Numerical and experimental analysis of the flow around a two-element wingsail at Reynolds number 0.53 × 106

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Eprints ID: 16666

To cite this version: Fiumara, Alessandro and Gourdain, Nicolas and Chapin, Vincent and

Senter, Julien and Bury, Yannick Numerical and experimental analysis of the flow around

a two-element wingsail at Reynolds number 0.53 × 106. (2016) International Journal of

Heat and Fluid Flow, vol. 62. pp. 538-551. ISSN 0142-727X

Numerical

and

experimental

analysis

of

the

flow

around

a

two-element

wingsail

at

Reynolds

number

0.53

×10

6

Alessandro Fiumara

a,b,∗

_{, Nicolas Gourdain}

b

_{, Vincent Chapin}

b

_{, Julien Senter}

a

_{, Yannick Bury}

b a Assystem France, 13, Rue Marie Louise Dissard, 31024 Toulouse, France

b ISAE Supaéro, 10, Avenue Edouard Belin, 31400 Toulouse France

Keywords: Wingsail High lift Two-element Wind tunnel Experimental data Unsteady RANS

a

b

s

t

r

a

c

t

Therigidwingsailisapropulsionsystem,utilizedinsailingcompetitionsinordertoenhancetheyacht performance inbothupwind anddownwind conditions.Nevertheless, thisnewrig is sensitiveto up-streamflowvariations,makingitssteeringdifficult.Thisissuesuggeststheneedtoperformastudyon wingsailaerodynamics.Thusthispaperreportssomeinvestigationsdonetobetterunderstandtheflow physicsaroundascaledmodelofanAmerica’sCupwingsail,basedonatwo-elementAC72profile.Firsta windtunneltestcampaignwascarriedouttogenerateadatabaseforaerodynamicphenomenaanalyses andCFDvalidation.UnsteadyRANSsimulationswereperformedtopredictandvalidatetheflow charac-teristicsonthewingsail,inthewindtunneltestconditions.Thewindtunneldomainwasfullymodeled, inordertotakeintoaccountthefacilityconfinementeffects.Numerical simulationsinfreestream and windtunnelconditionswerethencomparedwithexperimentaldata.Thisanalysis showsthenecessity toconsiderthewindtunnelwallswhenexperimentalandnumericaldataarecompared.Numerical sim-ulationscorrectlyreproducetheflowfieldforlow-to-moderateflowangles.However,discrepancieson thepressuredistributionincreasewhentheboundarylayerstartstoseparatefromthewingsail.Inthis regard,the flowgeneratedbytheslotbetweenbothelements ofthe wingsailisofparamount impor-tance.ThisslotflowisanalyzedindetailsthroughPIVmeasurementsandnumericalsimulations.While thenumericalsimulationcorrectlypredictsthejetflowitself,itonlypartiallyreproducestheinteraction betweenthejetflowandthemainflow,especiallyathighangleofattacks.Moreprecisely,thenumerical simulationfailstopredictthecorrectjetflowtrajectory,whichaffectstheliftcapabilitiesoftheentire wing.Theinfluenceofthewingsaildeformationduringexperimentalcampaignshasbeeninvestigatedto explainthisbehavior.

1. Introduction

Wingsailsareincreasinglyusedinsailingcompetitionto substi-tuteconventionalsoftsails.Thisnewrig,joinedtofoils,allowsthe yacht to achieve better performance. However, at the same time sailorsmayhaveproblemscorrectlysettingandmaneuveringthe wingsailinallsailingconditions.Somespectacularanddangerous capsizesoccur duringthe last editionof theAmerica’s Cup com-petition, due to this issue. To date, the global performance en-velope of wingsailsis not completely understood sincethe aero-dynamic phenomena have not been fully investigated. Moreover, the navalenvironment introducessome perturbations (like atmo-spheric boundary layer andupstream turbulence) that should be

∗ _{Corresponding author at: Assystem France, 13, Rue Marie Louise Dissard, 31024} Toulouse, France.

E-mail address: afiumara@assystem.com (A. Fiumara).

takenintoconsideration.Furthermore,theaerodynamic character-ization hasbecome increasingly important after the introduction offoils,allowingthe catamaranto“fly” onthesea(Fig.1). With-outsufficienthydrodynamiclift,significantyachtdecelerationcan occur,therebymakingtheresearch ofstablenavigationconditions essential.

Typically,wingsailsarecomposedofamainelementandaflap, setina waytoobtainmaximumperformancesonthewater.Due tohighflapdeflectionanglevariations(from15° to40°)duringthe navigation,theflow around a wingsail presentssome similarities withtheflow around an aeronauticalwingin high-liftcondition. Thisanalogyexplainswhysailorshavealreadydrawnonthe aero-nauticalknow-howto enhancethewingsailperformance, likethe slottedflap.Unfortunately, the wingsail designimposes some re-strictions;forexample,to reduce theweight ofthe wingsail, the flapmechanism is based ona unique rotation while,on aircraft, theflaphasmorecomplexkinematics.Thisconstraintreducesthe

Nomenclature

α

Angleofattack

γ

Intermittencyfactor

δ

Flapdeflectionangle

δ

BL Boundarylayerthickness



Differenceforparametersestimations

BL BoundaryLayer

c Chord

c1 Mainelementchord

c2 Flapchord

CD Dragcoefficient

CL Liftcoefficient

Cp Pressurecoefficient

FSNS FreeStreamNumericalSimulation

g Gapdimensionoftheslot

H Wingsailheight

k Turbulentkineticenergy

ISAE InstitutSupérieurdel’Aéronautiqueetdel’Espace

l Localdistancefromthewingsurface

L.E. LeadingEdge

LLSB Laminarseparationbubblelength

LSB Laminarseparationbubble

o Overlapdimensionoftheslot

PIV ParticuleImageVelocimetry

RANS ReynoldsAveragedNavierStokes

Re Reynoldsnumber

Reϑ MomentumthicknessReynoldsnumber

T.E. TrailingEdge

U Velocitycomponentinthefreestreamdirection

U_∞ Freestreamvelocity

V Velocitymagnitude

WTNS WindTunnelNumericalSimulation

WTT WindTunnel(experimental)Tests

x,y,z Axesofthewingsailreferencesystem XLSB x-coordinateofthelaminarseparationbubble

xrot x-coordinateoftheflaprotationaxis

xv,yv,zv Axesofthewindtunnelreferencesystem

yF ypositionofflapL.E.

y+ Dimensionlesswalldistance

z∗ Normalizedheightpositionz/H

abilitytocorrectlysettheslotsize.Furthermore,theneedtotack frombothcatamaransidesconstrainsthewingsailtotheusageof onlysymmetricairfoilswhichhavealower performancethanthe asymmetriconesnormallyusedinaeronautics.

