validation of a vortex panel method for aerodynamics and …1198230/...2 master of science thesis...

Validationofavortexpanelmethodforaerodynamicsandaero-elasticityof

WindTurbineMasterThesis

AntoineThibiergeKTHsupervisor: Adwensupervisors:PaulPetrie-Repar PaulDeglaire BastienDuboc

LaurentBeaudet

MasterofScienceThesisTRITA-ITM-EX2018:20

Validationofavortexpanelmethodforaerodynamicsandaero-elasticityofWindTurbine

AntoineTHIBIERGE

Approved

Examiner

PaulPetrie-ReparSupervisor

PaulDeglaire

Commissioner

Contactperson

PaulDeglaire

AbstractArdema3D isanewtypeofvortex freemodelcodethatcansimulatewindturbines.Thiscodehasbeendevelopedinordertoreplacethestateoftheartmodel,thebladeelement momentum (BEM). Indeed, the BEM is using strong assumptions andempirical correction,which are relevant for standard operation, however, there is adoubtonthevalidityofthismodelforcomplexsituation.Ardema3DisdevelopedtobesubstitutefortheBEMwhenitisnotvalid.Thiscodehasbeenimplementedinacoupledcode,FARDEMAST,takingintoaccounttheelasticityofthebladeandthecontroller.FARDEMASTisacodebasedonFAST,acode developed by the National Renewable Energy Laboratory (NREL), where theaerodynamic module has been replaced by Ardema3D. Both codes are undervalidation.ThecouplecodeFARDEMAST iscomputing the loadson thewindturbine,whichareusedtodesigntheblade.SincevortexpanelcodessuchasArdema3Dareusingmuchlessassumptionsthanthestateoftheartmodelfortheindustry,theyaresupposedtogive more accurate results which can lead to safe and cheaper design for windturbines.TheMasterThesisproposedwillcovertwomaintopicsofresearch:

1. ValidationofthefarwakemodelofArdema3DThe free wake vortex model ARDEMA3D is accurate in terms of description of theunsteady forces on the blades and on the rotor nearwake velocities. The farwakedescriptionisnotsoaccurate.For thewakes, Adwen and the CORIAhave beendeveloping an actuator linemodelinside the Large Eddy Simulation code YALES2 for very advanced and detailedwakesimulations. Several validations of the actuator linemodel have been initiated withrespecttotheexistingbibliography.Themostusefulexperimentalresultsconsideredtheanalysisofwakevelocitydeficitsdownstreamofasmallscalewindturbineplacedonawindtunnel intheNorwegianUniversityofScienceandTechnology(NTNU)inNorway.BasedontheNTNUexperimentalsetup,theworktobeperformedduringthisMasterThesiswillbetocomparetheresultsofArdema3Dandtheactuatorlinemodelbothintermsof localrotorquantitiessuchas forces,angleofattacks,etc,onblades,whereARDEMA3D is assumed to bemore accurate togetherwith the velocity deficit closeandfarfromtherotorwhereYALES2shouldhaveabetterdescriptionandanalyzethesourcesofthedifferences.

2. ValidationofthecoupledcodeFARDEMASTAfterthevalidationoftheaerodynamiccode,thestudentwillvalidatetheuseofthecode for aero-elasticity purposewith the code FARDEMAST. The comparisonwill bedonewith FAST. Theonlydifferencewith FARDEMAST is theuseof anaerodynamicmodelbasedonthemomentumequation,thusfasterbutlessaccurate.ThevalidationwillbedonealsowithtwostructuralmodelsofFAST:ElastoDynandBeamDyn.

AbstraktArdema3Därennytypavvortexfrimodellkodsomkansimuleravindkraftverk.Dennakodharutvecklatsförattersättadensenastetekniken,bladelementetsmomentum(BEM).FaktumärattBEManvänderstarkaantagandenochempiriskkorrigering,somärrelevantaförstandardoperation,mendetärtveksamtomgiltighetenavdennamodellförkomplexasituationer.Ardema3DärutveckladförattersättaBEMnärdeninteärgiltig.Dennakodharimplementeratsienkoppladkod,FARDEMAST,medhänsyntillbladetselasticitetochkontrollenheten.FARDEMASTärenkodbaseradpåFAST,enkodsomutvecklatsavNationalRenewableEnergyLaboratory(NREL),därdenaerodynamiskamodulenharersattsavArdema3D.Bådakodernaärundervalidering.ParkodenFARDEMASTberäknarlasternapåvindturbinen,somanvändsförattdesignabladet.EftersomvortexpanelkodersomArdema3Danvändermycketmindreantagandenäntoppmodernmodellenförindustrin,skadegemerexaktaresultatsomkanledatillsäkerochbilligaredesignförvindkraftverk.

Denföreslagnauppsatsenskaomfattatvåhuvudämnenavforskning:1.ValideringavArdema3DslångvaktmodellFrivåtsvortexmodellenARDEMA3Därkorrektnärdetgällerbeskrivningavdeostadigakrafternapåknivarnaochpårotornnäraväckthastigheter.Beskrivningenavlångtkölvattnetärintesåexakt.FörväckningarnaharAdwenochCORIAutvecklatenmanövermodelliLargeEddySimulation-kodenYALES2förmycketavanceradeochdetaljeradevakningssimuleringar.Fleravalideringaravmanöverlinjemodellenharinitieratsmedhänsyntilldenbefintligabibliografin.DemestanvändbaraexperimentellaresultatenbetraktadeanalysenavväckthastighetsbristernanedströmsenlitenvindturbinplaceradpåenvindtunneliNorgesteknisk-naturvetenskapligauniversitet(NTNU)iNorge.UtifrånNTNU:sexperimentellainställningärdetarbetesomskautförasunderdennaexamensarbeteattjämföraresultatenfrånArdema3Dochmanövermodellen,bådenärdetgällerlokalarotorkvantitetersomkrafter,angreppsvinkelmmpåblad,därARDEMA3DantasvaramerexakttillsammansmedhastighetsunderskottetnäraochlångtifrånrotorndärYALES2skahaenbättrebeskrivningochanalyseraskillnadskällorna.2.ValideringavdenkoppladekodenFARDEMASTEftervalideringavdenaerodynamiskakodenkommerstudentenattvalideraanvändningenavkodenföraeroelasticitetsändamålmedkodenFARDEMAST.JämförelsengörsmedFAST.DenendaskillnadenmedFARDEMASTäranvändningenavenaerodynamiskmodellbaseradpåmomentumekvationen,såsnabbaremenmindrenoggrann.ValideringenkommerocksåattgörasmedtvåstrukturellamodelleravFAST:ElastoDynochBeamDyn.

AcknowledgementIwouldliketothankAdwen,thecompanydevelopingArdema3DandFARDEMAST,tohostmefordoingthismasterthesis.IwouldalsothankPaulDeglaire,BastienDubocandLaurentBeaudet,mysupervisorsin Adwen, and Paul Petrie-Repar, my supervisor in KTH. But also, Nobert Warncke,PanagiotisPanousisandFelixBarnaud,whichwerepartoftheINWITproject,andwithwhichIhavealsoworked.IwouldalsoliketothankPierreBénard,GhislainLartigueandVincentMoureau,whoworkatCORIAlaboratoryandhavedevelopedthecodeYALES2.

ContentsAbstract............................................................................................................................3

Abstrakt............................................................................................................................4

Acknowledgement...........................................................................................................5

1. Introduction.............................................................................................................9

2. Context...................................................................................................................10

2.1. OverviewofHorizontalAxisWindTurbine....................................................10

2.2. INWITproject.................................................................................................11

2.3. ARDEMA3D.....................................................................................................12

2.4. YALES2............................................................................................................12

2.5. FAST................................................................................................................13

2.6. FARDEMAST....................................................................................................13

3. Aerodynamicsandstructuralmodels.....................................................................15

3.1. Generalaerodynamicsaroundanairfoil........................................................15

3.1.1. Forcesarounda2Dairfoil......................................................................15

3.1.2. 3DAerodynamics....................................................................................16

3.2. BladeElementMomentumTheory................................................................16

3.2.1. MomentumTheory................................................................................16

3.2.2. BladeElementMomentumTheory........................................................19

3.3. VortexModelingMethod...............................................................................20

3.3.1. Mainideaandhypotheses.....................................................................20

3.3.2. Governingequation................................................................................21

3.3.3. VortexPanelMethod.............................................................................25

3.3.4. Angleofattackandviscouscorrections.................................................27

3.4. LESwithActuatorLineModel........................................................................28

3.4.1. LESmethod.............................................................................................28

3.4.2. ActuatorLineModel...............................................................................29

4. ValidationofthefarwakemodelinArdema3D.....................................................31

4.1. TheExperimentandnumericalhypotheses...................................................31

4.1.1. TheExperiment......................................................................................31

4.1.2. Numericalhypotheses............................................................................32

4.1.2.1. Generalassumptions..........................................................................32

4.1.2.2. AssumptionsforARDEMA3D..............................................................32

4.1.2.3. AssumptionsforYALES2.....................................................................34

4.2. ResultsforRotorOnlysimulation..................................................................35

4.2.1. Simulations.............................................................................................35

4.2.2. TSR3.......................................................................................................36

4.2.2.1. Bladesaerodynamics..........................................................................36

4.2.2.2. Wake...................................................................................................38

4.2.3. TSR6.......................................................................................................40

4.2.3.1. Bladesaerodynamics..........................................................................40

4.2.3.2. Wake...................................................................................................42

4.2.4. Conclusion..............................................................................................45

4.3. Resultsforthefullgeometry..........................................................................45

4.3.1. Simulations.............................................................................................45

4.3.2. TSR3.......................................................................................................46

4.3.3. TSR6.......................................................................................................48

4.3.4. Conclusion..............................................................................................51

5. Validationoftheaero-elasticscode.......................................................................52

5.1. Aero-elasticityformodernwindturbine........................................................52

5.1.1. Introduction................................................................................................52

5.1.2. Structuralmodel.........................................................................................52

5.1.3. Aero-elasticstudy.......................................................................................53

5.1.3.1. Deformationoftheblade...................................................................53

5.1.3.2. Equivalentloads.................................................................................54

5.2. Simulationparameters...................................................................................54

5.2.1. Simplification..........................................................................................54

5.2.2. Simulations.............................................................................................55

5.3. ConstantWind................................................................................................56

5.4. Turbulentwind...............................................................................................58

5.4.1. Generalparameters................................................................................58

5.4.2. Deformations..........................................................................................60

5.4.3. EquivalentLoads.....................................................................................61

....................................................................................................................................61

5.5. Start-up:turbulentwindwithcontroller.......................................................61

5.5.1. Generalparameters................................................................................61

5.5.2. Deformations..........................................................................................63

5.5.3. EquivalentLoads.....................................................................................64

5.6. Conclusion......................................................................................................65

6. Conclusion..............................................................................................................66

Bibliography...................................................................................................................67

Appendix:Ardema3DWake......................................................................................68

1. Introduction The awareness of the emission of pollution and the global warming hasincreased over the last few years causing the energy system of all the countries toslowlyshiftfromafossilenergytocleanersourcesofenergy.Windpowerisoneofthesourcesofrenewableenergythatisthemostcompetitiveinthemarket. Wind power has been developed world-wide for more than 20 years, goingfrom 6.1 GW of power installed in 1996 to 487 GW in 2016 [1]. China is themainleaderininstalledcapacitytoday,butintheEuropeanUnion,Denmarkgenerates40%ofitselectricalpowerfromwindandGermanyhasinstalledmorethan5GWofwindpowercapacityin2016.InFrance,theglobalcapacityreached12GWin2016,whichrepresent 3.5 to 4% of the electrical production. Yet France has the second largestoffshorewindresourcesinEurope,butitisnotusedfornowandalltheFrenchwindfarmsareonshore.In2012and2014,sixoffshorewindfarmstendersof500MWwerelaunched. The design of a wind turbine is a complex process, in which considerationsabouttheaerodynamic,thestructureelasticityandthecontrollermustbeconsidered.Thereisstrongcouplingbetweenthesedifferentaspects.Thestateoftheartmethodsto simulate wind turbine in an aero-elastic-servo code are using the Blade ElementMomentum (BEM)model for the simulationof the aerodynamicpart.However, thismodel is based on strong assumptions and correction. With the development ofmodernwindturbines,questionsariseoverthevalidityofthismodel.TheIntegratedNumericalWindTunnelforOffshorewindturbines(INWIT)projecthasbeenlaunchedforthreeyearstodevelopanewcodeofsimulationbasedonvortexmethodtobeasubstitutefortheBEMmodelsinthedesignoffuturewindturbine. Amoreaccuratemodelwillallowabetterunderstandingandabetteruseofthecouplingbetweentheaerodynamicandtheelasticityofthestructure.Moreover,sincethevalidityoftheBEMisquestionableforsomedimensionalcase,asafetyfactoris applied. With a model like the vortex panel method, this safety factor could bedecrease,thereforedecreasingthecostofthewindturbine. Thismasterthesiswillbefocusedonthevalidationofthevortexpanelmethodinthefarwake,butalsocomparedtoaBEMcouplecode,onacaseonwhichtheBEMisknowntobeaccurate.

