Flow Control over the Blunt Trailing Edge of Wind Turbine Airfoils Using Circulation Control

26 Pages·2017·3.54 MB·English

energies
Article
Flow Control over the Blunt Trailing Edge of Wind
Turbine Airfoils Using Circulation Control
He-YongXu1,2,*,Qing-LiDong1,Chen-LiangQiao1,2andZheng-YinYe1
1 SchoolofAeronautics,NorthwesternPolytechnicalUniversity,Xi’an710072,China;
[email protected](Q.-L.D.);[email protected](C.-L.Q.);[email protected](Z.-Y.Y.)
2 Research&DevelopmentInstituteofNorthwesternPolytechnicalUniversityinShenzhen,
Shenzhen518057,China
* Correspondence:[email protected];Tel.:[phone]
Received:16February2018;Accepted:8March2018;Published:10March2018
Abstract: Anewpartialcirculationcontrol(PCC)methodisimplementedontheblunttrailingedge
DU97-Flatback airfoil, and compared with the traditional full circulation control (FCC) based on
numericalanalysis. WhentheCoandajetisdeactivated,PCChasanattractiveadvantageoverFCC,
sincethedesignofPCCdoesn’tdegradeaerodynamiccharacteristicsofthebaselineflatbacksection,
incontrasttoFCC,whichisimportantinpracticaluseincaseoffailureofthecirculationcontrol
system. WhentheCoandajetisactivated,PCCalsooutperformsFCCinseveralrespects. PCCcan
producemuchhigherliftcoefficientsthanFCCovertheentirerangeofanglesofattackaswellas
the entire range of jet momentum coefficients under investigation, but with slightly higher drag
coefficients. TheflowfieldofPCCislesscomplexthanthatofFCC,indicatinglessenergydissipation
inthemainflowandhencelesspowerexpenditurefortheCoandajet. Theaerodynamicfigureof
merit(AFM)andcontrolefficiencyforcirculationcontrolaredefined,andresultsshowthatPCChas
muchhigherAFMandcontrolefficiencythanFCC.ItisdemonstratedthatPCCoutperformsFCC
intermsofeffectiveness,efficiencyandreliabilityforflowcontrolintheblunttrailingedgewind
turbineapplication.
Keywords: circulationcontrol;blunttrailingedge;windturbineairfoil;aerodynamicfigureofmerit;
controlefficiency;Coandajet
1. Introduction
The world’s ever-growing energy demand posts a huge challenge for humans in the context
of gradual depletion of fossil-fuel reserves. The serious energy crisis and stricter environmental
regulationshavepromptedpeopleandgovernmentsaroundtheworldtomakegreateffortstodevelop
windenergywhichisoneofthemostpromisingandfastestgrowingcleanrenewableenergyforms
duetoitswideavailability[1]. Advancedhorizontalaxiswindturbines(HAWTs)withever-larger
sizesandexcellentaerodynamiccharacteristicsaredesignedaimingtoreducethecostofenergyand
keep wind energy economically competitive with traditional and other renewable energy sources.
Larger turbines are desirable because the cost of energy can be reduced by increasing the lifetime
poweroutputwhichisproportionaltothesweptareaoftherotordisk[2]. Astherotorbladesize
grows, the blade mass increases at approximately the cube of the blade length, leading to a rapid
increase of gravitational loading. In addition, the aerodynamic loads on the blade increases with
approximately the square of the blade length, producing ever larger thrust perpendicular to the
rotationalplane. AstheloadsontheHAWTresultfromtheaddedcontributionsofeachairfoilalong
theblade,thegravitationalandaerodynamicloaddistributionsonthebladesinducesconcernsinthe
bladestructure,themostimportantofwhichistheflap-wisebendingmomentandthechord-wise
torsionmomentalongtheblade,whichisrathersevereintheinboardregion[3]. Demandforwyasof
Energies 2018,11,619;doi:10.3390/en11030619 www.mdpi.com/journal/energies
Energies 2018,11,619 2of26
addressingthisstructuralconcerngivesrisetotheneedforthickairfoilsintheinboardregionofthe
largewindturbine,sincethickairfoilscouldenhancestructuralstrength. However,traditionalthick
airfoilswithsharptrailingedgestendtohaverelativelypooraerodynamicperformancecharacteristics.
Inparticular,theliftcharacteristicsofthetraditionalsharptrailingedgethickairfoilissensitiveto
flow transition due to surface contamination and strong adverse pressure gradient on the upper
surface,leadingtoreductionofliftcurveslopeandmaximumliftcoefficient. Thesenegativeeffects
aredetrimentaltowindturbinepoweroutput[4].
Flatback airfoils with blunt trailing edges have been proposed to improve the aerodynamic
performancecharacteristicsoftraditionalsharptrailingedgethickairfoilsintheinboardregionoflarge
windturbines. Aflatbackairfoilisusuallycreatedbysymmetricallyaddingthicknesstoeithersideof
thecamberlineofatraditionalsharptrailingedgethickairfoilafterthemaximumthicknesslocation.
Thisaddingofthicknessmethodcanpreservetheimportantgeometricaspectsofairfoils, suchas
thenosegeometry,airfoilthicknessandcamber,whileprovidingablunttrailingedgewithdesired
bluntness[5]. Comparedwiththesharptrailingedgeairfoilswiththesamethickness,flatbackprofiles
arelessdemandingintermsofpressurerecoveryandhencehavebetterstallcharacteristics,leadingto
reduction of leading-edge roughness sensitivity [6]. As a result, flatback airfoils can increase the
maximumliftaswellastheliftcurveslope[6]. Moreover,flatbackprofileshavelargercross-sectional
areaandbetterstructuralcharacteristics,duetotheaddedthickness. Leeetal.[7]designeddigital
modelsofthree-dimensionalbladeswithdifferentlevelsofblunttrailing-edgethicknessbymodifying
theinboardportionoftheoriginalNRELPhaseVIblade[8],andobtainednumericalaerodynamic
characteristicsatvariouswindspeeds,demonstratingthatgenerallytheblunttrailingedgeairfoilcould
alleviatestructuralandmanufacturingconstraintswhileincreasingtheblade’spowerperformance.
