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  • 8/10/2019 FLUENT 14.0 Turbulence

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    IntroductiontoANSYS

    FLUENT

    Lecture6Turbulence

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    LectureTheme:

    Themajorityofengineeringflowsareturbulent. Successfullysimulatingsuchflowsrequiresunderstandingafewbasicconceptsofturbulence

    theoryandmodeling. Thisallowsonetomakethebestchoicefromtheavailableturbulencemodelsandnearwalloptionsforanygivenproblem.

    LearningAims:Youwilllearn:

    Basicturbulentflowandturbulencemodelingtheory

    TurbulencemodelsandnearwalloptionsavailableinFLUENTHowtochooseanappropriateturbulencemodelforagivenproblemHowtospecifyturbulenceboundaryconditionsatinlets

    LearningObjectives:

    Youwillunderstandthechallengesinherentinturbulentflowsimulationandbeabletoidentifythemostsuitablemodelandnearwalltreatmentforagivenproblem.

    Introduction

    Introduction Theory Models NearWallTreatments InletBCs Summary

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    Flowscanbeclassifiedaseither:

    Laminar(Low Reynolds Number)

    Transition(Increasing Reynolds Number)

    Turbulent(Higher Reynolds Number)

    Observationby OsborneReynolds

    Introduction Theory Models NearWallTreatments InletBCs Summary

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    Observationby OsborneReynolds

    TheReynoldsnumberisthecriterionusedtodeterminewhethertheflowis

    laminarorturbulent

    TheReynoldsnumberisbasedonthelengthscaleoftheflow:

    Transitiontoturbulencevariesdependingonthetypeofflow:

    Externalflow

    alongasurface :ReX > 500 000 aroundonobstacle :ReL > 20 000

    Internalflow :ReD > 2 300

    . .ReLU L

    etc.,dd,x,L hyd

    Introduction Theory Models NearWallTreatments InletBCs Summary

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    Aturbulentflowcontainsawiderangeofturbulenteddysizes

    Turbulentflowcharacteristics:

    Unsteady, three-dimensional, irregular, stochastic motion in which transported

    quantities (mass, momentum, scalar species) fluctuate in time and space

    Enhanced mixing of these quantities results from the fluctuations

    Unpredictability in detail

    Large scale coherent structures are different in each flow, whereas smalleddies are more universal

    TurbulentFlowStructures

    Smallstructures

    Largestructures

    Introduction Theory Models NearWallTreatments InletBCs Summary

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    TurbulentFlowStructures

    Energyistransferredfromlargereddiestosmallereddies

    (Kolmogorov Cascade)

    Largescalecontainsmostoftheenergy

    Inthesmallesteddies,turbulentenergyisconvertedtointernalenergybyviscous

    dissipation

    Energy Cascade

    Richardson (1922),

    Kolmogorov (1941)

    Introduction Theory Models NearWallTreatments InletBCs Summary

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    BackwardFacingStep

    Instantaneousvelocitycontours

    Timeaveragedvelocitycontours

    Asengineers,inmostcaseswe donotactuallyneedtoseeanexactsnapshotof

    thevelocityataparticularinstant.

    Instead formostproblems,knowingthetimeaveragedvelocity(andintensityof

    theturbulentfluctuations)isallweneedtoknow. Thisgivesusausefulwayto

    approachmodellingturbulence.

    Introduction Theory Models NearWallTreatments InletBCs Summary

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    Ifwerecordedthevelocityataparticularpointinthereal(turbulent)fluidflow,

    theinstantaneousvelocity(U)wouldlooklikethis:

    Time-average of velocity

    Velocity

    U Instantaneous velocity

    U

    u Fluctuating velocity

    Atanypointintime:

    Thetimeaverageofthefluctuatingvelocity mustbezero:

    BUT,theRMSof isnotnecessarilyzero:

    Noteyouwillhearreferencetotheturbulenceenergy,k.Thisisthesumofthe3

    fluctuatingvelocitycomponents:

    uUU

    0u

    u 02 u

    2222

    1wvuk

    u

    Time

    MeanandInstantaneousVelocities

    Introduction Theory Models NearWallTreatments InletBCs Summary

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    OverviewofComputationalApproaches

    Different approaches to make turbulence computationally tractable

    DNS

    (DirectNumericalSimulation)

    Numericallysolvingthefull

    unsteadyNavierStokesequations

    Resolvesthewholespectrumof

    scales

    Nomodelingisrequired

    Butthecostistooprohibitive!