Only few experimental works exist today (e.g. Turnock et al., 2014; Blakeleyetal., 2012)anda descriptionofflow phenomena israrely proposed. Blakeley’s work hasalso shown theinfluence oftheflapdeflectionangleandtheslotsizeonmulti-element air-foilperformances(Blakeleyetal.,2015).Additionally,anexhaustive windtunnelcampaignwasperformedby Violaetal.(2011)forthe aerodynamicscharacterization of soft sailsin upwind conditions, butacomparableanalysisonwingsailsstilldoesnotexist.

Toclosethisgap,anexperimentalcampaignwassetonascale model of an America’s Cup AC 72 wingsail in the ISAE-Supaero windtunnelfacility.Oilsurfaceflowvisualizationsandparticle im-agevelocimetrytestswereperformedduringthewindtunnel cam-paignto describethecharacteristics ofthe boundarylayer transi-tion,both onthe main andon theflapelements, andto investi-gatethe physics of the flow inthe slot. The aimwas to provide a description of the flow features over a two-element wingsail, trackingthemostsensitiveandcriticalzonesintheflowfieldand tounderstandtheabilitiesoftheRANS approachtomake

numer-Fig. 1. America’s Cup catamaran AC72 propelled by wingsail foiling in the Bay of S. Francisco (photograph Carlo Borlenghi).

H = 1.8 m

Reroot = 6.4×105

Retip = 2.9×105

g = 6 mm

xrot/c1 = 95%

Fig. 2. Geometry of the wingsail with its main parameters.

ical predictions.Bothlow and highflapdeflection angle configu-rations were analyzed, corresponding respectivelyto upwindand downwindsettings.Reynoldsnumberonthescalemodelinwind tunnelconditionsis0.53_{× 10}6_{,20timessmallercomparedto}

ac-tualAC72wingsailsduringnavigation(Collieetal., 2015). Never-thelesssmallerwingsailsarecurrentlyusedonC-classcatamarans (Re₌0.8_{× 10}6_{),inthe“littleAmerica’sCup” competition.}

Inthefirstsectionofthispaperanewmethodologyisproposed to reproduce the wind tunnel domain and its validation is pre-sented.Thesecondsectioncomparestheresultsofnumerical sim-ulations(basedonunsteadyRANS)inwindtunnelandfreestream conditions,withtheexperimental database.Numericalpredictions are thenfurther investigatedby comparisonwithoil flow visual-izations, toemphasize the role oflaminar toturbulent transition andboundarylayer separations.Finally,a physicalanalysisofthe jetflow isdoneby comparingthenumericalvelocityscalarmaps andthenumericalsolutionwiththePIVdataanddiscussedinthe thirdsectionofthepaper.

2. Experimentalmethodology

A wingsail scalemodel ofthe America’s Cupclass AC72 was designedandusedforthetests(Fig.2).Itiscomposedoftwo ele-ments, themain element andthe flap,divided by aslot through which the air can flow. The flap can be set at different angles, pivotingonits axislocatedat95%ofthemain axis.The two

ele-st. 1 st. 2 st. 3 st. 4 st. 0 st. 5 zV xV x z XV/C = 0 XV/C = 2.40 XV/C= 4.34 XV/C = 8.00 XV/C = 20.00 XV/C = -13.46

duct shape: elliptical duct section: 3m×2m

duct length: 2 m vmax: 42 m/s

Fig. 3. Scheme of the S4 wind tunnel facility and main parameters.

mentsarecomposedbyNACAsymmetricalairfoils,allowing wing-sailtackingfrombothsides.

Pressureportshavebeensetonthreesectionsofthemain ele-ment(respectively)locatedat25%,50%and75%ofthewingspan. The pressure sensorused forthe measurement is a temperature correctedscanwitha+/−5kParangeandanaccuracyof+/−0.15%. The wind tunnel used for the experimental campaign is the S4 facility ownedby “Institut Supérieur de l’ Aéronautique et de l’ Espace” ISAE-Supaero in Toulouse,an open returnwind tunnel withopentestsection (Fig.3).Theduct hasanellipticalshape of 3m_{× 2}m.Theflowiscreatedbytheaspirationofthreefandrives of90kWeach,locatedattheendofthediffuser(st.5in Fig.3).

The maximum speed in the duct is 42m/s. To eliminate low frequencyoscillationsinsidetheduct (inherenttosuchopen loop configurations), a gap wascreated inthe first section of the dif-fuser (st. 4). In doing so, the oscillations are dumped by the creation of a secondary flow, exterior to the diffuser, which re-circulates air from the gap to the intake of the diffuser itself (st.3).

Thewingsailmodelwasmountedverticallyintheduct(st.2)on arotatingplatethatallowsadjustingtheangleofattack.Toreduce theinteractionsbetweenbalanceandthewingsail,adiskplatform wasposedatthebaseofthewingscalemodel.

The aerodynamic forces are estimated with a six-component balance.The maximumloadsbearableby thebalanceare 2.40kN for the longitudinal force, 3.00kN for the transversal force and 0.50kNmfortheheelingandthepitchingmoments. Fig.3details thetwo referencesystemsused inthispaper.The firstoneisthe duct system (xv,yv,zv), whose originis located at the end ofthe convergent section in correspondence to the symmetry plane of theductandatthebottomoftheconvergent.Thex-axisisinthe convergent-diffuserdirectionwhilethez-axisisdirectedupwards. The wingsailreferencesystem(x,y,z) istranslatedtothe previous oneinawaythattheoriginislocatedontheleadingedgeofthe wingroot section, keepingits positionin thesymmetry plane of theduct(x=xV+2.4c,y=yv,z=zV+0.022H).

3. Numericalmethodology

Theextentofseparatedregionsonwingsailsurfacemaybe rel-evanttoprefer LargeEddySimulations (LES)that aresupposedto bethemostadaptedmodelingintheseflowconditions. Neverthe-lessbecause of thehuge computingcost of LES andofthe large

numberofconfigurationstobestudied,itwasdecidedtouse un-steadyRANSforallnumericalsimulations.Thechallengewillbeto obtainthebestresultspossiblewiththismodel.

Numericalsimulations were performedtoreproduce thewind tunneltestconditionsonthewingsail scaledmodel.Thewingsail geometrywas numerically reproduced in both the low andhigh flap deflection angle configurations recreating at the same time theinterface diskon thewingroot. Becauseof thelow Reynolds number,basedonthemeanchordofthewingsail(Re=0.53× 105_),

thetransitioneffects havealsobeenconsidered bytheuseofthe transitionmodel

γ

-Reϑ.Thismodelwasproposedby Menteretal. (2004a, b),based ontwo transportequationsmodeling the inter-mittencyfactor

γ

andReϑ inturbulentk

ω

-SSTmodel.

Twoapproacheswere tested forthewingsail environment: 1) aclassicalapproachwithfreestreamconditions(theperturbations induced bythe windtunnel wallsare neglected)and2) an envi-ronmentintegratedapproach wherethe fullwind tunnel domain istakenintoaccount.