2. Context

2.1. OverviewofHorizontalAxisWindTurbine Awindturbineisamechanismproducingmechanicalworkthankstothekineticenergyofthewind,usingtheaerodynamicsofrotorbladesrotatingalongahorizontalorverticalaxis.HorizontalAxisWindTurbines(HAWT)(Figure1)aretheturbineswiththerotorfacingthewind.Itisawell-knowntechnologyandthereforethestandardoftheindustry.VerticalAxisWindTurbines(VAWT)alsoexist(Figure2),butthismasterthesis is not dedicated to this technology, even though the software presented iscapableofhandlingbothtypesofwindturbine.

Figure1:AdwenOffshoreHAWT[2]

Figure2:NENUPHARVAWT[3]

Horizontal axiswind turbineshavebeendesignedandbuilt for yearsand theprinciplehasbeenusedforcenturieswiththefirstwindmills.Theyarecomposedofatower,anacelle,ahubandarotorwhichisfacingthewind.Theprincipleistoharvesttheenergyofthewindthankstothebladesthatareprofiledtoturnwiththewinddueto the aerodynamics forces. This rotation is transmitted to a shaft connected to ageneratorwhichwillproduceelectricity. Servomotorswillbeusedinordertoorientatetherotorandchangethepitchofthebladesinordertomaximizetheenergyharvestedortodecreaseit,inordernottousetheturbinewithtooextremewindspeed. Wind turbines exist for all sorts of applications and an important range ofpower,from100Wforhomeapplicationandsailboat,to8MWturbinesforthemostpowerful.Rotordiametersrangefromlessthan1mto180m.Tobuildsuchimpressivestructures,largerwindturbinesaregroupedinwindfarmsinordertoreducethecostoftheinfrastructureneededtobuildit.

2.2. INWITproject The INWIT project (Integrated Numerical Wind Tunnel for offshore windturbines)aims todevelop, implementandvalidateanewandaccuratemethodologyfor the simulationof loadsandperformanceofoffshorewind turbinesbasedon thevortexmethodscode:ARDEMA3D. Theprojectissetfor3years,andtheteamisbasedatAdwenR&DcenterinLeMadrilletTechnopôleclosetoRouenandisfundedbyNormandyregion.Itcomprisestwopartners:

• AdwenOffshore:oneoftheleadersoftheoffshorewindturbinemarket.• CORIA:acombinedresearchunitbetweentheCNRS,RouenUniversityand

INSARouen.Theyarespecializedincombustionsimulationsandspecificallyinfluidmechanics,doingbothexperimentationsandsimulations.Theyhavealso a strong expertise on the use of massive clusters through highperformanceparallelcomputinganddevelopedYALES2,aCFDcodebasedonLargeEddySimulation(LES).YALES2isthoughttohaveahighpotentialfor the accurate simulation of flows around profiles [4] used in windturbines blades and use an actuator line method to simulate real windturbine.Adwenwould like to exploit the fluidmechanics expertiseof theCORIA,andtheCORIAtheexpertiseinwindturbineofAdwen.

Thetechnicalchallengesthattheprojectshouldaddressare:

• TobemoreaccuratethanthestateoftheartBladeElementMomentum(BEM)models (see 3.2), which are based on a main bi-dimensional steady stateassumption for the flow,andcompletedwithempirical corrections.Themaininnovation consists in the development of a new model for the unsteadyaerodynamics,usingvortexmodels.Thepurposewillbetodemonstratethatin

some simple cases the vortexmodel and the BEM are identical, but that oncomplexcases,thevortexmodelismoreaccurate.

• To couple the aerodynamic model with existing models for the elasticity,control and hydrodynamic models. The main strategy is to couple theaerodynamic module ARDEMA3D with FAST, an aero-servo-hydro-elasticcomputer-aidedengineeringtoolforhorizontalaxiswindturbinedevelopedbythe National Renewable Energy Laboratory (NREL), by replacing itsaerodynamicmodule Aerodyn based on a BEMmodel with ARDEMA3D. ThecoupledmodelwithARDEMA3DisnamedFARDEMAST.

• TobeatthesameorderofmagnitudeasBEMtoolsintermsofcomputationaltimeinordertobeasuitabletoolfordesigningwindturbine.Thistargetisveryambitious but essential for the integration of the model in industrial designprocess.

2.3. ARDEMA3D ARDEMA3D (acronym of Areva-Delft-Madrillet, from the names of the firstcompany and labs involved in the creation of the project, respectively Areva, theTechnicalUniversityofDelft,AerospaceEngineeringDepartment,SectionWindEnergyand CORIA lab located on the Madrillet Technopôle in Rouen) is a 3-dimensionalunsteady inviscid flow solver based on a Lagrangian specification of the field anddedicated to rotor systems like wind turbines. It uses a panel method code on apotentialflow,onwhichlocalviscouscorrectionsareapplied. Thecodeisprimarilydevelopedforwindturbines(bothhorizontalandverticalaxiswindturbines)butisdesignedtobeflexibleenoughtomodelvirtuallyanykindofsimplerotororliftingornon-liftingmovingbodies. ItisdevelopedwithCforlow-levelfunctions(VertexVelocitiescalculations,…)andMatlabforhigh level functions(RunScripts, Inputs,post-processing,…).The low-level functions of the code are finally parallelized with different applicationprogramminginterface(API),suchasOpenMP[5](anAPIthatsupportsmulti-platformshared memory multiprocessing programming) and CUDA [6] (an API and parallelcomputingplatformthatallowstouseGPUforgeneralpurposeprocessing),thataredesigned to work with programming languages such as C, C++, Fortran, …. Thesimulationsareusually launchedon the supercomputerMyria, fromCRIANN (CentreRégionalInformatiqueetd’ApplicationsNumériquesdeNormandie),butcanbeusedonapersonallaptopforlittletimeconsumingsimulations. ARDEMA3Dhasaninterfacetobecoupledwithstructure,hydrodynamicsandcontrolmodules.

2.4. YALES2 YALES2 isa code that solves low-MachversionofNavier-Stokesequationsonunstructured meshes [7], using Direct Numerical Simulation (DNS) and Large EddySimulations(LES)formulation.YALES2includesalibraryofsolverdevelopedbyVincent

MoureauandGhislainLartiguesince2007atCORIAlaboratory.Itismainlydevotedtocombustion,chemistry,sprayandatomizationmodeling,butitofcourseveryefficientfornon-reactiveaerodynamic flows. It iswritten inobjectorientedFORTRAN90andcanuseaPythoninterface.Itusessolversoptimizedformassivelyparallelcomputing(>32000CPU)withacentral4th-ordernumericalschemeforspatial integrationanda4th-order4-stepRunge-Kuttamethodforthetimeintegration. In order to parallelize the calculation, YALES2divides themesh intodifferentareaswhichwillbecomputedbyoneCPU.ThecodewilloptimizethisdivisioninorderforeachCPUtohavethesamecalculationloads.ThisisoneofthestrengthofYALES2whichisthuscapableofhandlinggridswithseveralbillionsofelements.

2.5. FAST FASTisacodedevelopedbytheNationalRenewableEnergyLaboratory(NREL)[8]usedforsimulatingthecoupleddynamicresponseofHAWT.FASTisacoupledcodejoining aerodynamics models, structural dynamics module, control and electricalsystem, but also hydrodynamics models for offshore structures, moorings and icemodels. FAST is based on advanced engineering models but with appropriatesimplificationsandassumptions. Inthismasterthesis,onlythefollowingoptionsareactivated:

• AeroDyn,theaerodynamicsmodel:solvingtherotor-wakeeffectsforanytypeofwind (with the interfaceof InFlowWind) and computing the aerodynamicsloads on each blade-element. Themethod is the Blade ElementMomentum(BEM),explainin3.2.

• ServoDynwithCardasys,thecontrol :ServoDynisan interfacethatallowstochooseeitherFASTcontrolleroranyothercontroller.Inthismasterthesis,thecontrollerCardasys,acontrollerdevelopedbyAdwen,willbeused.

• ElastoDynorBeamDyn,thestructuralmodel:applythemotionprescribedbythecontrollerandapplyallthedifferentloads(aerodynamics,hydrodynamics,gravitational), and simulate the elasticity of the rotor and the supportstructure.EitherElastoDynorBeamDynwillbeuseandareexplainin5.1.2.

FASTisthemodularinterfaceandcouplerbetweenthesedifferentmodels.

2.6. FARDEMAST FARDEMAST(forFASTandARDEMA)isthecoupledcodefortheINWITproject,using FAST as the interface but replacing the aerodynamics module AeroDyn byArdema3D(seeFigure3).

Figure3:IntegrationofARDEMA3DintoFARDEMAST

3. AerodynamicsandstructuralmodelsIn this part, the theoriesbehind thedifferent aerodynamicsmodels, thathavebeenimplementedinthedifferentcodesusedinthismasterthesis,areexplained.

3.1. Generalaerodynamicsaroundanairfoil

3.1.1. Forcesarounda2Dairfoil Considera2Dairfoilinsideaflowcomingfromtheleftwithacertainangle,callangleofattack(AoA),withtheincidentflow.Theangleofattackαisusuallydefinedasthe angle between the chord line of the airfoil and the relative flow direction. Therelativeflowdirectioncanbehardtodefine,sincetheairfoilwillaltertheflow,buta“geometric”angleisusuallydefined,usingtheflowvelocitytheairfoil’s locationas iftherewasnoairfoil.

Figure4:GeometryandaerodynamiccoefficientsdefinitiononaNACA0018airfoil

The flow around the airfoil will create, due to the Bernoulli theorem, a highpressurezoneontheintrados(lowersurface)andalowpressurezoneontheextrados(uppersurface).Theintegrationofthepressurearoundtheairfoilcreatesaresultantforce 𝐹. This reacting force from the flow can be projected onto the directionperpendicular to thevelocityat infinity,𝑈#,whichwill give the lift𝐿, andprojectedontoadirectionparalleltotherelativevelocity,thedrag𝐷.

𝐹 = 𝐿 +𝐷 Withcthechordoftheairfoilandρthefluiddensity,thenon-dimensionalliftand drag coefficients are defined as (if the forces are wingspan forces per unit oflength):

𝐶* =𝐿

12𝜌𝑈#

. 𝑐

𝐶0 =𝐷

12𝜌𝑈#

. 𝑐

Forcertainflow,likeforawindturbine,thedefinitionofthevelocityatinfinityisnotaccurateenoughanddifferentmodelcanbeused,forexampleconsideringthevelocityatacertainpointconsideringtheairfoilisnothere. Tohaveanaccuratemodelof the forceson theairfoil, it isalsonecessary toknowthemomentMatapoint in theprofile.Thispointcanbethecenterof thrustwhich isusually locatedonthechordlineatthequarterchordfromthe leadingedgefor a thin airfoil with an attached boundary layer (the point where the forces areappliedonFigure4).Themomentcoefficient canbedefined thesameway than forthedragandlift:

𝐶1 =𝑀

12𝜌𝑈#

. 𝑐.