Therefore,theincorporationofblunttrailingedgeairfoilswouldallowbladedesignerstomorefreely
addressthestructuraldemandswithouthavingtosacrificeaerodynamicperformance.
Throughimplementationofflatbackairfoils,thestructuralandaerodynamicissuesassociated
withlargewindturbineshavebeenmitigated. However,effortsremaintobemadetofurtherenhance
theaerodynamicperformancecharacteristics. Theinboardregionforflatbackairfoilsmightaccountfor
upto40%ofthewholeblade[7,9],andtheenhancementofaerodynamiccharacteristicswilldefinitely
increasethepoweroutputandhencedecreasethecostofenergy. Flowcontrolisrecognizedasan
effectivemethodtoimprovetheblade’saerodynamiccharacteristics,andhasbeenwidelyinvestigated
for decades [3]. For flow control on flatback wind turbine airfoils, most current efforts focus on
reducing drag by passive-steady flow control methods. The significant base drag is an inherent
penalty of flatback airfoils, which is mainly due to bluff-body vortex shedding and the resulting
drop in pressure behind the blunt trailing edge. Numerical and experimental studies on flatback
airfoils [10–12] have shown that devices such as a simple splitter, a base cavity, or an offset cavity
canreducedragbyupto50%. Othercontrolmethodsanddeviceswerealsoproventobeeffective,
suchasaslottedcavity[13],aventilatedcavity[13],splitterwedges[14],serratedtrailingedges[14,15],
asteppedafterbody[16],andsoon. However,itisnotedthatthedragreductiondevicesalsoreduce
theliftundercertaincircumstances. Forexample,whenthesplitterplateisparalleltothechordand
extendsdownstreamoftheflatbacktrailingedge,theeffectivecamberoftheairfoilwillbereduced,
resultinginalowerliftcoefficient. Incontrasttotheabovedrag-reduction-basedmethod,Nikoueeyan
etal.[17]conductedanexperimentalresearchaimingtocontroltheliftoftheflatbackairfoilrather
than the base drag by using a Gurney flap. Compared to the baseline flatback airfoil, the Gurney
flap mounted on the pressure side with a height of 5% chord length can significantly increase the
liftcoefficientbyabout38–41%. TheyalsotestedGurneyflapswithdifferentheightsoneitherthe
pressuresideorthesuctionside, showingeffectivecontrolontheliftandmomentovertheentire
rangeofanglesofattackuptostall. However,itisexpectedthatthedragwillincreasesubstantially
duetotheobviousincreaseinbluntnessofthetrailingedgewithaGurneyflap,althoughthedrag
datawasnotreportedintheirwork.
Energies 2018,11,619 3of26
Tothebestofcurrentauthors’knowledge,researchofactiveflowcontrolofflatbackwindturbine
airfoilsisrare. Someactiveflowcontrolstudiesbasedonplasmaactuatorswereconductedonsome
generalbluntorroundtrailingedgeprofiles[18–20],demonstratingthattheactuatorcanenhancethe
mixingofthewakenearthetrailingedge,butonlylimitedenhancementinaerodynamicperformance
wasachieved. Recently,thecurrentauthors,Xuetal.[21],proposedaneffectiveandefficientactive
controltechniquefortheflatbackwindturbineairfoilusingcirculationcontrol(CC).Theblunttrailing
edgeofaDU97-flatbackairfoil[22]islocallymodifiedtoaroundshapewithapairofsmallstepson
thesuctionsideaswellasthepressureside. Ajetslotisdesignedattheupperstepperpendicularto
thecircularsurface. CCreliesontheCoandaeffect[23]andisimplementedbytangentiallyblowing
asmallhighvelocityjetoverthecircularCoandasurface. ItwasfoundthatCCnotonlysignificantly
increasestheliftbyenhancingthecirculation,butalsogreatlyreducesthebasedragbyeliminating
thewakevortex,indicatingapromisingactiveflowcontroltechniqueintheapplicationoflargewind
turbineswithblunttrailingedgeairfoils. However,itwasalsofoundthatthemodifiedroundtrailing
edgeairfoilundergoessignificantdegradationintheliftcharacteristicsduetothemodificationwhen
CC is deactivated, compared with its baseline flatback airfoil. This poses a problem for practical
use. Activecontroltechniquesaregenerallydesignedtoenablehighperformanceunderoff-design
conditions. Undertheconditionsofthedesignoperationpointorafailuretheactiveflowcontrol
systemmayencounter,thewindturbinewilloperatenormallywithoutcontrolactivated. Anideal
activecontroltechniqueshouldatleastmaintaintheaerodynamicperformancecomparabletothe
baselineflatbackairfoil. Therefore,effortsarestillneededtomaketoimprovethepreviouslyproposed
CCtechnique.
Inthepresentstudy,animprovedCCschemeisproposedfortheflatbackwindturbineairfoil.
Itisdesignedonthebasisofthepreviousone[21]. Thisnewdesigninvolveslessmodificationtothe
baselinetrailingedge,butprovidessignificantimprovementsintheliftcharacteristics. Theobjectiveof
thepresentstudyistomakeacomprehensivecomparisonbetweenthenewlyproposedCCtechnique
andthepreviousoneusingcomputationalfluiddynamics(CFD).Thisstudyisorganizedasfollows:
Section2describesthedetaileddesignofthemodifiedCCairfoils. Section3providesmethodologies
includingCFDmethods,implementationofCC,aerodynamiccharacteristicsanalysismethodand
anewlydefinedaerodynamicfigureofmerit. Section4addressesthevalidationofthepresentCFD
code. Section5presentstheresultsanddiscussions. Section6givessomeconclusionsdrawnfromthe
presentstudy.
