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Simulation of Wave Impact on a Horizontal Deck Based on SPH Method

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Simulation of Wave Impact on a Horizontal Deck Based on SPH Methodof,on,a,wave,deck,based,SPH,Wave,Deck,Based

    Simulation of Wave Impact on a Horizontal

    Deck Based on SPH Method

    J.MarineSciApp1.f201O,9:372378

    DOI:101007/sl1804.010l0225

    ,???I.

    lmUlatl0n0I

    BasedonSPHMethod

    Jia.wenSun,Shu.xiuLiang,Zhao.chenSunandXi.zengZhao

    i.StateKeyLaboratoO,ofCoastalandOffshoreEngineeringDalianUniversi~.jTechnology,Dalianl16024,China,

    2.R1AM,Kyushu,2n,ersit3;Kasuga,Fukuoka8168580,Japan

    Abstract:Anumericalmodelwasestab1ishedforsimulatingwaveimpactonahorizonta1deckbyanimproved

    incompressiblesmoothedparticlehydrodynamics(ISPH).Asagrid

    lessparticlemethod,the1SPHmethodhas

    beenwidelyusedinthefree?

    surfacehydrodynamicflowswithgoodaccuracy.Theimprovementincludesthe employmentofacorrectivefunctionforenhancementofangularmomentumconservationinaparticlebased

    calculationandanewestimationmethodtopredictthepressureonthehorizonta1deck.Thesimulationresults

    showagoodagreementwiththeexperiment.Thepresentnumericalmodelcanbeusedtostudywaveimpact

    ioadonthehorizonta1deck

    Keywords:incompressiblesmoothedparticlehydrodynamics(ISPH);waveimpact;kernelgradientcorrection

    ArticleID:l67I9433(2010)040372O7

1Introduction

    Wavejmpactloadoncoasta1andofirshorestructuresisa majorcauseofdamagetothemarinestmctures.Toavoidthe damageofthosemarinestructuresarousedbythewave impactforces.manylaboratoryexperimentalresearcheshave beencarriedouttoestimatethewavejmpactload(Wangeta1.. 1970;KaplanetaL.1992,1995:GuoandCai1980;Wang a1.,1998;RenandWang,2005:Reneta1.,2007;Zhoueta1., 2004).Becausethewaveimpactphenomenonisextremely complicatedandinvolvesthestrongnonlinearityofwaves.

    instantaneouseffect,fluidviscosityandturbulence,andthe stronginteractionbetweenthewaveandstructure,the progressinresearchisstillunsatisfactory.

    Withtherapiddevelopmentofcomputersandcomputational fluiddynamics,thenumericalmodelsbasedonthe Navier-Stokesequationshavebecomepopularintheresearch ofwavejmpact1oad.RenandWangfl999,2003);Rel3el a1..(2007)investigatedanumerica1wavetankbasedOil improvedVOFmethodtostudythewaveslammingona horizontaldeckinthesplashzone.Kleefsmaneta1.(20041put forwardanjreprovedVOFmethodComflowusingthefinite

    volumemethod.ThefreesurfaceistracedusingtheVOF methodtogetherwitha1ocalheightfunction.resultingina strictmassconservingmethod.Thechoiceofboundary conditionsatthefreesurfaceappearstobecrucia1forthe accuracyandrobustnessofthemethod.HuandKashiwagi (2004)appliedtheCIPmethodtosimulatethewaveimpacton thestmcturewithquitesatisfactoryresults,Zhengeta1.(2009) Reeeiveddate:2Ol0O70I.

    Foundationitem:SupportedbytheNationalHighTechnologyResearch

    andDevelopmentProgramofChina(863Program,Grant No2007AA1IZ130)

    C0rresp0ndin2authorEmail:SUnZC@dlutedu.cn HarbinEngineeringUniversityandSpringer-VerlagBerlinHeidelberg2010

    appliedthestandardISPHtothestudyoftheinteraction betweenwavesandstructures,simulateddamcollapsing impactpressureonawallandthewaveslammingona horizontaldeck.Butthenumericalpressureresultexhibits largepressureoscillations.

    Thepurposeofthispaperistosimulateatransientwave impactonahorizontaldeckbasedonanimprovedISPH method.Thenumericalwaveimpactforceresultsare comparedwithexperimentalresultsbyReneta1.(2003)and numericalresultsbyZhengeta1.r2009).

