浮式风机气动荷载模拟1

ContentslistsavailableatScienceDirectRenewableEnergyjournalhomepage:www.elsevier.com/locate/reneneUnsteadyaerodynamicsofoffshorefloatingwindturbinesinplatformpitchingmotionusingvortexlatticemethodMinuJeona,*,SeungminLeea,SoogabLeebabDepartmentofMechanicalandAerospaceEngineering,SeoulNationalUniversity,Seoul151-742,RepublicofKoreaCenterforEnvironmentalNoiseandVibrationResearch,EngineeringResearchInstitute,SeoulNationalUniversity,Seoul151-744,RepublicofKoreaarticleinfoArticlehistory:Received22February2013Accepted9September2013Availableonline15October2013Keywords:FloatingwindturbineUnsteadyaerodynamicloadBladeelementmomentumtheoryVortexlatticemethodabstractAstheflowstatesofanoffshorefloatingwindturbine(OFWT)differfromthoseofanonshorefixedwindturbine,itisquestionableastowhethertheaerodynamicloadpredictionofaturbineusingconventionalbladeelementmomentumtheory(BEMT)isaccurate.Theaimofthispaperistoshowthecharacteristicsofaerodynamicloadpredictionsusingthevortexlatticemethod(VLM).Washizu’sexperimentaldata,whichwasmeasuredunderasimilarflowstateofafloatingwindturbine,isusedforvalidation.Thepredictionshowsgoodresultscomparedtothoseofanexperiment.Todeterminetheunsteadyaero-dynamicsofafloatingwindturbine,theNREL5MWwindturbinemodelisusedforthesimulationofafloatingwindturbine.Theseresultsshowthataturbulentwakestate(TWS),whichisundesirableconditionandcannotpredictedinBEMTsimulation,ariseswhenafloatingwindturbineisoperatedatalow-speedinflowcondition.Inaddition,therotorexperiencesaTWSwhenthefloatingplatformun-dergoesupwardpitchingmotion.Ó2013PublishedbyElsevierLtd.1.IntroductionWindenergyisoneofthemostpromisingrenewableenergysources.Itiscleanenergyandisavailableatveryclosetothepriceoffossilfuels.Currently,theuseofoffshorewindturbinesisincreasingrapidlyduetonoiseandvisualproblemsassociatedwithanonshorewindturbine.Also,thewindquality,whichplaysasignificantpartindrivingtheaerodynamicpower,ismuchbetteroffshore,astherearenowindbarriers.Windsarestronger,moreconsistent,withlessturbulenceintensityandsmallershearthanonland.However,becausethewaterdepthisalsodeeperatsea,fixed-bottomsystemsarenoteconomicallyfeasible.Instead,floatingsupportsystemsaremorecompetitiveindeeperseas[1].Also,thefeasibilityoffloatingplatformshasbeendemonstrated,asdemonstratedbythelong-termuseofoffshorefloatingsub-structuresintheoilandgasindustry.Inafloatingstate,astheyareoperatedundercomplexcondi-tion,offshorewindturbinesshouldbeanalyzeddifferentlyfrom*Correspondingauthor.Rm.218,Bldg.35,DepartmentofMechanicalandAerospaceEngineering,SeoulNationalUniversity,Daehak-dong,Gwanak-gu,Seoul151-744,RepublicofKorea.Tel.:þ8228807299;fax:þ82287360.E-mailaddress:ase55@snu.ac.kr(M.Jeon).0960-1481/$eseefrontmatterÓ2013PublishedbyElsevierLtd.http://dx.doi.org/10.1016/j.renene.2013.09.009fixedwindturbines.Inparticular,whileafixedwindturbinehassimpleflowstate,theoffshorefloatingwindturbine(OFWT)ex-periencescomplexflowstateswhenthefloatingplatformisinmotion.Theseincludethenormalworkingstate(NWS),thetur-bulentwakestate(TWS),thevortexringstate(VRS)andthewindmillbrakingstate(WBS).Fig.1showshowvariousflowstatesoccurwhenthefloatingplatformundergoespitchingmotion.TheflowassociatedwiththeWBSissmoothanddefiniteslipstream,whichisthenormalconditionofawindturbine.Whentheplat-formstartspitchingbackward,theflowexperiencesahighlevelofturbulence.AttheboundarybetweentheWBSandTWS,theflowstatewithasmoothslipstreamchangesabruptlytoastatechar-acterizedbyrecirculationandturbulence,asthevelocityinthefarwakechangesdirection.Astheplatform’spitchingvelocityin-creases,thedefiniteslipstreamdisappearsandtheflowneartherotordiskbecomeshighlyunsteadyandturbulent.Thomasetal.[2]showthattheoccurrenceofabreakdownoftheslipstreamistwiceaslikelytooccurwithafloatingwindturbineascomparedtoanoffshorewindturbineofthemonopiletypeunderalowwindspeedcondition.Theaerodynamicmodelingofwindturbinesreliesonthreeapproaches:bladeelementmomentumtheory(BEMT),thevortexlatticemethod(VLM)andcomputationalfluiddynamics(CFD).BEMTisverysimpleengineeringmodelbasedonsimple208M.Jeonetal./RenewableEnergy65(2014)207e212

Fig.1.HypotheticalflowstatesofOFWTduringplatformpitchingmotion[2].

momentumandstriptheory.Owingtothecomprehensibleassumptionsofthismethod,itshouldbeusedinconjunctionwithcorrectionmethods,suchasthedynamicstall,Glauert’sthrustcorrection,Prandtl’stiplossfunction,andthestalldelaymodel.InspiteofthevariousassumptionsandapproximationsassociatedwiththeBEMT,itcanprovidegoodpreliminarypredictionsinrelativelysimpleflowstatessuchastheWBSandTWS[3].However,itisincompletewhenusedtoconsideralltypesofcomplexflowstatesthatarisewithanOFWT.BEMThastwomajorweaknessesinsuchananalysis.First,itassumesthatthewakeisfrozen,thoughthewakeofafloatingwindturbineishighlyunsteady.Tocounterbalancethiscondition,dynamicinflowmodelshavebeendeveloped.Ageneralizeddynamicwakemodel,whichismainlyusedasadynamicinflowmodelduringwindturbinesimulations,isnotsuitableinhighlyloadedrotorconditionssuchasrecirculatingflows,asitassumesthatthemeaninducedvelocityissmallrelativetothemeaninflowvelocity[4].Second,BEMT’sslipstreamassumptionisnotsatisfiedwhenthefreestreamvelocityisgreatertwicethantheinducedvelocityattherotor.AlthoughGlauert’sempiricalformulaisappliedinthiscondition,thefeasibilityofGlauert’sempiricalcorrectionisquestionableinVRSbecausetheformulawascreatedusingmeasurementdataintheTWS.Also,asplatformpitchingandyawingmotionintroducesignificanteffectivewindshearconditions,correctionasregardsanon-axialflowisunsatisfactory.Anothermethod,CFD,whichsolvesEulerorNaviereStokesequations,providesmorephysicallyrealisticsimulations;however,itisnotyetapracticalmethodinthedesignprocessbecauseitincursasignificantcomputationalcost.Inotherwords,asanengi-neeringmodel,VLMisaviablemethodasitcanrepresentthenon-uniforminducedeffectsassociatedwiththeverticalwaketrailingfromtheturbine.Thismethodhastheflexibilitytoincludeawiderangeofvalidatedsub-componentmodelsrepresentingvariousphysicaleffectsthataredifficulttomodelfrom1Dmomentumtheory.Ithasbeenwidelydevelopedforuseinhelicopterrotoranalyses,datingfromthe1960s,buthasstillyettoseesignificantuseforwindturbineapplications.Therefore,inthisstudy,weinvestigatedthecharacteristicsoftheaerodynamicsofanoffshorefloatingwindturbineundergoingplatformpitchingmotionusingVLMtoprovidemorephysicalinsightintounsteadyaerodynamics.2.NumericalmethodAmoreexplicittreatmentoftherotorwakerequiresamethodthatcanrepresentthespatiallocationsandstrengthsofthevortexthataretrailingeachbladeandareconvectedintothedownstreamwake.ThiscanbesatisfiedusingtheVLM,whichisbasedontheassumptionsandtheorydescribedbelow.Thefluidsurroundingthebodyisassumedtobeinviscid,irro-tational,andincompressibleovertheentireflowfield,excludingthebody’ssolidboundariesanditswakes.Hence,thevelocitypotential,F,becomestheLaplaceequation.UsingGreen’sthe-orem,thegeneralsolutiontoaLaplaceequationcanbeFig.2.Thrustcoefficientversusverticalflightvelocityfactorfordifferentvaluesofthepitchanglewhenthebladesectionxequals0.75.