2. DescriptionofCCAirfoilConfigurations
TheDU97-Flatbackairfoil,aflatbackversionoftheTU-DelftDU97-W-300airfoil[24],isemployed
inthepresentstudyasthebaselineblunttrailingedgeairfoil,asshowninFigure1withabluedashed
line. TheDU97-Flatbackairfoiliscreatedbyaddingthicknesssymmetricallytotheaft60%ofthe
DU97-W-300airfoil,givingablunttrailingedgewithathicknessof10%chord. Comparingwiththe
pastapproachoftruncatinganamountfromtheaftparttoformablunttrailingedge,thismethodhas
theadvantageofholdingtheblunttrailingedgeairfoil’smaximumthicknessandcamberconstant
withitsbaselinethintrailingedgeairfoil.
TheDU97-Flatbackairfoilinherentlydisplaysthenecessaryshapecharacteristicsofblunttrailing
edgethatjustmeettherequirementofCCimplementationifanappropriatelocalmodificationismade
tocreateahighlycurvedsmoothCoandasurfaceatthetrailingedge. Inthepresentstudy,theCoanda
surfaceisdesignedtobeacircularshape. Figure2showsthesketchmapofthetrailingedgeCoanda
surfacedesign. Theprocedureisgivenasfollows: (1)Copytheupperandlowersurfaceprofilelines,
andtranslatetheminwardbyadistanceof0.5%chord,forminglinesmandn;(2)Constructacircle
withtheconstraintthatthecircleistangenttotheupperandlowertranslatedlinesmandn,aswell
asthetrailingedgeline,formingthreetangencypointsE,FandP;(3)ConnectthecenterpointOof
thecircletothetwotangencypointsEandF,respectively, andthenextendthetwolinesegments
OEandOFtointersectwiththeupperandlowerprofilelines,obtainingtwointersectionpointsC
Energies 2018,11,619 4of26
Energies 2018, 11, x 4 of 26
aEnndergDies; 2(401)8F, 1o1r, xtr aditionalcirculationcontrol,thewholepartofthecircularsurfaceEPFistreate4d ofa 2s6
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Fcmiagvouirtreye r1se.haTalirhseetsic loa, wap eahrritgs uhorf-f patrhceees oscufirrtcheu eclacarav vistiuytyr fisash cdeae rEessiFg,a nependasr,u tarosifn stghh etohwcairnt c tuihnlea rFjeisgtu uarfrta etc he1e.E TsFlh,oeet nElsoHuwr ieinsr g tsatunhrgaftaecnthet e toojfe ttthhaete
tCchaoevasintloydt asE hsHaurriefsas tcaae n.p gaernt totfo tthhee cCirocaunldara ssuurrffaaccee .EF, ensuring that the jet at the slot EH is tangent to the
Coanda surface.

Figure 1. Profiles of the flatback and CC (Circulation Control) airfoils.
Figure1.ProfilesoftheflatbackandCC(CirculationControl)airfoils.
Figure 1. Profiles of the flatback and CC (Circulation Control) airfoils.

(a) (b) (c)
(a) (b) (c)
Figure 2. Details of the blunt trailing edge design: (a) DU97-Flatback; (b) DU97-Flatback-FCC (Full
FCFiiiggrucuurrelea 2t2i.o. nDD Ceetotaanilitslrs ooolf) f;t h(tche) e bDlbUulnu9t7n -ttFraltarialtibinlaignc kge-dPegCdeCg de (ePdsaiegrsntiig:a nl( a:C) i(DracU)ul9Da7tU-iFo9ln7a -tCFbolaanctktbr;a o(clb)k.); D(bU)9D7-UFl9a7tb-Falcakt-bFaCckC- F(FCuCll
Circulation Control); (c) DU97-Flatback-PCC (Partial Circulation Control).
(FullCirculationControl);(c)DU97-Flatback-PCC(PartialCirculationControl).
3. Methodologies
3. Methodologies
3. Methodologies
3.1. Numerical Methods
3.1. Numerical Methods
3.1. NumericalMethods
The numerical simulations in the present study are carried out using an in-house CFD code
The numerical simulations in the present study are carried out using an in-house CFD code
whicThh ies ncuapmaebrliec aolf scimomulparteiossnisblien Rtheeynporledsse-natvesrtuagdeyda Nreacvaierrri-eSdtookuest u(RsiAnNgSa)n siinm-huolautisoenC bFaDsecdo doen
which is capable of compressible Reynolds-averaged Navier-Stokes (RANS) simulation based on
wthhei cShpiaslacratp-Aablllmeoarfacso monper-eesqsuibalteioRne tyunrobludlse-nacvee rmagoeddelN [a2v8]i.e rT-hSteo ckleasss(iRcA cNenSt)rasli mfiuniltaet ivoonlbuamseed moenththode
the Spalart-Allmaras one-equation turbulence model [28]. The classic central finite volume method
S[2p9a]l aisrt -uAselldm faorra sthoen de-iescqrueatitzioantiotunr obfu gleonvceernminodg eelq[u28a]t.ioTnhse. Tclhaes siincvciesncitdra fllfiunxeitse avroel udmiscermetieztehdo dus[2in9g]
[29] is used for the discretization of governing equations. The inviscid fluxes are discretized using
itshue seudpwfoirntdh eRdoies crsecthizeamtieo n[3o0f]g owvietrhn ian gtehqiruda-toirodnesr. TMheoninovtoisncei dUflpusxteresaamre-cdeinstcerreetdiz eSdchuesmineg tfhoer
the upwind Roe scheme [30] with a third-order Monotone Upstream-centered Scheme for
uCpownsinerdvRatoioens chLeamwes [(3M0]UwSiCthL)a trheicrodn-sotrrduecrtiMono n[o3t1o].n eTUhep svtriescaomu-sc efnlutexreesd aSrceh ecmomefpourtCedo nusesirnvga titohne
Conservation Laws (MUSCL) reconstruction [31]. The viscous fluxes are computed using the
Lseacwosnd(M-oUrdSeCrL c)ernetcroaln dstirfufecrteionnci[n3g1.] .TThhe eLvoiwsceoru-Uspflpuexre sSyamremcoemtripcu-Gteadususs-iSnegidthele (sLeUco-SnGdS-o) rmdeerthcoendt [r3a2l]
second-order central differencing. The Lower-Upper Symmetric-Gauss-Seidel (LU-SGS) method [32]
is used to march pseudo time steps. The convergence of iteration is accelerated by implementing
is used to march pseudo time steps. The convergence of iteration is accelerated by implementing
the OpenMP parallel computing technique [33].
the OpenMP parallel computing technique [33].