    Notpracticalforindustrialflows!

    SolvesthespatiallyaveragedNS

    equations

    Largeeddiesaredirectlyresolved,

    buteddiessmallerthanthemesh

    aremodeled

    LessexpensivethanDNS,butthe

    amountofcomputational

    resourcesandeffortsarestilltoo

    largeformostpractical

    applications

    SolvetimeaveragedNavierStokes

    equations

    Allturbulentlengthscalesare

    modeledinRANS

    Variousdifferentmodelsareavailable

    Thisisthemostwidelyusedapproach

    forindustrialflows

    LES

    (LargeEddySimulation)

    RANS

    (ReynoldsAveragedNavier

    StokesSimulation)

    Introduction Theory Models NearWallTreatments InletBCs Summary

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    RANSModeling:Averaging

    Thus,theinstantaneousNavierStokesequationsmayberewrittenasReynolds

    averagedequations:

    TheReynoldsstressesareadditionalunknownsintroducedbytheaveraging

    procedure,hencetheymustbemodeled(relatedtotheaveragedflowquantities)in

    ordertoclosethesystemofgoverningequations

    jiij uuR j

    ij

    j

    i

    jik

    ik

    i

    x

    R

    x

    u

    xx

    p

    x

    uut

    u

    (Reynolds stress tensor)

    2

    2

    2

    ' ' ' ' '

    ' ' ' ' '

    ' ' ' ' '

    u u v u w

    u v v v w

    u w v w w

    jiij uuR

    6 unknowns

    Introduction Theory Models NearWallTreatments InletBCs Summary

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    EddyViscosityModels

    Boussinesq hypothesisReynoldsstressesaremodeledusinganeddy(or

    turbulent)viscosity,T

    Thehypothesisisreasonableforsimpleturbulent

    shearflows:boundarylayers,roundjets,mixing

    layers,channelflows,etc.

    ijij

    k

    k

    i

    j

    j

    ijiij k

    x

    u

    x

    u

    x

    uuuR

    3

    2

    3

    2TT

    RANSModeling:TheClosureProblem

    TheReynoldsStresstensor mustbesolved

    TheRANSmodelscanbeclosedintwoways:

    Note:Allturbulencemodelscontainempiricism

    Equationscannotbederivedfromfundamentalprinciples

    Somecalibratingtoobservedsolutionsandintelligentguessingiscontainedinthemodels

    ReynoldsStressModels(RSM)

    Rijisdirectlysolvedviatransportequations

    (modelingisstillrequiredformanytermsinthe

    transportequations)

    RSMismoreadvantageousincomplex3D

    turbulentflowswithlargestreamlinecurvature

    andswirl,

    butthemodelismorecomplex,computationally

    intensive,moredifficulttoconvergethaneddy

    viscositymodels

    jiij uuR

    ijijTijijijjikk

    ji DFPuuu

    x

    uu

    t

    Introduction Theory Models NearWallTreatments InletBCs Summary

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    TurbulenceModelsAvailableinFLUENT

    RANSbased

    models

    OneEquationModel

    SpalartAllmaras

    TwoEquationModels

    Standardk

    RNGk

    Realizablek*

    Standardk

    SSTk*

    ReynoldsStressModel

    kklTransitionModel

    SSTTransitionModelDetachedEddySimulation

    LargeEddySimulation

    Increasein

    Computational

    Cost

    PerIteration

    * Recommended choice for standard cases

    Introduction Theory Models NearWallTreatments InletBCs Summary

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    TwoEquationModels

    Twotransportequationsaresolved,givingtwoindependentscalesforcalculating t Virtuallyallusethetransportequationfortheturbulentkineticenergy,k

    Severaltransportvariableshavebeenproposed,basedondimensionalarguments,andusedforsecondequation. Theeddyviscositytisthenformulatedfromthetwotransportvariables.