3.1.2. 3DAerodynamics The2Dairfoilcanalsobeconsideredasa3Dwingofinfinitelength. Inreality,abladeorawingisabeamoffinitelengthwithaerodynamicprofilesas cross sections.Hence, therewillbeapressuredifferencebetween theupperandlowersideofthewing,andthesameaerodynamiccoefficientscanbedefined. Thedifferencesofpressureontheintradosandextradoscreateajumpinthetangential velocity at the trailing edge, creating, as a result, a continuous sheet oftangentialvorticityinthewakebehindthewing. Moreover, at the tip of the blade, 3D effects are observed. The tip vorticesfollow the tipof theblade, thus creating circular patternsof rotating air, associatedwithinduceddrag. For large unsteady angle of attack, the boundary layer detachment is late,compared to the steady state, therefore changing the lift, drag and momentcoefficient, before the aerodynamics becomes steady again. It is called the dynamicstall.

3.2. BladeElementMomentumTheory

3.2.1. MomentumTheory Themomentumtheory isamodeldescribingthemomentumlossofthewindwhen it flows through a turbine. The hypotheses of themodel are that the flow is

steady,incompressible,irrotational,withanidealfluidwithnofrictionandnoexternalforces. Itconsidersacircularcontrolvolumearoundthewindturbine (Figure5).Therotor isconsideredasapermeablediscwhichonlyslowsdowntheaxialspeed𝑈#ofthewind.Thediscisideal:therearenofrictionandnorotationalvelocitycomponentinducedinthewake. Closeupstreamoftherotor,thereisapressurerise,p1,beforeadiscontinuouspressure drop to p2, after the rotor. Downstream the pressure recovers to theatmosphericlevel.

Figure5:Circularcontrolvolumearoundthewindturbine[9]

ApplyingtheBernoulliequationstothesystem,withtheprevioushypotheses,upstreamanddownstreamtherotorplane,thepressuredropcanbedetermined:

∆𝑝 = 𝑝. − 𝑝6 =12𝜌(𝑈#. − 𝑈89:. )

IntroducingthethrustFwhichistheforceappliedontherotorfromthestream(streamwise)andthepowerPabsorbedbytheshaft,itgivesthankstothemomentumequation and the energy conservation on the integral form of the circular controlvolumearea(withnotationfromtheFigure5,andUd,thevelocityattherotor):

𝐹 = ∆𝑝. 𝑆 = 𝜌𝑆𝑈0(𝑈# − 𝑈89:)

𝑃 = 12𝜌𝑆𝑈0(𝑈#. − 𝑈89:. )

Combiningtheequationgivesthevelocityattherotor,Ud.

𝑈0 =12(𝑈# + 𝑈89:)

Sotheaxialinductionfactoracanbeintroducedas:

𝑈0 = (1 − 𝑎)𝑈#

𝑎 = 1 −𝑈0𝑈#

Theperformanceof thewind turbine is calculatedwith thepowercoefficientCp,whichisthepowerPadimensionalizedwiththewindpoweravailablebythesweptarea:∆𝐸A =

6.𝜌𝑆𝑈#B .

𝑪𝒑 =𝑷

𝟏𝟐𝝆𝑺𝑼#

𝟑= 𝟒𝒂(𝟏 − 𝒂)²

Thispowercoefficienthasamaximum(Cp,max)whichcanbeeasilycalculated:

𝜕𝐶P𝜕𝑎

= 0 ⇔ 𝑎 = 13

ThisCp,maxiscalledtheBetzlimitfortheaxialinductionfactorof𝑎 = 6

𝑪𝒑,𝒎𝒂𝒙 =𝟏𝟔𝟐𝟕

≈ 𝟓𝟗. 𝟑% The effect of the rotation of the rotor can be taken into account with thetangential inductionfactora’. ItdependsontherotationalspeedVθ, theblade localradiusrandtherotationspeedoftherotorΩ.

𝑎] = 𝑉_2𝑟Ω

TheTipSpeedRatio(TSR)λisdefinedastheratiobetweenthewindspeedandthetipspeed,withRtheradiusoftheblade.

𝜆 = Ω𝑅𝑈#

Withthetangential inductionfactor,thepowercoefficientcanbedeterminedwiththeintegrationofatermdependingonthetipspeedratioandthetwoinductionfactors:

𝑪𝒑 =𝟖𝝀𝟐

𝒂′(𝟏 − 𝒂)𝒙𝟑𝒅𝒙𝝀

However, themomentumtheory isnomorevalid fora >0.4,becauseof theformationofaturbulentwakestateduetoahighdifferencebetweenthefreestreamwind speed and the speed after the rotor. It creates perturbations by transportingmomentum from the outer flow into the wake. In this case, it is usual to use theGlauertempiricalcorrection[10]toobtainplausibleresults.

3.2.2. BladeElementMomentumTheory The Blade ElementMomentum (BEM)method is the use of themomentumtheorywithalocalapproachoftheeventstakingplaceattheblade.Thestreamtubeofthe momentum theory is discretized in N annular elements of height dr andstreamlines as boundaries. At the disk place there is an airfoil for each annularelement.Theseairfoilsaretheretogivethepressureforcesthankstothedragandliftcoefficient. Theassumptionsare:

• For the flow : stationary, incompressible, frictionless with no external forcesapplied

• Thereareno3Deffectsandoneelementdoesnotinfluencetheother• The blade applies a constant force on the flow for each element. This is

equivalenttoarotorwithaninfinitenumberofblades.Hence,theBEMusesanalgorithmtocomputetheforcesonthesegmentoftheblade:

1. Initializationofaanda’,usually𝑎 = 𝑎] = 0

2. Theanglebetweentheplaneofrotationandtherelativevelocity,theflowangle φ is computed using the equation :

tan 𝜑 =(1 − 𝑎)𝑈#(1 + 𝑎])Ω𝑟

3. Withθthetwistthelocalangleofattackiscomputed:𝛼 = 𝜑 − 𝜗

4. ReadCl(α)andCd(α)fromthepolartables(theliftanddragcoefficientsfor

theprofilevs.theangleofattack)5. ComputeCNandCTfromtheequations:

𝐶o = 𝐶* cos 𝜑 + 𝐶0 sin 𝜑 , 𝐶t = 𝐶* sin 𝜑 − 𝐶0 cos 𝜑

6. Calculateaanda’fromtheequations,usingtherotorsolidity:𝜎 = vowxyz|

𝑎 =1

4𝑠𝑖𝑛²(𝜑)𝜎𝐶o

− 1,𝑎 =

14𝑠𝑖𝑛(𝜑)cos(𝜑)

𝜎𝐶t− 1

7. Ifaanda’havechangedformorethanacertaintolerance,gobacktostep

(2),Elsefinished

8. Computethelocalforcesonthesegmentoftheblades.

Thisalgorithmcanbecorrectedtoconsidermoreeffects:

• Prandtl’stiplossfactor[11]:whichwillcorrectstheassumptionthatthereisaninfinitenumberofblades,

• Glauertcorrection:anempiricalrelationbetweenthethrustcoefficientCTandtheaxial interferencefactorα fora>0.4,wherethemomentumtheory isnolongervalid[10].

• Many other models can added for tip vortices correction, spanwise flow,turbulentwakeordynamicinflow.

TheBEMmethod isrelativelyreliableandprecise. Itcanbecalculatedveryfast (lessthanrealtime)anddoesnotneedalotofstorageforthedata.Nevertheless,therearealotofassumptionsthatcannotbefulfilledinmostofthecases.Asaresult,therearemanyempiricalcorrectionfactorstotakeintoaccountalltheeffects.Moreover,BEMarenotabletoestimateaccuratelyunsteadyloadsfordesigningfatiguecases.

3.3. VortexModelingMethod TheBEMmodelusesverysimplifiedphysicswithstrongassumptions,thereforemore advanced and sophisticated aerodynamic tools are needed. CFD can be asolution, but it is too time consuming for industrials. An alternative method is thevortexmodelsthataremoreaccuratethantheBEMmethodandlesstimeconsumingthanCFD.ThevortexpanelmethodusedinARDEMA3Disdescribedinthissection.

3.3.1. Mainideaandhypotheses Thepanelmethodisbasedonalinearequationthankstostrongassumptionsontheflow.Thislinearequation,theLaplace’sequation,admitselementarysolutionswhich thanks to the linearity can be added andmultiplied by a scalar to give othersolution.Theflowcanbesetintoanintegralformthatwillonlydependonfindingtheboundaryvalues.Therefore,findingtheboundaryvalueswillbeenoughtonumerically

calculate the solution at any point in the fluid domain. Consequently, it is notnecessary to mesh the whole flow as in CFD, which explains why it is much lessexpensive.Becausethesystemislinear,theboundaryvaluescanbeconstructedasalinearcombinationoftheelementarysolutionsofLaplace’sequation. The boundary is split into panels, defined in the geometry, and the flow iscalculated using a linear combination of the induced perturbations of each of thesepanels.Itiswherethename“PanelMethod”camefrom. Themainassumptionsarethattheflowis:

• Incompressible,sowithalowMachnumber(𝑀 < 0.3)• Inviscid,inthefluiddomain• Irrotational apart from singularities because the vorticity is concentrated in

theboundaryofthefluiddomain.Indeed,awayfromthesolidboundariesandfromthewakes,theeffectofviscousforcestendstobenegligiblecomparedtotheeffectsofinertialforces.Thus,theboundarylayersforthesolidbodiesandthewakesareconsideredasinfinitelythin.

3.3.2. Governingequation ThebehaviorofthefluidisdescribedbytheNavier-Stokesequations,andwiththe hypotheses of incompressibility, inviscidity and irrotationality (except at thesingularities),itgives:Navier-Stokesequations:

𝜕𝑈𝜕𝑡

+ 𝑈. ∇ 𝑈 = 1𝜌∇𝑝 + 𝜈∆𝑈

Massconservation:

∇. 𝑈 = 0Irrotational:

∇×𝑈 = 0

3.3.2.1. LaplaceEquation ThevelocitycanbedecomposedthankstoaHelmholtzdecompositionintoanirrotational term ∇Φ and a rotational term ∇×𝐴 that is neglected thanks to theassumptions.Therefore:

𝑈 =∇Φ +∇×𝐴 = ∇Φ

Thanks to the mass conservation for an incompressible flow, the LaplaceequationisrespectedforthepotentialΦ:

∆Φ = 0

3.3.2.2. BoundaryCondition Theflowcannotpenetratetheboundaries(solidbodies),accordinglythereisaNeumann boundary condition for the Laplace equation : on the solid surface nonormalvelocitycanappear:

𝑈. 𝑛 = ∇Φ. 𝑛 = 𝜕Φ𝜕𝑛

= 0 Theotherboundaryconditionisthatfarfromthesolidsurfacetheflowreachthesamevelocityvalueasthefreestreamvelocityupstreamofthebody,whichgivesthecondition(withrthenormoftheposition):

lim~→#

∇Φ =𝑈#

3.3.2.3. Kutta-Joukowskitheorem Thevorticity𝛾andtherotation𝜔ofthefluidaredefinedas:

𝛾 = 2𝜔 = ∇×𝑈 The circulation Γ is the integral of the fluid element velocity along a closedcurveL,surroundingasurfaceSwithaunitnormal𝑛:

Γ = 𝑈. 𝑑𝑙 = 𝛾𝑑𝑆.

Avortex line isdefinedasa linewhose tangent iseverywhereparallel to thelocalvorticityvector. A vortex tube is volume inside all the vortex lines drawn at each point of aclosedcurve. A vortex filament is a vortex tube whose cross-section is of infinitesimaldimensions. Hence, a vortex filament is a line of concentrated vorticity Γ, that willinduces flowvelocities in itsneighborhood,dependingon thedistance𝑟 of the flowelementtothefilament. Sometheoremsthatdescribethevortexfilamentarerecalled.Helmholtz’stheorems:

In an incompressible and inviscid flow, Helmholtz’s theorems describes themotionofthefluidattheproximityofavortexfilament:

• Helmholtz’s1sttheorem:Thestrengthofavortexfilamentisconstantalongitslength

• Helmholtz’s 2nd theorem : A vortex filament cannot end in a fluid; it mustextendtheboundariesof the fluid.Thevortex linemustbeclosed,extendtoinfinity,orendatasolidboundary.

