Dynamic Stall Control on the Wind Turbine Airfoil via a Co-Flow Jet

25 Pages·2016·4.58 MB·English

energies
Article
Dynamic Stall Control on the Wind Turbine Airfoil
via a Co-Flow Jet
He-YongXu*,Chen-LiangQiaoandZheng-YinYe
NationalKeyLaboratoryofScienceandTechnologyonAerodynamicDesignandResearch,
NorthwesternPolytechnicalUniversity,Xi’an710072,China;[email protected](C.-L.Q.);
[email protected](Z.-Y.Y.)
* Correspondence:[email protected];Tel.:[phone]
AcademicEditors:LanceManuelandRuppCarriveau
Received:18March2016;Accepted:30May2016;Published:2June2016
Abstract: Dynamic stall control of a S809 airfoil is numerically investigated by implementing a
co-flow jet (CFJ). The numerical methods of the solver are validated by comparing results with
thebaselineexperimentaswellasaNACA6415-basedCFJexperiment,showinggoodagreement
in both static and dynamic characteristics. The CFJ airfoil with inactive jet is simulated to study
the impact that the jet channel imposes upon the dynamic characteristics. It is shown that the
presenceofalongjetchannelcouldcauseanegativeeffectofdecreasingliftandincreasingdrag,
leadingtofluctuatingextremeloadsintermsofdragandmoment. Themainfocusofthepresent
researchistheinvestigationofthedynamiccharacteristicsoftheCFJairfoilwiththreedifferentjet
momentumcoefficients,whicharecomparedwiththebaseline,givingencouragingresults. Dynamic
stallcanbegreatlysuppressed,showingaverygoodcontrolperformanceofsignificantlyincreased
lift and reduced drag and moment. Analysis of the amplitude of variation in the aerodynamic
coefficients indicates that the fluctuating extreme aerodynamic loads are significantly alleviated,
whichisconducivetostructuralreliabilityandimprovedlifecycle. Theenergyconsumptionanalysis
showsthattheCFJconceptisapplicableandeconomicalincontrollingdynamicstall.
Keywords: dynamicstall;windturbine;flowcontrol;numericalsimulation;co-flowjet
1. Introduction
The depletion of fossil-fuel reserves, stricter environmental regulations and the world’s
ever-growingenergydemandhavegreatlypromotedtheusageofalternativerenewableenergysources.
Amongthevariousrenewableenergyalternatives,windenergyisoneofthemostpromisingandthe
fastestgrowinginstalledalternative-energyproductiontechnologyduetoitswideavailability[1].
IntheHalfYearReportofWorldWindEnergyAssociation[2],itwasreportedthatthegrowthofthe
windenergyindustrywillcontinuewiththerapidincreaseinenergydemand,thereforemoreefforts
are stillneededto increase the efficiencyof windenergy generationinordertokeep windenergy
economicallycompetitivecomparedwithtraditionalfossilfuelsandotherrenewableenergysources
suchashydroelectricenergy,solarenergyandbio-energy.
Twofactorsthataffectthecostofwindenergyarelifetimeenergycaptureandmaintenancecost.
Therefore,sincethebeginningofthecommercialwindindustry,therotordiameterandturbinesize
havegraduallyincreasedinordertocapturemoreenergyduringthelifetime. Asturbinesgrowinsize,
thestructuralandfatigueloadsbecomemorenoticeable. Theextremestructuralandfatigueloadsare
importantfactorsinturbinedesignandmostoftheseloadsresultfromthedynamicstall. Adynamic
stallphenomenontakesplacewhenthewindturbinebladesectionissubjectedtounsteadyvariation
ofangleofattack. Duetothecomplicatedatmosphericenvironmentatwindfarms, windturbine
bladesusuallyexperienceadverseconditionsunderwhichthelocalangleofattackofaparticularblade
Energies2016,9,429;doi:10.3390/en9060429 www.mdpi.com/journal/energies
Energies2016,9,429 2of25
sectionwillvarywithtime,includinggroundboundarylayereffects,horizontalorverticalwindshear,
towershadowing,yawandtiltmisalignment,andunsteadyinflowduetoatmosphericturbulence
or wake from other turbines. All these conditions can give rise to the dynamic stall phenomenon.
Theunsteadyaerodynamicloadproducedbydynamicstallisalsoamainsourceofthevibration[3]
andaero-acousticnoise[4]. Withincreasingdeployment,morewindturbineswillbelocatedwithin
residentialareas,wheretheaerodynamicnoiseemittedbytherotorsmayhaveanegativeimpacton
thecomfortoflivinginthevicinity. Tominimizethesefactors,reducemaintenancecosts,prolongthe
turbinelifetimeandreducenoiselevel,oneeffectivewayistoexploreeffectiveflowcontrolmethods,
passiveoractive,toalleviatethefluctuationsofaerodynamicloads. Ontheotherhand,windfarms
innaturalconditionsmayfrequentlyexperienceadverseworkingconditionswherethewindspeed
isverylowandhenceconventionalwindturbinesgeneratelittleornousablepower. Thisissuehas
limitedthedeploymentofwindturbinestorelativelyfewsiteswherefavorablewindconditionsexist.
Therefore,thereisademandtodevelopeffectiveflowcontrolmethodswhichcansignificantlyincrease
theliftofthebladeatlowwindspeedsandallowtheturbinetocut-inearlierandcaptureadditional
energy. Hence,foraflowcontrolmethod,itisimportanttoprovidethebladewithboth,goodstatic
anddynamic,aerodynamicperofmance.
Variousflowcontrolmethodshavebeeninvestigatedtoenhancewindturbinebladeperformance,
includingtrailingedgeflaps[5],microtabs[6,7],vortexgenerators[8],blowingjets[9,10],circulation
control[11],Gurneyflaps[11],syntheticjets[12],andplasmaactuators[13]. Hannsetal.[10]carried
outanexperimentalstudytoexploreconstantblowingasaflowcontrolconceptforwindturbine
blades. Theirresultsshowedthatcontrolfromtheleading-edgeslothadasignificantpotentialforload
controlapplications,whilecontrolfromthemid-chordslotsignificantlyenhancedliftatpre-stallangles
ofattackbutwasineffectiveforsuppressingleading-edgestall. Tongchitpakdeeetal.[11]studiedand
comparedthestaticaerodynamicperformancesofawindturbinerotorequippedwithtrailing-edge
blowing and Gurney flaps. The results indicated that for attached flow conditions, trailing-edge
blowingandGurneyflapbothcanproduceanetincreaseinpowergenerationcomparedwiththe
baselineturbinerotor. However,theresultsalsoindicatedthatathigh-windspeedconditionswhere
theflowseparates,thetrailing-edgeblowingandtheGurneyflapbothbecameineffectiveinincreasing
thepoweroutput. YenandAhmed[12]implementedsyntheticjetstostudythewindturbinedynamic
stallcontrolanddemonstratedthatsyntheticjetscouldimprovelowspeedvertical-axiswindturbine
performancebutwithoutsubstantiallyalleviatingstallseparation. Greenblattetal.[13]experimentally
measuredtheeffectsofplasmapulsationondynamicstallcontrolontheupwindhalfofaturbineand
alsolimitedphase-lockedparticleimagevelocimetrymeasurementswereperformedunderbaselineas
wellastwocontrolledconditions. Itwasfoundthatatlowermaximumanglesofattack,theeffectof
pulsationsonthedynamicstallwasgreater,butseparationwasnotfullycontrolled,andthepower
requiredtodrivetheactuatorswassignificantlylargerthantheresultingturbinepowerincrease.
