螺旋桨叶剖面优化设计比较研究(英文)

船舶力学

JournalofShipMechanicsArticleID：1007-7294(2011)12-1344-09AComparativeInvestigationonOptimizationof

PropellerBladeSectionDesignZENGZhi-bo(ChinaShipScientificResearchCenter,Wuxi214082,China)Abstract：Amethodofbladesectiondesignoptimizationformarinepropellerswithmaximumcavitationinceptionspeediscomparativelyinvestigated.Thedesignoptimizationmethodconsistsofthreeparts:parametricrepresentationofsections,cavitationbucketpredictionandGeneticAlgorithm(GA)usedtosearchtheoptimizedfoilsprovidingexcellentcavitationinceptionperformance.TheEpplermethod,whichdescribesaprofilebytenparameters,waseffectivelyutilizedforpropellerbladesectiondesignoptimizationformaximuminceptionspeed.BesidesdesignparametersinEpplermethod,parametricrepresentationofsectionscanbealsorealizedbycontrol[x)intsofB-splinecurve.Acomparativeinvestigationofbladesectiondesignoptimizationonthesetwoparametricrepresentationsispresented,someconclusionsaredrawn.Keywords:bladesectiondesignoptimization;geneticalgorithm;B-spline;Epplermethod；comparativeinvestigationCLCnumber:U661.313Documentcode:AIntroductionCavitationisakeysubjectofshippropellerdesign.Inmanycases,suchasfornavalships,ilisnecessarytodelaycavitationinceptionuptothehighestpossibleshipspeed.Traditionallythemarginagainstcavitationisincreasedbyincreasingthebladearea.However,itleadstothinandwidesections,whichreducestheabilityofcavitationfreewhenitoperatesatangleofattackwithtimedependentvaryingbecauseofnon-uniformwake.Furthermore,increasingbladeareareducespropellerefficiency.Forimprovingthecavitatingperformanceoffoilsection,Epplermethod"】wasprovedtobesignificantlysuccessfultoenlargecavitationbucketofsectionsandithadbeenverifiedbyexperiments121.Inrecentyears,morepracticaldesignmethodsofsectionsbasedonoptimizationhavebeendeveloped"』ZengandKuiper151developedanoptimizationtechnique,usingageneticalgorithmtointegratetheprogramofEppler-Shen,makesEpplerfoildesignmethodmoreaccessibleandconvenient.Inthispaper,theoptimizationtechnique151wasadoptedtocomparativelyinvestigateeffectsofdifferentparametricrepresentationsonoptimizedsectionsofpropeller.Twoparametricrepresentations:designparametersinEpplermethod,coordinatesofcontrolpointsofB-splineReceiveddate：2011-08-23Biography：ZENGZhi-bo(1980-),male,engineerofCSSRC.

curvewereinvestigated.Theoptimizationstrategyappliedgeneticalgorithmswhichwereprocessedbymeansofgeneticoperators,includingcrossover,mutationandselection.Theobjectivesderivefromacavitationbucketagainstanoperatingcurveofasectionofapropeller,whichconsistofpressuresheetcavitationmargin,suctionsheetcavitationmarginandsuctionbubblecavitationmargin.Theevaluationofthefitnessofobjectiveadoptedatwodimensionalpanelcode.Foraspecificoperatingcurveofabladesection,acomparativeinvestigationonthetwoparametricrepresentationsinoptimizationhasbeencarriedout.Theanalysiswaspresentedandsomeconclusionsweredrawn.Thegeometricaldifferencesamongtheoptimizedfoilsbasedontwoparametricrepresentationstellthatthesignificanceofeachparameterofeachrepresentationneedstobestudiedfurther.MethodologyMethodologyofsectiondesignoptimizationtodelaycavitationinceptionisgenerallycomposedofthreeparts:thefirstisparametricrepresentationofgeometryofsections,thesecondispredictionofcavitationbucketoffoilsandthethirdisoptimizationtool.Bladesectionparameterizationisadifficultprobleminoptimization,whichsignificantlyaffectsoptimizedresults.Anidealparametricrepresentationshouldbesimpleandcompletelyextractcharacteristicsofbladesectioninitsparametricspace.