• Helmholtz’s3rd theorem : Intheabsenceofrotationalexternal forces,a fluidthatisinitiallyirrotationalremainsirrotational.

Kelvin’scirculationtheorem:In a barotropic ideal fluidwith conservative body forces, the circulation Γ around aclosedcurvemovingwiththefluidremainsconstantwithtime:

𝐷Γ𝐷𝑡

= 0Kutta-Joukowskitheorem: Inan inviscid irrotationalflow,any2Dbody inrelativemotiontotheambientfluid, with a velocity U, a circulation Γ and a density of ρ, has a lift force L,perpendiculartoU,ofmagnitude:

𝐿 = −𝜌𝑈Γ ForafinitebladeofspanbwithaconstantairfoilandacirculationΓboundatthequarterchord:

𝐿 = −𝜌𝑈 Γ890 𝑦 𝑑𝑦.

3.3.2.4. LiftingLineMethod Theliftinglinemethodisamethodusedinordertosimulatea3Dfinitewingina flowstreamwithavelocityof𝑈#andagivenangleofattackα,withacalculationmethodbasedonvortexfilaments.Theideaofthismethodisthattheliftproducedbya 3D wing can bemodeled by a series of vortex filament oriented in the spanwisedirectionof thewing, calledboundvortices. Indeed theKutta-Joukowski theoremasdescribed in 3.3.2.3 gives a value for the lift force per unit span in function of thecirculation,sothevorticityoverasurface. UsingHelmholtz’s firstandsecondtheoremstatingthatthecirculationoveravortex filament is constant and that the vortex filamentmust forma closed loopor

extendsouttoinfinity,therefore,theliftcanbemodeledasahorseshoevortexbehindthewing.Thethirdtheoremimpliesapotentialflow.Asaresult,acompletewingcanbemodeledbyaseriesofclosedvortexfilamentsΓi. Foran incompressibleand inviscid flow, thewingcanbemodeledasa singleboundvortexline, locatedatonequarterofthechord,behindtheleadingedge,andtheassociated shedvortex sheet. Foreach lifting line spanelement, aboundvortexcorresponds to one control points, one shed vortex per time step and two trailingvorticiesovertimestep.Theyaremovedawayfromthewingbythewakeevolutionintime(Figure6).

Figure6:Liftinglinemodelwithboundvortices,collocationpointsandwakeelements[12]

The lifting line method algorithm is initialized with an approximate value ofΓbound.Then,foreachiteration,thealgorithmcalculatestheinducedvelocityduetothewake𝑢0,andthebodyinfluence𝑢0,80atthecontrolpoints.Hence,therealAoAisdeterminedfromtherelativevelocity:

𝑢~* = 𝑈# +𝑢0,80 +𝑢0, −𝑈18:8 The lift is deduced from polar curves, relative to the blade elements, thusallowing the calculation of Γbound, thanks to the Kutta-Joukowski theorem, and thedeductionofΓshedandΓtrailviatheformulas:

Γ890 = Γ 0

Γ 0 𝑧, 𝑡 = Γ890 𝑧, 𝑡 − Γ890 𝑧, 𝑡 − ∆𝑡

Γ:~¢* 𝑧, 𝑡 = Γ890 𝑧, 𝑡 − Γ890 𝑧 − ∆𝑧, 𝑡

3.3.2.5. Vortexmethods Forthevortexmethod,thevorticityisacharacteristicvariableoftheflowanditcanbemodeledviavortexpanels, trackedovertime inaLagrangianway inordertoreshapethewake.TheLagrangianmethodin3Davoidsdiffusionandtheconservationof vorticity is donewith the surfacemeshes’ connectivity on the vortex panels. Thebladesaremodeledbysingularvorticesdistributedalongalineforaliftinglinemodeloralongasurfaceinapaneldescriptionofthebladeforavortexpanelmethod. Howeveritisdifficulttomodelproperlyinteractionbetweenwakepanelwhentheyarestretched,advectedorinacomplexreconnection.

3.3.3. VortexPanelMethod The vortex panel method considers a real profile, so a continuous profile, acontinuous wake and a boundary layer, representing the real behavior of the flow(Figure7, left).With theprevioushypothesis, thewakeand theboundary layersareconsideredasinfinitelythin.Thewakeisthendiscretizedwithaliftinglinemethodinto3Dsurfacesthatwillrepresentashearlayerintheflow(Figure7,middle).Finallytheprofileisdiscretizedandreplacedbyafinitenumberofflatpanels(Figure7,right).

Figure7:Realflowbehavior,wakediscretizationandvortexpanelmethoddiscretization

Figure8:Representationofonepanelwithitsvortexringandcontrolpoint

Foreachpanel,avortexringfollowsitsbordersandthevorticesrotatearoundthis ring (seeFigure8).Thesevortices induceavelocityat thecontrolpoint𝑢0. Inthisvelocitythereisthewakeinfluence𝑢andthebodyinfluence𝑢80.

𝑢0 = 𝑢 +𝑢80 Moreover, the freestream velocity𝑈# and the motion of the blade𝑈18:8should be added to calculate the relation speed𝑢~* of the panel,which should beparallel to thepanel surface in order to respect theNeumann condition. Thewholepanelvortexalgorithmisbasedonthedeterminationoftheseinducedvelocities.

𝑢~* = 𝑈# +𝑢0 −𝑈18:8 TheinducedvelocityisproportionaltothevortexstrengthandiscalculatedbythelawofBiot-Savart,with𝑟thevectorbetweenthecontrolpointandthevortexring,𝑑𝑙alongthatringand𝛾theintensityofthesingularity:

𝑢0 = 𝛾2𝜋

𝑟×𝑑𝑙𝑟 B

Usually, this integral issplit intofour integrals foreachsegmentofthevortexring. For a panel of control point 𝑖, there is𝑢0(𝑖)¤, the velocity induced by thevortex ring 𝑗. Accordingly, an influence coefficient 𝑎 can be defined as the panelinducedvelocityforavortexstrengthof𝛾 = 1.

𝑎 𝑖, 𝑗 = 𝑢0(𝛾 = 1)(𝑖)¤ As a consequence, it is possible to write the velocity induced at the controlpoint𝑖ifthereare𝑛vortexrings:

𝑢0 𝑖 = 𝛾𝑎(𝑖, 𝑘)

TheNeumannconditionhas tobe satisfiedat every controlpoint. Therefore,thefreestreamvelocityhastocompensatetheinducedvelocityinthenormaldirectionofthepanel:

𝑢0. 𝑛 = −𝑈#. 𝑛 Combiningthetwopreviousequations,asystemcanbeobtainedforthewholewingandtheinfluenceofthewake,andwritteninmatrixform.ThematrixA=ai,jisofdimension (mxn),withm thenumberofcontrolpointsandn thenumberofvortexrings. This matrix is called Aerodynamic Influence Coefficient (AIC). It takes intoaccount the influence of panels on each other. After projection along the normalvectors,thesystembecomes:

𝑎6,6 𝑎6,. ⋯ 𝑎6,𝑎.,6 𝑎.,. … 𝑎6,⋮ ⋮ ⋱ ⋮

𝑎1,6 𝑎1,. ⋯ 𝑎1,

𝛾6𝛾.⋮𝛾

𝑈#,6𝑈#,.⋮

𝑈#,1

Thisprovidesasetofequationswhichcannotbesolvedforallthe𝛾ofthebodyandthewake,becausetherearetoomanyunknowns.However, theKuttaconditionstatesnovelocityandnocross-flowatthetrailingedge.Hence,somesolutionsofthesystemcanbefoundbysettingthestrengthofthelastvortexringsofthebladeequaltothestrengthofthefirstvortexringsofthewake. Oncethematrixissolved,thevorticesstrengthgivesthelocalforce𝐹foreachcontrolpointthankstotheKutta-Joukowskitheorem. Thatmodeltakesintoaccounttheinfluenceofthewakeonthebody,butnotthe influence of the body on the wake nor the influence of the wake on itself.Consequently,somesupplementarymatricesareimplementedinthecodetotakeintoaccounttheimpactofthebladesonthewake,aswellastheinfluenceofeachbladeontheotherones,andtheadvectionofthewake.

3.3.4. Angleofattackandviscouscorrections Sincethevortexpanelmethodassumesaninviscidflow,itisnecessarytoapplya correction. This part describes briefly how the aerodynamic coefficients arecalculatedandhowtheviscouscorrectionisapplied.Pressure,AoAandAerodynamiccoefficients: ThepressureinsidetheflowdomainΩisofnointerest,butthepressureattheboundaryof thedomain,𝜕Ω,canbecalculatedfromthegradientof thedisturbancepotentialΦandthecontributionoftheouterflow,thankstotheBernoulliequation,whosehypothesesarefulfilled. The AoA and the lift and drag coefficients can be calculated with differentmethods,usingpolartablesalreadymeasuredfortheairfoil.TheAoAmeasurementisacomplextopicforwindturbinesbecausethefreestreamvelocityinawindturbineismoreambiguousduetotherotationoftheblade.Accordingly,theAoAcanbedefinedgeometrically, from the velocity at a certain point or from the integration of thepressure around the airfoil. The aerodynamic coefficients are thenderived from themeasurementoftheAoA. For Ardema3D computation, the method used is the integration of thepressure.Theinviscidflowaroundtheairfoilisintegrated,hencegivingavaluefortheliftforce,whichisthenusetofindthevalueoftheAoAwiththeinviscidpolars. In section 4, the comparison of the AoA between YALES2 and Ardema3D isdoneusingtheAoAofArdema3Dcomingfromthevelocityatthequarterchord,even

thoughthisAoAisnotthesameastheAoAusedtomakethecalculation(whichcomesfromtheintegrationofthepressure).Viscoussimulations:forceandwakereduction: Inordertotakeintoaccounttheviscosityofthefluid,thevalueofliftanddragcoefficient will be read from the viscous polars. To define the viscous forces, areductionfactoriscalculatedviatheliftcoefficientfrominviscidandviscouspolarsforaselectedAoA:

𝑅𝐹 = 𝐶*,¬¢v89𝐶*,¢¬¢v¢0

Thisreductionfactorwillbeusedtocorrecttheinviscidforces. Amodel for the dynamic stall can also be used. The viscous forces keep thedirectionoftheinviscidforces(comingfromtheintegrationofthepressurearoundtheblade)forthelift,andthenitismodifiedtotakeintoaccounttheviscousdragappliedon thedirectionof the relative flow toagivenelement.There itwilldependon theAoAdefinition. Inthesameway,areductionfactorcanbeusedtoreducethewaketotakeintoaccounttheviscosityeffects. PicturesofthewakeinArdema3DareintheappendixA.

3.4. LESwithActuatorLineModel ComputationalFluidDynamic(CFD)isaclassicalmethodofsimulation.Itisverypreciseanddoesnotrequirehavingstrongassumptionsorexperimentalcorrections,but the cost in terms of calculation time is very high, compared to vortex panelmethodsorBEM. DifferentmodelexisttosolveaflowwithCFD.TheDirectNumericalSimulation(DNS)isthemostaccurate,sinceitsolvesthefullrangeofturbulencescales,withfinemeshbutinsuchconfigurationofspaceandtimescalesrequiredforawindturbine,itisnotaffordable,duetothemeshrequirement.Asaresult,theLargeEddySimulation(LES)willbeusedfortheflow,sinceitsolvesthelargestscalesoftheturbulencewhilethesmallscalesaremodeled,butnotcomputed,allowingastrongincreaseofthecellsize. Asfortheturbine,thebladegeometrycannotbemeshedevenwithLESsincevery smalls meshes will be required, accordingly the method of the Actuator LineModel(ALM)willbeused[13].Forthismasterthesis,thesizeofthemeshcellisaboutthesizeofthechordoftheblade.InanotherstudyofAdwenwiththeCORIA,anairfoilismodeledandthecellsizeisabout10e5smallerthanthechord. BothLESandALMmethodsaredescribedinthefollowingparts.