Zhaetal.[14–20]havedevelopedanewflowcontrolmethodbyimplementingaco-flowjet(CFJ)
on the suction surface, which has been proved an effective way to significantly increase lift, stall
marginanddragreductionforstationaryairfoilsandenhancetheperformanceofpitchingairfoils
in the aircraft research field. The working mechanism of a CFJ is different from the conventional
circulationcontrolwhichreliesonlarge-radiusleadingedgeortrailingedgetoinducetheCoanda
effectandenhancecirculation. TheCFJreliesonthejetmixingwiththemainflowtoenergizethemain
flowandovercometheadversepressuregradient. Moreover,thejetsuctioneffectnearthesuction
slotfurtherenhancesflowstabilitytoremainattachedtothesurfaceathighanglesofattack(AoA),
thusinducingmuchhighercirculationthanconventionalcirculationcontrolwithoutjetsuction. Ina
previousstudy,Xuetal.[21]introducedthisconcepttowindturbineairfoilapplication,focusingon
thestaticperformancewithactiveaswellasinactiveCFJ.Theresultsshowedthatsteadyco-flowjethad
agreatpositiveeffectinliftenhancement,stallmarginexpansion,anddragreduction.Forcaseswithjet
momentumcoefficientslargerthan0.12,thetotaldragevenbecamenegativeduetothejetreactionforces.
Energies2016,9,429 3of25
Inthepresentstudy,theCFJconceptisextendedtothedynamicstallcontrolonawindturbine
Energies 2016, 9, 429  3 of 25 
airfoil. TheprimarypurposeistoinvestigatethedynamicperformanceoftheCFJinsuppressing
Energies 2016, 9, 429  3 of 25 
wwiinndd tuturbrbinineea iarfiorfiolidl ydnyanmaimcsicta lsltaanlld acnodn sceoqnuseenqtluyeanltlleyv iaaltlienvgiafltuincgtu afltuincgtuaaetriondgy anearmodicylnoaamdsi.cE lnoeardgsy. 
cEwoninnesrdug mytu ecrdobnbisnyuetm haeeirdCf obFiJyl  ptdhuyemn CpamFiJsi cpa nusamtlaypllz  eiasd naadnn adclyocznoesmdeq pauanerden dtcloywm iatphllaetrhveeidaa twimnigoth u fntlhuteco tfaugmaatoiinnuegnd t aeoenfr eogrdagiyynnetaodm aesincse erlsogsaytd htsoe.  
eaEcsnoseenrsogsmy t hyceoo nefcsiuomnmpoelmedmy b eoynf t tihimneg pCltFehmJe peCunFmtJinopgn i stth haeen CawlFyiJnz odednt  utahrnbedi wn ceointmodp ctaournrebtdrion wled ittoyh n ctaohmnet iarcomsl todaulyln.nta omf igca sitnaelld.  energy to 
assess the economy of implementing the CFJ on the wind turbine to control dynamic stall. 
2. DesignoftheCFJAirfoil
2. Design of the CFJ Airfoil 
2. DeTshigenN oRfE thLeS C80F9J wAiinrfdotiul rbineairfoilisusedinthepresentstudyasthebaselineanditsdetailed
The NREL S809 wind turbine airfoil is used in the present study as the baseline and its detailed 
parametersaregivenin[22]. ThecorrespondingCFJconceptualairfoilisshowninFigure1,withan
paramTheete NrsR aEreL  gSi8v0e9n  wini n[2d2 t]u. rTbhien ec oarirrfeosipl oisn duisnegd  CinF tJh ceo npcreepsetunta ls tauirdfyo ial sis t hshe obwasne liinn Fe iagnudre i t1s,  dweittahi laend  
injection slot near the leading edge and a suction slot near the trailing edge on the airfoil suction
ipnajeractmioente srlso at rnee gairv ethne i nle [a2d2i]n. gT heed gcoer arensdp oan sduicntgio CnF sJl ocot nnceeaprt uthael  atirrafioliinl gis  esdhgowe non i nt hFeig auirrefo 1il,  wsuitchti oann  
surface. Theseslotsareformedbytranslatingdownwardaportionofsuctionsurface,givingriseto
sinujrefcatcioe.n T shloest en selaort st haere l efoardminegd  ebdyg ter aannsdla ati nsug cdtioown nswloat rnde aa rp tohreti otrna iolfin sgu cetdiogne  sounr ftahcee ,a girivfoinilg s uricstei otno  
thepresenceofajetchannel. Whentheco-flowjetisactivated,ajetisinjectedtangentiallyintothe
tshuer fparcees. eTnhcees eo fs lao jtest  acrhea fnonrmel.e Wd bhye ntr tahnes lcaot‐inflgo wd ojewt nisw aacrtdiv aa tpeodr,t aio jne to ifs  siuncjeticotend s utarnfagceen, tgiaivlliyn gin rtios et htoe  
mainflow,andasameamountofmassflowissuckedintothesuctionslot,formingaclosed-loopjet
mthaei np rfelosewn,c aen odf  aa  sjaetm ceh aamnnoeul.n Wt ohf emn atshse f cloow‐fl iosw su jectk eisd a icnttiov athteed s, uac tjeiot nis s ilnojte, cftoerdm tianngg ae ncltoiaslelyd ‐ilnotoop t jheet  
circuit. Apumpcanbeusedtopowertheco-flowjetflow. Byusingaclosed-loopjetrecirculation,
cmiraciuni tf.l oAw p, uanmdp a c saanm bee a umseodu ntot  opfo mwaesrs  tfhloew co i‐sf lsouwck jeedt  filnotwo .t hBey s uuscitniogn a s clolot,s feodr‐mloionpg  jae tc lroesceirdc‐ulolaotpio jnet,  
theflowattachmentonthesuctionsurfacewillbegreatlystrengthened,allowinganattractiveability
tchirec fuliotw. A a tptaucmhmp ecnant  obne  tuhsee sdu ctoti opno wsuerrf atchee  wcoil‐lf lboew g rjeeat tfllyo wst.r eBnyg tuhseinnged a,  aclloloswedin‐lgo oapn  ajettt rraecctiirvceu alabtiiloitny,  
toresistsevereadversepressuregradientsathighanglesofattack. Thesourceofjetflowisprovided
ttoh er efsloiswt  saetvtaecrhe madevnet rosne  tphree sssuucrteio gnr asudriefanctes  wati hlli bgeh  garnegaltelsy  ostfr aetntagcthk.e Tnehde ,s aolulorwcei nogf  jaent  falottwra cist ipvreo avbiidlietdy  
bysuckinganequalamountofflowmassfromthesuctionslotratherthantheengine,whichmakes
btoy  rseusciskti nsegv aenre e aqduvael rasme pourensts uofr ef lgorwa dmieanstss  farto mhig thh ea nsugcletiso onf  saltotta crakt.h Tehre t hsoaun rtchee o efn jegti nfleo, ww ihsi cphr omvaidkeeds  
theco-flowjetazeronetmassflow.
tbhye  scuoc‐kflionwg  ajent  eaq zuearlo a nmeto munats os ff lfoloww.  mass from the suction slot rather than the engine, which makes 
the co‐flow jet a zero net mass flow. 