TwodimensionalpanelmethodisemployedtopredictthepressuredistributionandtheOptimiutionBoxOptimiutionBoxOptimiutionBoxParameterBoxFunctionBoxFig.lTheflowchartofsectiondesignoptimizationcavitationbucketonafoil.Cavitationbucketisdefinedbytheminimumpressureonthefoilversusangleofattackorliftcoefficient.SoafterthecalculationofthepressuredistributionsonafoilataseriesofOptimiutionBoxParameterBoxFunctionBoxFig.lTheflowchartofsectiondesignoptimizationTheoptimizationwasrealizedwithgeneticalgorithms,availableundertheiSIGHT9.0environment,aproductfromEngineousSoftware.Thesectiondesignoptimizationissetupbyintegratingaparametricrepresentation,atwodimensionalpanelmethodandanoptimizationtool.Fig.1showstheflowchart.ParametericrepresentationsAsmentionedabove,bladesectionparameterizationisaworthystudyingproblemrelatedtoaspecificoptimizationobject.Twomethodswereinvestigatedinthepresentstudy.B-splineLettingP（t）bethepositionvectoralongthecurveasafunctionoftheparameteraB-splinecurveisgivenby/l+lPU）二£bM（£）虹芦心皿,2WkWgl⑴i=lwherearethepositionvectorsofthen+1verticesofthecontrolpolygon,andNikarethenormalizedB-splinebasisfunctions.Differenttypesofcontrol'handles'areusedtoinfluencetheshapeofB-splinecurves,inwhichchanging/adjustingpositionofthecontrolpolygonverticesisthemostpracticalandsignificantone.Asanusualway,asectionofpropellerbladeisconsideredasasuperpositionofathicknessdistributionandacamberdistribution.Inordertomaketwocurvesreflectpossiblecharacteristicsofsectionsinoptimization,thecontrolpointsofB-splineshouldbeselectedreasonably.ThecontrolpointsforthicknessandcambercanbeselectedasinFig.2andFig.3,andthecoordinatesofthemareshowninTab.landTab.2.Thethicknessisrepresentedby9controlpointsand8parameterswithtwopointscorrespondingtotheleadingedgeandtrailingedgebeingfixed:（xt,ytvyt4,yfmax,yt5,yf6）.Thecamberisrepresentedby8controlpointsand7parameters:（xf,yfi，泌，yfy）/薄，yf）,Sothereare15parametersintotaltorepresentasectioninB-splineparametricrepresentationmethod.Fig.2ThecontrolpointstorepresentthicknessFig.3ThecontrolpointstorepresentcamberdistributiondistributionTab.lThecontrolpointscoordinatesforthicknessdistributionX00.0IxfOAxt0.25心0.5xzxt（\+2xt）/3（2+以）/31y0yhyhytAyGyt60Tab.2ThecontrolpointscoordinatesforcamberdistributionX00.0"0.15V0.25xf0.5xfxf0.5（1+矿）1y0yf\xfiyfi寸4yfgyfs0EpplermethodTheprogramofEppler-Shen[l）fordesigningasectioncanbeconsideredtodescribeasectionbytenparametersasfollows地巾i，a},a2.©3,ar巾妙a4,a5,u,k

when04Fig.4SegmentationofthesectiongeometryFig.4issegmentationofthesectiongeometryandshowsparametersoneachsegment.Inthefigure,from巾州to巾】isthemainpressureregionanda}isthecorrespondingangleofattackforconstantpressuredistributioninthisregion,where（f）PRisthelocationofthebeginningoftherecoveryandfixedat51degrees,whichisthesamevalueasusedbyKuiperandJessup161;From巾ito巾？，巾210巾3and</）3to（j）4arethesheetcavitationsuppressionregions,inwhich（f）2iscalculatedintheprogramanda29anda4arethecorrespondinganglesofattackintheseregions;a5correspondstotheregionfrom如to-</>5,inwhich如determinestheclosureregionatthetrailingedgeandfixedat24degrees;Thesuctionpressurerecoveryregionisonthesuctionsidefrom+（/>5to巾地；uandkareusedtocontrolthepressuredistributiononwhen04Fig.4SegmentationofthesectiongeometryComparativeinvestigationAcomparativeinvestigationontheeffectsoftwoparametricrepresentationmethods,i.e.B-splinemethod,andEpplermethodontheoptimizedresultsiscarriedout.Eachoptimizationhasitsownparametricrepresentationbutusingthesamepanelmethodforproducingcavitationbucketandthesameoptimizationtool.Anoperatingcurveofthesectionin0.8RofapropellerworkingbehindDTMB5415151wasadoptedasexampletofindtheobjectives.Fig.5givestheoperatingcurveandabucketof+a=0.8sectionwithamaximumthickness0.035NACA66mod+a=0.8sectionwithamaximumthickness0.035andthesectionisshowninFigs.13~15,itcanbeseenthatthebucketcannotenvelopetheoperatingcurve+a=0.8sectionwithamaximumthickness0.0354.1OptimizationproblemTheobjectiveoftheoptimizationistodesignasectionwithacavitationbucket,whichenvelopstheoperatingcurveinFig.6.Theoperatingcurvecanbecalculatedbyunsteadypanelcode.TheobjectiveconsistsofdClvdClHanddacThevaluedC”istheverticaldistancebetweenthecavitationbucketandthelowestpointoftheoperatingcurve,andgivesthemarginagainstpressuresidesheetcavitation.ThevaluedCLBistheverticaldistancebetweenthecavitationbucketandthehighestpointoftheoperatingcurve,andgivesthemarginagainstsuctionsidesheetcavitation.Similarlythevalueda(:comesfromtheminimumhorizontaldistancebetweentheoperatingcurveandthebucketanditdepictsthemarginagainstsuctionsidebubblecavitation.Theoptimizationproblemisformedwithaconstraintofmaximumthicknessoffoilsasfollows,Max.dCIA(X),dC^(X)9dcrc(X)XeC(2)whereXiscombinationofparameters,Cisaconstraintspaceofparameters,T临isthelimitofmaximumthicknessofsection.Therangeofeveryparameterineachparameterrepresentationmethodshouldbefirstlyspecified,whichhassomeeffectsonthedesignresults.TheconstraintofmaximumthicknessTIimissetas0.04.Inordertooptimizedesignvariablestheobjectivesaretranslatedintoonefitnessparameterwithsuitableweightforeachofthedesignobjectives.AGeneticAlgorithm(GA)optimizationmethodisusedtogenerateanewbetterpopulation.Optimizationsareprocessedbymeansofgeneticoperators,includingcrossover,mutationandselection.Thebestsolutionforamulti-objectiveoptimizationproblemisoftenatrade-off,soaParetooptimumisusedinsteadoffindingonlyonesolution.Thereisaseriesoffeasibleandnon-dominatedsolutionsintheParetoanddesignerscanselectasuitableoneaccordingtopracticalrequirements.ThedesignoptimizationisexecutediniSIGHT,thefeaturesofoptimizationtool,geneticalgorithm,areselectedasfollows:populationsizeis20,maximumgenerationsarespecifiedas25,crossovertypeistwopointsandcrossoverrateis0.4,mutationrateissetas0.1.Objectiveisdefinedas,Objective=-(WdCuxdC^+Wdc^^LB^c)⑶withtheweightofdC”,dclBofdCIRandofdac.SotheoptimizationbecomesaproblemsearchingminimumvalueofObjective.Inthepresentoptimizationproblem,(4)isselected.ComparisonontheoptimizationprocessTheoptimizationprocesseswiththetwoparametricrepresentationmethodsareshowninFig.7.ThefiguregivesthedevelopmentofbestObjectiveversusgenerations.ItcanbeseenthateachbestObjectiveisimprovedwiththeincreasingofgenerations,howevertheconvergenceissignificantlydifferent.Epplermethodcanarriveatminimumvalueafter5generationsbutB-splinemethodshowsagraduallyimprovedprocessandreachestheminimumObjective

in20generations.RegardingtheminimumObjective,B-sp]inemethodandEpplermethodhavethesamevaluewhichiscloseto-0.1.Fig.6AtypicaloperatingcurveandcavitationFig.6AtypicaloperatingcurveandcavitationFig.7ComparisonoftheoptimizationprocessbetweenbucketB-splinemethodandEpplermethod4.3ComparisonontheoptimizationresultTheParetodistributionisusedtodemonstratetheoptimizationdesignresultsinthemulti-objectiveproblem.Figs.8~9giverespectivelytheParetosineachmethod.TherearefourParetos:dC”anddac;dClAanddClB;dClBanddac\da(.andObjective.Inthesefigurestherearealltheindividualsineverygenerationduringtheprocessofoptimizationinwhichthedarkbluedotsarethefinaloptimumindividuals.ForObjectiveinthetwomethods,itcanbeseenfromthedarkdotsthatObjectiveisimprovedandtheminimumvaluesareinthesamelevel;Fordac,EpplermethodhasthehigherlevelthanB-splinemethodandthevalueinbothmethodsislargerthan0.FordClAanddCLBJtwomethodsgeneratevaluesdistributedonthebothsidesof0,andB-splinehaslargerrange.dCIAanddCIRhavetheobviouslycon-•CUraet«ri>ticPoiaU(A.B.0(WsifnedBvditt・・..4>.