3.1. Wingsailinfreestream

Thefreestreamdomainconsideredisabox:lengthL₌31c(12c upstreamthewingand28cdownstream),widthl=40candheight h=2H(Fig.4),withcthewingsailrootchordandHthewingspan. Thewingsailisassumedtocontactthebottomsurfaceofthebox (norootleakageflow).

The referencesystem has the same characteristics asthe one describedfor the wind tunnel domain,i.e. the originlies on the leadingedgeofthemainrootsection,thex-axis hasthe leading-to-trailingedgedirection,thez-axisisdirectedupward.Theentire domain wasmeshed using a polyhedral mesh with prism layers onthewingsurface.Theboundaryconditionsimposedonthebox are:

• Velocityinlet:ontheinlet,leewardandwindwardandtop sur-faces;

• Pressureoutlet:ontheoutletsurface; • Slipwall:onthebottomsurface.

Thesettingschosenforthewingsailare(Fig.5):

SET1:flapangle

δ

=15° andinletflowangle

α

=0°;

SET2:flapangle

δ

=25° andinletflowangle

α

=0°.

The simulations were run using the unsteady RANS approach withthek-

ω

SSTturbulencemodeland

γ

-Reϑ transitionmodel. 3.2.Windtunnelmodeling

Theboundaryconditioninteractionwiththewindtunnelwalls fora high-liftconfigurationisawell knownproblem,asreported in Rogers et al. (2001) and Nayani et al. (2015). Since it is dif-ficult to determine the flow characteristics inside a wind tun-nel, directly with measurements, a CFD-based database and ex-perimental database are becoming increasingly necessary in or-dertohavea simpleestimationoftheaerodynamicsandtohave an accurate flow description during the wind tunnel tests. This field of investigation is paramount for the fluid dynamics com-munity; recent studies have reported investigations done to cor-rectwindtunnelmeasurementsandimprovedextrapolation tech-niques to free flight conditions (Melber-Wilkending and Wich-mann, 2007; Melber-Wilkending and Wichmann, 2009; Ciobaca et al., 2013). These works showed the wind tunnel influence on thewing, by increasingthe effectiveangleofattack compared to freestreamconditions.Inthecaseofsoftsailconfigurations, Viola etal.(2013) also suggestedtaking intoaccount forwind tunnels effects.Inthiscase, afirstsimulationwascarriedouttoestimate

Inlet Outlet Windward Leeward 28 c 20 c 12 c 20 c

Fig. 4. Box domain and mesh section for the freestream simulation.

Fig. 5. Lateral view of the wingsail and sections at half wingspan for Set1 (top) and Set 2 (bottom) configurations.

theblockage of thewind tunnel equippedwhen withthe mock-up.Theextractedvelocityfieldwasthenusedasaboundary con-dition(avoiding anyconsiderations offull windtunnelduringthe numericalsimulationof thesail). Inthe analysisreportedin this paper,thenumericalmodeling oftheS4 facilitywascomplicated notonlybytheblockage ofthewindtunnelbutalsobyits ellip-ticalshapeandtheopenwindtestsection,introducingsignificant modificationsintheflowfield.Forthisreason,theentirewind tun-nelgeometryhadtobereproduced,asalreadyshownby Fiumara etal.(2015).

The wind tunneldomain was createdreproducing at firstthe convergent and diffuser geometries (Fig. 3). The difficulty is to properlyclosethe duct zone inorder tomake the domain avail-ableforthenumericalsimulation.Initiallytheductwasclosed us-ingaloftsurfacefromtheconvergentendsection(st.1in Fig.3)to thediffuserintakesection(st.3in Fig.3).Howeverthistechnique didnotleadtoaproperreproductionofthewindtunnelflow.An

overestimationofthepressuregradients wasobservedintherear partoftheductandthejetflowoftheduct hadthetendencyto contract. To overcome these problems, the entire test room was created(framedareain Fig.3)reproducingalsothegapexistingin thediffuser(st.4in Fig.3)totakeintoaccountfortheexternal re-coveryflow.Theemptydomainwasmeshedwithpolyhedralcells withprismlayersontheconvergentwallsonly(Fig.6).Theentire meshismadeof1.3millioncells.

A RANS simulation was then run withSTAR-CCM+9.02 using theturbulencemodelk-

ω

SSTtomodelturbulence.

Anon-slipconditionwasused ontheconvergent surfaceonly in order to account forthe effects of the boundary layer on the flow inside the duct. On theremaining surfaces,a slipcondition wasimposed.

Toreproducetheaspirationofthefandrives,apressureoutlet conditionwaschosenforboththeintakeoftheconvergent(st.0in

Fig. 6. Section at y = 0 of the polyhedral mesh for the empty wind tunnel domain. 0,75 0,8 0,85 0,9 0,95 1 1,05 0 1 2 3 4 V/ V0 xV/c

S4 - CFD

S4 - Real

0,75 0,8 0,85 0,9 0,95 1 1,05 0 0,2 0,4 0,6 0,8 1 1,2 V /V 0 (sta tio n 2 ) zV/H

S4 - CFD

S4 - Real

Fig. 7. Velocity distribution V/V0 in the duct length (x V ) and in the vertical (z v ) direction on the station 2.

betweentheinletandtheoutletwereset tomodifythepressure value attheoutletinawaytoobtainaflowvelocityof20m/sin thetwopointswherethepressureprobesoftherealwindtunnel arelocated.TheanalysiswasrunonanIntelI7processor2.70GHz, 32GBofRAM.Thetimeofconvergencewasabout2hon4cores.

ThisRANSsimulationwasperformedusinganemptywind tun-neltocomparewithexperimentaldata.

3.3. Validationofemptywindtunnelsimulations

The numericalvelocity magnitude (V)distribution ofthe duct wasextractedandcomparedtotheexperimentaldata(Fig.7).The velocitywasnormalizedwithrespecttothevalueassumedto cor-respond to station 2, at the center of the elliptical section (i.e. yv=0,zv=0.56H).

Table 1

Aerodynamic coefficients for SET2 configuration in WTNS at four dif- ferent mesh refinements.

MESH0 MESH1 MESH2 MESH3 Cell count (Millions) 18 24 32 45 C L 1 .239 1 .176 1 .124 1 .090 C D 0 .150 0 .146 0 .143 0 .142

Alongthex-axis,theCFDandtheexperimentaldataagreewell. Thedifferencebetweenthetwocurvesislessthan3%atstations0 and3.ThetendencyoftherealS4istokeepaconstantvelocityin thefirsthalfoftheductandthenreduceitsignificantlyinthelast quarteroftheduct.Thislossinvelocityiscausedbytheblockage effectduetothepresenceofthediffuserintake.Inthenumerical results,thiseffectis notreproduced andthe distributionis quite constanton therear partontheduct. Inthe forwardpartofthe duct,theCFD underestimatesthevelocity distribution.Inthe nu-merical simulationthe flow hasa favorablepressuregradient for the first part of the duct andzero-pressure gradient in the rear part.

