Fluid Mechanics and Thermodynamics of Turbomachinery PDF
Preview Fluid Mechanics and Thermodynamics of Turbomachinery
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. SeniorFellowattheUniversityofLiverpool FOURTH EDITION in SI/METRIC UNITS Butterworth-Heinemann LinacreHouse,JordanHill,OxfordOX2 8DP 225Wildwood Avenue, Woburn,MA01801-2041 Adivision of Reed Educational and ProfessionalPublishing Ltd Amember ofthe ReedElsevierplcgroup FirstpublishedbyPergamon Press Ltd1966 Second edition 1975 Third edition 1978 Reprinted 1979,1982(twice),1984, 1986, 1989, 1992, 1995 Fourthedition1998 ª S.L.Dixon1978,1998 All rightsreserved.Nopartof this publication maybereproducedinany materialform(including photocopyingorstoring inanymedium by electronic means andwhetherornot transientlyorincidentally tosome otheruseofthispublication)without the written permissionof thecopyrightholder except inaccordancewith theprovisionsof theCopyright, Designs andPatents Act 1988orunderthe termsofa license issued by theCopyright LicensingAgency Ltd, 90Tottenham CourtRoad, London,England W1P 9HE. Applicationsfor the copyright holder’s writtenpermission toreproduceanypartofthispublication shouldbe addressed tothe publishers BritishLibraryCataloguinginPublicationData Acatalogue record forthisbook is availablefromtheBritish Library ISBN 0750670592 Libraryof CongressCataloguing in Publication Data Acatalogue record forthisbook is availablefromtheLibraryof Congress TypesetbyLaserWords,Madras, India Printed and bound in Contents PREFACETO FOURTH EDITION ix PREFACETO THIRD EDITION xi ACKNOWLEDGEMENTS xiii LISTOF SYMBOLS xv 1. Introduction: Dimensional Analysis: Similitude 1 Definitionofaturbomachine 1 Unitsanddimensions 3 Dimensionalanalysisandperformancelaws 4 Incompressiblefluidanalysis 6 Performancecharacteristics 7 Variablegeometryturbomachines 9 Specificspeed 10 Cavitation 12 Compressiblegasflowrelations 15 Compressiblefluidanalysis 16 Theinherentunsteadinessoftheflowwithinturbomachines 20 References 21 Problems 22 2. Basic Thermodynamics, Fluid Mechanics: Definitions of Efficiency 23 Introduction 23 Theequationofcontinuity 23 Thefirstlawofthermodynamics internalenergy 24 Themomentumequation Newton’ssecondlawofmotion 25 Thesecondlawofthermodynamics entropy 29 Definitionsofefficiency 30 Smallstageorpolytropicefficiency 35 Nozzleefficiency 41 Diffusers 43 References 53 Problems 53 vi Contents 3. Two-dimensional Cascades 55 Introduction 55 Cascadenomenclature 56 Analysisofcascadeforces 57 Energylosses 59 Liftanddrag 59 Circulationandlift 61 Efficiencyofacompressorcascade 62 Performanceoftwo-dimensionalcascades 63 Thecascadewindtunnel 63 Cascadetestresults 65 Compressorcascadeperformance 68 Turbinecascadeperformance 70 Compressorcascadecorrelations 71 Fanbladedesign(McKenzie) 80 Turbinecascadecorrelation(Ainley) 81 Comparisonoftheprofilelossinacascadeandinaturbinestage 86 Optimumspace-chordratioofturbineblades(Zweifel) 87 References 88 Problems 90 4. Axial-flow Turbines: Two-dimensional Theory 93 Introduction 93 Velocitydiagramsoftheaxialturbinestage 93 Thermodynamicsoftheaxialturbinestage 94 Stagelossesandefficiency 96 Soderberg’scorrelation 97 Typesofaxialturbinedesign 99 Stagereaction 101 Diffusionwithinbladerows 103 Choiceofreactionandeffectonefficiency 107 Designpointefficiencyofaturbinestage 108 Maximumtotal-to-staticefficiencyofareversibleturbinestage 112 Stressesinturbinerotorblades 114 Turbineflowcharacteristics 120 Flowcharacteristicsofamultistageturbine 122 TheWellsturbine 124 References 132 Problems 133 5. Axial-flow Compressors and Fans 137 Introduction 137 Two-dimensionalanalysisofthecompressorstage 138 Velocitydiagramsofthecompressorstage 140 Thermodynamicsofthecompressorstage 141 Contents vii Stagelossrelationshipsandefficiency 142 Reactionratio 143 Choiceofreaction 143 Stageloading 144 Simplifiedoff-designperformance 145 Stagepressurerise 147 Pressureratioofamultistagecompressor 148 Estimationofcompressorstageefficiency 149 Stallandsurgephenomenaincompressors 154 Controlofflowinstabilities 159 Axial-flowductedfans 160 Bladeelementtheory 162 Bladeelementefficiency 163 Liftcoefficientofafanaerofoil 164 References 165 Problems 166 6. Three-dimensional Flows in Axial Turbomachines 169 Introduction 169 Theoryofradialequilibrium 169 Theindirectproblem 171 Thedirectproblem 179 Compressibleflowthroughafixedbladerow 180 Constantspecificmassflow 181 Off-designperformanceofastage 183 Free-vortexturbinestage 184 Actuatordiscapproach 186 Bladerowinteractioneffects 190 Computer-aidedmethodsofsolvingthethrough-flowproblem 191 Secondaryflows 193 References 195 Problems 196 7. Centrifugal Pumps, Fans and Compressors 199 Introduction 199 Somedefinitions 