Application of genetic algorithm for ship hull for

APPLICATIONOFGENETICALGORITHMFORSHIPHULLFORMOPTIMIZATIONR.Dejhalla,Z.Mrsˇa,S.Vukovi´cFacultyofEngineering,UniversityofRijeka,CroatiaInt.Shipbuild.Progr.,48,no.2(2001)pp.117-133Received:February2000Accepted:September2000Acomputationalmethoddevelopedforsolvingtheminimumshipwaveresistanceproblemispresentedinthepaper.Themethodinvolvescouplingideasfromtwodistinctresearchfields:numericalshiphydrodynamicsandgeneticalgorithms.Toapproachtheminimumshipwaveresistanceproblemnumerically,thegeneticalgorithmiscoupledwithanumericalmethodforsolvingthethree-dimensionalpotentialflowpastashipmovingatconstantspeedincalmwater.ThenumericalmethodisbaseduponawellknownDawson’smethod.ThedevelopedoptimizationprocedureisdemonstratedbyselectingtheSeries60(CB=0.60)hullasmother-modelforthedevelopmentoftheoptimalshiphullforms.Thenumericalresultsofoptimizationprocedureindicatethattheoptimizedhullformsyieldareductioninwaveresistance.1.IntroductionThenumericalshapeoptimizationtechniqueisapromisingmethodforthedesignproblemsinengineeringbecauseitcansupplementanexperienceandguidewhendesigningnewgeometriesortryingtoimprovetheefficiencyoftheexistingones.Approachofusingadirectflowsolverandverygeneralrobustconstraintmethodsisacceptedin3Dindustrialaerodynamicsdesign[1].Forthesimplegeometriesandsimpleflowmodels,suchas2Dairfoilsorwingprofiles,theshapeoptimizationmethodsarewidelyused[2],buttheyremainquiteunusedforcomplexconfigurationsandcomplexflow.Inthecontextofshiphydrodynamics,themostfundamentalandeverlastingproblemisthedesignoflowresistanceshipssatisfyinggivenrequirementsofdisplacementvolumeandspeed.Shipdesignersandshiphydrodynamicistshavealwaysbeeninterestedinfindingshipformsofminimumresistance.Anumberofinvestigatorshavetriedtoemployoptimizationtechniquesinordertominimizesomeuserdefined118Applicationofgeneticalgorithmforshiphullformoptimizationobjectivefunction[3,4,5,6,7,8,9].Someoftheseattemptsseemtobeencouragingasnumericalcomputationsshowimprovementsoftheoptimizedshape.Forsimplification,theshipresistancemaybeseparatedintotwoparts:africtionalresistanceandawave-makingresistance.Ingeneral,forconventionallyshapedshiphullsitisnotpossibletoreducethefrictionalresistancesignificantlybyredesignofthehull.Experienceandobservationshaveshownthatoptimaldesignsareundoubtedlythosewithleastwaves.Minimizationofwaveresistanceofshipshasbeen,andstillis,oneofthefundamentalproblemsfornavalarchitects.Inthispaper,thenewoptimizationprocedurethatdealsdirectlywiththeactualgeometryoftheshipispresented.Thisoptimumhullformproblemisapproachedbymeansofanumericalanalysis.Forthatreason,thenumericalmethodforsolvingthethree-dimensionalpotentialflowaroundashipmovingatconstantspeedincalmwateriscoupledwiththegeneticalgorithm.TheprocedureforsolvingtheshipsteadyinviscidflowcalculationwithfreesurfacebelongstothefamilyofmethodsbasedonboundaryelementsandRankinesources,andbasicallyisDawson’smethod[10].2.TheproblemformulationTheshipisassumedtobearigidfloatingbodythatmoveswithconstantvelocityU∞relativetothefluidatinfinity.Aright-handedCartesiancoordinatesystem(0,x,y,z)fixedwithrespecttotheshipisadopted.Theoriginissituatedattheintersectionoftheplanesoftheundisturbedfreesurfaceandthemidshipsection,thex-axisisdirectedasternandthez-axisverticallyupwards,Figure1.Figure1.CoordinatesystemIntheabsenceofviscousstressesthefluidmotionwillbeirrotationalhenceasteadyflowpasttheshipcanbedescribedbyavelocitypotentialφ(x,y,z),whichsatisfiestheLaplaceequation∇=20φ(,,)xyz(1)y∞UzxR.Dejhalla,Z.MrsˇaandS.Vukovi´c119inthefluidregion.Theboundaryconditiononthewettedshipsurface,wherezh(x,y)isφ⋅=n0,(2)wheren=(nx,ny,nz)istheoutwardnormalunitvectortothehullsurface.Onthefreesurfacez=h(x,y),wherehisthewaveelevation,thevelocitypotentialneedstosatisfythekinematicandthedynamicboundarycondition∂φ∂∂φ∂∂φxxyyzhh+−=0(3)ghUxyz+[++−]=∞1222220()()()∂φ∂φ∂φ(4)Eliminatingh,(3)and(4)reduceto122222220∂{∂++[]+∂∂++[]=xxxyzyyxyzφ∂φ∂φ∂φφ∂φ∂φ∂φ()()()()()()}(5)Finally,itisalsorequiredthatthefunctionφapproachestheuniformstreampotentialatinfinityandthattherearenowavesupstreamfromtheship(radiationcondition).Thefreesurfaceproblemformulatedaboveisnon-linear,duetothenon-linearityofthefreesurfaceboundaryconditionsandsincethepositionofthecorrespondingboundaryisinitiallyunknown.Thereforethenon-linearprocedureisnecessarytoobtainanexactsolution.However,insteadofsolvingafullynon-linearproblemalinearformulationisusedtoobtainthenumericalsolution.ThetotalvelocitypotentialφisthenexpressedasthesumoftwopotentialfunctionsφDandφoas:φφφφ=+=+DoUx'.(6)TheφDisthedoublemodelsolution,whichmightbethoughtofasafirstapprox-imationofφ,andφoisaperturbationpotential,representingtheeffectofthefreesurfacewave.Substituting(6)into(5),thelatterislinearizedaboutthedoublemodelsolutionφDbyneglectingthenon-lineartermsofφo.Furthermore,assumingthat(5)holdsonh=0insteadofonthefreesurface,expandingalltermsin(5)thelinearizedfreesurfaceconditionbecomes:∂++∂++∂∂+∂∂+∂∂+xyxDxxyDyyxDyDxyacbdVVVVφφφφφ'()'()()(')()(')((')22+∂∂+∂=−∂+[−∂+∂]∞∞yxzxDxxDyDyxDxyDgVcUVVdUVV('))'(())(()())φφ22,(7)where:120A