3.4.1. LESmethod

TheLargeEddySimulation (LES)methodhasbeenusedsince1970andhasalargerangeofapplication.Itisbasedonthesimulationofthelargeeddiesandtheuseofmodels for thesmallerones. Itallowshaving less refinedmesh than forDNS thatwillbelesscostlyintermsofcalculationtime,butthatwillallowagoodprecisiononlargescale. Inordertodoit,theNavier-Stokesequationisnotsolved,butitisafilteringoftheequationthatwillbesolved.ThefilteringoperatorisaconvolutionwithkernelGwhichcanbeassimpleasanaverageoragaussiencurvehenceusinganoperatorofthetype(withΩthewholedomain,rthedistanceand𝜑aparameteroftheflow):

𝜑(𝑟) = 𝜑(𝑟])𝐺(𝑟 − 𝑟])𝑑𝑟′

So the Navier-Stokes equations for an incompressible flow to which thisoperatorisappliedbecomes:

∇. 𝑢 = 0

𝜕𝑢𝜕𝑡+ 𝑢. ∇ 𝑢 = −

1𝜌∇𝑝 + 𝜐∇.𝑢 + ∇. 𝜏± + 𝜇

Withρthedensity,pthepressure,νthekinematicviscosity.𝜏±isthemodeledsubgrid-scalestresstensorwhichisamodelfortheflowforthescalesmallerthanthemesh;thismodelisrequiredinordertocompensatethelossofinformationduetothefiltering of the equation. A source term𝜇 is introduced in the equation in order tomodeltheeffectoftherotorofthewindturbineontheflow. Thesubgridscaleusedinthisstudyisa𝜎-model.The𝜎-modelprovidesresultsofasimilarqualitythantheSmagorinskymodel,butfora lowercostwhentherearewalls[14].

3.4.2. ActuatorLineModel Due to themulti-scale nature of the problem, a simultaneous solving of theboundary layersof thebladeof the turbineand thewakeover longdistances isnotcomputationallyaffordable.TheActuatorLineModel(ALM)isamodelthatconsistsinmodeling the influence of the wind turbine on the flow, by imposing body forcesdistributedalongrotatinglines.Thisisrepresentedasthesourceterm𝜇inthefilteredNavier-Stokesequations.Asaconsequence,theboundarylayerisnotsimulatedanditallowsusingalessrefinedmesh. IntheALM,thebladesarediscretizedalongthespanandarotationmotionisprescribed.Theforcesusedarecomingfromthepolarsfortheliftanddragcoefficientfortheairfoilcomposingtheblade(see3.1).Thepolarsarefittedwithfittingcurveinorder to avoid using look-up tables.With L the lift and D the drag force, the forceappliedis:

𝑓 = 𝐿𝑒 + 𝐷𝑒µ

In order to have a continuous force in the flow, a model of mollication isintroduce (see Figure 9). Therefore the forcewill not introduce a singularity on oneelementinthemesh,butasmoothforceonseveralelementofthemesh(seeFigure10)

Figure9:MollicationfortheActuatorLine

Figure10:Mollificationeffectatthemeshscale

Themollifierisdefinedas(withdthedistancetotheapplicationpoint):

𝜂 𝑑 =1

𝜖B𝜋B/.exp −

𝑑𝜖

With the regularization parameter𝜖 such as𝜖 = 2𝛿,where𝛿 is the actuatorline element size. Thus, the force f will be, with N the number of element of theactuatorlineand𝑟thepositionoftheelementioftheactuatorline:

𝑓 𝑟, 𝑡 = (𝐿𝑒 + 𝐷𝑒µ

)𝜂( 𝑟 − 𝑟 )

TheactuatorlineistheprevailingmethodinLESsimulationsforwindturbines.Indeed,itallowsstudyingthewakeofawindturbinewithanimportantaccuracyandwithanaffordablecomputationaltime.

4. ValidationofthefarwakemodelinArdema3D

4.1. TheExperimentandnumericalhypotheses

4.1.1. TheExperiment It isverydifficulttovalidateanaerodynamiccodeforwindturbinesbasedonfull scale turbine measurement. Indeed, the result of the simulation will be highlydependent on the turbulent inlet wind which is difficult to measure. Furthermore,modernwindturbinesaremoreandmoreelastic,thustheaerodynamiccodemustbecoupledtoastructuralsolvertogetcorrectsimulationsofsuchturbines(fortheINWITproject,thisisthepurposeofthecodeFARDEMAST). TheNTNUWindTurbineExperiment(Figure11)wasanexperimentofEriksenand Krogstad at the Norwegian University of Science and Technology (NTNU) inTrondheim in Norway [15]. It is an experiment in a wind tunnel, hence with acontrolled wind, for a small wind turbine, accordingly with negligible elasticdeformations.Itisconsequentlyaveryinterestingcasetovalidateaerodynamiccodes. TheexperimentusesasmallwindturbineofD=0.90mofdiameterinawindtunnel1.8mwide,2.7mhighand11.15m long.Theaimof theexperimentwas tohaveabetterunderstandingoftheaerodynamicsofthewake. Theexperimentranwithawindat10m/s,withturbulence intensityof0.3%,foraTSRof3,6and10.TheresultsarethemeasurementsofthevelocityofthewakeatadistanceXoftheturbine,suchas:X/D=1,3and5. Thebladeshaveanon-uniformtwistangleandchordlengthdistributions.Theprofile isaNRELS826.Thehubhasaradiusof0.045m,hencethebladehasaspangoingfrom0.045mto0.45m.Thehubisat0.817mabovetheground.

Figure11:PhotooftheNTNUwindturbine

4.1.2. Numericalhypotheses

4.1.2.1. Generalassumptions Inordertorunthesimulations,severalassumptionshavebeendone. Theturbulenceintensityissetto0%,sinceitisverylowintheexperiment,asaresult,auniformwindisconsidered. Thebladeshaveatwistangleandachord lengthwhichhavebeencalculatedbasedonthedescriptionofthecase,andthenusingafittingcurve,inordertobeabletochoosethenumberofelementintheblade.Moreover,becausethevortexmethodandtheactuatorlinemethodareusingpolarstocomputetheforces,thepolarsoftheprofilearealsocomputedthankstoafittingcurve. Since YALES2 has no module to take into account the dynamic stall, thecorrectionofthiseffectinArdema3Dhasbeenremoved. ThesimulationshavebeendoneonlyforTSR3and6.Thesimulationsaredonefirstonlyusingtherotor,withnomodellingofthehuborthetower.Thesecondpartwasusingallthegeometry,withalsothewallsthatarepresentintheexperiment.

4.1.2.2. AssumptionsforARDEMA3D

Figure12:GeometrysetupforArdema3D

InArdema3D,thesimulationhasbeendonewithasegmentationofthebladeinto20sections.Anelementisthevolumedefinedbetweentwosections.The5firstsections (fromaspanof0.045 to0.0675meter)aredefinedasnon-liftingelements,meaningthattheelementswillnotproducewakepanels. Indeed, inorder tohaveasmoothgeometry, thesections for theseelementsaregoingfromacylindershapetoaS826profile.Becausetherearenocleartrailingedges, it is difficult to create a wake panel for these profiles. Moreover, the polar

associatedwiththesesectionsarethepolarforacylindershape,sinceitwasdifficulttocomputeitforamixedprofile. The 15 others sections are distributed along the span following a cosinefunction,inordertohaveavortexroll-upofthetrailingvortices. In Ardema3D, there is choice for the user to use single or double digitprecisions. This choice is a tradeoff between precision and simulation cost,which isindeedabouttwicehigherindoubleprecision.FormostsimulationsinArdema3Dthesingleprecisiongivesenoughsatisfactoryresults. However, the NTNU case pointed out a bug in the implementation ofArdema3D.Indeed,becausethescaleoftheNTNUturbineisabout100timessmallerthan for a realwind turbine, the functionwas ironing out a lot of vortices in singleprecision, consequently leading to a wrong calculation. The function has beencorrected,inordertoimproveitsefficiencyforsmallscale,still,someeffectswerestillnoticeable,sothesimulationswereranwithdoubledigitprecisions. For the complete geometry case (Figure 12), a wake deficit model is used.Indeed,Ardema3Ddonotmodelthemassivedetachedflowthatcanbeobservedforthe tower. As a result, an empirical correction has been added to create a velocitydeficitdownstreamthetowerandthenacelle.Nonetheless,thecorrectionwillonlybeareductionfactor,thusnotaddinganyradialvelocity. Moreover, a regularization parameter will be added in order to smooth thesingularities,whichwillmakeamorestableandrealisticadvectionof thewake.Thisfactor will allow avoiding a too important speed close to a vortex, so reducing thenumericalnoiseinthewake. The sensitivity tests on Ardema3Dwere previously done to know howmanyturnsoftheturbineshouldbedoneinordertohaveaconvergencetolessthan0.5%ofthefinalresultsintorque.Thestudyshowedthatittakes10turnsatTSR4and25turnsatTSR8,due tomore important inductions in thewake.Because this study isfocusedonthewake,thenumberofturnshasbeenincreasedabit(seeTable1). Asforthecomputationalhardware,torunArdema3D,oneGPUisusedforthemostcostlyoperation.About10CPUareused,however,thisisnotafixnumber. ThecomputationaltimeisquitelowcomparedtoYALES2(seeTable2),whichcantakemorethanadaytorunasimulation,withevenmoreCPUs.

Numberofturns Time Requirements

TSR3RotorOnly

15turns 36min 1GPU~10CPUs

TSR6RotorOnly

25turns 1h16min 1GPU~10CPUs

TSR3CompleteGeometry

TSR6CompleteGeometry

Table1:ComputationalparametersforArdema3D

4.1.2.3. AssumptionsforYALES2 ThesimulationwithYALES2wererunwithanunstructuredmesh.Themeshcanberefinedto increasethesizeofthemesh. Indeed,thesimulationwererunat leasttwo timeswith aminimummesh size of 0.04m (RAF0), in order tomake sure thattherearenoobviousissueandthenwithaminimummeshsizeof0.02m(RAF1). Onecase,theTSR6,hasalsobeenlaunchedwithaminimummeshsizeof0.01(RAF2),however,sensitivitytestsshowedthattherewasasmuchinformationinRAF1asinRAF2. Dependingonthecase,theactuatorlineisdividedinmoreorlesssections.InRAF0,thereare17sectionsperblades,inRAF149sectionsperbladesand99sectionsperbladesinRAF2. In YALES2, the forces are applied on the fluid, thus, there is a need to knowtheseforces.Itcanbedoneusingthepolarcurves,butalsousingtheforcesextractedfromArdema3DandputbackintoYALES2.Fromnow,thecasewhereapolarcurveisusedwillbereferredas“Polar”andthecaseusingtheforcesfromArdema3Dwillbereferred as “A3D forces”. Because of the long computational time for YALES2, thecomparisonbetween the case “Polar” and “A3D forces” has only beendone for theTSR6rotoronlycase. The simulation shouldnotbe lookedatafter10 radiuses. Indeed, inorder toavoidsomebackflowattheoutletofthemesh,somenumericaltreatmentsaredoneinordertodissipatethevorticesattheoutletofthemesh. Thesimulationtimeissettobetheequivalentof10turnsoftheturbine. AsummaryoftheparametersisprovidedintheTable2.