    2IncompressibleSPHmodel

    2.1Governingequations

    TheNSequationdescribedbyLagrangianfunctioncanbe writtenintheforlTlasfoIlows:

    

    1

    _

    dp

    +.:0(1)d,

    :

    lVp

    +F+vzu(2)

    dtD

    whereP:pressure.P=density,U=velocity,o0=laminar kinematicviscosity.

    IntheLESframework,Eqs.(1)and(2)insubgridscalecan bederivedfromtheNSequationbyusingaspatialfilterand

    representedasfollows:

    

    1

    

    dp

    +.:0(3)

    Pdt

    dU

    =

    V+g+DoV2+1V

    ,

    r(4)

    whereg-s~ndsforsubgridscaleturbulencestressesandare

    expressedasfollows:

    JournalofMarineScienceandApplicationf201019:372378 (2)一号?Il

    Inwhich,C0.0066,turbulenceeddyviscosity coefficient,k=turbulentkineticenergy,isthestress tensorofsubparticlesscale:

    =

    1

    '

    Oui

    +)

    Turbulenceviscositycoefficientiscalculatedbyusing

    standardSmagorinskymodel: =

(?)ll

    Inwhich.Cs=0.12isSmagorinskyconstant.1ocalstrainrate

    isexpressedinformofI=(2s?osq),andAstandsforthe

    initialspacingofparticles.

    2.2ThecorrectedincompressibleSPH

    TheSPHmethodisbasedontheinterpolationtheory.In SPH,thefimdamentalprincipleistoestimateanyfunction A,anditsgradienthasthefollowingform: Zmj3

    ,

    -

    (r-rj,h)

    VA(AjV(

    r-rj,h)

    ThefinalformofEqs.(3)and(4)canbewrittenas dPl

    ,

    dU

    dt

    f81

    ++g+c++

    (9)

    whereW(r-rj~h)isthekernelfunctionIWr.h)=gradient ofthekemelwithrespecttothepositionofparticlei.Inthis paperweusecubicsplinekernelfunction,whichcanbe W(R,h)=

    

    R2+IR3

    2

0?R<1

    1R<2

    ?2

    whereR=,for2-dimensionalproblems,thenormalization factortakesthevalue~a=15/7h.,h=smoothlength. IntheSPHmethod,theparticlesneartheboundariesand freesurfacehaveakernelfunctiontruncatedduetothe absenceofneighboringparticles.Theconditionsof consistencyandnormalizationfail.Khayyereta1.(2008) appliedacorrectivetechniquetocorrectthegradientof kernelfunctionincalculatingviscousforcestoavoiderrors fromacorruptedinterpolationfunction.Inthispaperweuse 373

    acorrectmethodthesameasKhayyer'smethod.The correctedgradientofkernelfunctionshouldbeusedto calculatetheforceintheequationofmotioninsteadofthe gradientofthekernelVW(r-r,h).Thecorrectedgradientof kernelfunctionsisgivenasfollows:

    WH=L_wu

    '=(?V0(0))

    (11)

    (12)

    2.3Solutionprocedure

    Inthesolutionprocessofpressure.wewilldivideeach

    timestepintotwosteps.Themethodissimilartothe movingparticlesemiimplicitmethod.Thefirststep,the velocityanddisplacementvariables".generatedbythe nonpressureiternsaresolvedusingthesourceiternatthe timeoft=n.andthenmakeamendmentaccordingto continuityequationandmomentumequation,wecanobtain

thefollowingequations:

    Au=fat

    (13)

    (141

    r=r"+"At(15)

    Forthesecondstep.assumethatun+I:"+?".whereisthe

    changeofspeedgeneratedbythepressureitem: 1

    ?"=1VPAt(16)

    p

    Tointroducethisspeeditemintothecontinuityequation, Poissonequationforpressurecanbederivedasfollows: V?

    (V]=

    ByusingthisPoissonequationforpressure,wecanobtain thespeedgeneratedbypressureitemandthusderivethe speed""andr"atthetimeoft=-n+1.

    r.=r+~/n+lAt(18)

    Theimprovedformofthepressuregradientitemproposed byShaoisused:

    V?

    (V,Pl,,?w(++

    where,Pl|PrPpandrl=rrlisasmallquantitythat guaranteesthedenominatornotbeingzerointhemiddle stepsofcalculation,generallytakes0.1timesofthesmooth length.Thecoefncientmatrixofthisequationissymmetric positivedefiniteandthemaindiagonalisdominant. Therefore.itisconvenienttousehigh.eciencycalculation

    methodforsolution.Inthispaper,biconjugategradient

    methodisemployed.

