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Simulation of Cavitating Flow around a 2-D Hydrofoil

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Simulation of Cavitating Flow around a 2-D Hydrofoilof,a,2D,Flow,flow

    Simulation of Cavitating Flow around a 2-D

    Hydrofoil

    JMarine.Sci.Appl(201019:6368

    DOI:10.1O07/s11804.0108090.4

    SimulationofCavitatingFlowaroundalDHydrofoil

    ShengHuang,MiaoHe,ChaoWangandXinChang

    CollegeofShipbuildingEngineeringUniversity,HarbinEngineeringUniversity,Harbin150001China

    Abstract:Inordertopredicttheeffectsofcavitationonahvdrofoil,thestateequationsofthecavitationmode1

    werecombinedwitha1inearviscousturbulentmethodformixedfluidsinthecomputationalfluiddynamics

    (CFD)softwareFLUENTtosimulatesteadycavitatingflow.Atafixedattackangle.pressuredistributionsand

    volumefractionsofvaporatdifferentcavitationnumbersweresimulated,andtheresultsonfoilsections

    agreedwel1withexperimentaldata.Inaddition,atthevariouscavitationnumbers,thevaDorfractionsat

    differentattackangleswerealsopredicted.ThevaDorregionmovedtowardsthefrontoftheairfoi1andthe

    lengthofthecavitygrewwithincreasedattackangle.TheresultsshowthatthismethodofapplyingFLUENT

    tosimulatecavitationisreliable.

    Keywords:2Dhydrofoil;cavitationmodel;cavitationflow

    ArticleID:16719433(201o)ol006306

    1Introduction

    cavitationisaphenomenonthatplaysamaiorroleinsurface

    seagoingvesseldesignandoperation,aswellasinhydraulic equipment.Propellers,hydrofoilships,hydraulicturbinesand pumpsmaysutterfromitsconsequencesinmanyways. Cavitationcanleadtofata1failuresofhydraulicmachinery andhydraulicstructures.Therefore.ithastobeavoidedorat leastcontrolled.Thisdemandsthatcavitationinceptionhasto bepredictedbymeansofexperimentsornumerical

    investigationsduringthedesignphase.Duetotherapid developmentandbroaderapplicationofpowerfulcomputers andtheabilltytosavecostsandtimeincomparisonwith experiments.numericalmethodshavebecomeincreasingly popularinrecentyears.

    Anumberofresearchershavebeeninvestigatingcavitation numerically.Kubotaeta1.r1992)assumedthatthefluid initiallycontainsuniformlydistributedsmallgasbubblesthat willbehaveasdescribedbytheRayleighPlessetequationin achangingpressurefield.Songeta1.(1997)assumedthat,for anaturalcavitation.the1iquidandgasphasesarerepresented byasinglecontinuousequationofstate.Kunzeta1.(20001 developedamultiphaseflowmodelinwhichthedensityof eachcomponentisassumedtobeaconstant.Singhaleta1. (2001,developedthel1cavitationmodelwhichassumesthe workingfluidtobeamixtureofliquid.1iquidvaporand noncondensablegasfNCG,.

    Inthiswork,thefullcavitationmodelisadopted.A user-definefunctionisaddedintothesoftwareFLUENT. PressurecoefficientsarepresentedforflowsoverNACA66 2Dhydrofoilsandthecomputedresultsarecomparedwith experimentaldata.VolumefractionsofvaporonNACA66

Receiveddate:2008.1223.

    correspondingauthorEmaihmiaomiao591213@yahoo.coin.ca HarbinEngineeringUniversityandSpringer-VerlagBerlinHeidelberg2010

    hydrofoilsarealsopredicted.