At st. 2(where the model wasplaced), experimental and nu-merical data are in good agreement along the z direction. Here, thenumericalsolutionmatchescompletelywiththeexperimental resultsupto zv/H=0.9.Movingupwards, theCFDsolutionshows the tendency of the flow to contract, reducing the local veloci-tiesonthe borderoftheduct. Thisloss isestimatedto be3% at zv/H=1.04,azonenearthewingsailtip,butnotazonethat influ-encesthewingdirectly.

Overall,theanalysisofnumericalresultsdemonstratesthatthe numericalwindtunnelisabletoreproducetheflowatthe mock-uplocationintherealduct.

3.4.Wingsailinwindtunnel

Numericalsimulationsofthewingsailinthewindtunnelwere thencarriedout.Thewingsailwasconsidered inthetwo configu-rationsalreadytestedinthefreestreamcase(SET1andSET2)and placedatstation2asintherealcase.

The entire domain was meshed using Star-CCM+ 9.02 with polyhedra. Prismlayers were added on the wingsail,on the disk andonthewindtunnelconvergentsurface.Thelayersweresetin awayto achievea normalizeddistanceto thewall y+ below0.5 (Fig. 8)on thewingsail andbelow20 onthe convergentsurface. Thechoice ofa low wall y+ on thewingsail surfacewasderived fromthevalidationteststhathadshownthesensitivityofthe

γ

-Re_{ϑ model} to thenear wall discretization. Inthe validation tests forthetransitionmodeldevelopedby Suluksnaetal.(2009) (im-plementedinSTAR-CCM+), Malanetal.(2009)refers,forthehigh liftcase, to a y+ atwall ranging from0.1to 0.8. This alternative formulationofthe

γ

-Reϑ model wasproposed by Suluksnaetal. (2009)inorder tomake up forthelack ofthe originaltransport equationofintermittencyformulatedby Menteretal.(2004a,b).

Themeshwasrefinedparticularlyforthegapbetweenthetwo elementsofthewingsailandthewakeregion.Refinementwas im-posedalsoonthe shearlayersofthe borderoftheduct. Amesh sensitivity study was performed for the SET2 case. The coarsest mesh(Mesh0)counts18Millioncells.Themeshwasthenrefined modifying the cell size on the wingsail surface and the polyhe-dronsizeintherefinedzones.Therefinementratioisrespectively 0.85, 0.71 and 0.59for Mesh1, Mesh2 andMesh 3 with respect toMesh0.Simulationswere performedinordertoextract thelift anddrag coefficientsof the wingsail atthe different grid refine-ments(Table1).Theliftandthedragcoefficientsstarttoconverge withMesh2having a difference oflessthan 3% on CL and1% in

Fig. 8. Scalar map on the wingsail upper surface in the SET1 configuration, colored with the normalized distance to the wall y + _. Table 2

Aerodynamic coefficients comparison between experimental data and numerical solutions in both freestream and WT domains for SET 1 configuration.

WTT FSNS WTNS FSNS/WTT (%) W TNS/W TT (%) C L 0 .773 1 .032 0 .845 + 33 .5 + 9 .3 C D 0 .089 0 .049 0 .065 −44 .9 −26 .9

CDcomparedtoMesh3.Thefinalmeshretainedforthesimulation

wasMesh2(32millioncells).

RANS simulations were run witha k-

ω

SST turbulence model andactivatingthe

γ

-Reϑ.Theboundaryconditionsimposedatthe inletandatthe outletofthe windtunnel are thesameused for theemptywindtunnelsimulationinawaytokeepaflowvelocity of20m/sintheduct.

Simulations were computed onbi-XeonbE5-2670 Octo proces-sors,2.60GHz,64GBRAM.Thecomputationtimewasabout6days on16cores.Afirstconvergencewasobtainedontheaerodynamic coefficient after 4000 iterations. At the same time the pressure distributionover the wingsail and particularlythe transition and thelaminarbubblezonesstillpresentedstrongoscillationscaused by the unsteady characteristics of the transitionphenomena. For this reason the RANS simulations were completed using an un-steadyRANS approach, for a total time of 1s using a time step of 2× 10−3_{s, corresponding to 50 through flow times (the time}

neededforaparticletomovefromtheleadingedgetothetrailing edge).

4. Results

4.1.Comparisonofthewingsailresultsinfreestreamandinthewind tunneldomain

Windtunnelnumericalsimulations(WTNS)andfreestream nu-merical simulations (FSNS) were compared to wind tunnel tests (WTT).Theliftanddragaerodynamiccoefficientswerecalculated aswellastheCPdistributiononthethreewingsailreference

sec-tions (i.e. z∗=0.25, 0.50 and 0.75). The error introduced by the balanceduring experimental testshasto be considered. The tool usedduring theexperimental testscan bear,in fact, loadsup to 2.40kN forthedragand3.00kNforthelift.Comparedto aerody-namicforces producedby the wingsail in theSET2 configuration (i.e.D₌0.027kN,L₌0.20kN),itrepresentsrespectively1%and6% offullscale.Therefore,testsonthebalancewereexpresslycarried outtogiveanestimationofthemeasurementerrorduetothe bal-ancesensitivityincaseoflowloads.TheCLuncertaintieswere

es-timatedtobeupto8%fortheSET1andupto3%fortheSET2.For thedrag,theuncertaintyisupto5%forboththewingsail config-urations.

The comparisonon the aerodynamic coefficientsfor the SET1 configuration (Table 2) shows a discrepancy of 33.5% on CL

be-tweentheexperimentalvalueandtheFSNS.Thedifferenceiseven moreelevatedwithadiscrepancyof44.9%onthedragcoefficient. The wind tunnel numerical reproduction enhanced the CFD

pre-Table 3

Flow deflection angles in the local xy plane at y = 0 and at the upstream distance of 20% of the local chord from the local main L.E. on the x-direction for the wing in WTNS and FSNS for the SET1 configuration.

WTNS FSNS

z∗_{= 0.25 7 ° 13 °}

z∗_{= 0.50 15 ° 22 °}

z∗_{= 0.75 13 ° 18 °}

Table 4

Aerodynamic coefficients comparison between experimental data and numerical solutions in both freestream and WT domains for SET 2 configuration.

WTT FSNS WTNS FSNS/WTT (%) W TNS/W TT (%) C L 1 .254 1 .365 1 .124 + 8 .8 −10 .4 C D 0 .171 0 .119 0 .143 −30 .4 −16 .4

dictionsonthewingsail:theerrorsdropdownto9.3%onthelift and26.9%on thedrag. Thisenhancementin thenumerical mod-eling canbe furtherobserved comparingthe Cp distribution over

thethreewingsailsections(Fig.9).

IntheFSNSthesuctionpeakontheuppersurfaceoftheairfoil isoverestimatedfromaminimumof0.3toamaximumof0.5with respecttotheexperimental data(A1,B1 andC1).Furthermorethe

transitiontakes place quicker than inthe experimental case (A2,

B2, andC2). Theseproblems are completelysolved in theWTNS.