M.Jeonetal./RenewableEnergy65(2014)207e212209

Fig.3.Normalvorticityfieldsandstreamlinesatq0.75¼4.5󰀂À(a)Vz¼6.6m/s,(b)Vz¼5.0m/s,(c)Vz¼3.2m/s,(d)Vz¼1.1m/s.

formulatedbythesumofthesourceanddoubletdistributionsontheboundary.1F¼4p*Zbodyþwake󰀂󰀃1gn,VdSþFNrSourceanddoubletdistributionsaresolvedbyimplementingtwoboundaryconditions.Thefirstboundaryconditionrequiringazeronormalvelocityacrossthebody’ssolidboundariesiscalledtheNeumannboundarycondition.Thesecondboundaryconditionrequiresthattheflowdisturbancesarisingduetothebody’smotionthroughthefluidshoulddiminishfarfromthebody.Finally,aerodynamicforcegeneratedbythevortexsheetiscalculatedbytheKuttaeJoukowskitheorem(seemoredetailsinRef.[5]).Toconsiderthethicknessandviscouseffects,anonlinearvor-texcorrectionmethod(NVCM)wasused.ThisiscorrectedbymatchingupthesectionalliftfromtheVLMwiththatfromthetwo-dimensionaltablelook-up[6].Tocorrectthethree-dimensionaleffectsoftherotorblades,theDuandSeligstalldelaymodelisimplemented[7].TheBladewasdividedintotwenty-eightpanelsinallsimulations.Theadditionalcalculationcomparedtocalculationofonshorewindturbineisneededasthiswindturbinesystemismoving.So,thelatticeofrotorbladeisshiftedintheglobalcoordinatesys-tem.Also,relativevelocityontherotorbladebyfloatingplat-form’smotionisaddedwhencalculatingvelocityonthebladesurface.Therotorbladeisassumedtoberigid.Aeroelasticeffectsmayhavebeeninfluencedaccuracyofaerodynamicload.However,aeroelasticityisalittleeffectonthetendencyofresultsasthechangeofrotorbladeissmallcomparedtofloatingplatform’sun-steadymotion.3.Results&discussion3.1.ValidationTovalidatethein-housenumericalcodeinVRS,predictionsarecomparedwithWashizu’sexperimentaldata[8],whichisaFig.4.Floatingturbinestancesduringpitchingmotion.

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Fig.5.NormalvorticityfieldsandstreamlinesatVz¼4.5m/se(a)fixedwindturbine,(b)floatingwindturbine.

