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Using CFD Software to Calculate Hydrodynamic Coefficients

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Using CFD Software to Calculate Hydrodynamic Coefficients

    Using CFD Software to Calculate

    Hydrodynamic Coefficients

    J.Marine.Sci.App1.f201019:149155

    DoI:10.1007/s11804.010.9009.9

    UsingCFDSoftwaretoCalculateHydrodynamicCoefficients

    HeZhang,YuruXuandHao.pengCai

    KeyLaboratoryofScienceandTechnologyforNationalDefenseofAutonomousUnderwaterVehicle

    HarbinEngineeringUniversity,Harbin150001,China

    Abstract:Applicationsofcomputationalfluiddynamic(CFD1tothemaritimeindustrycontinuetogrowwith

    theincreasingdevelopmentofcomputers.Numericalapproacheshaveevolvedtoalevelofaccuracywhich

    allowsthemtobeappliedforhydrodynamiccomputationsinindustryareas.Hydrodynamictests,especially

    planarmotionmechanism(PMM)testsaresimulatedbvCFDsoftware

    FLUENandal1ofthe

    correspondinghydrodynamiccoefncientsareobtained.whichsarisfytheneedofestablishingthesimulation

    systemtoevaluatemaneuverabilityofvehiclesduringtheautonomousunderwatervehicleschemedesignstage

    Theestablishedsimulationsystemperff'rmedwellintests.

    Keywords:FLUENT;planarmotion

    mechanismfPMM);hydrodynamiccoefficients;motionsimulation

    ArticleID:16719433(2010)02014907

    1IntrOductiOn

    AutonomousunderwatervehiclefAUV1isakindof

    submarinevehiclethatworksindeepwaterwhichisofa rangefromtenstothousandsofmetersdepthwhereits maneuverabilityalmosthasnoinfluenceonfreewater surface.wavemaking(Xueta1.,2006).Inrecentyears,there havebeenintensiveeffortstowardthedevelopmentOfAUV (Wemli.2002).TodesignanAUV.itsmaneuverabilityand controllabilitymustbeexaminedinadvancepreferably basedonamathematicalmode1.Themathematicalmodel containshydrodynamicforcesandmomentsexpressedin termsofhydrodynamiccoefficients.Therefore,itis importanttoknowthevaluesofthesecoecientsto

    simulatetheperformanceoftheAUVaccurately. Thehydrodynamiccoefficientsmaybeclassifiedintothree types:1ineardampingcoefficients.1inearinertialforce coefficients,andnonlineardampingcoefficients.Among thesecoemcients.thelineardampingonesaf.fectAUV's maneuverabilitymostlywhenAUVnavigatesinsteadystate

    flow(Sen.2000);whileinunsteadystateflow.1inearinertial

    forcecoecientsandnonlinearonesmustbetakeninto considerationtoo.Thesecoefficientsareusuallydetermined byexperiments.numericalanalysis,systemidentificationor empiricalformula.Becauseofnumbersofappendageand variantshapeOfAUVs'bodies.thereisnosystematicdesign informationwhichcouldbeusedtoestimatecoecientsof

    AUVyet.WhenestimationworkofAUViscompleted accordingtotheempiricalformulaforshipsubmarineand torpedo,amassoferrorsareunavoidable.Themethodof systemidentificationperfoITnswellinnavigationdata Receiveddate:2009.O3.04.

    Foundationitem:SupposedbytheOpenResearchFoundationof

SKLabAUVHEUunderGrantNo2008003

    c0rresp0nd-ngauthorEmaii:yihe0908@163.tom HarbinEngineeringUniversityandSpringer-VerlagBerlinHeidelberg2010

    analysesandhydrodynamiccoefficientscorrection,butit doesn'tworkwellduringtheAUVmaneuverabilitydesign stage(HuZQ,2007).Althoughplanar-motionmechanism

    (PMM)testsarethemostpopularonesamongallofthe experimentalhydrodynamictests.measureddatafromthese testsarenotcompletelyreliablebecauseofexperimental difficultiesanderrorsinvolved.meanwhiletestscostlotsof timeandmoney.

    Withtheincreasingdevelopmentofcomputers,applications OfCFDinthemaritimeindustryarefeasibleandimportant. Numerica1approacheshaveevolvedtoalevelofaccuracy whichallowsthemtobeappliedtopracticalshipresistance andpropulsioncomputationsinindustryareas.Inrecent years,CFDisalsobeingappliedtodeterminesomeof hydrodynamiccoefficientsthatareneededinevaluating maneuveringcharacteristicsofmarinevehiclesfFerziger andPeric,2002;Sarkareta1.,1997;Wilsoneta1.,2006; TyagiAetal2006).

