidentallyto some other use of this publication) without thewritten permission of the copyright holder exceptin accordance with the provisions of the Copyright,Designs and Patents Act 1988 or under the terms of alicense issued by the Copyright Licensing Agency Ltd,90 Tottenham Court Road, London, England W1P for the copyright holder s written permissionto reproduce any part of this publication should be addressedto the publishersBritish Library Cataloguing in Publication DataA catalogue record for this book is available from the British LibraryISBN 0 7506 7059 2 Library of Congress Cataloguing in Publication DataA catalogue record for this book is available from the Library of CongressTypeset by Laser Words, Madras, IndiaPrinted and bound inContentsPREFACE TOFOURTHEDITIONixPREFACE TOTHIRDEDITIONxiACKNOWLEDGEMENTS xiiiLIST OFSYMBOLSxv1.

3 Introduction: Dimensional Analysis: Similitude1 Definition of a turbomachine1 Units and dimensions3 Dimensional analysis and performance laws4 Incompressible Fluid analysis6 Performance characteristics7 Variable geometry turbomachines9 Specific speed10 Cavitation12 Compressible gas flow relations15 Compressible Fluid analysis16 The inherent unsteadiness of the flow within turbomachines20 References21 Problems222. Basic Thermodynamics , Fluid Mechanics: Definitions of Efficiency23 Introduction23 The equation of continuity23 The first law of thermodynamicsinternal energy24 The momentum equationNewton s second law of motion25 The second law of thermodynamicsentropy29 Definitions of efficiency30 Small stage or polytropic efficiency35 Nozzle efficiency41 Diffusers43 References53 Problems53viContents3.

4 Two-dimensional Cascades55 Introduction55 Cascade nomenclature56 Analysis of cascade forces57 Energy losses59 Lift and drag59 Circulation and lift61 Efficiency of a compressor cascade62 Performance of two-dimensional cascades63 The cascade wind tunnel63 Cascade test results65 Compressor cascade performance68 Turbine cascade performance70 Compressor cascade correlations71 Fan blade design (McKenzie)80 Turbine cascade correlation (Ainley)81 Comparison of the profile loss in a cascade and in a turbine stage86 Optimum space-chord ratio of turbine blades (Zweifel)87 References88 Problems904. Axial-flow Turbines: Two-dimensional Theory93 Introduction93 Velocity diagrams of the axial turbine stage93 Thermodynamics of the axial turbine stage94 Stage losses and efficiency96 Soderberg s correlation97 Types of axial turbine design99 Stage reaction101 Diffusion within blade rows103 Choice of reaction and effect on efficiency107 Design point efficiency of a turbine stage108 Maximum total-to-static efficiency of a reversible turbine stage112 Stresses in turbine rotor blades114 Turbine flow characteristics120 Flow characteristics of a multistage turbine122 The Wells turbine124 References132 Problems1335.

5 Axial-flow Compressors and Fans137 Introduction137 Two-dimensional analysis of the compressor stage138 Velocity diagrams of the compressor stage140 Thermodynamics of the compressor stage141 ContentsviiStage loss relationships and efficiency142 Reaction ratio143 Choice of reaction143 Stage loading144 Simplified off-design performance145 Stage pressure rise147 Pressure ratio of a multistage compressor148 Estimation of compressor stage efficiency149 Stall and surge phenomena in compressors154 Control of flow instabilities159 Axial-flow ducted fans160 Blade element theory162 Blade element efficiency163 Lift coefficient of a fan aerofoil164 References165 Problems1666.

6 Three-dimensional Flows in Axial Turbomachines169 Introduction169 Theory of radial equilibrium169 The indirect problem171 The direct problem179 Compressible flow through a fixed blade row180 Constant specific mass flow181 Off-design performance of a stage183 Free-vortex turbine stage184 Actuator disc approach186 Blade row interaction effects190 Computer-aided methods of solving the through-flow problem191 Secondary flows193 References195 Problems1967. Centrifugal Pumps, Fans and Compressors199 Introduction199 Some definitions200 Theoretical analysis of a centrifugal compressor202 Inlet casing203 Impeller203 Conservation of rothalpy204 Diffuser205 Inlet velocity limitations205 Optimum design of a pump inlet206 Optimum design of a centrifugal compressor inlet208 Slip factor213 Head increase of a centrifugal pump218viiiContentsPerformance of centrifugal compressors219 The diffuser system227 Choking in a compressor stage230 References232 Problems2338.

7 Radial Flow Gas Turbines236 Introduction236 Types of inward flow radial turbine237 Thermodynamics of the 90 deg IFR turbine239 Basic design of the rotor241 Nominal design point efficiency242 Mach number relations246 Loss coefficients in 90 deg IFR turbines247 Optimum efficiency considerations248 Criterion for minimum number of blades253 Design considerations for rotor exit256 Incidence losses260 Significance and application of specific speed263 Optimum design selection of 90 deg IFR turbines266 Clearance and windage losses269 Pressure ratio limits of the 90 deg IFR turbine269 Cooled 90 deg IFR turbines271 References272 Problems2739.

8 Hydraulic Turbines277 Introduction277 Hydraulic turbines278 The Pelton turbine281 Reaction turbines290 The Francis turbine290 The Kaplan turbine296 Effect of size on turbomachine efficiency299 Cavitation301 References305 Problems306 Bibliography309 Appendix 1. Conversion of British and US Units to SI Units310 Appendix 2. Answers to Problems311 Index315 Preface to the Fourth EditionIt is now twenty years since the third edition of this book was published and inthat period many advances have been made to the art and science of turboma-chinery design. Knowledge of the flow processes within turbomachines has increaseddramatically resulting in the appearance of new and innovative designs.

9 Some ofthe long-standing, apparently intractable, problems such as surge and rotating stallhave begun to yield to new methods of control. New types of flow machine havemade their appearance ( the Wells turbine and the axi-fuge compressor) andsome changes have been made to established design procedures. Much attentionis now being given to blade and flow passage design using computational fluiddynamics (CFD) and this must eventually bring forth further design and flow effi-ciency improvements. However, the fundamentals do not change and this book isstill concerned with the basics of the subject as well as looking at new book was originally perceived as a text for students taking an Honours degreein engineering which included turbomachines as well as assisting those undertakingmore advanced postgraduate courses in the subject.

10 The book was written for engi-neers rather than mathematicians. Much stress is laid on physical concepts ratherthan mathematics and the use of specialised mathematical techniques is mostly keptto a minimum. The book should continue to be of use to engineers in industryand technological establishments, especially as brief reviews are included on manyimportant aspects of Turbomachinery giving pointers to more advanced sources ofinformation. For those looking towards the wider reaches of the subject area someinteresting reading is contained in the bibliography. It might be of interest to knowthat the third edition was published in four fairly large number of additions and extensions have been included in thebook from the new material mentioned as well as tidying up various sectionsno longer to my liking.


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