    Kolmogorov,: t k /, l k1/2 / k /

    isspecificdissipationrate

    definedintermsoflargeeddyscalesthatdefinesupplyrateofk

    Chou,: t k2/, l k3/2 /

    Rotta,l: t k1/2l, k3/2 / l

    ijijt

    jkj

    SSSskeSPPx

    k

    xDt

    Dk2)(; 2t

    production dissipation

    Introduction Theory Models NearWallTreatments InletBCs Summary

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    Standardk- ModelEquations

    Empiricalconstantsdetermined

    frombenchmarkexperimentsof

    simpleflowsusingairandwater.

    ijijtjkj

    SSSS

    x

    k

    xDt

    Dk2;2t

    2

    2

    t1

    t CSCkxxDt

    D

    jj

    k-transport equation

    -transport equationproduction dissipation

    2,,, CCik

    coefficients

    turbulent viscosity

    2

    k

    Ct

    inverse time scale

    Introduction Theory Models NearWallTreatments InletBCs Summary

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    RANS:EVM:Standardk (SKE)Model

    TheStandardKEpsilonmodel(SKE)isthemostwidelyusedengineeringturbulencemodelforindustrialapplications

    Modelparametersarecalibrated byusingdatafromanumberofbenchmarkexperimentssuchaspipeflow,flatplate,etc.

    Robustandreasonablyaccurateforawiderangeofapplications

    Containssubmodels forcompressibility,buoyancy,combustion,etc.

    KnownlimitationsoftheSKEmodel: Performspoorlyforflowswithlargerpressuregradient,strongseparation,highswirlingcomponent andlargestreamlinecurvature.

    Inaccuratepredictionofthespreadingrateofroundjets.

    Productionofkisexcessive(unphysical)inregionswithlargestrainrate(forexample,

    nearastagnationpoint),resultinginveryinaccuratemodelpredictions.

    Introduction Theory Models NearWallTreatments InletBCs Summary

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    RANS:EVM:Realizablekepsilon

    Realizablek (RKE)model(Shih):

    Dissipationrate()equationisderivedfromthemeansquarevorticity fluctuation,whichisfundamentallydifferentfromthe

    SKE. Severalrealizability conditionsareenforcedforReynolds

    stresses.

    Benefits: Accuratelypredictsthespreadingrateofbothplanarandroundjets

    Alsolikelytoprovidesuperiorperformanceforflowsinvolvingrotation,boundarylayersunderstrongadversepressuregradients,

    separation,andrecirculation

    OFTEN PREFERRED TO STANDARD K-EPSILON

    Introduction Theory Models NearWallTreatments InletBCs Summary

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    RANS:EVM:SpalartAllmaras (SA)Model

    SpalartAllmarasisalowcostRANSmodelsolvingasingletransportequationforamodifiededdyviscosity

    Designedspecificallyforaerospaceapplicationsinvolvingwallboundedflows

    Hasbeenshowntogivegoodresultsforboundarylayerssubjectedtoadversepressuregradients.

    Usedmainlyforaerospaceandturbomachinery applications

    Limitations: Themodelwasdesignedforwallboundedflowsandflowswithmildseparation

    andrecirculation.

    Noclaimismaderegardingitsapplicabilitytoalltypesofcomplexengineering

    flows.

