Introduction to computational fluid dynamics

398 Pages·2005·2.361 MB·English

by  Date A.W.

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INTRODUCTION TO COMPUTATIONAL FLUID DYNAMICS
IntroductiontoComputationalFluidDynamicsintroducesalltheprimarycom-
ponentsforlearningandpracticingcomputationalfluiddynamics(CFD).The
bookiswrittenforfinalyearundergraduatesand/orgraduatestudentsinme-
chanical, chemical, and aeronautical engineering who have undergone basic
coursesinthermodynamics,fluidmechanics,andheatandmasstransfer.Chap-
ters cover discretisation of equations for transport of mass, momentum, and
energyonCartesian,structuredcurvilinear,andunstructuredmeshes;solution
ofdiscretisedequations,numericalgridgeneration,andconvergenceenhance-
ment.Thebookfollowsaconsistentphilosophyofcontrol-volumeformulation
ofthefundamentallawsoffluidmotionandenergytransferandintroducesa
novel notion of “smoothing pressure correction” for solution of flow equa-
tions on collocated grids within the framework of the well-known SIMPLE
algorithm.
Thereareover50solvedproblemsinthetextandover130end-of-chapter
problems.Practicingindustryprofessionalswillalsofindthisbookusefulfor
continuingeducationandrefreshercourses.
ProfessorAnilW.Dateobtainedhisbachelor’sdegreeinmechanicalengineer-
ingfromBombayUniversity;hismaster’sdegreeinthermo-fluidsfromUMIST
Manchester, UK; and his doctorate in heat transfer from Imperial College of
Science and Technology, London. He has been a member of the Thermo-
Fluids-Engineering group of the Mechanical Engineering Department at IIT
Bombaysince1973.Overthepastthirtyyears,hehastaughtcoursesatboth
undergraduateandpostgraduatelevelinthermodynamics,energyconversion,
heatandmasstransfer,andcombustion.Hehasbeenengagedinresearchand
consultinginthermo-fluidsengineeringandisanactivereviewerofresearch
proposalsandpapersforvariousnationalandinternationalbodiesandjournals.
He has been Editor for India of the Journal of Enhanced Heat Transfer and
has contributed research papers to several international journals in the field.
HehasbeenavisitingscientistatCornellUniversityandavisitingprofessor
attheUniversityofKarlsruhe,Germany.Hehasdeliveredseminarlecturesat
universitiesinAustralia,HongKong,Sweden,Germany,UK,USA,andIndia.
Professor Date derives great satisfaction from applying thermo-fluid science
torural-technologyproblemsinIndiaandhastaughtcoursesinscience,tech-
nology, and society and in appropriate technology at IIT Bombay. Professor
DateisaFellowoftheIndianNationalAcademyofEngineering(FNAE).
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Introduction to
Computational Fluid Dynamics
ANIL W. DATE
IndianInstituteofTechnology,Bombay
iii
cambridge university press
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo
Cambridge University Press
TheEdinburghBuilding,Cambridgecb22ru,UK
Published in the United States of America by Cambridge University Press, New York
www.cambridge.org
Informationo nthi stitle :www.cambri dge.org/9780521853262
© Cambridge University Press 2005
Thispublicationisincopyright.Subjecttostatutoryexceptionandtotheprovisionof
relevant collective licensing agreements, no reproduction of any part may take place
without the written permission of Cambridge University Press.
Firstpublishedinprintformat 2005
isbn-13 978-0-511-13052-6 eBook (NetLibrary)
isbn-10 0-511-13052-x
eBook (NetLibrary)
isbn-13 978-0-521-85326-2 hardback
isbn-10 0-521-85326-5 hardback
CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyofurls
forexternalorthird-partyinternetwebsitesreferredtointhispublication,anddoesnot
guaranteethatanycontentonsuchwebsitesis,orwillremain,accurateorappropriate.
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Dedicatedtothememoryof
Aai,Kaka,andWalmik
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Contents
Nomenclature pagexiii
Preface xvii
1. Introduction..........................................1
1.1 CFDActivity 1
1.2 TransportEquations 2
1.3 NumericalVersusAnalyticalSolutions 5
1.4 MainTask 6
1.5 ANoteonNavier–StokesEquations 9
1.6 OutlineoftheBook 12
Exercises 13
2. 1D Heat Conduction................................17
2.1 Introduction 17
2.2 1DConductionEquation 17
2.3 GridLayout 19
2.4 Discretisation 20
2.4.1 TSEMethod 21
2.4.2 IOCVMethod 23
2.5 StabilityandConvergence 24
2.5.1 ExplicitProcedureψ =0 25
2.5.2 PartiallyImplicitProcedure0<ψ <1 28
2.5.3 ImplicitProcedureψ =1 29
2.6 MakingChoices 31
2.7 DealingwithNonlinearities 32
2.7.1 NonlinearSources 33
2.7.2 NonlinearCoefficients 33
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viii CONTENTS
2.7.3 BoundaryConditions 35
2.7.4 Underrelaxation 37
2.8 MethodsofSolution 38
2.8.1 Gauss–SeidelMethod 38
2.8.2 TridiagonalMatrixAlgorithm 38
2.8.3 Applications 40
2.9 ProblemsfromRelatedFields 45
Exercises 47
3.1DConduction–Convection ........................55
3.1 Introduction 55
3.2 ExactSolution 55
3.3 Discretisation 57
3.4 UpwindDifferenceScheme 59
3.5 ComparisonofCDS,UDS,andExactSolution 60
3.6 NumericalFalseDiffusion 61
3.7 HybridandPower-LawSchemes 63
3.8 TotalVariationDiminishingScheme 63
3.9 StabilityoftheUnsteadyEquation 65
3.9.1 ExactSolution 65
3.9.2 ExplicitFinite-DifferenceForm 66
3.9.3 ImplicitFinite-DifferenceForm 67
Exercises 68
4. 2D Boundary Layers................................71
4.1 GoverningEquations 71
4.2 AdaptiveGrid 73
4.3 Transformationto(x,ω)Coordinates 74
4.4 Discretisation 76
4.5 Determinationofω, y,andr 79
4.6 BoundaryConditions 80
4.6.1 Symmetry 80
4.6.2 Wall 81
4.6.3 FreeStream 82
4.7 SourceTerms 85
4.7.1 PressureGradient 85
4.7.2 Q(cid:2)(cid:2)(cid:2) and R 86
k
4.8 TreatmentofTurbulentFlows 87
4.8.1 MixingLengthModel 88
4.8.2 e−(cid:3) Model 89
4.8.3 Free-ShearFlows 91
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CONTENTS ix
4.9 OverallProcedure 91
4.9.1 CalculationSequence 91
4.9.2 InitialConditions 92
4.9.3 ChoiceofStepSizeandIterations 93
4.10 Applications 93
Exercises 101
5.2DConvection –CartesianGrids .................105
5.1 Introduction 105
5.1.1 MainTask 105
5.1.2 SolutionStrategy 106
5.2 SIMPLE–CollocatedGrids 109
5.2.1 MainIdea 109
5.2.2 Discretisation 110
5.2.3 Pressure-CorrectionEquation 112
5.2.4 FurtherSimplification 117
5.2.5 OverallCalculationProcedure 119
5.3 MethodofSolution 120
5.3.1 IterativeSolvers 120
5.3.2 EvaluationofResiduals 121
5.3.3 Underrelaxation 122
5.3.4 BoundaryConditionsfor(cid:4) 123
5.3.5 BoundaryConditionfor p(cid:2) 125
m
5.3.6 NodeTagging 126
5.4 TreatmentofTurbulentFlows 128
5.4.1 LREModel 128
5.4.2 HREModel 129
5.5 NotionofSmoothingPressureCorrection 133
5.6 Applications 139
Exercises 152
6.2DConvection –ComplexDomains ..............161
6.1 Introduction 161
6.1.1 CurvilinearGrids 161
6.1.2 UnstructuredGrids 162
6.2 CurvilinearGrids 164
6.2.1 CoordinateTransformation 164
6.2.2 TransportEquation 165
6.2.3 InterpretationofTerms 166
6.2.4 Discretisation 168
6.2.5 Pressure-CorrectionEquation 170