An experimental and numerical study of the vortex

*Correspondingauthor.DepartmentofAeronauticalandAstronauticalEngineering,UniversityofIllinoisatUrbana,Champaign,306TalbotLab.,104S.WrightSt.Urbana,IL61801,USA.Tel.:#[phone];fax:#[phone];e-mail:[e-mail]andIndustrialAerodynamics84(2000)1}21AnexperimentalandnumericalstudyofthevortexstructureinthewakeofawindturbineJ.Whale!,*,C.G.Anderson,R.Bareiss#,S.Wagner#!DepartmentofMechanicalEngineering,TheUniversityofEdinburgh,TheKing+sBuildings,Edinburgh,EH93JL,UKAerpacUKLtd,13FaradayRd,Glenrothes,FifeKY62RU,UK#Institutfu(rAerodynamikundGasdynamik,Universita(tStuttgartPfawenwaldring21,D-70550Stuttgart,GermanyReceived11August1997AbstractAnexperimentalinvestigationintothepropertiesofthevortexwakebehindawindturbinerotorhasbeencarriedoutatmodelscale,usingParticleImageVelocimetry(PIV).Thetwo-blademodelwasoperatedattipspeedratiosintherangej3}8,andchordReynoldsnumbersRe6400}16000.Thebladeswereuntwisted,with#at-plateaerofoilprole.Measurementsofwakevelocityandvorticitywereobtainedforatwo-dimensional#oweldrepresentinganaxialcross-sectionofthewake,extending2.9rotordiametersdownstreamoftherotor.ThevorticitymapswerecomparedwithcalculationsmadeusingtheRotorVortexLatticeMethod(ROVLM),aninviscidfree-wakecoderecentlydevelopedattheUniversityofStuttgart.ThePIVandROVLMdatashowqualitativeagreementintermsoftheshapeofthewakeboundary,includingdownstreamwakecontraction,andquantitativeagreementintermsofthetipvortexpitch.ItappearsthatthefundamentalbehaviourofthehelicalvortexwakemayberelativelyinsensitivetobladechordReynoldsnumber,solongassimilarityoftipspeedratioisobserved.(2000ElsevierScienceLtd.Allrightsreserved.Keywords:Windturbinewakes;ParticleImageVelocimetry;Vortexwakemodel;Tipvortexbehaviour1.IntroductionCurrentindustry-standardcodesforcalculatingwindturbinerotorloadsandpoweroutputarebasedonblade-elementmomentumtheory(BEMT).Itiswidely0167-6105/00/$}seefrontmatter(2000ElsevierScienceLtd.Allrightsreserved.PII:S0167-6105(98)00201-3NomenclatureDdiameteroftherotor(m)Rradiusoftherotor,RD/2(m)cbladechord(m)Xrotationalspeedoftherotor(rad/s)xradialcross-wakedistance,measuredfromthehuboftherotor(m)zaxialdownstreamdistance,measuredfromthehuboftherotor(m)dspacingofvectoreldgrid=freestreamvelocity(m/s)rrelativevelocityattheblade(m/s)zaxialtransportationvelocityofthetipvortex(m/s)1vorticity(s~1)lkinematicviscosity(m2/s)jtipspeedratio,j(XR)/=RechordReynoldsnumber,Re(rc)/l1/normalisedvorticity,1/41d/=ptipvortexpitch,p2pz/XRacknowledged,however,thatBEMTcontainsfundamentallyinvalidassumptions[1],whichareovercomeinpracticebyempiricaladjustments.ThereisawidespreaddesireinthewindindustrythatamoretheoreticallycorrectapproachshouldsupplantBEMTinthelongterm.Todoso,itshouldembodyamodeloftherotorwakewhichisvalidinalloperatingconditions,asitisthestructureofthewake,andinparticularitsvorticitycontent,whichultimatelydictatesthe#uidloadingonthebladesofthewindturbine.Thepresentpaperaddressestheneedfordetailedmeasurementsoftherotorwake,inordertodevelopandvalidatenewnumericalpredictioncodes.NovelimageshavebeenobtainedattheUniversityofEdinburgh,usingparticleimagevelocimetry(PIV)tovisualisethewakeofatwo-bladerotoratmodelscale,andthusobtaindetailedrecordsofvelocityandvorticity.ThePIVresultswerecomparedwithnumericalsimulationsfromasophisticatedvortex-wakecode,recentlydevelopedattheUniversityofStuttgart.2.Windturbinewakes2.1.AerodynamicsTheair#owdownwindofawindturbinerotorsu!ersalossinmomentumresultinginaregionofreducedmeanvelocity,i.e.thewake.Thewakeishighlystructured,owingitsformtotheinteractionofthefreestreamwiththevorticitysheetsgeneratedJ.Whaleetal./J.WindEng.Ind.Aerodyn.84(2000)1}212atthebladesandtraileddownstreamoftherotor.Thistrailingvorticityissynony-mouswiththe`horseshoevortexasystemcreatedbyaconventionalwingofnitespan,duetothespanwisevariationinboundcirculation[2].Onawindturbinerotorthevortexsheetsterminateattherootandtipofeachblade,whereboundcirculation,andhencelift,areforcedtozero.Thechangeincirculationisparticularlygreatatthebladetip,whereastrongtrailingvortexresults.Thetrailingvorticitycreatesahelicalpattern,inwhichthevortexsheetsformscrewsurfaces.Thediameterandpitchofthesheetsdonotremainconstantdownstreamoftherotorplane,however,duetospatialvariationofthewakevelocity.Thepatternisnottriviallymodelled,astheinducedvelocity(thevectorcomponentcausedbytheactionoftherotor)atanypointinthewakeisdeterminedbythevorticityatallotherpointsaccordingtotheBiot}Savartlaw[3].Inaddition,thevortexsheetstendto`rollupashortlydownstreamoftherotor,withthevorticitybecomingconcentratedattheouteredgeofthewake.Thewakedeformsintoasystemcomprisinganouterregioncontaininganintensetipvortexspiral,andaninnerregioncontainingaweakdi!usedvortexsheet.Thein#owvelocitiesacrosstherotordisc,whichdictatethe#uidloadingontherotorblades,aredenedbythecompletewakevortexsystem,anditisforthisreasonthatanaccuratedescriptionofthelatterissoeagerlysought.2.2.TheoreticalmodelsAsnotedabove,BEMTformsthemostcommonbasisforwindturbineperformancepredictioncodes(e.g.[4,5]).BEM