movingtracktestofarotor1.1mindiameterindescentforaxialconditions.AsthisexperimentcomprisesallflowstatesandisatypicalVRSexperiment,itisappropriateforthevalidationofafloatingwindturbine.Thethree-bladedrotorusedforthevali-dationprocesshasasolidityvalueof0.0573withan8.33degtwist.Therpmis1000rpmandthechordvalueis0.033m.TheairfoilofeachbladeisaNACA00012.DatafortheaerodynamiccoefficientsoftheNACA0012weresourcedfromexperimentalresults[9].ThemeasuredandpredictedthrustcoefficientsareshowninFig.2.ThepredictionshowsthatVLMpredictsthevaluenearupperborderoffluctuationswellforacompleteintervalofVz/UR.ThenormalvorticityfieldsperpendiculartotheYaxisasthedescentvelocityareshowninFig.3.Fig.3clearlyshowssmoothslipstreamsforWBS.ForaTWS,thegenerationofthetipvorticescanbeseen.Theenvelopeoftheswirlyareasgraduallyarisesabovetherotordiskplane.Wealsonotedthepresenceofanareaofhighamplitudeofthevorticityattherootoftheblade.Itislinkedtoahighleveloflocalthrust.ForVRS,thetipvorticesareclusteredatthetipoftheblades.Theenvelopesoftherecirculationzonesbecomelargerandatthispointbecomemainlylocatedontherotordiskplane.Hence,thevalidationshowsthattheVLMcanfeasiblypredictthenumericalvaluesaswellastheflow-fieldsofaturbulentwakestateandavortexringstate.3.2.SimulationforfloatingwindturbinesThewell-knownNRELoffshorefivemega-wattwindturbine[10]waschosen,andtofocusontheaerodynamicsofthefloatingwindturbine,aprescribedsimpleharmonicplatformpitchanglewasused(Fig.4).Thepitchamplitudeis3m,andtheperiodis12s,bothofwhicharesimilartothepitchingmotionofabargeplatform.Thesimulationoftheoperatingconditionisdefinedbyawindspeedof4.5m/sandarpmof7.6.Thisislowwindspeedconditionwhichisknownashighlyunsteadyaerodynamicstate.First,toverifytheoutbreakofanunsteadyflowinthefloatingwindturbineunderalowwindspeedcondition,wecomparedtheflow-fieldofafixedwindturbineandafloatingwindturbine.InFig.5(a),thefixedturbineshowsaslipstreamflowatalowwindspeedcondition.However,inFig.5(b),thefloatingwindturbineshowsanunsteadyflowfield,similartoaturbulentwakestate.Thisarisesbecausethenetconvectionofthegrowingtipvortexbe-comeslow,asperiodicdisturbancesareaddedbythefloatingplatformmotion.Hence,wecouldverifytheoccurrenceofanun-steadyflowinthefloatingwindturbine.Next,weexaminedthecauseoftheturbulentwakestate.Accordingtopreviousresearch,anunsteadyflowarisesfromplatformpitchingmotioninthedownwarddirection.Duringthismovement,theinductionfactor,whichistheinducedvelocitydividedbytheinflowvelocity,ishigherthan0.5.Typically,thissignifiesahighthrustcoefficientandunsteadyflow.TheinductionfactorisveryhighatthetopoftherotorplaneatlocationthreeinFig.6.Wecoulddeterminethepossibilityofaturbulentwakestate.Next,weinvestigatedthesectionalthrustateachlocationofthefloatingwindturbineifahighinductionfactorcauseshighloading.AsshowninFig.7,incontrasttoexpectations,wefoundthatthesectionalthrustisthelowestatlocationthree.Inaddition,atlocationseven,thesectionalthrustisthehighestdespitethefactthattheaxialinductionfactorislowerthanitisatlocationthree,astherelativewindattherotorisminorduetothebackwardpitchingmotionatlocationthree.Inotherwords,althoughtheinductionfactorcausesahighthrustcoefficient,thethrustislowbecausethedynamicpressureisverylowatlocationthree.Hence,weinspectedlocationsevennext.Fig.8showsthenormalvorticitycontourandstreamlinesatlocationseven.Atthetopoftherotor,arecirculatingflowcanbeseen,astherelativevelocityofthetopofthebladeishighduetoupwardpitchingmotionoftheplatform.Moreover,therpmin-creasestosupplymorepower.Thisservestoincreasethetipspeedratio.Withahightipspeedratio,clusteringofthetipvortexin-creasesgiventhattheconvectionofthetipvortexislow.Therefore,incontrasttothehypotheticalconcepts[2],thisshowsthatacomplexflowcanoccurduringtheupwardpitchingmotionoftheplatform.M.Jeonetal./RenewableEnergy65(2014)207e212211

Fig.6.LocalinductionfactorateachplatformpitchinglocationÀ(a)e(i):locations1e9inFig.4.