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    Ink models,thetransportequationfortheturbulentdissipationrate,,isreplacedwithanequationforthespecificdissipationrate,

    Theturbulentkineticenergytransportequationisstillsolved

    SeeAppendixfordetailsof equation k modelshavegainedpopularityinrecentyearsmainlybecause:

    Muchbetterperformancethankmodelsforboundarylayerflows Forseparation,transition,lowReeffects,andimpingement,kmodelsaremore

    accuratethankmodels

    Accurateandrobustforawiderangeofboundarylayerflowswithpressuregradient

    Twovariationsofthek modelareavailableinFLUENT

    Standardkmodel(Wilcox,1998) SSTkmodel(Menter)

    komegaModels

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    ShearStressTransport(SST) Model TheSSTmodelisanhybridtwoequationmodelthatcombinestheadvantagesofboth

    kandkmodels

    kmodelperformsmuchbetterthankmodelsforboundarylayerflows

    Wilcoxoriginalk modelisoverlysensitivetothefreestream value(BC)of,

    whilekmodelisnotpronetosuchproblem

    ThekeandkwmodelsareblendedsuchthattheSSTmodelfunctionslikethekwclosetothewallandthekemodelinthefreestream

    SSTisagoodcompromisebetweenk andk models

    SSTModel

    Wall

    k-

    k-

    Introduction Theory Models NearWallTreatments InletBCs Summary

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    RANS:OtherModelsinFLUENT

    RNGk model Modelconstantsarederivedfromrenormalizationgroup(RNG)theoryinsteadof

    empiricism

    Advantagesoverthestandardk modelareverysimilartothoseoftheRKEmodel

    ReynoldsStressmodel(RSM) InsteadofusingeddyviscositytoclosetheRANSequations,RSMsolvestransport

    equationsfortheindividualReynoldsstresses

    7additionalequationsin3D,comparedto2additionalequationswithEVM.

    MuchmorecomputationallyexpensivethanEVMandgenerallyverydifficulttoconverge

    Asaresult,RSMisusedprimarilyinflowswhereeddyviscositymodelsare

    knowntofail Thesearemainlyflowswherestrongswirlisthepredominantflowfeature,for

    instanceacyclone(seeAppendix)

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    TheStructureofNearWallFlows

    TurbulenceNeartheWall

    Introduction Theory Models NearWallTreatments InletBCs Summary

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    Neartoawall,thevelocitychangesrapidly.

    Ifweplotthesamegraphagain,where: Logscaleaxesareused

    Thevelocityismadedimensionless, fromU/U ( )

    Thewalldistancevectorismadedimensionless

    Thenwearriveatthegraphonthenextpage. Theshapeofthisisgenerallythesameforallflows:

    TurbulencenearaWall

    Velocit

    y,

    U

    Distance from Wall, y

    Introduction Theory Models NearWallTreatments InletBCs Summary

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    Byscalingthevariablesnearthewallthevelocityprofiledatatakesonapredictableform(transitioningfromlineartologarithmicbehavior)

    Sincenearwallconditionsareoftenpredictable,functionscanbeusedto

    determinethenearwallprofilesratherthanusingafinemeshtoactuallyresolvetheprofile

    Thesefunctionsarecalledwallfunctions

    Linear

    Logarithmic

    Scaling the non-dimensional

    velocity and non-dimensional

    distance from the wall results in a

    predictable boundary layer profile

    for a wide range of flows

    TurbulenceNeartheWall

    Introduction Theory Models NearWallTreatments InletBCs Summary

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    ChoiceofWallModelingStrategy.

    Inthenearwallregion,thesolutiongradientsareveryhigh,butaccuratecalculationsinthenearwallregionareparamounttothesuccessofthesimulation.

    Thechoiceisbetween:ResolvingtheViscousSublayer

    Firstgridcellneedstobeatabouty+ =1

    Thiswilladdsignificantlytothemeshcount

    UsealowReynoldsnumberturbulencemodel(likekomega)

    Generallyspeaking,iftheforcesonthewallarekeytoyoursimulation(aerodynamicdrag,turbomachinery bladeperformance)thisistheapproachyouwilltake