Herethematchwiththewindtunneldataisgood.TheCp

distri-bution onthe pressure sideis correctlyreproduced aswell asin thesuctionside.Thesuctionpeakhasamaximumdiscrepancyof 5%(A1,B1,C1)whilethe transitionzone isdelayedby 1to2%of

thechord.Onthetrailingedgezone(A3,B3,C3),boththe

numer-ical solutions keep alower pressure value than the experimental case, wherethe pressuretends to increase inthe last 10% ofthe localchord.

The FSNS cannot correctly reproduce the experimental condi-tions because ofthe confinementeffects introduced by the wind tunnel walls. In Table 3 theflow deviation angleon thelocal xy planeisreportedforboththenumericalcasesWTNSandFSNSand comparedto thethreereferencesections,aty₌0andatthe up-stream distance(-xdirection) of20% ofthe localchord fromthe localmainL.E.Theflowdeviationforthefreestreamsimulationis 5°–7° more elevated than in the wind tunnel case. The effect of thewindtunneldomainreducestheactualangleofattack feltby theairfoils.Thesuctionpressurecapabilitiesarethenworsenedby thisincidencereduction affectingtheliftcapabilitiesoftheentire wing.

IntheSET2case, thediscrepancyonthedragcoefficientis re-ducedfrom 30.4%to 16.4% using thewind tunnel modeling. The liftisunderestimatedby10.4%inWTNSwhileisoverestimatedby 8.8%inFSNS(Table4).

-3 -2,5 -2 -1,5 -1 -0,5 0 0,5 1 0 0,2 0,4 0,6 0,8 1

C

p (

z*=

0,25)

x/c

1 WTNS FSNS WTT

A

2

A

1

SET 1

δ=15° α=0°

A

3 -3 -2,5 -2 -1,5 -1 -0,5 0 0,5 1 0 0,2 0,4 0,6 0,8 1

C

p (

z*=

0,50)

x/c

1 WTNS FSNS WTT

B

2

B

1

SET 1

δ=15° α=0°

B

₃ -3 -2,5 -2 -1,5 -1 -0,5 0 0,5 1 0 0,2 0,4 0,6 0,8 1

C

p (

z*=

0,75)

x/c

1 WTNS FSNS WTT

C

₂

C

₁

SET 1

δ=15° α=0°

C

3

Fig. 9. Comparison of the Cp distributions on the three sections of the wingsail for SET1.

The Cp distribution analysis on the three wing sections (Fig.

10) is more complex. On the lowest section a correct match is found between WTT data and WTNS data, while the freestream caseoverestimates the Cp (A1). Onthissame section the

transi-tion pointiscorrectlyestimatedwithan errorofonly afew per-cent on the chord compared to the experimental case(A2). For

z∗=0.5, the pressure side distribution iscorrectly reproduced by theWTNS;onthesuctionside onthecontrarytheFSNSproperly estimatesthe Cp on theturbulentzone (B2) whilethe peak

suc-tion zone (B1) is overestimatedby theWTNSand overestimated

by the FSNS. On the highest section (z∗=0.75), the best match with theexperimental dataon the suction side is obtained with

theFSNS,whiletheWTNSunderestimates thesuctiononthe en-tire chord (C1, C2, C3). The wind tunnel here also reduces the

angleofattackfeltbythewing(Table5).

The reason why WTNS does not perform better than FSNS

acrosstheentirewingspanismorecloselyinvestigatedinthenext section.ThemainreasonisthattheSET2configurationhasa par-ticularflow pattern, withtheflow attachedonly onthe low half sectionsoftheflapwhileonthemid-highsectionstheflowis sep-arated.Thisdifferentconditionontheflapinfluences directlythe jetflowinginsidetheslotdividing themainfromtheflap.Inthe attachedcase (i.e. on the lowest section) the slot jet lies on the flapsurfacekeepingthedirectiongivento itby thegeometry. In

-3 -2,5 -2 -1,5 -1 -0,5 0 0,5 1 0 0,2 0,4 0,6 0,8 1

C

p (

z*=

0,25)

x/c

1 WTNS FSNS WTT

A'

2

A'

1

SET 2

δ=25° α=0°

-3 -2,5 -2 -1,5 -1 -0,5 0 0,5 1 0 0,2 0,4 0,6 0,8 1

C

p (

z*=

0,50)

x/c

1 WTNS FSNS WTT

B'

1

B'

2

SET 2

δ=25° α=0°

-3 -2,5 -2 -1,5 -1 -0,5 0 0,5 1 0 0,2 0,4 0,6 0,8 1

C

p (

z*=

0,75)

x/c

1 WTNS FSNS WTT

C'

2

C'

1

SET 2

δ=25° α=0°

C'

3

Fig. 10. Comparison of the Cp distributions on the three sections of the wingsail in the SET2 configuration.

theseparated case(i.e. onthe highsections), the jet isdetached fromtheflapsurfaceassuming adirectiondependentonthesize oftheflaprecirculationzone.

Because of the wind tunnel influence, the flow in the WTNS is less deviated in the slot, giving a jet that has a low tangen-tialmomentumcomponent.OnthecontrarytheFSNS,thathasno straightening effects,predicts a jet witha higher tangential mo-mentumcomponent. The differencein jetdeflectionbetweenthe twocaseswasestimatedtobe2°.

As described by Smith (1975) the jet direction modifies the T.E.conditionon themainelement,changingits circulation.Ajet

deflection enhances the main circulation and hence its lift. This explains the differences found in the two numerical cases but nonetheless itdoesnot justify whythe experimental datamatch betterwiththefree-streamcase.Anotherexplanationcomesfrom the wing deformation that occurs during the wind tunnel tests. Particularly,theupperpartoftheflapmovesawayfromthemain element, wideningthe slotsize. Havinga larger slot,the jet was characterized by a lower velocity, thus preventingits capabilities todeviateinthesamewayasintheWTNS,wheretheslotis nar-rower.Inactuality,theflowjetislessdeviatedintheFSNSandin

Table 5

Flow deflection angles in the local xy plane at y = 0 and at the upstream distance of 20% of the local chord from the local main L.E. on the x-direction for the wing in WTNS and FSNS for the SET2 configuration.

WTNS FSNS

z∗_{= 0.25 15 .8 ° 28 .4 °}

z∗_{= 0.50 15 .0 ° 22 .0 °}

z∗_{= 0.75 14 .5 ° 22 .2 °}

Laminar flow Laminar bubble Turbulent flow Separated flow

z*=0.75 z*=0.50 z*=0.25

WTNS

z*=0.75 z*=0.50 z*=0.25

WTT

Fig. 11. Scheme of the different flow zones on the suction side of the wingsail in WTT (up) and in WTNS (down) for SET1.

theWTT, improvingthemaincirculationandthereforeenhancing thepressuresuctiononthehighwingsections.