200 Theoreticalanalysisofacentrifugalcompressor 202 Inletcasing 203 Impeller 203 Conservationofrothalpy 204 Diffuser 205 Inletvelocitylimitations 205 Optimumdesignofapumpinlet 206 Optimumdesignofacentrifugalcompressorinlet 208 Slipfactor 213 Headincreaseofacentrifugalpump 218 viii Contents Performanceofcentrifugalcompressors 219 Thediffusersystem 227 Chokinginacompressorstage 230 References 232 Problems 233 8. Radial Flow Gas Turbines 236 Introduction 236 Typesofinwardflowradialturbine 237 Thermodynamicsofthe90degIFRturbine 239 Basicdesignoftherotor 241 Nominaldesignpointefficiency 242 Machnumberrelations 246 Losscoefficientsin90degIFRturbines 247 Optimumefficiencyconsiderations 248 Criterionforminimumnumberofblades 253 Designconsiderationsforrotorexit 256 Incidencelosses 260 Significanceandapplicationofspecificspeed 263 Optimumdesignselectionof90degIFRturbines 266 Clearanceandwindagelosses 269 Pressureratiolimitsofthe90degIFRturbine 269 Cooled90degIFRturbines 271 References 272 Problems 273 9. Hydraulic Turbines 277 Introduction 277 Hydraulicturbines 278 ThePeltonturbine 281 Reactionturbines 290 TheFrancisturbine 290 TheKaplanturbine 296 Effectofsizeonturbomachineefficiency 299 Cavitation 301 References 305 Problems 306 Bibliography 309 Appendix 1. Conversion of British and US Units to SI Units 310 Appendix 2. Answers to Problems 311 Index 315 PrefacetotheFourthEdition It is now twenty years since the third edition of this book was published and in that period many advances have been made to the art and science of turboma- chinerydesign.Knowledgeoftheflowprocesseswithinturbomachineshasincreased dramatically resulting in the appearance of new and innovative designs. Some of the long-standing, apparently intractable, problems such as surge and rotating stall have begun to yield to new methods of control. New types of flow machine have made their appearance (e.g. the Wells turbine and the axi-fuge compressor) and some changes have been made to established design procedures. Much attention is now being given to blade and flow passage design using computational fluid dynamics (CFD) and this must eventually bring forth further design and flow effi- ciency improvements. However, the fundamentals do not change and this book is still concerned with the basics of the subject as well as looking at new ideas. ThebookwasoriginallyperceivedasatextforstudentstakinganHonoursdegree in engineering which included turbomachines as well as assisting those undertaking more advanced postgraduate courses in the subject. The book was written for engi- neers rather than mathematicians. Much stress is laid on physical concepts rather thanmathematicsandtheuseofspecialisedmathematicaltechniquesismostlykept to a minimum. The book should continue to be of use to engineers in industry and technological establishments, especially as brief reviews are included on many important aspects of turbomachinery giving pointers to more advanced sources of information. For those looking towards the wider reaches of the subject area some interesting reading is contained in the bibliography. It might be of interest to know that the third edition was published in four languages. A fairly large number of additions and extensions have been included in the book from the new material mentioned as well as “tidying up” various sections no longer to my liking. Additions include some details of a new method of fan blade design, the determination of the design point efficiency of a turbine stage, sections on centrifugal stresses in turbine blades and blade cooling, control of flow instabilities in axial-flow compressors, design of the Wells turbine, consideration of rothalpyconservationinimpellers(androtors),definingandcalculatingtheoptimum efficiency of inward flow turbines and comparison with the nominal design. A number of extensions of existing topics have been included such as updating and extending the treatment and application of diffuser research, effect of prerotation of the flow in centrifugal compressors and the use of backward swept vanes on their performance, also changes in the design philosophy concerning the blading of axial-flow compressors. The original chapter on radial flow turbines has been split into two chapters; one dealing with radial gas turbines with some new extensions and the other on hydraulic turbines. In a world striving for a ‘greener’ future it was felt that there would now be more than just a little interest in hydraulic turbines. It is a subject that is usually included in many mechanical engineering courses. This chapter includes a few new ideas which could be of some interest.
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