Figure 1. Co‐flow jet conceptual airfoil. 
Figure1.Co-flowjetconceptualairfoil.
Figure 1. Co‐flow jet conceptual airfoil. 
The computational model of S809 CFJ airfoil is shown in Figure 2a, which includes the cavities 
ThecomputationalmodelofS809CFJairfoilisshowninFigure2a,whichincludesthecavities
of injTechteio cno manpdu stautciotinoanl  imn oodrdele ro ft oS 8m0a9k CeF tJh aei rsfiomilu ilsa tsihoonw mno irne  Freigaulirseti c2.a T, wheh liochca itniocnlu odfe isn tjhecet icoanv istlioest  
ofinjectionandsuctioninordertomakethesimulationmorerealistic. Thelocationofinjectionslot
AofC i nisje scetito ant  a6n.0d% scu fcrtoiomn  tihne o lredaedri ntog  medagkee,  ptheer pseimnduilcautiloanr  tmo othree  rloeacalils tsiuc.r fTahcee  wloictaht iao nh eoifg hintj eocft 0io.6n5 s%loct.  
ACissetat6.0%cfromtheleadingedge,perpendiculartothelocalsurfacewithaheightof0.65%c.
TAhCe  islo sceatt iaotn 6 .o0f% scu fcrtoiomn  tshleo tl eBaDdi nisg  seedt gaet,  2p0e.r0p%ecn dfricoumla rth teo  ttrhaei llioncga le sdugref,a cpee rwpietnhd ai chueliagrh tto o ft h0e.6 l5o%cacl.  
ThelocationofsuctionslotBDissetat20.0%cfromthetrailingedge,perpendiculartothelocalsurface
sTuhref alcoec awtiiothn  ao hf esiugchtti oonf  1s.l3o8t% BcD. T ios  esnest uarte  2th0.a0t% thce f jreotm is  ttahneg ternaitliianl gto e tdhgee s, uprefarcpee,n ad jiectu clhara ntno etlh lein lkoicnagl  
withaheightof1.38%c. Toensurethatthejetistangentialtothesurface,ajetchannellinkingthe
tshuer fiancjee cwtiiothn  aa nhdei gsuhct toiof n1 .3sl8o%tsc .i sT oca ernesfuulrley  tdheast itghnee jdet  bisy  ttarnagnesnlattiianl gto d tohwe snuwrfaarcde ,a an dje ts clihgahntlnye lr olitnaktiinngg  
injectionandsuctionslotsiscarefullydesignedbytranslatingdownwardandslightlyrotatingthe
tthhee  pinojretcitoino nA aBn odf  sthuec tbioanse slilnoets s iusc ctiaornef suullryfa dcee stiog ntheed  tbaryg tertaends lloatciantgio dno CwDn.w Foarrd th aen cda sseli gohf tilnya crtoitvaattinedg  
portion AB of the baseline suction surface to the targeted location CD. For the case of inactivated
cthoe‐f lpoowrt jieotn,  tAheBr eo fi st hnee abralyse nlion me sauscst filoonw s tuhrrfoauceg hto t hthee s tloartsg,e ttheed h liogcha‐tpiornes CsuDr.e F aonrd t hloew ca‐psere osfs uinrae cctaivvaittieeds  
co-flowjet,thereisnearlynomassflowthroughtheslots,thehigh-pressureandlow-pressurecavities
acore‐f eloxwclu jedte, tdh feorre  sisim nepalirclyit yn,o a ms sahsos wflonw in t hFrioguugreh  2thb.e  slots, the high‐pressure and low‐pressure cavities 
areexcludedforsimplicity,asshowninFigure2b.
are excluded for simplicity, as shown in Figure 2b. 
(a)  (b)
(a)  (b)
Figure 2. The computational models of S809 CFJ airfoil: (a) Jet‐on; (b) Jet‐off. 
Figure 2. The computational models of S809 CFJ airfoil: (a) Jet‐on; (b) Jet‐off. 
Figure2.ThecomputationalmodelsofS809CFJairfoil:(a)Jet-on;(b)Jet-off.
3. Methodology 
3. Methodology 
3. Methodology
3.1. Numerical Methods 
33..11.. NNuummeerriiccaall MMeetthhooddss 
The unsteady Reynolds‐Averaged Navier‐Stokes equations and Spalart‐Allmaras one‐equation 
turbuTTlhehneec uuenn mssttoeedaadedlyy a RrReee yuynsneoodlldd isns-‐ AtAhvveee prraraeggseeeddn NtN ianav‐vhiieoerru-‐SsSteto ockkoeedsse e etqqouu caaattriirooynn sosu aatnn tddh eSS pnpauallmaarrett-r‐AiAclallllmm staaurradasys .oo Mnneeo-‐reeeqq uduaeatttaiiooilnns  
tatuubrrobbuuutll etehnnecc eeg momvooeddreneliln aagrre ee uqususeeaddti ioinnn ttshh aeen ppdrr ebessoeeunnnttd iinna-‐rhhyoo cuuossneed cciootiddoeen tstoo c accaanrr brryye  ofoouuuttn tthhdee i nnn uu[2mm1]ee.rr Tiicchaaell  ssdttuuuaddlyy‐.t.i MMmoeo rrseete ddpeepttaainiillgss  
amabbeootuuhtto ttdhh e[e2 gg3oo] vvisee rranndiinongpgt eeeqqduu taaott iiaoodnnvssa aannncdde  btbhooeuu ntnidmdaaerry‐ya cccocounnrddaiitctiyioo nsnossl cucaatnino bnbe ew ffooituuhnn pdds ieinnu [d[22o11 ]]t..i mTThheee m ddauuraacllh-‐ttiiinmmgee b ssytte empppepaiinnnggs  
omf etthheo dL U[2‐3S]G isS  amdeotphtoedd  t[o24 a]d. vTahnec Re othe es tcihmeem‐aec [c2u5r]a cwyi tsho lau ttihoinrd w oitrhd eprs eMuUdoS CtiLm ree mcoanrscthriuncgti boyn  m[2e6a] niss  
uofs etdh et oL Ud‐iSscGrSet imzee tthhoed  i[n2v4i]s.c Tidh ef lRuxoees s cahnedm see c[o25n]d w cietnht raa tl hdiridff eorrednecri nMg UisS CuLse dre cfoonr sctorumcptiuonti n[g26 t]h ies  
vuissecdo utso  flduixscerse. tOizpee tnhMe Pin pvairsaclilde l fcluoxmeps uatnindg  steeccohnndiq uceen [t2r7a]l  isd iafpfeprleinedci ntog  aicsc eulseeradt ef othr ec soimmpuulatitniogn .t he 
viscous fluxes. OpenMP parallel computing technique [27] is applied to accelerate the simulation.