Despitethisdiscrepancy,theWTNSisthemostappropriate ap-proach toreproduce the experimental caseandthe flow physics. OnlytheWTNSdatabaseremainstobefurtheranalyzedinthe fol-lowingsections.

4.2. Flowfieldcomparisonbetweenthenumericalanalysisinwind tunnelandtheexperimentaldata

Theskinfrictionfeaturesofthewingflowfieldhavebeen com-pared betweenthe WTNS andthe viscous oil visualizations. The wingsailmapcomparisonshowsaqualitativeviewoftheflow pat-ternonthesuctionside,especiallyregardinglaminartoturbulent transitionzonesandboundarylayer separations.Theflowis lam-inar on thefirst partof thewing chord (the zone nearthe L.E.). The flow separates, creatinga laminar bubble that extends until theflowreattachesonthewingsurfaceafterthetransitionin tur-bulentregimethathastakenplace.Theoilvisualizationhighlights thelocationoflaminarbubblesandseparationlineswheretheoil stagnates. In the numerical solution the laminar bubble and the separatedzoneshavebeendetected bymeansoftheskinfriction coefficient. The laminar and turbulent zones were then detected withtheintermittencyfactor(Suluksnaetal., 2009;Malan etal., 2009).

FortheSET1configurationtheflowmap isreportedin Fig.11, showinga good agreementon themain element between exper-imental andnumericalfields.Thelaminarbubblepositionis well detected ontheentirewingspanwithadiscrepancyby 2%to11% of the chord c1 (Table 6). An exception exists at the wing root, where the 3D flow phenomena, due to the flow interaction be-tween thewingandthe diskinterface, makeit hardertopredict thetransitionalregion.

Table 6

Numerical/experimental comparison for the posi- tion and the length of laminar separation bubble on the main element for SET1 configuration.

SET 1 X LSB (% c 1 ) L LSB (% c 1 ) WTNS WTT WTNS WTT z∗_{= 0.25 33 41 21 8} z∗_{= 0.50 30 32 21 16} z∗_{= 0.75 31 36 22 15}

Laminar flow Laminar bubble

Turbulent flow Separated flow

z*=0.75 z*=0.50 z*=0.25

z*=0.75 z*=0.50 z*=0.25

WTT

WTNS

Fig. 12. Scheme of the different flow zones on the suction side of the wingsail in WTT (up) and in WTNS (down) for SET2.

Thelaminar bubblelength isoverestimatedby 5%–13%by the simulation. Previous studies already reported this behavior with the transitional model used (Malan et al., 2009; Chapin et al., 2015).Afterthetransitioninturbulentregime,theflowisattached alloverthemainsurfaceexceptonthetrailingedgeregion.

The transition model predicts a transition on the flap that is induced by a laminar separation at half of the chord. However, in the oil flow visualizations, the transitionis detected near the flapL.E.withathinlaminarbubble.Thetransitionmodelconsiders thevalueofthelocalturbulentkineticenergy,aspredictedbythe turbulencemodel, toestimate the value of theReynolds number basedonthemomentumthickness.Indeed,theincorrecttransition detectionisrelatedtothedifficulty oftheRANS-based numerical simulation to accurately estimate the turbulent kinetic energy at thefrontierofthe flapboundarylayer, whichisprotectedby the jetfromtheslot.

FortheSET2configuration(Fig.12),thenumericalandthe ex-perimentaldataareingoodagreement.Theflowonthemainhas thesamecharacteristics asintheSET1. The laminarbubble posi-tioniswell detected on theentirewingspanwithadifference of lessthan4%ofchordasreportedin Table7.Itslengthis overesti-matedwithadifferencefrom2% to12%.The flowseparatesfrom themainat90%ofthechord.

Thetransitionmodelwelldetectstheflaplaminarzonethatlies betweenthe5%and10%oftheflapchord.Thenumerical simula-tioncapturesthedifferentflowfeaturesalongthewingspan.From rootto half span,the flow is attachedon mostparts ofthe sur-face,withaseparationthatoccursat95%oftheflapchord.Onthe upperpartoftheflap,theflowiscompletelyseparated.

Table 7

Numerical/experimental comparison for the posi- tion and the length of laminar separation bubble on the main element for SET2 configuration.

SET 2 X LSB (% c 1 ) L LSB (% c 1 ) WTNS WTT WTNS WTT z∗_{= 0.25 33 35 23 11} z∗_{= 0.50 28 28 19 17} z∗= 0.75 28 28 21 16

Fig. 13. Slot parameters: gap (g), overlap (o), y F .

Thisbehavioroftheflowaroundtheflapislinkedtothesizeof theslotalong thewingspan.Thejet oftheslotissensitive tothe gapsize,modifyingthelocationoftheflowseparationontheflap. Thesefindingsemphasizedthesloteffectinwingsailperformances asitwillbedescribedinmoredetailsinthenextsection.

5. Jetslotanalysis

In existing literature, the characterization of the slot is ex-pressed by two parameters: the overlap(o) andthe gap (g) dis-tance.Thefirstoneexpressesthehorizontaldistancebetweenthe mainT.E. and the flapL.E.;it assumes negative values when the flapisplaced rearwardtothe mainT.E.The gapsizeisthe mini-mumdistancebetweenthemainsurfaceandtheflapsurface. In-steadof thegapsize, the verticaldistance betweenthemain T.E andtheflapL.E.(yF)canalsobeusedasparameter(Fig.13).

Thepresenceofthejetimprovesthehighliftcapabilitiesofthe flapped wing configuration as reported by Smith (1975). The jet of the slot can be considered as a potential flow lying between theviscous shearlayer ofthemain element andtheflap bound-arylayer. Thehighvelocityregionofthejet, deviatedby theflap geometry,helps to increase the circulation on the main element enhancingits lift.The jetinfluences theflow nearthe T.E.of the main, decreasing its pressure recovery demands, bringing down thepossibilityofaflowseparationfromthemainsurface.The in-terferencewiththe T.E.ofthemain reducestheflowmomentum nearbytheflapL.E.,dumpingitspressurepeakandhencethe pres-suregradient on the flap surface, delaying the separation ofthe boundarylayer.

Theflapisseparatedfromthemainbytheslot,soitsboundary layeristhinnercomparedtothecaseofaflapfullyincorporatedin themainwing.Thestabilityofthisboundarylayerisimprovedby the“off-surface pressurerecovery”, moreefficientthan a conven-tionalrecovery incontactwiththewall. Thisphenomenon isdue tothe interactionamong thethree flow layerson the upperflap surface.The entrainingeffectduetothe viscositycausesa decel-erationoftheflow thattakesplaceon athick zoneandnot only incontactwiththesurface. Thedeceleration ishencelessabrupt withconsequentloweradversepressuregradients.