    Inthispaper.anewmethodusingCFDsoftwareFLUENT tosimulatehydrodynamictestsispresentedandthen hydrodynamiccoefficientswhichareneededinestablishing hydrodynamicmodelarecalculated.Thenewcalculation methodisconvenient.1owcost.andclean.The

    wel1.performedmaneuverabilitypredictionresultsobtained bythismotionsimulationsystemhaveproventhatthe calculatedhydrodynamiccoefficientscouldsatisfythe designrequirementofmaneuverabilityandprediction

duringtheAUVschemedesignstage.

    Thispaperisorganizedas

    LEUVmodelandbasic

    follows:SectionIIdescribesthe

    calculationtheory.SectionIII

    presentsthenewmethodofsimulatinghydrodynamictests usingFLUENTandcalculationresults.SectionIV establishesAUV'smotionsimulationsystem.SectionV showsmaneuverabilitypredictionresults.Finally,Section 150

    VIpresentsconclusions

    2Basictheory

    2.1Descriptionofthemodel

    Theobjectstudiedinthispaperisalongendurance

    underwatervehicle(LEUV)whichcanworkinawiderange

    seaareaanddealwithcomplextasks.

    Theentitymodelisaspheroid-shapedvehiclewithfour horizontalwingsandaverticalrudder.Accordingtothe entitymodel,calculationmodelwasestablishedusing GAMBITwithascaleof1:1(Fig.1),andthen

    correspondingdomainanddesigninggirdwereestablished. Fig.1EntitymodelofLEUV

    Theproportionbetweencuboidssolutiondomainandthe modelissetto7:1inordertosimulatethevehicle navigationindeepseaarea(Fig.2).Thenumberofthe calculationmode1girdswhicharetriangularunstructured onesis413565.Thenumberhasbeenconformedafter severaltrialsandcalculations.Thedistributionofgirdsis showninFig.2.

Fig.2GirdsdistributionofLEUV

    2.2Governingequation

    Amodelwasestablishedinordertosolvetheproblem causedbyflowaroundthevehicle.Themodelisbasedon theReynoldsAveragedNavier-Stokes(RANS)equations. Foraturbulentflow,thevelocityfieldandpressurefieldcan bedecomposedintotwoparts:themean(ensembleaverage) velocityandpressure(H)and(p),andthedeviatoric(or turbulent)velocityandpressureuandp.Thus, =

    (ui)+"andp:(p)+p,inwhichi=1,2,3fora3_D

    flow.Ifthefluidisassumedincompressible,themeanflow fieldisgovemedbytheRANSequations:

    aU

    ——=

    0(1)

    8Ui

    +

    ()=10P10(r一峨)(2)

    HeZhang,etalUsingCFDSoftwaretoCalculateHydrodynamicCoefficients

    InwhichPisthedensityofthefluid,Reynoldsstress tensoris

    

    =

    l-

    l

    l

    2.3Tlurbulentmodel

    TheksSSk一,hereafter,andReynoldss~ess

    transport,RSTMhereafter,turbulencemodelsareusedfor

turbulenceclosureinthepresentstudy.Thek一,modelis

    oneofthemostwidelyusedturbulencemodelsforexternal aerodynamicsandhydrodynamics.ksmodelischosenas

    turbulentmodelinthispaper.

    kfunction:

    +v.():.[(?+)v]+pe(3)

    dt

    function

    Ot

    (.[(+V小酬4)

    o,k

    where.

    ^

    =V?(vO+v0)_zV?[(3V?+)

    )

    k

    |lt:up——

    2.4Boundaryconditions

    SetboundaryconditionsinpreprocesssoftwareGAMBIT: (1)inflow(rightboundaryofsolutiondomain):velocity inlet;

    (2)outflow(1eftboundaryofsolutiondomain):outflow; (3)wall(surfaceofthevehicle):wall;

    r41fluiddomain:FLUID.

    Fig.3Spacedistributionofvehicleanddomain 3Simulationhydrodynamictestsusing

    FLUENT

    Simulationtestsproposedinthispaperconcludetwokinds ofconditions:steadystateandunsteadystate.

    Unsteadystatetestsincludefivemaneuverabilityteststhat operatedwithPMM,whilethesteadystateonesarelinear

    motionandloxodromicmotiontests.

    JournalofMarineScienceandApplicationf201019:149-155 3.1Simulatingunsteady-statetests

    3.i.iSettinginitialization

    SimulationtestsarecompletedusingFLUENTsoftware. Someparametersaresetasfollows.Choosethefirstorder implicitsolver.standardk一,model,standardwall

    function;theotheroptionsremainasdefault.SIMPLE algorithmisusedtocalculatepressurevelocitycoupling.

    PressurediscretizatiOnisPREST01.Momentum discretizationisthesecondorderUpwind,andtheother onesarethefirstorderUpwind.Forceandmomentumdata arerecordedineverystep.