Size ofthemesh

NumberSection

Numberofturn

Elementsin themesh

NumberofCPU

Numberof CPUhours

RAF0 0.04m 17sections

10 14M 16 69hCPU

10 115M 224 1824hCPU

10 920M 448 ~14000hCPU

Table2:ComputationalparametersforYALES2

4.2. ResultsforRotorOnlysimulation

4.2.1. Simulations ThelistofthesimulationsdoneisintheTable3. Code Refinement Forces

Ardema3D - -

YALES2 RAF1 UsingA3Dforces

Ardema3D - -

YALES2 RAF1 UsingA3Dforces

YALES2 RAF2 UsingPolars

Table3:Listofthesimulationsinrotoronly

Forthestudyofthebladeaerodynamics,thecomparisonwillbedoneon:

• AngleofAttack(AoA)• LiftandDragcoefficient(ClandCd)• AxialandTangentialforces(FzandFt)

• Theaxialandradialvelocityfieldataverticalcross-sectionat1diameteroftherotor(UaxandUrad)

Thestudyoftheaerodynamicscharacteristicsofthebladeisdirectlylinkedtothe effect of the flow on the blade. These parameters are essential for designing awindturbine. Forthestudyofthewake,thecomparisonwillbedoneon:

• TheAxialInductionFactor(definedin3.2.1)alonghorizontallinesdownstreamoftherotoratadistanceX/D=1,3and5,likeintheexperiment

• Theaxialvelocityfieldinanhorizontalcrosssection The study of the wake is more important for wind farms design or otherapplicationsinwindfarms,suchashelicopterdeliveryinwindfarms. Each factor (AoA,Cl,Cd,FzandFt)willbeplottedasa functionof thespanofoneblade.Thesimulationconvergedtoasteadystate,sotheseparametersshouldnotchangeover the time. Each velocity is an averaged velocity over the time, over onerotation.

4.2.2. TSR3

4.2.2.1. Bladesaerodynamics The AoA is one of the most important parameter, because the otherparametersarecomputeddependingon it.Accordingly, if theAoA (Figure13) isnotthesamebetweenYALES2andArdema3D,theliftanddragcoefficient(Figure14)willnotbethesame. Theissueinthecurveat18%ofthespancomesfromthechangeofmethodtocalculatetheAoA(seeErreur!Nousn’avonspastrouvélasourcedurenvoi.).Indeed,this is the separation between lifting and non-lifting elements, so there is a suddenchange in themethodof computationof theAoA:below18%theAoA is calculatedusingthe integrationofthepressure.Afterthat, it isusingtheAoAcomingfromthevelocity,whichisthesamemethodasinYALES2. However, the AoA used for the calculation of the coefficient is not the AoAplotted,buttheAoAcomingfromtheintegrationofthepressure,allalongthespan.

Figure13:AoAcomparisonTSR3,RotorOnly

FromtheAoA,theCdandClcoefficientsareeasilydefinedusingpolarcurves.TheforcesFtandFz(Figure15)canthenbecomputedbyprojectingthedragandliftcoefficient. In thecaseofYALES2, the forcesare imposedon the fluid thanks to theforcesalreadycomputedwithArdema3D. Thepeaks inArdema3Dare coming from the use of different geometries fornon-liftingelements.Moreover,forthesesections,thegeometryisamixedgeometrybetween the S826 profile and a cylinder, using the polar curves of a cylinder. Thisapproximationisdonebecausethenon-liftingelementswillnothaveaninfluenceonthewake.

Figure14:ClandCdcoefficientcomparison,TSR3,RotorOnly

Figure15:FtandFzcomparison,TSR3,RotorOnly

TheforcesgiventoYALES2weresmoothedinordertoreducethepeak,whichmaycreateissueinthecode.Theotherdifferencesarecomingfromthedefinitionoftheliftanddragcoefficientexplainedin3.1.1. Asfortheaxialandradialvelocityfieldsatonediameterawayfromtherotor,there isagoodmatchbetweenthetwocodes.Theaxialvelocitydifferencesandtheradialvelocitydifferencesarecomputeddifferently,duetothefactthattherewasnoreferencevaluefortheradialvelocity.

∆𝐴𝑥𝑖𝑎𝑙 = 𝑈¾¿ÀÁ. − 𝑈¾À~01

𝑈#∆𝑅𝑎𝑑𝑖𝑎𝑙 = 𝑈~0¿ÀÁ. − 𝑈~0À~01

Figure16:AxialandRadialvelocityfiel,TSR3,RotorOnly

Themaindifferencesareattherootofthebladewheretheyareduetonon-liftingelementsinArdema3D,thusthecreationofatrailingvortexattheedgeofnon-liftingsections(Figure16). The differences between the codes are differences thatwere expected sincethe two codes are using completely differentmodel, therefore, the results are verysatisfying.

4.2.2.2. Wake The wake given in both simulations will be compared to the experimentalresultsinsection4.3,wherethecompletegeometryisdone. TheaxialinductionfactormeasuredatX/D=1,3and5iscomparedsinceitisthevalueonwhichtheexperimentalresultsareprovided.

Figure17:AxialInductionFactor,TSR3,RotorOnly

TheimportantdifferenceisthediffusionforYALES2overthedistance,whereasthevalue inArdema3D isstillveryhigh. Itcomes fromtheviscousdissipationof thevorticeswhichisinherentlydoneinYALES2,sinceitusesLES.However,inArdema3D,the vortices are not dissipated, since the simulation is inviscid (even thoughcorrectionsareappliedtohaveviscousresults).TheinfluencesofthevorticesonthebladeareinverselyproportionaltothedistanceintheBiot-Savartequation(see3.3.3),still,thevortexintensityisconstant,so,therearenodissipationofthewake.Thesameeffectispresentinthehorizontalcrosssection(Figure18andFigure19).However,noexperimentaldatavalidateanymodels.

Figure18:Horizontalcrosssection,TSR3,RotorOnly

Figure19:Horizontalcrosssectiondifferences,TSR3,RotorOnly

This effect is obvious after 5 radiuses, where thewake starts to dissipate inYALES2andnotinArdema3D.

4.2.3. TSR6 ATSRof6isamoreusualoperationalconditionforthewindturbine.

4.2.3.1. Bladesaerodynamics ThecomparisonisdonebetweenArdema3D,YALES2usingArdema3DforcesinRAF1andYALESusingpolarsforcesinRAF2.ThedifferencesbetweenArdema3DandYALES2withArdema3DforcesaresimilartothedifferencesfortheTSR3. Thereareimportantdifferences,duetothedifferentmethodforcomputation,fortheAoA(Figure20),ClandCd(Figure21)forYALES2usingpolarsandYALES2usingthe forces from Ardema3D, however, since the forces Ft and Fz (Figure 22) arerelativelyclose,thedifferenceswillnotimpactmuchthewake.

Figure20:AoAcomparison,TSR6,RotorOnly

Figure21:ClandCdcomparison,TSR6,RotorOnly

Figure22:FtandFzcomparison,TSR6,RotorOnly

Asfortheaxialandradialvelocityfieldatonediameteraway,therearemoredifferencesthanforTSR3,this isduetothefactthatTSR6 isamoreheavily loadedcase,withmore inductions,andasaresult, thedifferencesareemphasized.There isalsoanissueduetothenumberofsectionsinArdema3DcomparedtoYALES2,whichisresponsiblefortheiso-velocityannuliintheplot. More differences are observed comparing Ardema3D to YALES2 using theArdema3Dforces(Figure23)orthepolars(Figure24).Indeed,duetothedifferencesintheforces,therearemoredifferenceswithArdema3D,howevertheresultsarestillsatisfying.

Figure23:AxialandRadialvelocitycomparisonforYALES2A3DforceRAF1,TSR6,RotorOnly

Figure24:AxialandRadialvelocitycomparisonforYALES2PolarsRAF2,TSR6,RotorOnly

4.2.3.2. Wake Theaxialinductionfactorisquitesimilarforthethreesimulations.ThereisstilladifferenceduetothediffusionofthevorticesintheLEScode.Moreover,Ardema3Duses a simple advection scheme to move the vortex, accordingly, the accuracy islimitedforfarwakeelements.

Figure25:AxialInductionFactor,TSR6,RotorOnly

ThevelocityfieldsshowthattherearesomeinstabilitiesinthewakeforYALES2after8 radii,due to thewakediffusion, thusaphysical instability. InArdema3D, thewakealsostartstobeunstableduetotheuseofanEulerschemefortheadvectionofthe wake panels, thus a numerical instability. However, the comparisons are verycorrectforbothcasesuntil6radii(Figure26,Figure27,Figure28&Figure29).

Figure26:Horizontalcrosssection,YALESA3D-RAF1,TSR6,RotorOnly

Figure27:Horizontalcrosssecttiondifferences,YALES2A3D–RAF1,TSR6,RotorOnly

Figure28:Horizontalcrosssection,YALESPolars-RAF2,TSR6,RotorOnly

Figure29:Horizontalcrosssectiondifferences,YALES2Polars–RAF2,TSR6,RotorOnly

4.2.4. Conclusion ThestudyoftherotoronlyshowedthatArdema3Dgaveverysatisfyingresultsfor the studyof the farwake,whichwasnot expected for a vortexpanel code. ThecomparisontotheexperimentandtotheYALES2codeswhichhandlesbetterthefarwake,alsohighlightsomeimprovementthatcouldbe implementedonArdema3Dtoimprovethedescriptionofthefarwake. As for YALES2, the comparison with Ardema3D for the close rotoraerodynamicsispromising,eventhoughthedefinitionsofthecoefficientsofdragandlift could be improved to have a bettermatchon those coefficientswhenusing theforcesfromArdema3D.

4.3. Resultsforthefullgeometry

4.3.1. Simulations ThelistofsimulationisinTable4. Thecomparisonwillbedoneonlyonthewakesinceit iswheretheresultsoftheexperimentwerecollected.

Code Refinement Forces

Ardema3D - -

Table4:Listofsimulationforthecompletegeometry

4.3.2. TSR3 TheaxialinductionfactorhadbeencomparedwiththeexperimentalresultsinFigure30.

Figure30:AxialInductionFactor,CompleteGeometry,TSR3

For x/D=1, the two codes give very similar results and are also similar to theexperimental datawith a peak at the level of the nacelle (in Ardema3D, due to thewakedeficitmodel).This isaninterestingresultsincetheinductionperceivedbytherotor is mostly due to the near wake induction. For x/D=3 and 5, the results fromYALES2haveasimilardynamicscomparedtotheexperiment.However,forArdema3D,thedynamicsissimilarfortheblade(fory/R=0.1to1),butthevelocitydeficitdueto

thenacelleisnotverywelldescribe.Thewakedeficitmodeltosimulatethedynamicsof the nacelle is not enough for this simulation, andwill be an axis of evolution forArdema3D.

Figure31:VelocityField,TopView,TSR3

Figure32:VelocityFieldDifference,TopView,TSR3

Onthevelocityfields,therearesomedifferencesatthewalls,whichcomefromthefactthattheflowisviscousinYALES2andthatthereisonlyaviscouscorrectioninArdema3D. Moreover, there is an increase of the speed at the nacelle level inArdema3D,sincethere isnoboundary layer.Finally, thewake inArdema3D ishighlyinfluenced by the wake deficit model, while the effect of the tower is inherentlysimulatedbyYALES2(Figure31,Figure32,Figure33&Figure34).

Figure33:VelocityField,SideView,TSR3

Figure34:VelocityFieldDifference,SideView,TSR3

4.3.3. TSR6 Ardema3DandYALES2arecomparedtotheexperimentalresultsonFigure35.TheresultsforYALES2areveryclosetotheexperimentforthefarwake.InArdema3D,theresultsarebetterclosetotherotor,butthereisstillanissueatthenacellelevel,

due to thewakedeficitmodel use. There is also adissymmetry in theexperimentalresultswhichisalsofoundinthetwocodes,eventhoughindifferentform. Atx/D=5,Ardema3Dhasasteeperslope,duetotheinviscidtransportofthevortices.

Figure35:AxialInductionFactor,CompleteGeometry,TSR6

ThevelocityfieldsaresimilarasforTSR3;however,theeffectofthenacelleonthewakeislessimportantinArdema3D.Thewakeclosetotherotorissimilarinbothcodes(Figure36,Figure37,Figure38&Figure39).