    UsingaWallFunction

    Firstgridcellneedstobe 30

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    Fewernodesareneedednormaltothewallwhenlogarithmicbasedwallfunctionsareused(comparedtomoredetailedlowRewallmodeling)

    u

    y

    u

    y

    Boundary layer

    Logarithmic-based Wall functions

    used to resolve boundary layerNear-wall resolving approach

    used to resolve boundary layer

    First node wall distance is reflected by y+ value

    TurbulenceNeartheWall

    Introduction Theory Models NearWall

    Treatments Inlet

    BCs Summary

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    ExampleinPredictingNearwallCellSize

    Duringthepreprocessingstage,youwillneedtoknowasuitablesizeforthefirstlayerofgridcells(inflationlayer)sothatY+ isinthedesiredrange.

    Theactualflowfieldwillnotbeknownuntilyouhavecomputedthesolution(andindeeditissometimesunavoidabletohavetogobackandremesh yourmodelonaccountofthecomputedY+ values).

    Toreducetheriskofneedingtoremesh,youmaywanttotryandpredictthecellsizebyperformingahandcalculationatthestart. Forexample:

    Foraflatplate,Reynoldsnumber( ) givesRel= 1.4x106

    (Recallfromearlierslide,flowoverasurfaceisturbulentwhenReL>5x105)

    Flat plate, 1m long

    Air at 20 m/s = 1.225 kg/m3

    = 1.8x10-5 kg/ms

    y

    The question is whatheight (y) should the first

    row of grid cells be. We

    will use SWF, and are

    aiming for Y+ 50

    VLlRe

    Introduction Theory Models NearWall

    Treatments Inlet

    BCs Summary

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    Reisknown,sousethedefinitionstocalculatethefirstcellheight

    Weknowweareaimingfory+ of50,hence:

    ourfirstcellheightyshouldbe

    approximately1mm.

    ExampleinPredictingNearwallCellSize[2]

    Beginwiththedefinitionofy+ andrearrange:

    Thetargety+ valueandfluidpropertiesareknown,soweneedU,whichis

    definedas:

    Thewallshearstress,w,canbefoundfromtheskinfrictioncoefficient,Cf:

    Aliteraturesearchsuggestsaformulafortheskinfrictiononaplate1 thus:

    2.0Re058.0 lf

    C

    mU

    yy 4-9x10

    221

    UCfw

    wU

    Introduction Theory Models NearWall

    Treatments Inlet

    BCs Summary

    U

    yy

    m/s0.82

    wU

    y

    Uy

    2221 smkg/0.83 UCfw

    .0034Re058.0 2.0 lfC

    1Anequivalentformulaforinternalflows,withReynoldsnumberbasedonthepipediameterisCf=0.079Red0.25

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    Insomesituations,suchasboundarylayerseparation,logarithmicbasedwallfunctionsdonotcorrectlypredicttheboundarylayerprofile

    Inthesecaseslogarithmicbasedwallfunctionsshouldnotbeused

    Instead,directlyresolvingtheboundarylayercanprovideaccurateresults

    Wall functions applicable Wall functions not applicable

    LimitationsofWallFunctions

    Non-equilibrium wall functions have been developed

    in FLUENT to address this situation but they are very

    empirical. A more rigorous approach is

    recommended if affordable

    Introduction Theory Models NearWall

    Treatments Inlet

    BCs Summary

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    EnhancedWallTreatment(EWT)

    Needfory+insensitivewalltreatment

    EWTsmoothlyvariesfromlowRetowallfunctionwithmeshresolution

    EWTavailablefork andRSMmodels

    Similarapproachimplementedfork equationbasedmodels

    Introduction Theory Models NearWall

    Treatments Inlet

    BCs Summary

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    StandardWallFunctions TheStandardWallFunctionoptions