    2.4Treatmentofboundaryconditionsandfreesurfaces Inthispaper,thetreatmentofboundaryconditionsandfree 236O

    374J/a

    wcnSun.etaLSimulationWaveImpactOPlAHorizontalDeckBasedonSPHMethoeds

    surfaceissimilartoShao(2005).Thesolidboundariesare representedbyfixedwallparticles,whicharesimilartothe fluidparticles.ThepressurePoissonequationisalsosolved onthesewallparticles.buttheirvelocitiesaresettozeroat theendofeachtime.step.Therefore,theirvelocitiesand positionsarefixed.Thefreesurfacecanbeeasilyand accuratelytrackedsincethecalculateddensitiesatparticles onthefleesurfacedropabruptlyduetolackofparticlesin theouterregionofthefreesurface.Thefollowingcriterion isconsideredforthedetectionoffreesurfaceparticles: =0.99P0(20)

    Inordertogetexactsolutionofthepressureonsomepoints onthedeck.anewestimationmethodisapplied.Basedon thesolidboundarydescribedabove.theparticlesonthedeck aretreatedasfluidparticlesbutinthesimulations,thesum overalltheneighboringparticlesisreplacedbythesumover theonlyneighboringfluidparticles,onlythefluidparticles areconsideredwhenthepressuresimulationiscarriedout. AsshowninFig.1.thepressurecanbewrittenas:

    F.

    P,=(21)

    whereens0r=2h,F~nisthetotalforceonthewall,anditcan bewri~enas

    =

?pym.,m,

    i,Deckparticle

    oooooooo.

    :

    OOoOoOO

    Fig.1Samplingarea

    3Modelapplication

    (22)

    3.1Waveimpactonahorizontaldeck

    Inthissection.theincompressibleSPHmodeIisusedto simulateagreenwaterwaveimpactonahorizonta1deck.In thecoastalandoffshoreengineering,unexpectedwave impactforceisthemajorcauseofdamagetothemarine structuressuchasopenwharfandplatform.RenandWang havedonealotofresearchesaboutthewaveimpactonthe horizontalplate.includingexperimentalresearchinthe laboratoryandnumeficalsimulationresearchbasedonVOF metbod.InordertotestOUTnumericalmodel,the experimentalresultsbyReneta1.(2003)areusedforthe comparison.

    3.2Introductionofexperiment

    Themoredetailedlaboratoryexperimentcanbefoundin Ren(2003).Onlysomeimportantparametersare1istedhere. Theexperimentswerecarriedoutinalargewavecurrent

    tankattheStateKeyLaboratoryofCoasta1andOffshore Engineering,DalianUniversityofTechnology.Thetankis 69mlong.2Inwideand1.8mhigh.Thedeckmode1wasa horizontalplate,1mlong,0.65mwideand0.02mthick, spanningonethirdofthewidthoftheflume,asshownin Fig.2.Thewaveimpactpressuresontheundersideofthe

modelweremeasuredusingamultipointpressure

    measuringsystem.Elevenpressuretransducerswerefixed ontheundersideofthemode1.andweremarkedaslt0l

    startingfromtheseasideasshowninFig.3.

    Fig.2Planeviewofexperimentalsetup

    1m

    5cm5cm

    ???????????

    fiffIllIIl

    I9cmJ9cmI9cmJcl9cmJ9cmll9clJJ

    Fig.3Sketchofpressuretransducersontheundersideofthe modelstructure

    3.3Thenumericalcomputationalparameters

    Thenumericalcomputationresultsofwaveimpactondeck fordifierentparametriccasesareverifiedbythe experimentalresults.Thecomputationregionisshownin Fig.4.Thelengthofthenumericalwavetankis35.0m.and thedistancebetweentheleadingedgeofthedeckandthe wavemakeris9.0m.thewaterdepthis0.6m,theendofthe tankisaslopingwal1.theslopangleis30degree.Theinitial fluidparticlespacingdx=dy1.5cm,thefixedparticles spacingdx=dy=1.0cm,includingthesolidboundary, movingpaddleandthehorizontaldeck.Thusthetotal numberoftheparticlesis59817.

    15m

    Fig.4Sketchofthecomputationdomain

    4Resultanalyses

    4.1Thetimehistoryofpressure

    Fig.5showsthenumericalandexperimentalresultsofthe timehistoryofimpactpressureonthedeck.Theleftfigures

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