3.2. Boundary Conditions
3.2. Boundary Conditions
Energies 2018,11,619 5of26
differencing. The Lower-Upper Symmetric-Gauss-Seidel (LU-SGS) method [32] is used to march
pseudotimesteps. TheconvergenceofiterationisacceleratedbyimplementingtheOpenMPparallel
computingtechnique[33].
3.2. BoundaryConditions
There are three different types of boundary conditions in the present study, namely, the wall
boundary,far-fieldboundaryandjetinletboundary.Onthewallboundary,theno-slipflowconditionis
Energies 2018, 11, x 5 of 26
applied.Thedensityandpressureonthewallboundaryareobtainedbyextrapolationfromtheinterior
solution.TOhenret haeref athr-rfieee lddifbfeoruenntd tayrpye,st hoef btroeuantdmaeryn tcoonfdbiotiuonnsd ainr ythceo pnrdeisteiontn sitsudbya,s endamoenlyt,h teheR iwemalla nn
invarbioaunntsdaforyr, afaorn-fei-edldim beonusniodnarayl flaonwd njeot rimnlaelt tbootuhnedbaoryu.n Odanr yth[e3 4w].aFllo brothuendDaUry9, 7t-hFel antboa-sclkip-F fCloCwa nd
DU9c7o-nFdlaittiboanc iks- aPpCpClieadi.r fTohiels dwenitshityt haendC poraensdsuareje otna cthtiev wataeldl ,btohuendhaigryh -aprer eosbstuarineecda bvyit yexitsraipnocllautdioend in
from the interior solution. On the far-field boundary, the treatment of boundary condition is based
simulations. Inpractice,anon-dimensionalsimilarityparametercalledjetmomentumcoefficientis
on the Riemann invariants for a one-dimensional flow normal to the boundary [34]. For the
specifiedatthejetslot,whichisdefinedas:
DU97-Flatback-FCC and DU97-Flatback-PCC airfoils with the Coanda jet activated, the
high-pressure cavity is included in simulations. In .practice, a non-dimensional similarity parameter
m V
j j
called jet momentum coefficient is specifCieµd =at t0h.e5 ρje∞t Vsl∞o2tS, w, hich is defined as: (1)
m V
where m. j is the jet mass flow rate, Vj is thCeμj=et0.v5eρlj∞oVcj∞i2tSy,, ρ∞ is the free-stream density, V∞(1i)s the
free-stream velocity, and S is equal to the chord length c for the present two-dimensional cases.
where m is the jet mass flow rate, Vj is the jet velocity, ρ∞ is the free-stream density, V∞ is the
Accordingtojthemomentumtheorem,thenumeratorisathrustforceintheoppositedirectionofthe
free-stream velocity, and S is equal to the chord length c for the present two-dimensional cases.
jetflowwhichisperpendiculartotheslotsurface. Therefore,Equation(1)canberewrittenas
According to the momentum theorem, the numerator is a thrust force in the opposite direction of the
jet flow which is perpendicular to the slot surface. TFherefore, Equation (1) can be rewritten as
C = Thrust , (2)
Thrust 0.5Fρ∞V∞2S
C = Thrust , (2)
Thrust 0.5ρV2S
where F represents the jet reaction force, and ∞C∞ is the jet thrust coefficient which is
Thrust Thrust
anonw-hdeimre eFnTshiruostn raelppraersaenmtse ttehrea njeat loregaocutisonto fCorLcae,n danCdD C.Thrust is the jet thrust coefficient which is a
nOonn-dthimeejentsiionnlaelt pbaoraumndetaerry a,ntahleogtooutas ltop CreL sasnudr eC,Dt. otal temperature and flow angle are specified,
andtheiOnfln otwhe vjeetl oinclietyt bisouenxdtraarpy,o tlhaete tdotfarlo pmretshsuerien, tteortiaolr tedmompearaintu.rTe haendto ftlaolwp raensgslue raerea tsptheecifjeietdi,n let
and the inflow velocity is extrapolated from the interior domain. The total pressure at the jet inlet
boundary is adjusted every 500 pseudo time-marching iterations until the flow is converged and
boundary is adjusted every 500 pseudo time-marching iterations until the flow is converged and
simultaneouslythedesiredjetmomentumcoefficientisachieved.
simultaneously the desired jet momentum coefficient is achieved.
AsshowninFigure3,thesolidsurfaceofthecavityisdefinedasthewallboundary. Whenthe
As shown in Figure 3, the solid surface of the cavity is defined as the wall boundary. When the
Coanda jet is deactivated, the jet slot EH is assumed to be a wall boundary since there is no flow
Coanda jet is deactivated, the jet slot EH is assumed to be a wall boundary since there is no flow
throughtheslot,andhencethecavityisnotincludedinthecomputation.
through the slot, and hence the cavity is not included in the computation.

Figure 3. Close-up of the trailing edge area of the DU97-Flatback-PCC airfoil.
Figure3.Close-upofthetrailingedgeareaoftheDU97-Flatback-PCCairfoil.