    isdesignedforhighReattachedflows

    Thenearwallregionisnotresolved

    Nearwallmeshisrelativelycoarse

    NonEquilibriumWallFunctions Forbetterpredictionofadversepressuregradientflowsand

    separation

    Nearwallmeshisrelativelycoarse

    EnhancedWallTreatment* UsedforlowReflowsorflowswithcomplex

    nearwallphenomena

    Generallyrequiresaveryfinenearwallmeshcapableofresolvingthenearwallregion

    Canalsohandlecoarsenearwallmesh

    UserDefinedWallFunctions Canhostuserspecificsolutions

    ChoosinganearWallTreatment

    * Recommended choice for standard cases

    Introduction Theory Models NearWall

    Treatments Inlet

    BCs Summary

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    TheSSTandk modelswereformulatedtobenearwallresolvingmodels

    wheretheviscoussublayer isresolvedbythemesh

    Totakefulladvantageofthisformulation,y+shouldbe

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    InletBoundaryConditions

    Whenturbulentflowentersadomainatinletsoroutlets(backflow),boundaryconditionsfork,,and/or mustbespecified,dependingonwhich

    turbulencemodelhasbeenselected

    Fourmethodsfordirectlyorindirectlyspecifyingturbulenceparameters:1)Explicitlyinputk,,,orReynoldsstresscomponents(thisistheonlymethodthat

    allowsforprofiledefinition)

    Notebydefault,theFLUENTGUIentersk=1m/s and =1m/s. These values

    MUST be changed, they are unlikely to be correct for your simulation.

    2)Turbulenceintensityandlengthscale

    Lengthscaleisrelatedtosizeoflargeeddiesthatcontainmostofenergy

    Forboundarylayerflows: l0.499

    Forflowsdownstreamofgrid: lopeningsize3)Turbulenceintensityandhydraulicdiameter(primarilyforinternalflows)

    4)Turbulenceintensityandviscosityratio(primarilyforexternalflows)

    ''jiuu

    Introduction Theory Models NearWall

    Treatments Inlet

    BCs Summary

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    InletTurbulenceConditions

    Ifyouhaveabsolutelynoideaoftheturbulencelevelsinyoursimulation,youcouldusefollowingvaluesofturbulenceintensitiesandviscosityratios:

    Usualturbulenceintensitiesrangefrom1%to5%

    Thedefaultturbulenceintensityvalueof0.037(thatis,3.7%)issufficientfornominalturbulencethroughacircularinlet,andisagoodestimateintheabsenceofexperimentaldata

    Forexternalflows,turbulentviscosityratioof110istypicallyagoodvalue

    Forinternal

    flows,

    turbulent

    viscosity

    ratio

    of10

    100

    ittypically

    agood

    value

    ForfullydevelopedpipeflowatRe=50,000,theturbulentviscosityratioisaround100

    Introduction Theory Models NearWall

    Treatments Inlet

    BCs Summary

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    RANSTurbulenceModelUsage

    Model Behavior and Usage

    Spalart-Allmaras Economical for large meshes. Performs poorly for 3D flows, free shear flows, flows with strongseparation. Suitable for mildly complex (quasi-2D) external/internal flows and boundary layer flows

    under pressure gradient (e.g. airfoils, wings, airplane fuselages, missiles, ship hulls).

    Standard k Robust. Widely used despite the known limitations of the model. Performs poorly for complex flowsinvolving severe pressure gradient, separation, strong streamline curvature. Suitable for initialiterations, initial screening of alternative designs, and parametric studies.

    Realizable k* Suitable for complex shear flows involving rapid strain, moderate swirl, vortices, and locally transitionalflows (e.g. boundary layer separation, massive separation, and vortex shedding behind bluff bodies, stall

    in wide-angle diffusers, room ventilation).

    RNG kOffers largely the same benefits and has similar applications as Realizable. Possibly harder to converge

    than Realizable.

    Standard k Superior performance for wall-bounded boundary layer, free shear, and low Reynolds number flows.Suitable for complex boundary layer flows under adverse pressure gradient and separation (external

    aerodynamics and turbomachinery). Can be used for transitional flows (though tends to predict early

    transition). Separation is typically predicted to be excessive and early.

    SST k* Offers similar benefits as standard k. Dependency on wall distance makes this less suitable for free

    shear flows.

