ComputationalFluidDynamicsforEngineers Computationalfluiddynamics(CFD)hasbecomeanindispensabletoolformanyengi- neers.ThisbookgivesanintroductiontoCFDsimulationsofturbulence,mixing,reac- tion, combustion and multiphase flows. The emphasis on understanding the physics of these flows helps the engineer to select appropriate models with which to obtain reliable simulations. Besides presenting the equations involved, the basics and limita- tions of the models are explained and discussed. The book, combined with tutorials, project and Power-Point lecture notes (all available for download), forms a complete course. The reader is given hands-on experience of drawing, meshing and simulation. Thetutorialscoverflowandreactionsinsideaporouscatalyst,combustioninturbulent non-premixedflowandmultiphasesimulationofevaporatingsprays.Theprojectdeals with the design of an industrial-scale selective catalytic reduction process and allows thereadertoexplorevariousdesignimprovementsandapplybestpracticeguidelinesin theCFDsimulations. Bengt Andersson is a Professor in Chemical Engineering at Chalmers University, Sweden. His research has focused on experimental studies and modelling of mass and heat transfer in various chemical reactors ranging from automotive catalysis to three-phaseflowinchemicalreactors. RonnieAnderssonisanAssistantProfessorinChemicalEngineeringatChalmersUni- versity.HeobtainedhisPhDatChalmersin2005andfrom2005until2010heworked asaconsultant atEpsilonHighTech asaspecialistinCFDsimulationsofcombustion andmultiphaseflows.Hisresearchprojectsinvolvephysicalmodelling,fluid-dynamic simulationsandexperimentalmethods. LoveHa˚kanssonworksasaconsultantatEngineeringDataResources–EDRinOslo, Norway.Hisresearchhasbeeninmasstransferinturbulentboundarylayers.Heisnow workingonsimulationsofsingle-phaseandmultiphaseflows. MikaelMortensenobtainedhisPhDatChalmersUniversityin2005inturbulentmixing withchemicalreactions.AftertwoyearsasapostdocattheUniversityofSydney,heis nowworkingwithfluiddynamicsattheNorwegianDefenceResearchEstablishmentin Lillehammer,Norway. RahmanSudiyoisaLecturerattheUniversityofGadjahMadainYogyakarta,Indonesia. HereceivedhisPhDatChalmersUniversityin2006.Hisresearchhasbeeninmultiphase flow. Berend van Wachem is a Reader at Imperial College London in the UK. His research projectsinvolvemultiphaseflowmodelling,rangingfromunderstandingthebehaviour ofturbulenceonthescaleofindividualparticlestothelarge-scalemodellingofgas–solid andgas–liquidflows. http://ebooks.cambridge.org/ebook.jsf?bid=CBO9781139093590 Cambridge Books Online © Cambridge University Press, 2012 http://ebooks.cambridge.org/ebook.jsf?bid=CBO9781139093590 Cambridge Books Online © Cambridge University Press, 2012 Computational Fluid Dynamics for Engineers BENGT ANDERSSON ChalmersUniversity,Sweden RONNIE ANDERSSON ChalmersUniversity,Sweden LOVE HA˚KANSSON EngineeringDataResources–EDR,Norway MIKAEL MORTENSEN NorwegianDefenceResearchEstablishment,Norway RAHMAN SUDIYO UniversityofGadjahMada,Indonesia BEREND VAN WACHEM ImperialCollegeLondon,UK http://ebooks.cambridge.org/ebook.jsf?bid=CBO9781139093590 Cambridge Books Online © Cambridge University Press, 