Energies2016,9,429 4of25
method[23]isadoptedtoadvancethetime-accuracysolutionwithpseudotimemarchingbymeansof
theLU-SGSmethod[24]. TheRoescheme[25]withathirdorderMUSCLreconstruction[26]isusedto
discretizetheinviscidfluxesandsecondcentraldifferencingisusedforcomputingtheviscousfluxes.
OpenMPparallelcomputingtechnique[27]isappliedtoacceleratethesimulation.
Theinflowandoutflowspecifiedatthefar-fieldboundaryarebasedonthecharacteristicsofthe
flow. Fortheinletandexitboundaries,EFandGH,inthehigh-pressurecavityandlow-pressurecavity
showninFigure2a,theflowconditionsaredefinedindifferentwaysinordertoeasilyimplementthe
CFJconcept. AttheinletboundaryEF,thetotalpressureP ,totaltemperatureT ,flowangleαare
t t
specifiedandinflowvelocityuisextrapolatedfromtheinterior. AttheexitboundaryGH,thestatic
pressureP isspecified,andthreeprimitiveflowvariablesu,vandρareextrapolatedfromtheinterior
s
domain. Inthesimulation,thetotalpressureP atboundaryEFandstaticpressureP atboundary
t s
GHaresubjecttochangeduringthenumericaliterationuntilthedesiredjetmomentumcoefficient
isachievedatbothinletEFandoutletGH.Thesolidsurfaceofairfoilandthecavitiesaredefinedas
non-slipwallboundaries. Densityandpressureonthesurfaceareobtainedbyextrapolationfrom
theinteriorsolution. Forthejet-offcase,thejetslotsACandBDareassumedtobewallboundaries,
andthehigh-pressureandlow-pressurecavitiesarenotincludedinthecomputation.
3.2. PitchOscillationMotionandRelevantParameters
The present study investigates the unsteady aerodynamic characteristics of the NREL S809
baselineandCFJairfoilsundergoingsinusoidalpitchoscillationsaboutthequarterchordpointwith
variousjetmomentumcoefficients. Thepitchoscillationmotionofanairfoilcanbedescribedina
sine-waveformexpressionwhichisdefinedintermsoftheinstantaneousangleofattackby:
αptq“α `α sinpωtq (1)
0 1
whereα andα arethemeanangleandpitchoscillationamplituderespectively. ω “ 2πf,withf
0 1
beingthefrequencyoftheoscillation. Foroscillatingairfoils,thereducedfrequencyκisusuallyused
todescribetheunsteadymotion,whichisdefinedas:
ωc
κ “ (2)
2V8
where c is the chord length, and V8 is the velocity of the free stream. This parameter represents
theinteractionbetweentheoscillationmotionaboutpitchaxisandthemainflowinthechord-wise
direction. Themagnitudeoftheparameterreflectsthedegreeoftheimpactthattheoscillationmotion
imposesuponthemainflow.
3.3. RelevantParametersinCFJAirfoilSimulation
Theimplementationofaco-flowjetisusuallycharacterizedbyasimilarityparameterC ,known
µ
asthemomentumcoefficient,whichisdefinedas:
.
m V
j j
C “ (3)
µ 0.5ρ8V82S
.
wheremj istheco-flowjetmassflowrate,Vjistheinjectionjetvelocity,ρ8isthefree-streamdensity,
V8isthefree-streamvelocity,andSisequaltocforthepresenttwodimensionalcases.
IntheCFJconcept,thepowerrequiredtopumpthejetisdeterminedbythejetmassflowrate
andtotalpressureratiotoovercomethetotalpressurelossoftherecirculatedjet. Thepowerisusually
describedbyanon-dimensionalsimilarityparametercalledpowercoefficientP ,whichisdefinedas:
c
. »ˆ ˙γ´1 fiO” ı
Pc “ mcfηjcpT01 – PP02 γ ´1fl 0.5ρ8V83S (4)
cfj 01 cfj
Energies2016,9,429 5of25
whereη isthepumpefficiency,c isspecificheatatconstantpressure,P istotalpressureatpump
cfj p 01
inletGH,P isthetotalpressureatpumpexitEF,andT istotaltemperatureatpumpinletGH.
02 01
3.4. DynamicMeshStrategy
The pitch oscillation motion of an airfoil is a classic unsteady flow problem which needs a
dynamic mesh to simulate the motion of the airfoil. The dynamic mesh is necessary for handling
theunsteadyproblemsinvolvinggeometricdeformationorrelativemotionbetweenmultiplebodies.
Usuallythedynamicmeshstrategiesaredividedintoseveralcategories,includingmeshdeformation,
meshregeneration,slidingmesh,andoversetmesh. Thecurrentauthorshavealsodevelopedanew
kindofrotationaldynamicoversetmesh,andsimulatedtheNACA0012pitchoscillation[28]aswell
asothercaseswithrelativelymovingbodies[29–33]. Alltheabovefourdynamicgridstrategiescan
beappliedtotheairfoiloscillationsimulation,butmoremanipulationisneededtoobtainaccurate
results. Inthepresentstudy,onlythesingleairfoilundergoingarigidoscillationmotionisconsidered
withoutregardinganyotherrelativelymovingbodies. Henceamoresimpledynamicmeshstrategy
thatdoesnotfallintotheabovefourcategoriesisappropriateforthepresentstudy,whichiscalled
rigidmovingmesh. Themeshperformsarigidrotationabouttheairfoilquarter-chordpointaccording
totheoscillationmotionandthegridvelocitycanbecalculatedinastraightforwardwaybydividing
themoveddistancefromonephysicaltimesteptothenextbytheintervaltimestep.
4. ResultsandDiscussion
4.1. BaselineSimulationandValidation
The static prediction precision of the solver has been validated in a previous study [21] by
comparing the numerical results of NREL S809 airfoil static characteristics with the experiment
conductedintheDelftUniversityofTechnology[34]. Here,thedynamicpredictionprecisionofthe
solverwillbevalidatedbycomparingresultswithexperimentconductedatOhioStateUniversity
(OSU)[22]. Thepitchoscillation, aswellasstaticcharacteristics, arebothinvestigatedintheOSU
experimentinordertoaidinthedevelopmentsofnewairfoilperformancecodesthataccountfor
unsteadybehavior. TheOSU-measuredsectionalstaticaerodynamiccoefficientsoftheS809airfoil
withangleofattackwillalsobesimulatedandcanbeusedtocomparewiththedynamiccounterparts.