    RSM Physically the most sound RANS model. Avoids isotropic eddy viscosity assumption. More CPU timeand memory required. Tougher to converge due to close coupling of equations. Suitable for complex

    3D flows with strong streamline curvature, strong swirl/rotation (e.g. curved duct, rotating flow

    passages, swirl combustors with very large inlet swirl, cyclones).

    * Recommended choice for standard cases

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    RANSTurbulenceModelDescriptions

    Model Description

    Spalart

    Allmaras

    A single transport equation model solving directly for a modified turbulent viscosity. Designed specifically

    for aerospace applications involving wall-bounded flows on a fine near-wall mesh. FLUENTs

    implementation allows the use of coarser meshes. Option to include strain rate in k production term

    improves predictions of vortical flows.

    Standard k The baseline two-transport-equation model solving for k and . This is the default k model. Coefficientsare empirically derived; valid for fully turbulent flows only. Options to account for viscous heating,

    buoyancy, and compressibility are shared with other k models.

    RNG k A variant of the standard k model. Equations and coefficients are analytically derived. Significant changesin the equation improves the ability to model highly strained flows. Additional options aid in predicting

    swirling and low Reynolds number flows.

    Realizable k A variant of the standard k model. Its realizability stems from changes that allow certain mathematicalconstraints to be obeyed which ultimately improves the performance of this model.

    Standard k A two-transport-equation model solving for k and , the specific dissipation rate ( / k) based on Wilcox(1998). This is the default k model. Demonstrates superior performance for wall-bounded and low

    Reynolds number flows. Shows potential for predicting transition. Options account for transitional, free

    shear, and compressible flows.

    SST k A variant of the standard k

    model. Combines the original Wilcox model for use near walls and thestandard k model away from walls using a blending function. Also limits turbulent viscosity to guarantee

    that T ~ k. The transition and shearing options are borrowed from standard k. No option to include

    compressibility.

    RSM Reynolds stresses are solved directly using transport equations, avoiding isotropic viscosity assumption ofother models. Use for highly swirling flows. Quadratic pressure-strain option improves performance for

    many basic shear flows.

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    Summary TurbulenceModelingGuidelines

    Successfulturbulencemodelingrequiresengineeringjudgmentof: Flowphysics Computerresourcesavailable Projectrequirements

    Accuracy Turnaroundtime

    ChoiceofNearwalltreatment

    Modelingprocedure1. CalculatecharacteristicReynoldsnumberanddeterminewhetherflowisturbulent.

    2. Iftheflowisinthetransition(fromlaminartoturbulent)range,considertheuseofoneoftheturbulencetransitionmodels(notcoveredinthistraining).

    3. Estimatewalladjacentcellcentroid y+ beforegeneratingthemesh.4. PrepareyourmeshtousewallfunctionsexceptforlowReflowsand/orflowswith

    complexnearwallphysics(nonequilibriumboundarylayers).

    5. BeginwithRKE(realizablek)andchangetoSA,RNG,SKW,orSSTifneeded.Checkthetablesonpreviousslidesasaguideforyourchoice.

    6. UseRSMforhighlyswirling,3D,rotatingflows.7. Rememberthatthereisnosingle,superiorturbulencemodelforallflows!

    Introduction Theory Models NearWallTreatments InletBCs Summary

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    Appendix

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    Example#1 TurbulentFlowPastaBlunt

    FlatPlate Turbulentflowpastabluntflatplatewassimulatedusingfour

    differentturbulencemodels.

    8,700cellquadmesh,gradednearleadingedgeandreattachmentlocation.

    Nonequilibriumboundarylayertreatment

    N. Djilali and I. S. Gartshore (1991), Turbulent Flow Around a Bluff Rectangular

    Plate, Part I: Experimental Investigation, JFE, Vol. 113, pp. 5159.

