FLUENT 14.0 Turbulence
Transcript of 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
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Flowscanbeclassifiedaseither:
Laminar(Low Reynolds Number)
Transition(Increasing Reynolds Number)
Turbulent(Higher Reynolds Number)
Observationby OsborneReynolds
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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
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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
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TurbulentFlowStructures
Energyistransferredfromlargereddiestosmallereddies
(Kolmogorov Cascade)
Largescalecontainsmostoftheenergy
Inthesmallesteddies,turbulentenergyisconvertedtointernalenergybyviscous
dissipation
Energy Cascade
Richardson (1922),
Kolmogorov (1941)
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BackwardFacingStep
Instantaneousvelocitycontours
Timeaveragedvelocitycontours
Asengineers,inmostcaseswe donotactuallyneedtoseeanexactsnapshotof
thevelocityataparticularinstant.
Instead formostproblems,knowingthetimeaveragedvelocity(andintensityof
theturbulentfluctuations)isallweneedtoknow. Thisgivesusausefulwayto
approachmodellingturbulence.
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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
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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)
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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
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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
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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
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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
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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
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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.
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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
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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-
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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
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Neartoawall,thevelocitychangesrapidly.
Ifweplotthesamegraphagain,where: Logscaleaxesareused
Thevelocityismadedimensionless, fromU/U ( )
Thewalldistancevectorismadedimensionless
Thenwearriveatthegraphonthenextpage. Theshapeofthisisgenerallythesameforallflows:
TurbulencenearaWall
Velocit
y,
U
Distance from Wall, y
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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
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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
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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
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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
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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
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EnhancedWallTreatment(EWT)
Needfory+insensitivewalltreatment
EWTsmoothlyvariesfromlowRetowallfunctionwithmeshresolution
EWTavailablefork andRSMmodels
Similarapproachimplementedfork equationbasedmodels
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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
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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
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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
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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!
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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