Nevertheless theseeffects onlyexist iftheslot isproperly di-mensioned. Smith(1975) proposeda criterionfortheslot dimen-sion,i.e.theslothasto ensurethatthewakeoftheupstream

el-Table 8

Optimal values for y F and overlap sizes at different flap deflection angles.

δ Ref. o/c1 yF /c 1

20 ° Woodward and Lean (1993) −1.25% to 0.25% 1.5%–3.25% 30 ° Biber and Zumwalt (1993) −2% to −0.2% 1.75%–3.25% 40 ° Woodward and Lean, (1993) −1.25% to 0.2% 0%–2.2%

Biber (2005) −1.5% to −1% 0.25%–0.75%

ement andthe flap boundarylayer do not merge.Otherwise the mergingofthesezonesisresponsibleforathickviscouslayerthat ismorepronetoseparation.Oncetheseparationhasoccurredon the flapsurface, theperformance of thehighlift configurationis reduced,potentiallyleadingtoamassivestall.

BiberandZumwalt(1993)describedadoublestallbehavioron GA(W)2highliftconfiguration:theflowseparates,atfirst,onthe flapsurface,causingafirstlossinlift,butwithoutinfluencingthe flow onthe mainthat will separate whenthe inletflow angleis stillincreased.Beforethefirststall,theliftslopetendstoincrease (Woodward andLean,1993). Infact, the increase ofthe angleof attack leadsto a thickening of the wake, pushing the jet of the slot on the flap surface and hence delaying the flow separation. Nevertheless theslope enhancement ischaracteristic ofhighflap deflectionangles(30°–40°)andinacertainrangeofgapand over-lapthatdefinestheslotoptimalsize.Arearwardmovementofthe flapfromtheoptimumposition,aswellasanyFincrease,leadsto alargeseparationontheflapsurface.Aforwardmovementofthe flaporareduction intheverticaldistance(yF)is notdetrimental totheliftatlowandintermediateincidences.Neverthelessathigh incidencestheliftslopeincreasedoesnottakeplace,limitingthus themaximumliftcoefficient.

Theslopeenhancementdoesnotappearforthe20° flap deflec-tionangle(WoodwardandLean,1993). Themaximumlift gradu-allydecays whenthe flapismoved away fromthis position.The optimaldimensionoftheslotgapdependsontheReynolds num-ber. At low Reynolds number, the boundary layer thickens, so it reducestheslotsizefeltbytheflow.Sotheoptimumsizemustto be largeratlow ReynoldsnumberthanathighReynoldsnumber (Haines,1994).Furthermoreonwingsailstheslotdimensionis de-pendenttotheflapdeflectionangle,becauseoftheflapkinematic. Theslotdimensionofthestudiedwingsailisrepresentedthrough itsyFandodistributionsalongthespanforthetwoconfigurations, Fig.14.Thenormalizedvalues(yF/c1ando/c1)arenotconstanton thewingspanbecauseofthetipwardchordreduction.

Clearly forthe SET1configuration, where thedeflection angle issmaller,the distancefromthemainto theflapyF is smalland thuswelladaptedtoavoidtheflowseparationovertheflap. How-ever for the SET2 configuration, the slot is adapted only on the lowestsectionofthewing.Ontheupperpartofthespan,the dis-tancefromthe main tothe flapyF isimportant andcorresponds to conditions where the boundary layer on the flapis separated (Woodward andLean,1993). Asreported in Table 8,forlow flap deflectionangles,theoptimumoverlapcorrespondstonegativeor small positive values, while for high deflection angles, the opti-mummovestowardsmorenegativevalues.Theoptimumdistance yF islargeratlowdeflectionanglesthanathighdeflectionangles. Because of its flaprotating mechanism, it is thus difficultto ob-taintheoptimalvalueforallflapdeflectionangles.Whentheflap angle isincreased, the overlap ofthe slot movestoward positive valuesandlargerdistanceyF dimension,whichisexactlyopposite towhatshouldbedonetoobtaintheoptimalsize.

To investigate the flow in the slot gap region, the numerical simulationiscomparedwith2DPIV-basedmeasurements.The in-vestigated configurationistheSET2configuration.Theanalysisof theflowisledatz∗=0.25(attachedboundarylayer)andz∗=0.75

0,0 0,2 0,4 0,6 0,8 1,0 -4,5 -3,5 -2,5 -1,5 -0,5

z*=z/

H

o/c

1

%

% o/c1 SET1 % o/c1 SET2 0,0 0,2 0,4 0,6 0,8 1,0 0,0 1,0 2,0 3,0 4,0

z*=z/

H

y

F

/c

1

%

% yF/c1 SET1 % yF/c1 SET2

Fig. 14. Distribution of the slot dimensions y F /c 1 and o/c 1 on the wingspan for the two configurations of the wingsail.

(separated boundarylayer).The scalarmapforthe normalized x-componentofthevelocityU/U_∞ispresentedforz∗=0.25(Fig.15) andforz∗=0.75(Fig.16).Thevelocityprofiles,U=f(l)(withlthe distanceto thewall)andtheturbulent kineticenergy, k=f(l)are plottedat90%ofthemainchord andat10% ofthe flapchord, at z∗=0.25(Fig.17)andz∗=0.75(Fig.18).

Thevelocityisnormalizedwithfreestreamvelocityandthe tur-bulent kinetic energy is normalized with the freestream kinetic energy. Thedistancefromthe wall surface(l) isnormalized with thelocalboundarylayerthickness(

δ

BL).Theturbulentkinetic

en-ergy measuredwith2D PIV onlytakesinto accountforaxial and tangentialfluctuatingvelocitycomponents (sothespanwise com-ponent is not taken into account). To compare numerical pre-dictions with measurements, turbulence kinetic energy must be scaleddownbyafactorof2/3(theturbulencemodelassumes tur-bulenceisisotropic).

Atz∗=0.25,closetotherootwheretheboundarylayerremains attached,experimentalandnumericaldataareingoodagreement, especially forthe main element. On theflap, some discrepancies appearalongthetrajectory ofthewakeinduced bythemain ele-ment.Numericalsimulationsuccessfullypredictsthejetbutitfails to reproduce properlythe mixinglayer between the jet andthe wake of themain element. The PIV scalarmap showsa velocity deficitinthewakeofthemainelementallalongtheflapchord.In thenumericalsimulationthisdeficitisobservedonlyinthe neigh-borsoftheflapL.E.butitisthenquicklydissipated.Sincethewake mergeswiththeflapboundarylayer(inthenumericalsimulation), itmakestheflowmoresensitivetotheadversepressuregradients

U/U

∞

-0.7 0 1 1.7

Fig. 15. Scalar maps colored with the normalized velocity on SET 2 at z ∗_{=25% from} CFD (top) and PIV (bottom). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

U/U

∞

-0.7 0 1 1.7

Fig. 16. Scalar maps colored with the normalized velocity on SET 2 at z ∗_{=75% from} CFD (top) and PIV data (bottom). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

0 1 2 3 4 5 -0,5 0,5 1,5 l/δBL U/U∞(main 90%c1) PIV URANS 0 1 2 3 4 5 0 0,025 0,05 l/δBL 2k/U∞2 (main 90%c1) PIV URANS 0 1 2 3 4 5 -0,5 0,5 1,5 l/δBL U/U∞ (flap 10%c2) PIV URANS 0 1 2 3 4 5 0 0,025 0,05 l/δBL 2k/U∞2 (flap 10%c2) PIV URANS

Fig. 17. Comparison between CFD and PIV data at two stations on the main (up) and on the flap (down) for the SET2 configuration, at z ∗_{=25%: velocity (left) and} turbulent kinetic energy (right).

andhenceto separation(asshownalsoin Fig.11). Theturbulent kineticenergyagreeswell withthePIVandnumericalsolutionas shownin Fig.17.