3.3. Aerodynamic Force Analysis for a CC Airfoil
For a CC airfoil, the analysis of lift and drag characteristics is quite different from that of a
conventional airfoil. For a conventional airfoil with a pure and closed solid boundary, the
aerodynamic force on the surface is due to only two basic sources, namely, pressure distribution
and shear stress distribution. The net effect of the pressure and shear stress distributions integrated
over the whole airfoil surface is the resultant lift and drag. However, as shown in Figure 3, taking
Energies 2018,11,619 6of26
3.3. AerodynamicForceAnalysisforaCCAirfoil
For a CC airfoil, the analysis of lift and drag characteristics is quite different from that
of a conventional airfoil. For a conventional airfoil with a pure and closed solid boundary,
theaerodynamicforceonthesurfaceisduetoonlytwobasicsources,namely,pressuredistribution
andshearstressdistribution. Theneteffectofthepressureandshearstressdistributionsintegrated
overthewholeairfoilsurfaceistheresultantliftanddrag. However,asshowninFigure3,takingthe
DU97-Flatback-PCC airfoil for example, there is an inlet boundary in the high-pressure cavity,
whichcausesadifferenceintheforceanalysis. Tosimplifytheanalysis,theinnertwosolidboundaries
andoneflowinletboundaryinthehigh-pressurecavity,asdrawnwithbluelinesinFigure3,arenot
includedintheaerodynamicforcecalculation. Theircontributionstotheoverallaerodynamicforces
aretakenintoaccountthroughthespecificaerodynamicanalysisattheslotsurfacedenotedbythered
dashedlineintheenlargeddrawinginFigure3.Therefore,theCCairfoilprofileshapeforaerodynamic
forceanalysisisconsideredastwoparts: theoutersolidsurfaceenclosedbytheblackboldprofile
line and the jet slot surface represented by the red dashed line. The slot surface is a jet passage,
andthejetcouldproduceareactionforce. Hence,onceitisconsideredasapartofairfoilprofilefor
aerodynamicforceanalysis,itsuffersfromthreetypesofforces,namely,pressure,shearstressand
areactionforce. Theshearstressisnegligiblebecausetheslotsurfaceisan“air”surfaceandthejet
directionisperpendiculartoit. Itshouldbenotedthatthepressureforceexertedontheslotsurface
cannot be neglected because it has a great contribution to the total aerodynamic force, especially
the drag. As sketched in the enlarged window in Figure 3, the force exerting on the slot surface
consists of the pressure force Fpressure and the reaction force Fm.Vjet, which are all pointing forward
and hence contribute to a reduced drag. Therefore, the overall aerodynamic force exerting on the
CCairfoilincludesnotonlythepressureandshearstressforcesontheoutersolidsurface,butalso
thereactionforceduetothejetemanatingfromtheslotandthepressureforceontheslotsurface.
Basedontheaboveanalysis,thetotalaerodynamicforceiscomputedbysummingthreecomponents:
thepressureforceontheoutersolidsurfaceaswellastheslotsurface,theshearstressforceonthe
outersolidsurface,andthejetreactionforceontheslotsurface. Correspondingnon-dimensionalforce
coefficientscanbeexpressedasC ,C ,C ,C ,C ,C ,respectively. Thus,thetotalliftand
L,p L,τ L,jet D,p D,τ D,jet
dragcoefficientscanbeexpressedas:
CL =CL,p+CL,τ+CL,jet =CL,p+τ+CL,jet, (3)
CD =CD,p+CD,τ+CD,jet =CD,p+τ+CD,jet, (4)
whereC ,C arecalculatedbythestandardintegraloperationjustassameasthatinthenormal
L,p+τ D,p+τ
simulation,whileC ,C arecomputedfrom:
L,jet D,jet
. →
m V →
jet jet
C = − •j, (5)
L,jet 0.5ρ∞V∞2c(1)
and:
. →
m V →
jet jet
C = − •i, (6)
D,jet 0.5ρ∞V∞2c(1)
→ → →
where(i, j)istheunitvectorrepresentingthedragandliftdirection,respectively,andV isthejet
jet
velocityvectorattheslotsurface.
3.4. AerodynamicFigureofMerit(AFM)andControlEfficiency
Asanactiveflowcontrolmethod,theCCimplementationrequiresacertainamountofauxiliary
power to energize the Coanda jet. Assessment of the active method should not only include the
enhancement of aerodynamic characteristics, but also take the power expenditure into account.
Energies 2018,11,619 7of26
Whether the increment of power output due to the flow control implementation can or cannot
exceed the power expenditure will definitely affect the method’s practicability and economy in
thewindturbineapplication. Itisnecessarytobuildanappropriateeffectivenesscriterionforthe
analysisofpowerexpenditure,powergainandcontrolefficiency. Aprerequisiteforcomparingthe
windturbineperformance,withandwithoutflowcontrol,isidentificationofappropriatefigureof
Energies 2018, 11, x 7 of 26
merit. ComparisonparametersforflowcontrolactuatorswerepreviouslydiscussedbySeifert[35].
TwoTaweroo daeyrnoadmynicamfigicu friegsuorefsm oef rmite(rAitF (MAFs)Mfos)r faocrt uaacttuoartpore rpfoerrfmoramnacnecceo cmopmapraisriosnonw wereeres usgugggesetsetedda nd
theiranredl athtievier rvealalutievse wvaelureesd wisecrues dseisdcufsosredv afroiro vuasritoyupse tsyopfesa cotfu aacttourasto.rHs. oHwoewveevre,rt,h tohsoeset wtwooA AFFMMss are
onlyasrue iotanblyle sfuoirtafibxlee dfo-rw fiinxgeda-pwpinligc aatpiopnlisc.atSiotanlsn. oSvtaelntoavl .e[t3 6a]l.d [e3fi6]n eddefianethdi rad tAhiFrdM AfoFMrw fionr dwtiunrdb ine
appltiucrabtiinoen sa,pwplhiciacthionwsa, swbhaicshe dwaosn btahseedr aotnio thbee trwatieoe nbegtweneeenra gteednepraotewde rpsowweirtsh wainthd awndit hwoiuthtoauctt ive
active flow control. But it was specifically tailored for wind turbines with zero-mass-flux
flow control. But it was specifically tailored for wind turbines with zero-mass-flux piezofluidic
piezofluidic actuators during the HAWT start-up process. All of the three AFMs are not suitable for
actuatorsduringtheHAWTstart-upprocess. AllofthethreeAFMsarenotsuitableforthecurrentCC
the current CC implementation. In the present study, a new figure of merit for the wind turbine
implementation. Inthepresentstudy,anewfigureofmeritforthewindturbineapplicationwithCC
application with CC is given as follows.
isgivenasfollows.