    2Governingequationsandcavitationmodel

    2.1Governingequations

    Thecavitaionmode1implementedisthemultiphasemixture mode1.Withpropercavitationmodel,itcansimulatethe processofvaporgenerationandcondensation.Itassumes that,inaflowingfluid,thereisnovelocityslipbetweenthe fluidandbubbles,andcavitatingflowworksatconstant temperature.Thesteadystategoverningequationsaregiven by:

    

    OYlP

    

    mUj

    :

    ox

    

    OY

    

    v

    =

    tO

    

    m

    

    Uj

    :

Sv

    dx-

    

    OY

    g

    P

    

    m

    Uj

    :0

    o

    (1)

    (3)

    ++g(4)++(4)

    oxlm

    ThesourcetermsSIandSv

    denotingvaporgenerationand condensationratesarecalculatedasfollows

    =

    (+),Sv=(+)

    Themixturedensityofliquid,vaporandNCGismodifiedas

    pmQipi+vPv+.cgPg(5)

    wherePl,Pv

    andPgaredensitiesoftheliquid,the vaporandNCG,respectively,,anda g

    arevolume

    fractionsrespectively,andYi=representsmass

    Pm

    fractionsofspecies

2.2Cavitationmodel

    BasedOrldifferentdefinitionsofdensityofasinglephase,the cavitationmodelscouldbecategorizedintotwogenera1 classes:thefirstemploysstateequationswhilethesecond employstransportequations.Thefu1lcavitationmodel focusingonthetransportequationsisadoptedhere. ;.ifP<Pv

    {}=e(;)ifp>

    where,therecommendedvaluesoftheempiricalconstants CcandCcareo.02ando.01respectivelg

    3Turbulencemodelsandnear-wallfuctions

    3.11,lrbulencemodels

    ByanalysingallturbulencemodelsinFLUENT,standard kmode1.RNGksmodelandRSMmodelare

    pickedoutbyintroduction.Theywillbecomparedandone ofthemwillbechosenforfurtherstudy.

    3i.1Standardk一,turbulencemodel

    Thestandardkmodel(LaunderandSpalding,1972)is

    asemiempiricalmode1basedonmodeltransportequations fortheturbulencekineticenergy(k)anditsdissipation rate(s1.Themodeltransporteqdationforkisderivedfrom theexactequation,whilethemodeltransportequationfor wasobtainedusingphysicalreasoningandbearslittle resemblancetoitsmathematicallyexactcounterpart.It assumesthattheflowfieldisonflow,andtheviscosity beeennumeratorisignored.sothestandardkmodel

    isavailabilityonlyintheonflow.

    Thetransportequationsofthestandaredksmodelare

    givenby

    =

[(+)]++

    :

    ++一?

    where,representsonflow

    averagespeedgrads,andGb

    energyarosedbyflotageeffect

    oftheonflowis

    C=0.09,o-k=1.0,

    kineticenergyarosedby

    representsonflowkinetic

    Theviscositycoefficient

    CI1.44,1.92,

    ShengHuang,eta1.SimulationofCavitatingFlowarounda2-DHydrofoil

    3.1.2Gksmodel

    TheRNGksmodel(Choudhury,1993)wasderived usingarigorousstatisticaltechnique(calledrenormalization

    grouptheory).Itissimilarinformtothestandardk一占

    mode1.butithasanadditiona1terminitsequationthat significantlyimprovestheaccuracyforrapidlystrained

    flows.ThetransportequationsoftheRNGkFmodel

    aregivenby:

    :

    1l++(9)Ir+

    酬讣J+,

    cI(+G)c2一庀

    where,C1~=1.42,C2~=1.68,=Sk

    S=0:4.28,:0.015,C:0.085,C3:[_1+ 2G3ml(n1)+(1).,/6cC~q]13?

    313RSMmodel

    Thebasa1Renaultstressmode1(RSM1(Laundereta1.,1975)

isalinearityRSMwherelinearityalgebraequationisused

    tosimulatestressvarietyitemandscalarquantitydissipation

    equationisusedtosimulatedissipationitern.Equationsin

    theRSMmodelaregivenby:

    (+(++aPU-

    where,isthediffuseitem,

    thestressvarietyitem,and

    aregivenasbelow:

    =

    8./4

    8u~uj)

    theproduceitem,

    thedissipationitem,which

    Pij~--(u'iu'

    k+u

    

    '

    ju'

    k

    tJt"J

    i)

    =--

    Cl+C2(ctkj-+

    C3kS~Gk(a,,sjk+ajkSQkIaH61+

    G(at'k+oc|t

    Comparingwiththedoubleequation七一mode1.the

    RSMmodeldoesn'tneedanytransportionequationto

    sulotion.