Atz∗=0.75,closetothetipwheretheboundarylayeris sepa-ratedfromtheflap surface, experimentalandnumerical dataare also in good agreement. The most important discrepancy is re-latedto thepredictionofthe slotjet direction,which isoriented

0 1 2 3 4 5 -0,5 0 0,5 1 1,5 l/δBL U/U∞(main 90%c1) PIV URANS 0 1 2 3 4 5 0 0,05 0,1 l/δBL 2k/U∞2 (main 90%c1) PIV URANS 0 1 2 3 4 5 -0,5 0 0,5 1 1,5 l/δBL U/U∞(flap 10%c2) PIV URANS 0 1 2 3 4 5 0 0,05 0,1 l/δBL 2k/U∞2 (flap 10%c2) PIV URANS

Fig. 18. Comparison between CFD and PIV data at two stations on the main (up) and on the flap (down) for the SET2 configuration, at z ∗_{=75%: velocity (left) and} turbulent kinetic energy (right).

inthetangentialdirectionmorewiththePIVflowfieldthaninthe URANSflow field.Beyondthe difficultyforURANS topredictthis flow,ithasbeenobservedduringtheexperimentalcampaignthat the aerodynamicforcesdeform themock-upgeometry, especially inthewingtipregion.Theextentofthescalemodeldeformation wasmeasured duringtheexperimental testsby photogrammetry. ThedeformeddistributionsinoverlapandyF havebeenplottedin Fig.19fortheSET2configuration.

Thisdeformationinducesanegativeoverlapbetweenthemain elementandtheflap.ItalsoreducesthedistanceyF betweenboth elements. Aspreviously discussed, thiseffectcan delaythe sepa-rationof theboundary layeron theflap. In Fig.18, experimental andnumerical data are in good agreement,showing a separated boundarylayerontheflapat10% oftheflapchord. However,the peak of turbulent kinetic energy, relatedto the mixing layer be-tween the jet flow and the wake of the main element, is found closertotheflapwallinthecaseofnumericalsimulation.This ob-servationconfirmsthat thenumericalsimulationdoesnotpredict accuratelythetrajectoryofthejetflow.

This discrepancy about the jet deviation does not depend on afault ofthenumericalapproachbutratheronamodificationof thegeometrycaused bythemock-updeformation duringthe ex-perimentalcampaign.

6. Conclusions

The rigid wingsail is an effective propulsion system that en-hances yacht performance. Such wingsails can operate in severe conditions,showingmassiveboundarylayerseparation,at moder-ate to highReynolds number.The objective of thisstudy wasto betterunderstandtheflowphysics ofa rigidwingsail,atlowand highflapdeflectionangles.Aparticularattentionwaspaid tothe behavior of the flow inthe vicinity of the slot betweenthe two elements.

0,0 0,2 0,4 0,6 0,8 1,0 1,0 2,0 3,0 4,0

z*=z/

H

yF/c1 %

% yf/c1 idea l % yf/c1 deformed 0,0 0,2 0,4 0,6 0,8 1,0 -4,5 -3,5 -2,5 -1,5 -0,5

z*=z/

H

o/c

1

%

% o/c1 idea l %o/c1 deformed

Fig. 19. Distribution of the slot dimensions y F /c 1 and o/c 1 on the wingspan in the ideal and in deformed case for the SET2 configuration.

The investigationswere supportedby awindtunnel campaign coupled with 3D unsteady RANS simulations on a scaled wing-sail.Wind-tunnelmeasurementsonthetwo-elementwingsail, typ-ical of an AC72 design, were performed at a Reynolds number Re=3×105 _{(basedonrootchord).Measurementsinclude:}

aerody-namic loads, steady pressure sensors, oil flow visualizations and PIVfields.

Two approaches were tested for the unsteady RANS simula-tions:theclassicalfreestreamconditionsandthewindtunnel en-vironment.Comparisonswerecarriedoutonthesedifferent situa-tionsemphasizingthefollowingpoints:

1. The numerical predictions are improved when the wind tun-nel environment is modeled (as generally reported for high lift configurations). Numerical simulations in freestream con-ditions overestimates aerodynamic coefficients (lift and drag) comparedtoexperimentaldata.

2. Thenumericalsimulationsinwindtunnelenvironment demon-strate its capability to predict the attached and separated re-gions as well as laminar and turbulent regions. Comparisons withPIV measurements confirm the abilityof unsteady RANS topredicttheflowaroundwingsailbothwithlowandhighflap deflectionangles.

3. Somedifferenceshavebeenidentifiedonthepredictionofthe mixinglayerbetweenthejetflowandthewakeofthemain el-ement.Suchflow isknowntobedifficultforturbulence

mod-els.Anothersourceofdiscrepancycomesfromthereal geome-tryofthewingsail,whichexperienceshapedeformationduring wind-tunneltests.

4.Theflowphysicsintheslotisakeyelementofwingsail perfor-mance.

Furthernumericalsimulationsare neededtoenhancethe pre-diction of the jet flow, with LES basedmethods that are able to deal with massively separated flows and mixing layers. The real slot geometry of the full-scaled wingsail, including its deforma-tions, should be quantified to estimate the uncertainties associ-ated to the real slot geometry. The effects of Reynolds number ontheflowshouldbeinvestigated,throughnumericalsimulations onafull-scale wingsail(Re=0.53×106 _{inthepresentwork while}

Re₌[3_×106_;10×106_{]forafullscaleAC72).}

Acknowledgments

ThisresearchwassupportedinpartbyASSYSTEMFrance,which kindly provided PhD funding. Particular thanks to Laurent Neau, whomadepossible thecreation ofthePhDprojecton the wing-sails.

ManythankstothetechnicalteamofISAE/DAEP,PatrickChèze andDanielGagneuxforthescalemodelmanufacturing,Hervé Bel-loc,ValérieAllan,HenriDedieuandEmmanuelRivetfortheir

valu-able support during the wind tunnel tests. Particular thanks to PhilippeBarricauforhishelpduringthePIVcampaign.

ThesupportprovidedbythecomputingcenteroftheUniversity ofToulouse(CALMIP)isalsoacknowledged(projectp1425).

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