Assume that the Coanda jet is generated by pumping the free stream around the nacelle into
AssumethattheCoandajetisgeneratedbypumpingthefreestreamaroundthenacelleintothe
the higher-pressure cavity. A pump is located in the nacelle and the high-pressure cavity is
higher-pressurecavity. Apumpislocatedinthenacelleandthehigh-pressurecavityisconnectedto
connected to the flow outlet of the pump through a well-designed air passage inside the blade and
theflhouwb. oTuhtel eptoowfethr eexppuemndpittuhrreo fuogr hCaC wise tlhl-ed pesoiwgnere dneaeidrepda tsos apgueminps tihdee Cthoeanbdlaad jeeta, nwdhihcuh bis. Tushueaplloyw er
expeenvdailutuarteedf obyr aC pCowisetrh ceoepffoicwieenrt nPec,jeet dtheadt itso dpeufinmepd aths:e Coanda jet, which is usually evaluated by
apowercoefficientP thatisdefinedas:
c,jet  γ−1 
PPc,cje,tjet==m.mjeηtjcηetpcjTept0T101(cid:18)PPPP000221(cid:19)jγeγ−γt1 −−11/(cid:104)00..5ρ5∞ρV∞V∞3∞3cc((11))(cid:105),, (7) (7)
jet 01 jet
where ηjet is the pump efficiency which is assumed to be 0.85 in the present study, cp is the specific
whereη isthepumpefficiencywhichisassumedtobe0.85inthepresentstudy,c isthespecificheat
heatj eatt constant pressure, P01 is the total pressure at the pump inlet, P02 is the totapl pressure at the
atconstantpressure,P isthetotalpressureatthepumpinlet,P isthetotalpressureatthepump
pump exit, and T01 is0 1the total temperature at the pump inlet. 02
exit,andT isthetotaltemperatureatthepumpinlet.
Fi0g1ure 4 depicts the relative orientation of lift and drag to the rotation plane with respect to the
rFeilagtuivree 4wdinedp iVc∞t,s wthheerree lαa tiisv eeffoerciteinveta atniognleo offl iaftttaacnkd, βd risa gthteo ttwhiestr oantagtlieo nat pal agniveewn irtahdriaels psteactitotno. the
relatTivhee wpoiwnderV co∞e,ffwiciheenrte gαeniesraetfefedc btiyv ae tawnog-ldeimofenastitoancakl, aβirfiositl hweitthw uisntita snpgalne isa tcoamgpivuetend rbayd: ialstation.
ThepowercoeffiPci=en(Ltrg−eDnre)rVart⋅eηdb=y0a.5tρw∞oV-∞2dc(i1m)eCnLssiionn(αal+aβir)f−oiClDwciotsh(αun+iβt)spVa∞ncoiss(cαo+mβp)u⋅ηted by:
PCC= (qL∞qr∞−cc(D1(1)r)V)VV∞∞r ·ηWWTT=η==WTη0.W5CρTL∞[VsCi∞2nLc((s1αi)n[C+(Lαβs+in)(−βα00+.).C55βρ−ρD∞)∞−VcVCC∞o3∞3DDscc(((cc11oα)o)ss(+α(+αββ+))]Vβc∞)oc]socs(o(ααs+(+αβ)β+·)ηβ, W) ,TWT (8) (8)
wherwehηeWreT ηiWsTt hise thwei nwdintdu rtubrinbienee fefifcfiiceinencycyo offp poowweerr ggeenneerraattiioonn frforomm thteh etotroqruqeu, ea,nadn ids aisssausmsuedm teod bteo be
0.850in.85th ien pthree spernestesntut sdtyu.dy.

FigFuirgeur4e. 4A. eAreordoydnyanmamicicf oforrcceea annaallyyssiiss ooff tthhee wwinindd tuturbribnien esesceticotnio. n.
Hence, the power coefficient of the baseline flatback airfoil is:
PC,flatback =ηWT CL,flatbacksin(α+β)−CD,flatbackcos(α+β)cos(α+β), (9)
Energies 2018,11,619 8of26
Hence,thepowercoefficientofthebaselineflatbackairfoilis:
(cid:104) (cid:105)
P = η C sin(α+β)−C cos(α+β) cos(α+β), (9)
C,flatback WT L,flatback D,flatback
andthepowercoefficientoftheflatback-CCairfoil(PCCorFCC)is:
(cid:104) (cid:105)
PC,flatback−CC = ηWT CL,flatback−CCsin(α+β)−CD,flatback−CCcos(α+β) cos(α+β). (10)
Therefore,thepowercoefficientenhancementduetotheimplementationofcirculationcontrolis:
PC,gain = PC,flatback−CC−PC,flatback. (11)
SinceCCisusedtoimprovetheaerodynamicandpowerproductioncharacteristicsofthebaseline
flatbackairfoil,anewAFMsuitableforCCisformulatedtoquantifythegainedpowerintermsofthe
multipleofthegeneratedpowerbythebaselineflatbackairfoil,whichisdefinedas:
P
C,gain
AFM = . (12)
CC
P
C,flatback
Moreover,toassesstheabilityofCCtoenhancewindpoweroutputintermsofaunitofpower
expenditure,thecirculationcontrolefficiencyη isdefinedas:
CC
P
C,gain
η = , (13)
CC
P
C,jet
whichistheratiobetweenthepowergainandpowerexpenditure.