4.1.1. StaticAerodynamicCharacteristicsandGrid-ResolutionStudy
Intheexperiment,theoriginalsharptrailingedgeofa457-mmchordS809airfoilwasthickened
to1.25-mmforfabricationpurposes. Thisthicknesswasaddedtotheuppersurfaceoverthelast10%
ofthechord. Inthepresentsimulation,thisminormodificationistakenintoaccountformodelingand
gridgeneration. Foralocallyblunttrailingedge,O-meshisabetterchoicethanC-meshwhichisused
forapreviousstaticperformancestudy[21]onasharptrailingedgeS809airfoil,sinceO-meshcan
easilyensurethemeshorthogonalityinthevicinityofablunttrailingedge.
The static simulation conditions are set in correspondence with its counterpart of oscillation
simulation,withMa=0.076,Re=1.0ˆ106.First,thegrid-resolutionstudyiscarriedoutforAoA=4.1˝.
Three different mesh resolutions are tested: a course mesh of 1.28 ˆ 104 cells, a medium mesh of
2.88ˆ104 cells, andafinemeshof5.12ˆ104 cells. Relevantdimensionsandspacingofthethree
meshesaregiveninTable1. Themeshrefinementiscarriedoutintheairfoil’snormaldirectionaswell
asthewrappingdirection. Thefirstlayerspacingisequaltoorlessthan1ˆ10´5toensurethatthey+
islessthan1. Figure3showsthemediummesh.
ThecomparisonsofaerodynamiccoefficientsfordifferentmeshlevelsarelistedinTable2. Thelift
andmomentcoefficientshaveafairlygoodagreementwiththeexperimentalresults, whereasthe
numericaldragcoefficientsaremuchlarger. Thisdiscrepancybetweennumericalandexperimental
dragcoefficientsisprobablybecausethenumericalsimulationsarecarriedoutundertheassumption
offullturbulencewhichcausesthedraglargerthanthatofalaminarflow. Intheexperimentthere
Energies2016,9,429 6of25
probablyexiststransitionatacertainlocationonthesuctionsurface,beforewhichtheflowislaminar,
and hence the resulting drag is lower than the assumed full turbulent flow. The introduction of a
transitionmodelintothesimulationisexpectedtoreducethediscrepancy. Fromanoverallviewof
Table2,theaerodynamiccoefficientspredictedwithafinermeshareclosertotheexperimentalresults,
andthereisasmalldifferencebetweenthemediumandfinemesh. Therefore, allthesimulations
are performed using the medium mesh. The jet-off CFJ airfoil mesh is obtained by adding the
correspondingpartofthejetchannelmeshtothebaselinemediummesh. Similarly,thejet-onCFJ
airfoilmeshisobtainedbyaddingthecorrespondingpartsofthejetchannelmesh,thehigh-pressure
andlow-pressurecavitiesmeshestothebaselinemediummesh.
Table1.DetailsofthegridemployedfortheS809baselineairfoil.
Parameters CoarseGrid MediumGrid FineGrid
Farfieldradius/c 50.0 50.0 50.0
NormallayersinO-mesh 80 120 160
Wrap-aroundpoints 160 240 320
Leading-edgespacing/c 0.0038 0.0025 0.0018
Trailing-edgespacing/c 0.0017 0.0010 0.0008
Firstlayerspacing/c,ˆ10´5 1.0 1.0 0.5
Spacingincreasingratio 1.20 1.13 1.08
Totalnumberofcells,ˆ104 1.28 2.88 5.12
Energies 2016, 9, 429  6 of 25 

Figure 3. O‐mesh for S809 airfoil (medium level). 
Figure3.O-meshforS809airfoil(mediumlevel).
The comparisons of aerodynamic coefficients for different mesh levels are listed in Table 2.  
Table2.Comparisonofaerodynamiccoefficientsfordifferentmeshlevels[Ma=0.076,Re=1ˆ106,
The lift and moment coefficients have a fairly good agreement with the experimental results, whereas 
AoA=4.1˝].
the  numerical  drag  coefficients  are  much  larger.  This  discrepancy  between  numerical  and 
experimental drag coefficients is probably because the numerical simulations are carried out under 
Parameters CoarseGrid MediumGrid FineGrid Experiment
the assumption of full turbulence which causes the drag larger than that of a laminar flow. In the 
experiment there pCrLobably exis0ts.5 t2r8a3nsition at a c0e.5r4ta0i6n location 0o.n5 4t6h4e suction 0s.u55r0fa0ce, before which 
C 0.0206 0.0161 0.0155 0.0050
the flow is laminarD, and hence the resulting drag is lower than the assumed full turbulent flow.  
C ´0.0371 ´0.0380 ´0.0383 ´0.0461
The introduction oMf a transition model into the simulation is expected to reduce the discrepancy. 
From an overall view of Table 2, the aerodynamic coefficients predicted with a finer mesh are closer 
Themediummeshisfurtherusedtosimulateawiderangeofanglesofattackfrom´20˝to24˝
to the experimental results, and there is a small difference between the medium and fine mesh. 
formorevalidations. Thecomputedaerodynamicforceandmomentcoefficientsarecomparedwith
Therefore, all the simulations are performed using the medium mesh. The jet‐off CFJ airfoil mesh is 
experimentalresultsinFigure4. AllthesimulationsarecarriedoutatsameMachnumber0.076and
obtained by adding the corresponding part of the jet channel mesh to the baseline medium mesh. 
ReSyinmoilldasrlny,u tmheb jeert‐1o.n0 CˆF1J 0a6i.rfTohile mpersehs eisn otbsttaatinicedre bsuy latsddwiinlgl btheeu csoerdretsopcoonmdipnagr epawrtisth oft htheen jeext tchdaynnnaeml ic
stamllersehsu, tlhtse whihgihc‐hprveasrsyurine aanrda nlogwe‐opfreasnsgulrees coafvaittiteasc kmbesehtwese teon th4˝e banasdel2in4˝e. mFreodmiumFi gmueresh4., fortherange
ofanglesofattackfrom´6˝to8˝,thenumericalresultsagreeratherwellwiththemeasurement.Afterthe
flowseTpaabralet i2o.n Coomccpuarrriseonnc eo,f taheeroldiyftniasmaicl ictoteleffiociveenrt-sp forer ddiicffteerdenbt umtewshi tlhevinelsa [nMaac =c e0p.0t7a6b, lReed =e 1g r×e 1e0,6a, ndthe
variatioAnotAre =n d4.1is°].w  ellcaptured.Overall,thepresentnumericalresultsagreefairlywellwithexperiment.