2012 CAMBRIDGEUNIVERSITYPRESS Cambridge,NewYork,Melbourne,Madrid,CapeTown, Singapore,Sa˜oPaulo,Delhi,Tokyo,MexicoCity CambridgeUniversityPress TheEdinburghBuilding,CambridgeCB28RU,UK PublishedintheUnitedStatesofAmericabyCambridgeUniversityPress,NewYork www.cambridge.org Informationonthistitle:www.cambridge.org/9781107018952 (cid:2)C B.Andersson,R.Andersson,L.Ha˚kansson,M.Mortensen,R.Sudiyo,B.vanWachem,L.Hellstro¨m2012 Thispublicationisincopyright.Subjecttostatutoryexception andtotheprovisionsofrelevantcollectivelicensingagreements, noreproductionofanypartmaytakeplacewithoutthewritten permissionofCambridgeUniversityPress. Firstpublished2012 PrintedintheUnitedKingdomattheUniversityPress,Cambridge AcataloguerecordforthispublicationisavailablefromtheBritishLibrary LibraryofCongressCataloguinginPublicationdata Computationalfluiddynamicsforengineers/BengtAndersson...[etal.]. p. cm. Includesbibliographicalreferencesandindex. ISBN978-1-107-01895-2(hardback) 1.Fluiddynamics. 2.Engineeringmathematics. I.Andersson,Bengt,1947June15– TA357.C58776 2011 532′.05–dc23 2011037992 ISBN978-1-107-01895-2Hardback Additionalresourcesforthispublicationat www.cambridge.org/9781107018952 CambridgeUniversityPresshasnoresponsibilityforthepersistenceor accuracyofURLsforexternalorthird-partyinternetwebsitesreferredto inthispublication,anddoesnotguaranteethatanycontentonsuch websitesis,orwillremain,accurateorappropriate. http://ebooks.cambridge.org/ebook.jsf?bid=CBO9781139093590 Cambridge Books Online © Cambridge University Press, 2012 Contents Preface pageix 1 Introduction 1 1.1 Modellinginengineering 1 1.2 CFDsimulations 1 1.3 Applicationsinengineering 2 1.4 Flow 2 1.4.1 Laminarflow 3 1.4.2 Turbulentflow 3 1.4.3 Single-phaseflow 4 1.4.4 Multiphaseflow 4 1.5 CFDprograms 4 2 Modelling 8 2.1 Mass,heatandmomentumbalances 9 2.1.1 Viscosity,diffusionandheatconduction 9 2.2 Theequationofcontinuity 12 2.3 Theequationofmotion 14 2.4 Energytransport 16 2.4.1 Thebalanceforkineticenergy 16 2.4.2 Thebalanceforthermalenergy 18 2.5 Thebalanceforspecies 18 2.6 Boundaryconditions 18 2.6.1 Inletandoutletboundaries 19 2.6.2 Wallboundaries 19 2.6.3 Symmetryandaxisboundaryconditions 20 2.6.4 Initialconditions 20 2.6.5 Domainsettings 21 2.7 Physicalproperties 21 2.7.1 Theequationofstate 22 2.7.2 Viscosity 22 http://ebooks.cambridge.org/ebook.jsf?bid=CBO9781139093590 Cambridge Books Online © Cambridge University Press, 2012 vi Contents 3 NumericalaspectsofCFD 24 3.1 Introduction 24 3.2 NumericalmethodsforCFD 25 3.2.1 Thefinite-volumemethod 25 3.2.2 Geometricaldefinitions 26 3.3 Cellbalancing 26 3.3.1 Theconvectiveterm 27 3.3.2 Thediffusionterm 28 3.3.3 Thesourceterm 28 3.4 Example1–1Dmassdiffusioninaflowinggas 29 3.4.1 Solution 29 3.4.2 Concludingremarks 33 3.5 TheGauss–Seidelalgorithm 33 3.6 Example2–Gauss–Seidel 34 3.7 Measuresofconvergence 37 3.8 Discretizationschemes 38 3.8.1 Example3–increasedvelocity 39 3.8.2 Boundednessandtransportiveness 40 3.8.3 Theupwindschemes 40 3.8.4 Taylorexpansions 42 3.8.5 Accuracy 43 3.8.6 Thehybridscheme 44 3.8.7 Thepower-lawscheme 45 3.8.8 TheQUICKscheme 45 3.8.9 Moreadvanceddiscretizationschemes 46 3.9 