4. ValidationofCFDCode
ThepresentCFDcodeisvalidatedinpreviouspublications,includingtheS809airfoilatdifferent
Reynoldsnumbers[37–39],theDU97-W-300andDU97-Flatbackairfoils[21],andtheCC020-010EJ
airfoil[21]. InXuetal.[21],thegridindependencystudywasperformedontheDU97-W-300airfoil
rather than the DU97-Flatback airfoil, and the grids for DU97-Flatback and CC airfoil are directly
generatedbasedonthescaleofthechosenmeshforDU97-W-300afterthegridindependencystudy.
Inthepresentstudy,asimilarstrategyisadopted. BecauseDU97-W-300isnotunderthecurrentstudy,
novalidationwillbecarriedoutforit. Therefore,agridindependencystudywillbeperformedforthe
DU97-Flatbackfirst. ThenthescaleofthechosengridisusedtogeneratepertinentCCairfoils.
4.1. GridIndependencyStudyfortheDU97-FlatbackAirfoil
TheDU97-Flatbackairfoilhasablunttrailingedgewitht =10%,whichisrelativelythickin
TE/c
comparisontomostothercommonairfoils. Oneissuethatmustbeaddressedisthetreatmentofthe
trailingedgeforgridgeneration. Inthestructuredgridmethod,therearetwotypicalgridtopologies,
namely,theC-gridandO-grid. AC-gridisusuallyusedfortheRANSsimulationsforsharptrailing
edgeairfoils,duetotheabilitytominimizetheskewnessofthenear-wallmesharoundthetrailingedge
andobtainbetterstabilityandconvergenceinthesimulation. Thefactthatthetrailingedgehassome
thicknessposesaproblemintermsofhowonetreatstheclosureofthetrailingedge. Standishetal.[4]
deemedreasonabletoextendthechordoftheairfoilby0.2%andfitaquadraticpolynomialtoboth
thetopandbottomsurfacesforablunttrailingedgeairfoilusingtheC-gridtopology,althoughthis
treatment actually changes a little the shape of the trailing edge. An alternative way is to use the
O-grid topology for such a blunt trailing edge airfoil, which is popular since it can provide better
orthogonalityingridlinesneartheblunttrailingedge,thusgeneratingabettergridthanaC-grid.
Moreover,theO-gridcanreducethegridnumberandavoidhighaspectratioofgridsinthefarwake.
Therefore,theO-gridisadoptedforthepresentDU97-Flatbackairfoil.
Energies 2018,11,619 9of26
Toperformthegridindependencystudy,fourgridsaregeneratedwithgraduallyincreasinggrid
numbers, namely, a coarse grid of 225 × 100, a medium grid A of 315 × 141, a medium grid B of
450×200,andafinegridof630×283. Asaresult,thecellnumbersofthefourgridsincreasebya
factorofabouttwo. Inaddition,someotherrelevantparametersofthefourgridsarechangedstepby
step,includingfirstlayerspacingandnormalspacingincreasingratio. Thelargestfirstlayerspacing
ofthegridsis1.2 × 10−5 whichissmallenoughtoensurethatthey+islessthan1. Accordingto
thegriddingguidelinesgiveninMavriplisetal.[40], thefirsttwolayersofcellsatthewallareof
similarspacing,andthegrowthrateofthenormalspacingthroughtheboundarylayerisbelow1.20.
ThedetailsofthefourgridsarelistedinTable1.
Table1.DetailsofthegridsemployedfortheDU97-Flatbackairfoil.
Wrap-around Normal TotalNumber FirstLayer Spacing
Parameters
Points Layers ofCells Spacing/c IncreasingRatio
Coarsegrid 225 100 22,500 1.2×10−5 1.20
MediumgridA 315 141 44,415 1.0×10−5 1.16
MediumgridB 450 200 90,000 0.8×10−5 1.13
Finegrid 630 283 178,290 0.6×10−5 1.10
For the DU97-Flatback airfoil, only a few experimental data for CFD code validation can be
found in the literature. Barone et al. [22] provided the measured aerodynamic coefficients for a
DU97-Flatbackairfoilatonlythreeanglesofattack(AoA),andallofthemarechosenforthepresent
CFDcodevalidation. Accordingtotheexperimentalsetup,thepresentvalidationconditionsaresetas
AoA=4.12◦,11.05◦,13.40◦,respectively,withthesameMa=0.168andRe=3.0×106. Theresultsof
lift,dragandmomentcoefficientsaregiveninTables2–4. Thecalculatedliftcoefficientsagreerather
wellwiththeexperiment,whilethedragandmomentcoefficientshavealittlelargerdiscrepancies
withtheexperimentaldatabutwithinanacceptableextent. Thediscrepancybetweenthecalculated
andexperimentaldragcoefficientsmightbeduetoseveralaspects,includingthelimitationofthe
RANSturbulencemodel,lackoftransitionprediction,uncertaintyoftheexperimentwhichissubject
toerror,unsteadinessandwindtunnelwallinterference,etc. Themomentcoefficientsarecalculated
from the corresponding lift and drag coefficients, and hence there is no surprising that they have
somediscrepancieswiththeexperiment. InTables2–4,itisshownthatthelift,dragandmomentum
coefficientsalldecreasealittlewithincreasinggridnumber. Lookedfromtheoverall, therelative
changesbetweentwosuccessivegridsarequitesmall,andthemaximumis5.26%whichcorresponds
toC comparisonbetweenthecoarsegridandmediumgridAatAoA=11.05◦. Themaximumrelative
D
changeis2.6%betweenthemediumgridsAandB,and1.8%betweenthemediumgridBandfine
grid. Therefore,themaximumrelativechangebetweenthemediumgridBandfinegridisthesmallest.
Therelativepercentageofvariationof1.8%isacceptableforthepresentgridindependencystudy,and
hencethepresentstudyadoptsthemediumgridBastheresultofthegridindependencystudyfor
DU97-Flatback. ThemediumgridBisshowninFigure5withaclose-upofthetrailingedge,anditis
demonstratedthatit’ssatisfactoryforthepresentRANSsimulation. ThecomputationalgridsforCC
airfoilswillbegeneratedbasedonthescaleofthecurrentmediumgridB.