Parameters  Coarse Grid Medium Grid Fine Grid Experiment 
CL  0.5283  0.5406  0.5464  0.5500 
CD  0.0206  0.0161  0.0155  0.0050 
CM  −0.0371  −0.0380  −0.0383  −0.0461 
The medium mesh is further used to simulate a wide range of angles of attack from −20° to 24° 
for more validations. The computed aerodynamic force and moment coefficients are compared with 
experimental results in Figure 4. All the simulations are carried out at same Mach number 0.076 and 
Reynolds number 1.0 × 106. The present static results will be used to compare with the next dynamic 
stall results which vary in a range of angles of attack between 4° and 24°. From Figure 4, for the range 
of angles of attack from −6° to 8°, the numerical results agree rather well with the measurement. After 
the flow separation occurrence, the lift is a little over‐predicted but within an acceptable degree, and the 
variation trend is well captured. Overall, the present numerical results agree fairly well with experiment. 
Figure 5 gives the comparison of surface pressure coefficient distributions with measurements 
for several AoA conditions, also showing rather good agreements except for large angles of attack 
over 20°.
Energies2016,9,429 7of25
Figure5givesthecomparisonofsurfacepressurecoefficientdistributionswithmeasurementsfor
severalAoAconditions,alsoshowingrathergoodagreementsexceptforlargeanglesofattackover20˝.
Energies 2016, 9, 429  7 of 25 
Energies 2016, 9, 429  7 of 25 

(a)  (b)

(a)  (b)
(c)
(c)
Figure 4. Comparisons of computed static aerodynamic coefficients with experiment: (a) Lift coefficient; 
Figure4.Comparisonsofcomputedstaticaerodynamiccoefficientswithexperiment:(a)Liftcoefficient;
(b)F Digruarge  4c.o Cefofmicipeanrtis; o(cn)s  Mofo cmomenptu cteode fsftiactiiecn ate.r odynamic coefficients with experiment: (a) Lift coefficient; 
(b)Dragcoefficient;(c)Momentcoefficient.
(b) Drag coefficient; (c) Moment coefficient. 
(a)  (b)
(a)  (b)
Figure 5. Cont. 
Figure 5. Cont. 
Figure5.Cont.
Energies2016,9,429 8of25
Energies 2016, 9, 429  8 of 25 
Energies 2016, 9, 429  8 of 25 
(c)  (d)
Figure 5. Comparisons of surface pressure coefficient distributions with experiment: (a) AoA = 6.1°; 
Figure5.Comparisonsofsurfacepressurecoefficientdistributionswithexperiment:(a)AoA=6.1˝;
(b)(bA)o AAoA= 1=2 1.22˝.2;°(;c ()c)A AooAA(= c=)1  188..11˝°;; ((dd)) AAooAA == 2244°˝. . (d)
4.1.2. DFiygnuarem 5i.c C Cohmapraarcisteorniss toifc ssu arnfadce T pimreses‐uRree scooleufftiicoienn St tduisdtryi butions with experiment: (a) AoA = 6.1°; 
4.1.2. DynamicCharacteristicsandTime-ResolutionStudy
(b) AoA = 12.2°; (c) AoA = 18.1°; (d) AoA = 24°. 
In the OSU experiment, unsteady data were obtained for the S809 airfoil model undergoing 
In the OSU experiment, unsteady data were obtained for the S809 airfoil model undergoing
si4n.u1s.2o.i Ddayln paimtcihc  oCshcailrlaacttioernisst wicsit han ad c Tomimper‐eRheesnosluivtieo sne St toufd teys t conditions, including two angle of attack 
sinusoidal pitch oscillations with a comprehensive set of test conditions, including two angle of
amplitudes, ±5.5° and ±10°; four Reynolds numbers, 0.75, 1.0, 1.25, and 1.4 million; three pitch 
attack amInp tlhiteu OdeSsU, ˘ex5p.5er˝imanendt,˘ u1n0s˝te;afdoyu rdaRteay wnoerled sobntuaimnebde rfso,r 0t.h7e5 ,S810.09, a1i.r2fo5i,l amnodd1e.l4 umndilelrigooni;ngth ree
oscillation reduced frequencies, 0.026, 0.052, and 0.077; and three mean angles of attack, 8°, 14°, and 
pitchsinouscsiolildaatilo pnitrcehd ousccieldlatfiroenqsu wenitchi ae sc,o0m.0p2r6e,h0e.n0s5iv2,e asnetd o0f .t0es7t7 c;oannddittiohnres,e inmcleuadninagn tgwleos aonfgalet toafc akt,ta8c˝k, 14˝,
20°. In the present study, the following conditions are selected for all of the validation simulations as 
andwaoe2msl0lc˝ pial.llsiaI tnttuhiodtehne s esru,e pbd±rs5uee.sc5qee°udn ea tnfnrstdet ucq ou±dm1ey0n,p°ct;ahi erfesao,tfu io0vr.l 0elRo2 sw6et,yu i0nnd.o0giel5dsc2:so,   mnanndeudiamt ni0ob .a0nen7rss7ga,;l  era0e n.o7sdf5e  a,tl hte1tcra.e0tcee,k d m1 α.f20eo 5a=r,n  a1 aal4nln°do,g  fal1ents.hg4 eo lemfv  aoaitlfltl iiaadoctnatkat;, ic 8otkh°n ,ra e1sme4im °pp,l uaiittlnucadhdti  eo ns
asαw12 e=0l °l1.a 0Is°n,t  tRhheeey spnurobelssdeesnq ntu suetmnutdbcyeo,r mt Rhpee  af=or 1all.to0iwv meinislgtlui ocdonin,e dasni:tdmio rneesad nauraecne sdge llfeerceotqefdua etftnoarcc yak lκlα  o=0f  =0t.h01e74 7v˝.a, Tlaihndeag tlaieoironff osaiilmt ptaueclrakftoiaormmnsps  altisht ue de
α1s=iwn1ue0sl˝lo ,aiRds eathyl epn iostulcdhbss oensqucuimlelnabtte icoronRm aepb=aoru1at.t0 iivtmse  qsiltuluiaodrnitee,sra:  cnmhdeoarrendd  apunocgienldet .o frf eaqttuaecnkc αy0 κ= 1=40°,. 0a7n7g.leT ohfe aatitrafcoki lapmeprlfioturmdes the
sinusoiTdhael pistcimhuolsactiilolantsi onaraeb oupteritfsorqmueadrt erucshinogr dpthorienet . different  non‐dimensional  time  steps  
α1 = 10°, Reynolds number Re = 1.0 million, and reduced frequency κ = 0.077. The airfoil performs the 
(nsoTinnhu‐edsoimidseiamnl spuioiltnachtai looizsnecsdill abatyiro ecn/ Vap∞b)oe rudftto  =irt sm0 q.0eu0da8r,t e0ur.0s ci1hn0og, r0d. 0tp1ho2ri,en ert.e spdeicffteivreelnyt, inn oornd-edri mtoe innsvieosntiaglatet itmhee timstee ps
(nosnte-pd ismeTnehsneit siivositinmya bulialzaseteiddon obsn y thacre/e aV e8rpoe)drfydontram=medi0c  .c0ou0e8sfi,fnicg0i .e0n1tth0sr.,e Fe0o .u0dr1 ic2fof,enrrseeensctpu eticnvtoeinv c‐eydlcyilm,esei nnarseioo snrudaflef ircitetimonte it nov sotebestptaisig n a te