Figure36:VelocityField,TopView,TSR6

Figure37:VelocityFieldDifferences,TopView,TSR6

Figure38:VelocityField,SideView,TSR6

Figure39:VelocityFieldDifference,SideView,TSR6

4.3.4. Conclusion Ardema3DandYALES2provideverygoodresultsonthisexperiment,bothforthedynamicsofthebladewiththecomparisonofrotoronlyandthedynamicofthewakewiththeexperiment.Itisgoodtonoticethatthevelocityiswelldescribedclosetotherotor,whichistheplacewheretheinductionofthewakeisthemostimportant.Eventhoughitwasn’texpected,thedescriptionofthefarwakeofArdema3Disverysatisfying. ForYALES2,themainaxisofimprovementshouldbethecalculationoftheAoA,whichisaprimaryimportanceforthecomputationoftheforcesofthebladesonthefluid. As for Ardema3D, a more stable scheme than the Euler scheme for theadvectionofthewake,butalsoamodelofthediffusionofthevortices,willgivemoreaccurate results for the far wake.Moreover, the wake deficit model has shown itslimitsintheNTNUexperimentandshouldbereplacedwithamoreaccuratemodel.

5. Validationoftheaero-elasticscode

5.1. Aero-elasticityformodernwindturbine

5.1.1. Introduction Themodernlargescalewindturbinearebecomingbiggerandbigger,withthelargestrotordiameterof180mfortheAD8prototypeofAdwen.Thematerialsusedforsuchbladesmustbelighter.Asaresult,thebladearemoreandmoreelastic.Thus,thereisaneedfornumericaltoolswhichtakeintoaccounttheelasticityoftheblade,henceprovidinganaero-elasticanalysisofthewindturbine. For designing a wind turbine, an aero-elastic analysis must on thousands ofDesignLoadCase(DLC),toensurethatthewindturbinewillnotbreakduringstandardoperation,butalsofordifferentscenarios,suchasveryhighwindspeedorimportantfailure. The stateof the artBEMmethodmaybe inaccurate for some scenarios, forexample for a flowwith a large spanwisewind, or for very elastic blades. The codeFARDEMAST, presented in section 2.6,may bemore accurate, thanks to the use ofArdema3Dfortheaerodynamicsmodule,thanAeroDyn,astateoftheartBEMcode. FARDEMAST has already been validated with one of FAST structural modelElastoDyn(presentedin5.1.2).Forthesecondpartofthemasterthesis,FARDEMASTwillbevalidatedwithamoreadvancedstructuralmoduleBeamDyn,allowingadegreeoffreedomintorsion.ThefourdifferentpossibilitieswithAeroDynorwithArdema3D,andwithElastoDynorwithBeamDynwillbecompared.It isacceptedthatforsimplecases like this one, the simple model AeroDyn and ElastoDyn is accurate. ThecomparisonwithmoreadvancedmodelArdema3DandBeamDynshouldinthesecasesgivesimilarresults,butformorecomplexDLCsandforbladeswithimportanttorsion,Ardema3DandBeamDynshouldbemoreaccurate. Thevalidationwillbedonewith theNREL5MWwindturbine [16],which isaprototypeofa5MWwindturbine,witharotorradiusof63m.Thiswindturbineisnotveryelastic,which is interesting for validation, since theBEMmodel is known tobevalid for more rigid blades. No experimental data were available, therefore thecomparison is only done with AeroDyn and ElastoDyn, which was validated by theNREL.

5.1.2. Structuralmodel The structuralmodel for the coupled aero-elastic codes FAST or FARDEMASTcanbeeitheramodalrepresentation(forElastoDyn)ortheGeometricallyExactBeamTheory(GEBT)(forBeamDyn).

Themodal representationof theblade isconsideringthat therearenoraxial,norshear,nortorsionaldeformations.Thus,onlyflapwiseandedgewisedeformationsaretakenintoaccount.Furthermore,thesolutionofthemomentumequationisgivenbyasuperpositionofthelowestmodes.Theshapesofthemodearecalculatedbeforethe simulation with another tool developed at NREL. This is the model used inElastoDyn,withthe5lowestmodes(themaximumnumberofmode). TheBeamDynisusingtheGeometricallyExactBeamTheorywhichissolvingthemomentum equation using the Beam approximation (validated for the blades of awindturbine).Itisafinite-elementsolver.Thismethodgivesadeformationintorsionoftheblade,whichisinterestingfortheaero-elasticitystudy,sinceitwillchangetheangle of attack of the section.Moreover, there is a possibility of coupling betweendifferentmodesthatcouldnotbemodeledinElastoDyn. However,withthismodel,nodeformationofthesectionsistakenintoaccount.Indeed, thedeformationof theprofilewill change thepolar curve,which cannotbedoneeasily. Themodel forBeamDyn isusedonly for theblades. ItstillusesElastoDynforthedeformationofthetowerandforimposingtherotationtotheblades.

5.1.3. Aero-elasticstudy In this section, the important parameters for the aero-elastic analysiswill bepresented.

5.1.3.1. Deformationoftheblade Thefirstthingtolookatisthedeformationoftheblade.Thisdeformationwillbelookedatthetipoftheblade.Itwillbeintermoftranslationaldeflectionoutoftheplaneofrotation(alongthewindaxis,x),whichisthebladebendingwiththewind;intermoftranslationaldeflectionintheplaneofrotation,whichisduetothetangentialforceandtheweight;andintermofrotationaldisplacementalongthebladeaxis. The rotational deflection along the blade axis is actually the torsion of theblade. It is a parameter of significant importance since the torsion of the bladewillresult in a change of angle of attack, and thus to different values of lift and dragcoefficient.ThisparameterisnotmodeledwithElastoDyn,whichexplainwhytheuseofBeamDynonFARDEMASTmustbevalidated. These parameters are looked at in term of time series and of Fast FourierTransform(FFT)forthefrequencyanalysisforthetorsion.

5.1.3.2. Equivalentloads Since the simulation time is limited to 750s, it is important to be able toquantifytheloadsthattheturbinewillexperienceduringitslifetime.Inordertodoit,theequivalentloadsarecalculatedforeachvalue. Theequivalent load isasingle loadamplitudeatagiven frequencyof1Hz inthiscase.Ifthisequivalentloadisappliedtothestructureduringacertaintime,itwilldamage the turbine asmuch as theoriginal load signal that contains a full rangeofdifferent frequencies. Thus the equivalent loads are containing the information thatcanbeobtainedintheFFT. Theequivalent loadswill be computed for the rotor thrust, the rotor torque,butalsoontheforcesatthebladeroot. Therotorthrustandtherotortorqueareparametersthattakeintoaccountallthephysicsinthewindturbine.Hence,thereareusedtohaveanoverviewofthewindturbine. Theforcesatthebladerootconsideronlytheforcesononeoftheblades.Theblade rootmomentalong the z axis is the torsionalmomentof theblade, thereforelinkedtothetiprotationaldeflectionintorsion.

5.2. Simulationparameters

5.2.1. Simplification Afewsimplificationsweremadeforthesimulations. Ardema3Dconsidersan inviscidflowandthen itusesacorrectiontomodelaviscousflow.Thiscorrectionisdonebychangingtheliftanddragcoefficients.Yet,themomentcoefficientisnotcorrectedandisinviscid.ItwasnotanissuewithElastoDyn,since therewasno torsion,but it iswithBeamDyn.Thus, themoment coefficient inFAST was changed to the inviscid moment coefficient obtained in Ardema3D.Nonetheless, there is still a dynamics stallmodel for themoment coefficient that isusedinFAST,butnotinFARDEMAST. Inwindturbine,betweentherotorandthegenerator,thereisadrivetrain.InFAST,theeffectofthetorsionofthisdrivetraincanbeenabled,asaresult,addingaperturbation intherotorspeed.However,whenusingBeamDyn,this torsioncreatesinstabilities. Itcanbeavoidedbyreducingthetimestep,butthecomputationaltimestartstoskyrocket.Asaresult,thisdegreeoffreedomofthedrivetrainwasdisabled. Moreover,theeffectofthetoweronthewake(suchaswiththewakedeficitmodelfortheNTNUwindturbine)wasnottakenintoaccount,neitherinFARDEMASTnorinFAST.Despitethattheaerodynamicsloadsonthetowerarestillcalculatedforthedisplacement.

Duringthemasterthesis,asensitivityanalysishasshownthattheoptimaltimestepis0.02sforElastoDynand0.01sforBeamDyn.However,Ardema3Dcannotberunat such lowtimesteps forcomputational time reasons.A sensitivity studywasdoneand the best time step forArdema3D, in termsof computational time, stability andconvergence of the results, is 0.08s. As a result, the simulation is done with twodifferent time steps, and Ardema3D is called every 4 or 8 time step of respectivelyElastoDyn or BeamDyn. For the time step were Ardema3D is not called, theaerodynamicsloadsarekeptconstant.ThisdoubletimestepisnottakenintoaccountwithAeroDynwhichusesthetimestepofthestructuralcode.

5.2.2. Simulations ThesimulationsthatwererunarelistedintheTable5. Allthesimulationswererunfourtimes:

• WithAeroDynandElastoDyn(referredas“AD-ED”,inorange)• WithArdema3DandElastoDyn(referredas“A3D-ED”,inturquoise)• WithAeroDynandBeamDyn(referredas“AD-BD”,inred)• WithArdema3DandBeamDyn(referredas“A3D-BD”,inblue)

The constantwind speed is at10m/sand the turbulentwindwasgeneratedusingTurbSim,acodethatcanbeusedinFASTforgeneratingwind[17].Theturbulentwindhasanaveragevalueof10m/s,withaturbulentintensityof18.34%andashearfollowingapowerlawof0.11,whicharethestandardvaluesforoffshoreconditions.The10m/sistheratedwindspeedoftheNRELwindturbine,thus,thesearethewindconditionswherethewindturbineisthemostheavilyloaded.Theturbulentwindis,ofcourse,thesameforthe4simulations. ThecontrollerCardasyscontrolsthepitchangle(angleofthebladetothewind)andthegeneratortorque(whichwillbesettokeepaconstantrotorspeedof12rpm).This enables to keep a constant power production for 10m/s to 30m/swind speed.Whenthecontrollerisused,thereisastart-upofthewindturbine,whichtakes300sinthiscase,thusasimulationof750s,inordertohave450sofsimulationforcomputingtheequivalentloads.Withoutthecontroller,thepitchangleissetto0°andtherotorspeedissetto12rpm,whichgaveaTSRofalmost8. Fortheconstantwindspeed,thecomputationoftheequivalentloadswasnotrelevant, since the solution is converging toa steady state,andwas replacedby themeanvalueovertwoturns(10s).Fortheturbulentwind,withoutcontroller, the last150swereusedtocomputetheequivalentloadssincethefirst100sareusedtogetridofnon-physicaltransientphaseduetomodelsinitialization.

Name Wind Controller SimulationTime

ComputationalTime

ConstantWind

Constant, uniform,10m/s

None 100s AD:3.9minA3D:1.1h

TurbulentWind

Turbulent,10m/s None 250s AD:8.8minA3D:3.3h

Start-up Turbulent,10m/s Cardasys 750s AD:58minA3D:8h

Table5:FARDEMASTandFASTSimulations

Asforthecomputationaltime,sameasfortheNTNUcase,thenumberofCPUsusedisnotrecordedandmayvary,dependingontheactivitiesoftheday.Asaresult,the computational time is more of an indication than an accurate data. Thecomputational time does not seems to be changed with the use of ElastoDyn orBeamDyn.ItwasexpectedtohavesuchdifferencebetweenAeroDynandArdema3Dincomputationaltime,duetothefactthattheBEMmethodsarenotsolvingaflow.

5.3. ConstantWind The constantwind analysis shouldpresent the samedynamics forArdema3Dand AeroDyn, and for ElastoDyn and BeamDyn, with only small differences in thevalues.Iflargedifferencesareobserved,itmeansthatthereisabuginthecode,andthatitshouldbesolvedbeforestartingwithturbulentwind. For a constant wind the wind turbine state will converge to a steady state,therefore,thesimulationcanbeshort,andthereisnoneedforacomputationoftheequivalentloads,sincetheloadsareconstant. Itisimportanttolookattherotortorque(Figure40,top)andtherotorthrust(Figure40,bottom)intimeseriessincebothvaluearecomingfromtheintegrationofthe forceson thewhole rotor,hence it ispossible toseequickly if thereweresomeissueduringthesimulation.Here,bothvaluesconvergetoasteadystateasexpected.