    D

    000,50Re DRx

    Recirculation zone Reattachment point

    0U

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    RNG kStandard k

    Reynolds StressRealizable k

    Contours of Turbulent Kinetic Energy (m2/s2)

    0.00

    0.07

    0.14

    0.21

    0.28

    0.35

    0.42

    0.49

    0.56

    0.63

    0.70

    Example#1 TurbulentFlowPastaBluntFlatPlate

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    Experimentally observed

    reattachment point is at

    x / D = 4.7

    Predicted separation bubble:

    Standard k (SKE) SkinFriction

    Coefficient

    Cf 1000

    SKE severely underpredicts the size of

    the separation bubble, while RKE

    predicts the size exactly.

    Realizable k (RKE)

    Distance Along

    Plate,x / D

    Example#1 TurbulentFlowPastaBluntFlatPlate

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    ReynoldsNumberReD=40750

    FullyDevelopedTurbulentFlowatInlet

    ExperimentsbyBaughn etal.(1984)

    q=const

    Outlet

    axis

    H

    H 40 x H

    Inlet

    q=0

    .

    d

    D

    Example#2:PipeExpansionwithHeatTransfer

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    PlotshowsdimensionlessdistanceversusNusseltNumber

    BestagreementiswithSSTandkomegamodelswhichdoabetterjobofcapturingflowrecirculationzonesaccurately

    Example#2:PipeExpansionwithHeatTransfer

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    40,000cellhexahedralmesh

    Highorderupwindschemewasused.

    ComputedusingSKE,RNG,RKEandRSM(secondmomentclosure)modelswiththe

    standardwallfunctions

    Representshighlyswirlingflows(Wmax=

    1.8Uin)

    0.2 m

    Uin = 20 m/s

    0.97 m

    0.1 m

    0.12 m

    Example#3 TurbulentFlowinaCyclone

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    Tangentialvelocityprofilepredictionsat0.41mbelowthevortexfinder

    Example#3 TurbulentFlowinaCyclone

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    ShearStressTransport(SST) Model Itaccountsmoreaccuratelyforthetransportoftheturbulentshearstress,which

    improvespredictionsoftheonsetandtheamountofflowseparationcomparedto

    kmodels

    SST result and experiment

    Standard k- fails to predict separation

    Experiment Gersten et al.

    Example4:Diffuser

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    TurbulentFlowStructuresRelatedtokand

    CharacteristicsoftheTurbulentStructures:

    Lengthscale : l [m]

    Velocityscale : [m/s]

    Timescale : [s]

    Shape(nonisotropiclargerstructures)

    kl

    k

    - Turbulent kinetic energy : [m2/s2]

    - Turbulent kinetic energy dissipation : [m2/s3] ~ k3/2/l

    - Turbulent Reynolds : Ret = k1/2.l/ ~ k2/ [-]

    - Turbulent Intensity : [-]

    2 2 21 ' ' '

    2

    k u v w

    3

    21

    k

    UU

    uI

    (dimensional analysis)

    Fluctuating

    component

    Timeaverage

    component

    Instantaneous

    component

    tutUtu iii ,,, xxx

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    k models areRANStwoequationsbasedmodels

    Oneoftheadvantagesofthek formulationisthenearwalltreatmentforlowReynoldsnumbercomputations

    designedtopredictcorrectbehaviorwhenintegratedtothewall thekmodelsswitchesbetweenalowReynoldsnumberformulation(i.e.directresolutionoftheboundarylayer)atlowy+

    valuesandawallfunctionapproachathighery+ values

    whileLowReynoldsnumbervariationsofstandardkmodelsusedampingfunctionstoattempttoreproducecorrectnearwallbehavior

    komegaModel

    j

    t

    jj

    i

    ij

    jk

    t

    jj

    iij

    t

    xxfx

    u

    kDt

    D

    x

    k

    xkf

    x

    u

    Dt

    Dk

    k

    2

    = specific dissipation rate

    1

    k

    ijij

    k

    k

    i

    j

    j

    ijiij k

    x

    u

    x

    u

    x

    uuuR

    3

    2

    3

    2TT

    Introduction Theory Models NearWallTreatments InletBCs Summary