thea t(pinmeorneio‐sddtieimcp essonelsuniotsiniotainlvi,z iateynddb b aiyns e ctd/hVeo∞ )np drteth s=ee n0a.te0 rs0ot8ud, d0yy.n0 1ap0mlo, it0ct.e0cd1o2 ce, ufrfirevcsipeesen cattsrive. eFoloybu,t airninc ooerdnd sfeerroc utmot  iitvnhevee cfsyotciuglreatsthea  ctryhecesl euti.mf fiTehc iee nt
tocoobsmtteappin asreainsospintei rvoiioft ydn biucamsseoedrlu ioctnail ot hnaee, raaoendrdoydniynanmtahimce icpco rceeofsefeifcfniicetinestntsut sdw. yFitohpu lreo cxtotpenedsreimccuuetrnivvteeas lc yamcrleeeasos aubrrteae sminueeffndictsife rnaortm eto g tohivbeteanfion iu nr th
cycFliaeg .upTreehr ieo6d,c ioschm soopwlauirtniiogsno a,n  aronefdan sionun mtahbeelr ypic rageloseaonedtr  osatdgurydenyea mpmleonitctte.c doH ecyfusfirtvceiereesn saitsrse wi so biptthareiensxeedpn tef rriionmm te htneht eaa lfeormuordetayhsn cuayrmcelmiec.  eTfnohtresc ea re
givceocneofmifnicpiFaeirngitsu ocrnue ro6vf,e nss huaomsw ewriienclgal la aas erterhoaeds oymnnoaammbleiycn tgc ooceoofedfficfaiiceginertenset  mwcuietrhnv tee..x HpItey irssitm earelsenost iasslh imoswepanrse utshreeanmtt seimnntasth llaeerrea  tegirmiovede nys tnienap ms ic
haFvigeu lirtet le6 ,e sffheocwtsi onng  tah er eaacscounraabcyly o gf othoed  reasgureltesm, aenndt.  hHenysctee trhesei sm iisd dplree stiemnte  isnte tph oe fa detr =o d0.y0n1a0m isi cs efloercctee d 
forcecoefficientcurvesaswellasthemomentcoefficientcurve. Itisalsoshownthatsmallertimesteps
toc coaerffriyc ioeuntt  acullr tvhees  sausb wseeqllu aesn tt hpei tmcho omsecniltl actoioenff iccaiesnest  fcourr vbeo.t hIt  tihs ea jlesto‐ osfhfo awnnd  tjehta‐to nsm coalnlefirg tuimraeti ostnesp. s 
havelittleeffectsontheaccuracyoftheresults,andhencethemiddletimestepofdt=0.010isselected
have little effects on the accuracy of the results, and hence the middle time step of dt = 0.010 is selected 
tocarryoutallthesubsequentpitchoscillationcasesforboththejet-offandjet-onconfigurations.
to carry out all the subsequent pitch oscillation cases for both the jet‐off and jet‐on configurations. 
(a)  (b)
(a)  Figure 6. Cont.  (b)
Figure 6. Cont. 
Figure6.Cont.
Energies 2016, 9, 429  9 of 25 
Energies2016,9,429 9of25
Energies 2016, 9, 429  9 of 25 
(c)
(c)
FiguFrieg ur6e.   6C. oCmopmapriasroisno no fo f aeareoroddyynnaammiicc   ccooeeffffiicciieenntt  lolooopps s fofro rr erdeudcuedce dfr efqrueeqnuceyn cκy  =κ  0.=0 770:. 0 77:  
Figure 6. Comparison of aerodynamic coefficient loops for reduced frequency κ = 0.077: (a) Lift
(a) L(aif)t L ciofte cffoiecfifeicnite;n (tb; )( bD) rDarga gc oceofeffifciiceiennt;t ;( (cc))  MMoommeenntt  ccooeefffifcicieiennt.t . 
coefficient;(b)Dragcoefficient;(c)Momentcoefficient.
In FInig Fuirgeu r7e,  7t,h eth ec aclcaulclualtaetded  reressuultltss  ooff  bbootthh  ssttaattiicc  aanndd o socsicllialltaintign gm omtiootniso nast  tahtr eteh rreeed urceeddu ced 
freqfurIneeqnFucieigenuscr i0ee.s70 ,02t.60h,2 e06c.,0 a05l.c02u5, 2l0a,. t00e7.d077r 7ae rsaeur elpt pslolootftttebedod t thtoogsgteeattthhiceerra,, n iindn  ooorsrdcdeilerl rat ottio nc lgcelameraloyrtl iyeox nehxsibhaiittb ttihhtr ete heefefr eeecdftfu eoccfe to doscff irolelsaqctuiinlelgna tciinesg 
0m.0o2t6mio,on0t. i0oa5nn2 d,a 0nr.de0 d7ru7edcaeurdcee pdfrl eofrqtetueqedunetcnoycg yeo tonhn et rht,heie n aaoiirrrffdooeiillr  aateoerrocolddeyaynrnalaymmeicxi chp ipebreiftroftrohmremaenafcfnee.c ceItt.  ocIfta oncs abcneil  lbfaoetui nfnogdu mtnhdoa tti tohthnaet a tnhde 
redumceodtiofrne oqfu aeinrfcoyil oanndt htheea pirafroaimlaeeterro dofy rneadmuciecdp ferrefqouremncayn chea.vIet ac asunbbsetafnotuianl dimtphaacttt ohne tmheo ftlioown foiefladi.r foil
motion of airfoil and the parameter of reduced frequency have a substantial impact on the flow field. 
andTthhee posacriallmatientger mooftrieodn ulecaedds ftroe qthuee napcypehaaravnecae souf bhsytsatenrteiasilsi mlooppasc tfoorn atllh aeeflroodwynfiaemldic. Tcoheeffoicsiecniltlsa,t ing
The oscillating motion leads to the appearance of hysteresis loops for all aerodynamic coefficients, 
motiaonnd lae aladrsgetro rtehdeucaepdp feraerqaunecnecyo lfehadyss tteor eas liasrlgoeor pospefonirnagl lina ethroe dhyynstaemreiscisc looeofpfisc. iTenhets ,hiagnhdesta llifatr ger
and a larger reduced frequency leads to a larger opening in the hysteresis loops. The highest lift 
coefficient obtained during oscillation is correspondingly much higher than its static counterpart. The 
reducedfrequencyleadstoalargeropeninginthehysteresisloops. Thehighestliftcoefficientobtained
coefficient obtained during oscillation is correspondingly much higher than its static counterpart. The 
higher the reduced frequency, the higher the highest lift coefficient. It is also shown that a higher 
duringoscillationiscorrespondinglymuchhigherthanitsstaticcounterpart. Thehigherthereduced
higher the reduced frequency, the higher the highest lift coefficient. It is also shown that a higher 
reduced frequency can generate even larger drag and moment peaks at high angles of attack, causing 
frequency, the higher the highest lift coefficient. It is also shown that a higher reduced frequency
reduced frequency can generate even larger drag and moment peaks at high angles of attack, causing 
a greater extreme aerodynamic load which could lead to structural fatigue or even worse the total 
cangenerateevenlargerdragandmomentpeaksathighanglesofattack,causingagreaterextreme
a grdeaamtear geex otrfe tmhee  satreuroctduyren.a Omniec  plouardpo wseh oicf hth ceo purleds elenat dre tsoe asrtcrhu cist utora rle fdauticgeu teh ios rk ienvde no fw flourcstue atthineg t otal 
aerodynamicloadwhichcouldleadtostructuralfatigueorevenworsethetotaldamageofthestructure.