    3..2Usingdynamicmeshes

    TherearetwokindsofUserDefinedFunction(UDF)for simulatingPMMtests——translationonesandrotationones accordingtothecharacteristicoftests.UDFisprogrammed tomakethewallofthevehiclemodelmovingasmotion equationinthesolutiondomain.

    Taketheheavemotiontestasanexample(translationUDF) {;=asino)t..

    whereverticaldisplacementofAUVmodel;

    a-amplitudeoftheheavemotionofAUVmodel;

    ?

    circularfrequencyofheavemotionofAUV

    model

    0,0angleandangularvelocityrotatedalongYaxis; w.-verticalvelocityandacceleration.

    Takethepitchmotiontestasanexample(rotationUDF), 0=O0sineotwhere0,0angleandangularvelocityrotatedalongYaxis; q,angleandangularvelocityinpitchmotion;

    

    circularfrequencyofpitchmotionofAUV

    model;

    w.verticalvelocityandacceleration.

    Thenumericaltestsfollowtheruleshereinatier.Thevehicle surgesinthesolutiondomainatdifferentfrequenciesr0.2 Hz,0.25Hz,0.3125Hz,0.4Hz,0.5Hz,0.625Hz,and0.8 Hz)anditsamplitudeis0.04m.Theparametersare nondimensionalizedwithinletvelocity1m/sand characteristiclengthL.Onemotionperiodisdividedinto 400stepsduringthecalculation.

    151

    3.1.3Dataprocessing

    Simulationcalculationgoeson6-7cyclestogetstable curvesofforceandmomentwithtimeindisregardof oscillationfromthebeginning.Themeanvalueofthelast threecyclesstabledataisusedforpost-processing.Replace thecharacteristiclengthbythesupposedareavaluewhen doingthenondimensiona1work.

    ResultsderivedfromFLUENTsoftwareareaseriesof discretepointsthatarefit)withregardtot.

    namely,

    )=a0+.c.s+sin

    ZZsinax+ZbCOSO)t+Z

    MM.sincot+M6coso)t+M:

    (8)

    (9)

    where,Listhecharacteristiclengthofmodel,Visthe incomingflowvelocity.

    =

    ago2L

    z:;Zh=a(o(10)

    .

    =

    2

    ;=

    ac

    

    oM,)

    Accordingtotheformulaeabove,dealwiththeresultdataas FourierexpansionusingMATLABsoftware,then derivez,Zb,Ma,Mb,furthermorederiverelevant hydrodynamiccoefficientsfromeachmotionofPMMtests. Then,PMMsimulationtestsarecompleted.

    3.2Simulatingsteady-statetests

    321Settinginitialization

    Simulatingsteady.statetestsarecompletedusingFLUENT softwareandsomeparametersaresetasfollows.Choosethe firstorderimplicitsolverwithsteadyoption(KandEpsilon, parameterTurbulentKineticEnergy=1m/s.Turbulent DissipationRate=lm/s1,standardwal1function,while otheroptionsremaindefault,withoutenergyfunction. SIMPLEalgorithmisusedtocalculatepressure.velocity coupling,pressurediscretizationisthefirstorderupwind discretemode.andmomentumdiscretizationisthefirst orderupwinddiscretemode.Forceandmomentumdataare recordedineverystep.

3.2.2Simulationoflineartest

    Thevehiclebuoysfiatinthesolutiondomain.magnitudeof longitudinalforcesarerecordedwithvelocityseries.Onthe basisofdataabove,thelongitudinalresistancecoefficient couldbecalculated.Operationconditionintheflame restrictsthesimulatinginletflowvelocityvaryingfrom0.3 to1.7m/swithanincrementof0.1m/s.

    3.2.3Simulationofloxodrometest

    Whensimulatingloxodrometest,sethorizontalinletflowat theinletofthedomainandthenrotatethemodelinthe l52

    domainastheattackangleoftheplanewhichvariesfrom .

    10.tO10.withanincrementOf2..Holdthehorizontal velocityataconstant,andrecordforceandmomentofthe lOXOdrometest.Dealwithmedatasoastocalculatethe correspondinghydrodynamiccoefficients.

    3.3Calculationresults

    Allthesimulatingtestsarecompletedinthefirsttwo sectionsofthischapter.Hydrodynamiccoefficientsare presentedhereinTable1.

    BasedonthecoefficientspresentedinTable1,24other coefficientscanbederivedaccordingtocorrelativearticle (Shi,1995).

    Table1Calculatedhydrodynamiccoefficients

    CoecientFLUENTCoefficientFLUENT

    乏一0.04575z;0.000494

    z:0.3376Z.0.01656g

    :0.00053M;0.00253

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