・.・•006-.♦•ooe-.•...•.Soot-♦••••.o1004-•■a002-002-3-00020040002DCLBDCLA004-.,006-•i.002-%.•.•也0-•••.•ow-•002-<11■F0050-002•1■0ObjectiveDCLA・・..4>.・.・•006-.♦•ooe-.•...•・・..4>.・.・•006-.♦•ooe-.•...•.Soot-♦••••.o1004-•■a002-002-3-00020040002DCLBDCLA004-.,006-•i.002-%.•.•也0-•••.•ow-•002-<11■F0050-002•1■0ObjectiveDCLAFig.8ThePareto:Thedistributionintheobjectivespaceofalltheindividuals(B-splinemethod)0901DCLB4*010DCLA092ow-••001-DSigmaCo«»—4__L-9.80006-g0-06・■085・C'*•oi-ooeQOtObjects■0010001DCLA002Fig.9ThePareto:Thedistributionintheobjectivespaceofalltheindividuals(Epplermethod)Inordertodistinguishthedifferencebetweenthesetwomethods,thecomparisonsonthethreecavitationmarginsinthreepracticalcasesweresinglycarriedout.TheresultsareshowninTab.3.Tab.3TheresultsofthecomparisonsdC”djBsplineEpplerBsplineEpplerBsplineEpplerBsplineEppler0.0080.0070.0130.0140.0650.0740.03350.03880.0130.0130.0190.0170.06150.07120.03330.03920.0180.0160.010.0090.0620.0740.03330.0393Case1:WhendCIAN0.007anddCLBN0.013,dacis0.065optimizedbyB-splinemethodand0.074byEpplermethod,whichshowsEpplermethodgives13.8%bettersuctionbubblecavitationmarginthanB-splinemethodduetoconstantpressuredistributiononthemainpressureregion.ThecomparisonofthetwobucketsweredepictedinFig.10.ThecorrespondingmaximumthicknessofEpplermethodis0.0388largerthanthatofB-splinemethod0.0335.0.)8o.0.080.060.040.02000.40.5a0.6Fig.10ThecomparisononsuctionbubblecavitationmarginCase2:WhendCIA20.013anddac0.06,B-splinemethodgeneratesdCLB=0.019andEpplermethodgeneratesdCIR=0.017whichisslightlylower.Fig.l10.)8o.0.080.060.040.02000.40.5a0.6Fig.10ThecomparisononsuctionbubblecavitationmarginFig.l1ThecomparisononsuctionsheetcavitationmarginFig.12ThecomparisononpressuresheetcavitationmarginCase3:WhendCIR>0.09andda0.06^dClAoptimizedbythetwomethodsarealsoverycloseandthebucketsareshowninFig.l1ThecomparisononsuctionsheetcavitationmarginFig.12ThecomparisononpressuresheetcavitationmarginInsummary,EpplermethodandB-splinemethodallcanoptimizesectionswithconsiderablebuckets.Epplermethodcanoptimizeasectionwithbetterbubblecavitationmargin,andslightlybettersheetcavitationmarginscanbeobtainedwithB-splinemethod.ThemaximumthicknessofB-splinemethodislessthanthatinEpplermethodThesectionsstructuredbyparametricrepresentationintheabovecasesareshowninFigs.13~15.ThemaximumthicknessofthemismovedtowardstheleadingedgeforincreasingthemarginagainstsheetcavitationandthemaximumcamberismovedtowardsthetrailingedgeformovingmoreloadstowardsthetrailingedgeincomparisonwiththeNACA66mod+a=0.8sectionalsoshowninthesefigures.o0.03>0.020.010.00-0.01-0.0290.03R0.020.010.00-0.01Fig.14Theoptimizedsections(Case2)-0.02Fig.15Theoptimizedsections(Case3)Thegeometricaldifferenceso0.03>0.020.010.00-0.01-0.0290.03R0.020.010.00-0.01Fig.14Theoptimizedsections(Case2)-0.02Fig.15Theoptimizedsections(Case3)ConclusionsAcomparativeinvestigationontheeffectsoftwoparametricrepresentationmethods:B-splinemethodandEpplermethodinthesectiondesignoptimizationmethodwascarriedout,someconclusionscanbedrawnasfollows:Thedesignoptimizationmethodwiththesetwoparametricrepresentationmethodscanallworkoutoptimumsections,andcanbe