    3.2Near-wallfunetions

    Forcavitationhappensnearthewall,near-walltreatments

JournalofMarineScienceandApplication(2010)9:6368

    influenceprecisionofcavitationflowsimulation.Near-wall treatmentscontainedintheFLUENTare:standardwall function,nonequilibriumwallfunctionandenhancedwall function.

    3.2.1Standardwallfunction

    ThestandardwallfunctionsinFLUENTarebasedonthe proposalofLaunderandSpalding(1974),andhavebeen mostwidelyusedforindustrialflows.Theequationsare givenby:

    =

    ?n()

    lU=Y

    v>11.225

    (12)

    v<11.225

    where,:0.42,E9.8,+:

    1/4

    .

    1/2

    tW|P

    pK1P

    /2YP

    3.2.2Nonequilibriumwallfunction

    Nonequilibriumwallfunctionadoptestressgradsonbasis ofstandardwallfimctionmethod,theequationsaregiven below:

    -

    c"1/k

    tWD

:

    11

    nfE

    I

    k"Y

    where,

    C?=U-

    2dr

    lpKx/kpK4klI.J

    Y=11.225.

    3.2.3Enhancedwallnction

    Enhancedwallfunctionformulatesthelaw.of-thewallasa singlewalllawfortheentirewallregion.Itblendslinear (1aminar)andlogarithmic(turbulent)lawsof-the-wallusing

    afunctionsuggestedbyJongen(1992):

    u=e"+eF"(14)

    where,=,n_0_0lc,6=

    /

    5/

    c1+6v

    65

    4.2Boundaryconditions

    Thenatureoftheequationsdictatestheapplicationofproper boundaryconditionsonallboundaries.Weapplythenoslip.

    nofluxboundaryconditiontothevelocityonthesurfaceof theairfoilandconstantvelocityonboundaryI(Fig.1,. PressureoutletconditionisappliedonboundaryII.A secondorderupwindschemeisusedtodiscretethe

    convectivefluxes.Thenatureoftheequationsdictatesthe applicationofproperboundaryconditionsonal1boundaries.

    Theworkingfluidiswaterat300K,withliquidandvapor densitiesof1000and0.02558k2/,saturationpressureof 3540Paandsurfacetensionof0.0717N/m.

    veIocinltet

    (a)Boundaryconditions

    (b)Meshdetails

    Fig.1Computationdomainandgrid,andgriddistributionnear thehydrofoilfor=4.

    4GridgeneratiOnandboundarycOnditi0ns5SimulatiOnresults 4.1Modelgeometryandgridgeneration

    ANACA66(mod)hydrofoilsectionwithcamberratioof 0.02.meanlinelengthof0.8andthicknessof0.09wasused A2Dworkingsectionofthehydrofoilsurfacewasmounted inawatertunne1.

    Itisknownthatoneofthemostsignificantparametersin numericalflowsimulationsisthequalityofmesh.This affectsdirectlytheaccuracyofsolutionandtherequired numberofiterations(CPUtime).Forthispurpose,the computationaldomainmodelingflowoverthehydrofoil contains30000structuredmeshes.Meshesneartheairfoil aredenser,asshowninFig.1

    Staticpressuresonhydrofoilsurfaceweremeasuredat differentanglesofaRackando-values.Simulationswere performedatRe=2×10..Thenondimensionalparameters

    ofinterestwere:

    Re=p

    |

    

    5.1Comparisonofdifferentturbulencemodels Inordertochooseaappropriateturbulencemodelforfurther

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