Figure40:RotorTorque(top)andThrust(bottom)forconstantwind

Thedeformationsoftheblade(Figure41)aresimilarforallsimulationwiththesame dynamics for ElastoDyn and BeamDyn and very little differences betweenArdema3DandAeroDyn.Thedeformation in torsion isnullwithElastoDynsince it isnot modeled. Hence, BeamDyn and Ardema3D seems to be well integrated in thecode.

Figure41:Deformationintranslationalongx(left),y(middle)andtorsion(right),forconstantwind

With the results in Figure 42, themean value for the rotor torque, the rotorthrust and the forces at the blade root are very similar, with less than 5% ofdifferences. Moreover, there is approximately the same difference betweenArdema3DandAeroDynfortheuseofElastoDynorBeamDyn,whichmeansthatthestructural model has not a huge impact on the aerodynamics model. The largedifferencefortheBladeRootMzisonlyanartifactduetooscillationsaroundzero.

Figure42:ConstantWindmeanvalue(fromlefttoright:RotorThrust,RotorTorque,BladeRootFx,Fy,Fz,Mz)

In conclusion, the results of the constantwind are very satisfying since evenwith a different aerodynamicsmodule and structuralmodule, thedifferences are oflessthan5%.Moreover, it is importanttoseethatthedifferencesbetweenAeroDynandArdema3DareindependentfromElastoDynorBeamDynandviceversa.Thefirststepwithaconstantwindwasnotintendedtoshowphysicaldifferencesbetweenthe

different structural and aerodynamic solvers, but to ensure that the latters areproperly implemented. The good agreement observed with the different casesconfirmsit.

5.4. Turbulentwind

5.4.1. Generalparameters Theturbulentwindcaseneedsmoreanalysissincethesolutionswillnotreachconstantvalues.It is importantthereforetolookatthetimeseries, inordertomakesurethattheglobaldynamicisthesame,butalsotolookattheFFTsinordertomakesurethatthemainfrequenciesproducedarethesame.It isexpectedthattheuseofBeamDyn will produce more frequencies since more phenomena are taken intoaccount.Thefrequencieshighlightedintheplotare:

• 0.2Hz,whichiscorrespondingtothefrequencyofrotation,called“1p”• 0.4Hz,whichiscalled“2p”• 0.6Hz,whichis3timesthefrequencyofrotation,called“3p”.Thisisoftenthe

most important frequency and is resulting from the symmetry of the threebladeofthewindturbine

• 12.5Hz,whichisequalto1/0.08s,whichisthetimestepofArdema3D.Beyondthat frequency the results are irrelevant since Ardema3D is not called. ThemainEigenFrequenciesof theNREL5MWare ranging from0.6 to9Hz, asaresult,thefrequencyof12.5Hzisenough.

TherotortorqueandthrustareplottedinFigure43,withthehorizontalwindspeed at the hub level. There are no important differences between the foursimulations and the forces are following well the variation of the wind speed. Thetransientpartatthebeginningofthesimulationdoesnothaveanyphysicalmeaning,which iswhythe loadsarecomputedonlyafteracertaintime. It isalsothetimeforArdema3Dtodevelopafullwake.

Figure43:Timeseries,WindSpeed(top),RotorTorque(middle)andRotorThrust(bottom),turbulentwind

The FFTs of the rotor thrust and rotor torque are in Figure 44. The lowfrequenciesarethesameandtherearemorefrequenciesasexpectedwithBeamDyn,duetoamoreadvancedmodel.The3ppeakispresentinallthesimulation,whichisexpectedduetotherotationofthethreeblades.TherearetwoimportantpeaksintherotortorqueusingBeamDyn,whichmaybeduetothetorsion.ThepeaksarehigherwithAeroDyn,and itmaycomefromthehigheroscillationsduetothedynamicstallmodelforthemomentcoefficient.

Figure44:FFTs,RotorThrust(left)andRotorTorque(right),turbulentwind

5.4.2. Deformations The deformations at the tip in translation for the turbulent wind are verysimilar(Figure45).However,thedeformationintorsionisdifferentbetween50sand100s(Figure46).IthasbeenfoundoutthatitcomesfromthedynamicstallmodelinAeroDyn,whichisnotmodeledinArdema3Dyet.Thedeformationscomethenfromacouplingbetweentheaerodynamicsandtheelasticityoftheblade.

Figure45:TranslationalDeformation,alongx(left)andy(right),turbulentwind

Figure46:Torsionaldeflectionatthetip,turbulentwind

5.4.3. EquivalentLoads Theequivalentloadshavebeencomputedforthelast150softhesimulation,inorder to get rid of the transient phase. However, it a small amount of time forequivalent loads, and some issues may be due to that. The usual duration forengineeringstudiesis600s.TheequivalentloadsarepresentedinFigure47.

Figure47:Equivalentloads,fromlefttoright:rotorthrust,torque,BladerootFx,Fy,Fz,Mz,turbulentwind

Thedifferencesareverysmallandthereareverysimilartotheconstantwindcase.Theresultsareverysatisfying.The importantdifference isduetothemodelofdynamicstallthathasnotbeenimplementedinArdema3D.However,thedifferencesare very large for the Blade RootMz, and therefore this is an important model toimplementinArdema3D.

5.5. Start-up:turbulentwindwithcontroller

5.5.1. Generalparameters Thestart-uptestcaseisveryinterestingbecauseitisoneofthecasesthatareusedforthecertificationofawindturbine.ThevalidationofFARDEMASTonsuchkindoftestsisamustfortheuseofthecodeinbladedesign. Thissimulationisdifferentfromthetwoothers,duetotheuseofthecontrollerCardasys.Thiscontrollerischangingthepitchangleoftheblade,whichwillchangetheangleofattackandthereforeincreasingordecreasingtheamountofenergyextractedfrom thewind, but also the generator torquewhichwill alter the rotation speed tokeeptheaconstantpowerproducedbythewindturbine. Therefore,inthistestcase,thetimeseriesarelessimportantthanpreviously,duetotheuseofthecontrollerwhichwillforcetheturbineintoonemode.Forthese

simulations,theequivalentloadsaretheimportantresults,sinceitistheseresultsthatwillbeconsideredforthedesignofthewindturbine. Thewindspeed,thepitchangleandtherotorspeedareinFigure48.Thisisastart-up case, therefore, the pitch angle starts at 82° in a position where the windturbineisstopped,andslowlygoesto0°tostartproducingpower.Thepitchangleisincreasingfromtimetotimewhenthewindistoostrong. The rotor torque and the rotor thrust are in Figure 49. There are strongeroscillationsusingAeroDyn,thanwithArdema3D.Itwasexpectedduetotheinertiaofthe wake that is not present in AeroDyn and that will cause Ardema3D to havesmoother reaction to quickwind speed variations.Nevertheless, the overall value issimilar.

Figure48:Timeseries,WindSpeed(top),Pitchangle(middle)andRotorSpeed(bottom),Start-up

Figure49:Timeseries,RotorTorque(left)andRotorThrust(right),Start-up

5.5.2. Deformations As for the deformations, the translational deflections are similar for the foursimulations (Figure50).As for the torsion, there is adifference like in the turbulentwindcaseduetothedynamicstallthatwasnotmodeledinArdema3D(Figure51).

Figure50:Timeseries,Translationaldeflectionatthetipofthebladealongx(left)andy(right),Start-up

Figure51:Timeseries,Torsionatthetipoftheblade,Start-up

5.5.3. EquivalentLoads The equivalent loads were computed for 450s of simulation. For thecertificationofawindturbine,the loadsarecomputedon600s,however, itwasnotdonehere,sincethestart-upistaking300sduetoahighturbulentwindspeedatthebeginningofthesimulation.Withotherturbulentwinditoftentakesabout150s.

Figure52:Equivalentloads,fromlefttoright:rotorthrust,torque,BladerootFx,Fy,Fz,Mz,Start-up

The results (Figure 52) arenot surprising after the studyof the constant andturbulent wind. The difference on the blade root momentum along z highlightsanother issuewith the torsionmodel. Indeed, the time series of the blade rootMz(Figure 53) shows very intense oscillations at the start-up. These oscillations appearonlywhenthepitchanglevaries.ThiscomesfromthemodelinBeamDyn. For a realwind turbine, once the controller has computed an angle of pitch,thereisamotorthatapplyatorqueontherootofthebladetomakeitturn. In ElastoDyn, since the torsion is notmodeled, the blade takes instantly thenewpitchangle. However, in BeamDyn, the pitch angle is only applied instantly on the firstsection, therefore, there is an important torsionbetween the first two sections, likewithaspring.Itwillthuscreatetheseimportantoscillations. TheoscillationsareevenlargerwithAeroDyn,duetothemodelofthedynamicstall.

Figure53:Timeseries,BladerootMomentumalongz,Start-up

5.6. Conclusion Thegoalof thestudywastovalidatethestructuralmodelBeamDynwiththeuseofArdema3D,butalsotofindwherethecodecouldbeimproved. This studywas very interesting since it has highlighted important differencesbetween the different models. The model of the dynamic stall for the momentcoefficient was shown to be very important for the coupled code using BeamDyn.Moreover,issueswiththestructuralmodelwithBeamDynhavebeendiscovered. Still,theresultsaresatisfying.Thedifferencesbetweenthetwocodesarenotsolargeandtheywillbereducedwiththecorrectionoftheissuesthatwerepointedout.Moreover,thedifferencesseemtobeindependentofthecoupling,withthesamedifferencebetweenArdema3DandAeroDyn,usingeitherElastoDynorBeamDyn. Nevertheless, differences of 5% will result in important differences for thedesign of the blade (for example in terms of costs or solidity of the materials).Therefore,itisveryimportanttohavethemostaccuratemodelandtocompareittoexperimentalresults.

6. Conclusion Ardema3D and the coupled code FARDEMAST are still under developmentinside the INWIT project which will continue until the end of 2018. In this masterthesis, the codes have been compared to other codes and they have producedsatisfying results.With thecomparison to theNTNUexperiment, thewakemodelofArdema3Dhasbeenshowntobeaccurate,eventhoughvortexpanelmethodsarenotsupposedtogiveagooddescriptionof the farwake.And,with thecomparisonwiththecoupledcodeFAST,FARDEMASThasprovidedsimilarresults. Still, a comparison with experimental data should be done to validate themodel. Inorder tobeable to compare FARDEMASTwith amodern large scalewindturbine,Ardema3Dmustbeprovidedwithagoodmodelofwakedeficittomodeltheeffect of the tower, better than the one used for the NTNU comparison; andFARDEMASTmusthaveagoodstructuralmodelthatcanbecoupledwithArdema3D,suchasBeamDyn. Moreover,oneofthefuturechallengesofArdema3DandFARDEMASTwillbetobebetterthanaBEMcode.Indeed,fornow,therearenotestcasesthatthevortexpanelmethod is solvingbetter thantheBEMmethod. It isnotobviouswith thetestcasedoneinsection5,sincethewindturbineisveryrigidandthisisacasewheretheBEMisusuallyvalid.However,therearecertainDLCswheretheBEMisknowntofail.TheseDLCsshouldbesimulatedwithArdema3DandFARDEMASTandbecomparedtoexperimental results, inorder toprove thebenefitsofusingavortexcodedespiteahighersimulationcost.

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multi-physicsfluiddynamics,"2018.[8] J.M.Jonkman,FASTUser'sGuide,NREL,2005.[9] L.Beaudet,"Modélisationdeséoliennes,"inUniversitédePoitiers,2013.[10]H. Glauert, Aerodynamic Theory, The Journal of the Royal Aeronautical Society,

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Appendix:Ardema3DWake The wake in Ardema3D is represented by the dipole panels with a colordependingontheirstrength.OnFigure54,after200mthewakestartstodegenerateduetotheadvectionscheme.ThesimulationisdonefortheNREL5MWwindturbine.

Figure54:Ardema3Dwake

Figure55:Ardema3Dwake,panelsclosetotherotor

validation of a vortex panel method for aerodynamics and …1198230/...2 master of science thesis...

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