Solvingthevelocityfield 47 3.9.1 Under-relaxation 49 3.10 Multigrid 50 3.11 Unsteadyflows 51 3.11.1 Example4–time-dependentsimulation 52 3.11.2 Conclusionsonthedifferenttimediscretizationmethods 57 3.12 Meshing 58 3.12.1 Meshgeneration 58 3.12.2 Adaptation 60 3.12.3 Numericaldiffusion 60 3.13 Summary 61 4 Turbulent-flowmodelling 62 4.1 Thephysicsoffluidturbulence 62 4.1.1 Characteristicfeaturesofturbulentflows 63 4.1.2 Statisticalmethods 66 4.1.3 Flowstability 69 4.1.4 TheKolmogorovhypotheses 70 http://ebooks.cambridge.org/ebook.jsf?bid=CBO9781139093590 Cambridge Books Online © Cambridge University Press, 2012 Contents vii 4.1.5 Theenergycascade 72 4.1.6 Sourcesofturbulence 74 4.1.7 Theturbulentenergyspectrum 75 4.2 Turbulencemodelling 76 4.2.1 Directnumericalsimulation 79 4.2.2 Large-eddysimulation 79 4.2.3 Reynoldsdecomposition 81 4.2.4 Modelsbasedontheturbulentviscosityhypothesis 86 4.2.5 Reynoldsstressmodels(RSMs) 96 4.2.6 Advancedturbulencemodelling 99 4.2.7 Comparisonsofvariousturbulencemodels 99 4.3 Near-wallmodelling 99 4.3.1 Turbulentboundarylayers 101 4.3.2 Wallfunctions 104 4.3.3 Improvednear-wall-modelling 107 4.3.4 Comparisonofthreenear-wallmodellingapproaches 109 4.4 Inletandoutletboundaryconditions 110 4.5 Summary 112 5 Turbulentmixingandchemicalreactions 113 5.1 Introduction 114 5.2 Problemdescription 115 5.3 Thenatureofturbulentmixing 117 5.4 Mixingofaconservedscalar 119 5.4.1 Mixingtimescales 119 5.4.2 Probabilitydensityfunctions 120 5.4.3 Modellingofturbulentmixing 124 5.5 Modellingofchemicalreactions 130 5.5.1 Da≪1 130 5.5.2 Da≫1 131 5.5.3 Da≈1 138 5.6 Non-PDFmodels 141 5.7 Summary 142 6 Multiphaseflowmodelling 143 6.1 Introduction 144 6.1.1 Characterizationofmultiphaseflows 144 6.1.2 Couplingbetweenacontinuousphaseandadispersedphase 146 6.2 Forcesondispersedparticles 147 6.3 Computationalmodels 149 6.3.1 Choosingamultiphasemodel 150 6.3.2 Directnumericalsimulations 151 6.3.3 Lagrangianparticlesimulations,thepoint-particleapproach 152 http://ebooks.cambridge.org/ebook.jsf?bid=CBO9781139093590 Cambridge Books Online © Cambridge University Press, 2012 viii Contents 6.3.4 Euler–Eulermodels 155 6.3.5 Themixturemodel 156 6.3.6 Modelsforstratifiedfluid–fluidflows 158 6.3.7 Modelsforflowsinporousmedia 160 6.4 Closuremodels 161 6.4.1 Interphasedrag 161 6.4.2 Particleinteractions 163 6.4.3 Heatandmasstransfer 168 6.5 Boundariesandboundaryconditions 169 6.5.1 Lagrangiandispersedphase 169 6.5.2 Euleriandispersedphase 170 6.6 Summary 171 6.6.1 Guidelinesforselectingamultiphasemodel 172 7 Best-practiceguidelines 174 7.1 Applicationuncertainty 175 7.1.1 Geometryandgriddesign 175 7.2 Numericaluncertainty 175 7.2.1 Convergence 175 7.2.2 Enhancingconvergence 176 7.2.3 Numericalerrors 176 7.2.4 Temporaldiscretization 177 7.3 Turbulencemodelling 177 7.3.1 Boundaryconditions 177 7.4 Reactions 178 7.5 Multiphasemodelling 178 7.6 Sensitivityanalysis 180 7.7 Verification,validationandcalibration 180 Appendix 181 References 185 Index 186 http://ebooks.cambridge.org/ebook.jsf?bid=CBO9781139093590 Cambridge Books Online © Cambridge University Press, 2012 Cambridge Books Online © Cambridge University Press, 2012