Table2.ComparisonofaerodynamiccoefficientsatAoA=4.12◦.
Parameters CoarseGrid MediumGridA MediumGridB FineGrid Experiment
C 0.8696 0.8688 0.8650 0.8598 0.833
L
C 0.04545 0.04311 0.04198 0.04145 0.0598
D
C −0.1419 −0.1410 −0.1404 −0.1390 −0.164
M
Energies 2018,11,619 10of26
Table3.ComparisonofaerodynamiccoefficientsatAoA=11.05◦.
Parameters CoarseGrid MediumGridA MediumGridB FineGrid Experiment
C 1.7339 1.7338 1.7292 1.7248 1.736
L
C 0.05095 0.04827 0.04715 0.04630 0.0545
D
C −0.1697 −0.1690 −0.1679 −0.1666 −0.2010
M
Energies 2018, 11, x 10 of 26
Table4.ComparisonofaerodynamiccoefficientsatAoA=13.40◦.
Table 4. Comparison of aerodynamic coefficients at AoA = 13.40°.
Parameters CoarseGrid MediumGridA MediumGridB FineGrid Experiment
Parameters Coarse Grid Medium Grid A Medium Grid B Fine Grid Experiment
CCLL 11.9.9991188 11.9.9991155 11..99886644 11.9.9883388 2.20.3033 3
C 0.05526 0.05238 0.05130 0.05063 0.0466
CDD 0.05526 0.05238 0.05130 0.05063 0.0466
C −0.1737 −0.1727 −0.1715 −0.1702 −0.210
CMM −0.1737 −0.1727 −0.1715 −0.1702 −0.210

Figure 5. Computational grid of a DU97-Flatback airfoil with close-up of the trailing edge.
Figure5.ComputationalgridofaDU97-Flatbackairfoilwithclose-upofthetrailingedge.
4.2. Validation of the GACC Airfoil
4.2. ValidationoftheGACCAirfoil
An experimental airfoil General Aviation Circulation Control (GACC) which is analogous to
AnexperimentalairfoilGeneralAviationCirculationControl(GACC)whichisanalogoustothe
the present FCC configuration is chosen to conduct the present CFD validation for CC
presentFCCconfigurationischosentoconductthepresentCFDvalidationforCCimplementation,
implementation, since there is no test data available for the present proposed CC wind turbine
sincethereisnotestdataavailableforthepresentproposedCCwindturbineairfoils. TheGACC
airfoils. The GACC airfoil was developed in a test program intended to address some technology
airfoilwasdevelopedinatestprogramintendedtoaddresssometechnologyissuesassociatedwith
issues associated with CC implementation in the aeronautical application [25]. It is a supercritical
CCimplementationintheaeronauticalapplication[25]. Itisasupercriticalairfoilmodelwithdual
airfoil model with dual slotted circulation control capability for low speed testing in the LaRC Basic
slottedcirculationcontrolcapabilityforlowspeedtestingintheLaRCBasicAerodynamicResearch
TAuenrnodely.nAacmcoicrd Rinegsetaorcthhe Tteusntnseelt.u Apcacnodrdteinstg dtaot athaev ateilsatb slee,tuthpe avnadli dteastito dnactoan advitaiiolanbilses, etthaes vAaoliAda=tio0◦n,
condition is set as AoA = 0°, Ma = 0.10, Re = 5.33 × 105, Cμ= 0.06. The pressure coefficient
Ma=0.10,Re=5.33×105,Cµ=0.06. Thepressurecoefficientdistributioniscalculatedandshown
distribution is calculated and shown in Figure 6, and the experimental data and CFD result by Jones
inFigure6,andtheexperimentaldataandCFDresultbyJonesetal.[25]usingtheFUN2Dcodeare
et al. [25] using the FUN2D code are shown for comparison. The FUN2D code employed the same
shownforcomparison. TheFUN2DcodeemployedthesameRANSequationsinconservation-law
RANS equations in conservation-law form along with the Spalart-Allmaras turbulence model as the
formalongwiththeSpalart-Allmarasturbulencemodelasthepresentsolver,exceptthatthegridis
present solver, except that the grid is fully unstructured. Hence, as expected, the present result
fullyunstructured. Hence,asexpected,thepresentresultagreesverywellwiththatfromFUN2D,
agrees very well with that from FUN2D, nearly coincident with each other. There is a favorable
nearly coincident with each other. There is a favorable comparison of the CFD and experimental
comparison of the CFD and experimental pressure coefficient distributions. The CFD results agree
pressurecoefficientdistributions. TheCFDresultsagreeverywellwiththeexperimentoveralmostthe
very well with the experiment over almost the entire airfoil surface except the bottom trailing edge
entireairfoilsurfaceexceptthebottomtrailingedgeareawherethelocalmeasuredpressurecoefficient
area where the local measured pressure coefficient even exceeds 2.0. This discrepancy may be due
evenexceeds2.0. Thisdiscrepancymaybeduetothelackofconfidenceintheexperimentaltrailing
to the lack of confidence in the experimental trailing edge pressure data and the associated error
edgepressuredataandtheassociatederrormagnitudes,asindicatedinJonesetal.[25]. Theflow
magnitudes, as indicated in Jones et al. [25]. The flow field with streamlines and Mach number
fieldwithstreamlinesandMachnumbercontourisgiveninFigure7,showingthatthefreestreamis
contour is given in Figure 7, showing that the free stream is deflected significantly due to the
deflectedsignificantlyduetotheCoandaeffectatthetrailingedge. Thisvalidationdemonstratesthat
Coanda effect at the trailing edge. This validation demonstrates that the present solver is reliable
thepresentsolverisreliableandadequateforthecirculationcontrolsimulations.
and adequate for the circulation control simulations.