4.ConclusionInthispaper,weinvestigatedtheflowstatesofafloatingwindturbineduringplatformpitchingmotionusinganumericalmethod,inthiscasetheVLM.Forvalidation,itwasfoundthattheVLMcanpredictwellthenumericalvalueaswellastheflow-fieldofaTWSandaVRS.Duringasimulationwithafloatingwindturbine,wedeterminedthataTWS,whichisunwantedaero-dynamicphenomena,occurswhenthefloatingwindturbineisoperatedatalow-speedinflowcondition.Also,incontrasttothehypotheticalflowstates,itwasshownthataTWSariseswhenthefloatingplatformispitchingintheupwinddirection.Inparticular,Fig.7.Localinductionfactorateachplatformpitchinglocation.

212M.Jeonetal./RenewableEnergy65(2014)207e212

Fig.8.Normalvorticityfieldsandstreamlinesofthefloatingwindturbineatlocationseven.

theworkpresentedheresuggeststhattheconvectionofthetipvortexplaysanimportantroleingoverningofthebehavioroftherotorinaTWS.AcknowledgmentThisworkwassupportedbytheHumanResourcesDevelop-mentprogram(No.20124030200030)oftheKoreaInstituteofEnergyTechnologyEvaluationandPlanning(KETEP)grantfundedbytheKoreagovernmentMinistryofTrade,IndustryandEnergy.ThisresearchwasalsosupportedbytheInstituteofAdvancedAerospaceTechnologyatSeoulNationalUniversity.References[1]MusialW,ButterfieldS,BooneA.Feasibilityoffloatingplatformsystemsforwindturbines.In:42ndAIAAaerospacesciencesmeetingandexhibit2004.p.476e86.[2]SebastianT,LacknerMA.Offshorefloatingwindturbines:anaerodynamicperspective.In:49thAIAAaerospacesciencesmeeting2011.[3]LeishmanJGordon.Challengesinmodellingtheunsteadyaerodynamicsofwindturbines.WindEnergy2002;5(2e3):85e132.[4]SuzukiA.Applicationofdynamicinflowtheorytowindturbinerotors.Doctoraldissertation.UniversityofUtah;2000.[5]KatzJ,PlotkinA.Low-speedaerodynamics.Cambridge,UK;NewYork:Cam-bridgeUniversityPress;2001.[6]KimH,LeeS,SonE,LeeS,LeeS.Aerodynamicnoiseanalysisoflargehori-zontalaxiswindturbinesconsideringfluid-structureinteraction.RenewEn-ergy2012;42:46e53.[7]DuZ,SeligMS.A3-Dstall-delaymodelforhorizontalaxiswindturbineperformanceprediction.In:ASMEwindenergysymposium,Reno,NV;UnitedStates1998.p.9e19.[8]WashizuK,AzumaA.Experimentsonamodelhelicopterrotoroperatinginthevortexringstate.JAircr1996;3(3):225e30.[9]ShendahlR,E,KlimasP,C.Aerodynamiccharacteristicsofsevensymmetricalairfoilsectionsthrough180-degreeangleofattackforuseinaerodynamicanalysisofverticalaxiswindturbines.TechnicalReport,SAND80-2114.SANDIALaboratories;March1981.[10]JonkmanJ,ButterfieldS,MusialW,ScottG.Definitionofa5-MWreferencewindturbineforoffshoresystemdevelopment.TechnicalReport,NREL/TP-500-38060.NationalRenewableEnergyLaboratory(NREL);2009.