dameaxgtree mofe  taheer osdtyruncatmuirce .l oOadn eb yp uimrppolesme eonft itnhge  ap croe‐sfelonwt  rjeets eoanr cthhe i sa irtofo irle sduucctieo nth siusr kfaicned a nodf  fwluilclt ubea ting 
Onepurposeofthepresentresearchistoreducethiskindoffluctuatingextremeaerodynamicloadby
extrpemresee naeterdo dlaytenra. mic load by implementing a co‐flow jet on the airfoil suction surface and will be 
implementingaco-flowjetontheairfoilsuctionsurfaceandwillbepresentedlater.
presented later. 
(a)  (b)
Figure 7. Cont. 
(a)  (b)
Figure 7. Cont. 
Figure7.Cont.
Energies2016,9,429 10of25
Energies 2016, 9, 429  10 of 25 
(c)
Figure 7. Comparison of aerodynamic coefficient loops for the static and oscillating motions under 
Figure7. Comparisonofaerodynamiccoefficientloopsforthestaticandoscillatingmotionsunder
three reduced frequencies: (a) Lift coefficient; (b) Drag coefficient; (c) Moment coefficient. 
threereducedfrequencies:(a)Liftcoefficient;(b)Dragcoefficient;(c)Momentcoefficient.
4.2. CFJ Simulation and Validation 
4.2. CFJSimulationandValidation
A CFJ airfoil based on the NACA 6415 airfoil was tested by Dano et al. [17] in the University of 
A CFJ airfoil based on the NACA 6415 airfoil was tested by Dano et al. [17] in the University
Miami 24″×24″ wind tunnel facilities. The CFJ airfoil was a NACA 6415 with the injection and suction 
ofMiami24”ˆ24”windtunnelfacilities. TheCFJairfoilwasaNACA6415withtheinjectionand
located at 7.5% and 88.5% of the chord, respectively. The injection and suction slot heights were 0.65% 
suctionlocatedat7.5%and88.5%ofthechord,respectively. Theinjectionandsuctionslotheightswere
and 1.42% of the chord. In the experiment, the CFJ is provided by a separated high pressure source 
0.65%and1.42%ofthechord. Intheexperiment,theCFJisprovidedbyaseparatedhighpressure
for the injection and a low pressure vacuum sink for the suction. The injection and suction flow 
sourcefortheinjectionandalowpressurevacuumsinkforthesuction. Theinjectionandsuctionflow
conditions were independently controlled. A compressor supplied the injection flow and a vacuum 
conditionswereindependentlycontrolled. Acompressorsuppliedtheinjectionflowandavacuum
pump generates the necessary low pressure for suction. Both mass flow rates in the injection and 
pump generates the necessary low pressure for suction. Both mass flow rates in the injection and
suction slots were measured using orifice mass flow meters. More experiment details can be found 
suctionslotsweremeasuredusingorificemassflowmeters. Moreexperimentdetailscanbefound
in [17]. The free stream Mach number was 0.03, and the chord‐based Reynolds number was 195,000. 
in[17]. ThefreestreamMachnumberwas0.03,andthechord-basedReynoldsnumberwas195,000.
The leading edge trip was used to achieve full turbulent boundary layer to be consistent with the 
The leading edge trip was used to achieve full turbulent boundary layer to be consistent with the
CCFFDD aannaallyyssiiss.. TThhee ooppeenn sslloott ccaassee iinn tthhee eexxppeerriimmeenntt wwiitthh mmoommeennttuummc cooeefffifcicieiennttC Cμ == 00..0088 iiss cchhoosseenn ttoo 
µ
validate the present solver for CFJ simulation. 
validatethepresentsolverforCFJsimulation.
Based on the grid‐resolution study in Section 4.1.1, the computational mesh for the present 
Basedonthegrid-resolutionstudyinSection4.1.1,thecomputationalmeshforthepresentNACA
NACA 6415 CFJ airfoil is generated in a similar way according to the medium mesh for the NREL 
6415 CFJ airfoil is generated in a similar way according to the medium mesh for the NREL S809
S809 CFJ airfoil. The computed lift, drag and power coefficients are presented in Figures 8 and 9, and 
CFJairfoil. Thecomputedlift,dragandpowercoefficientsarepresentedinFigure8andFigure9,
athned ftlhoewfl foiewldfi aetl dAaotAA =o 1A5°= i1s 5s˝hioswsnh oinw FniginurFeig 1u0r. eT1h0e. pTrheesepnrte nseunmtenruicmale rriecsaullrtse saurlet scoamrepcaormedp awreitdh 
experimental as well as CFD results by Lefebvre et al. [18], showing fairly good agreements, especially 
with experimental as well as CFD results by Lefebvre et al. [18], showing fairly good agreements,
for the power coefficient. For the lift coefficient, good agreement is achieved up to the highest AoA 
especially for the power coefficient. For the lift coefficient, good agreement is achieved up to the
hoifg 3h0e°s,t eAxcoeApto Af3o0A˝, oefx 2ce5p° twAhoeAreo tfh2e5 l˝iftw ihs eurnedthereplrifetdiiscutendd beryp trheed ipcrteedsebnyt sthoelvperre asse nwteslol lavse rLaesfewbverllea est 
al. [18]. The computed drag coefficient is underpredicted when the AoA is greater than 15°. Among 
Lefebvreetal.[18]. ThecomputeddragcoefficientisunderpredictedwhentheAoAisgreaterthan
1th5˝e. cAommponargistohnesc, othmep caormisopnust,etdh epocwomerp cuoteedffipcioewnte ragcroeeefsfi cthieen tbeasgtr eweisthth tehbe eesxtpweritihmtehnet.e Txhpee rriemaesonnt. 
may be that the total pressure and total temperature are integrated parameters using mass average, 
Thereasonmaybethatthetotalpressureandtotaltemperatureareintegratedparametersusingmass
which is easier to predict accurately than the drag that is determined by skin friction and pressure 
average,whichiseasiertopredictaccuratelythanthedragthatisdeterminedbyskinfrictionand
distribution. Overall, it is demonstrated that the present solver can predict the CFJ flow with a fairly 
pressuredistribution. Overall,itisdemonstratedthatthepresentsolvercanpredicttheCFJflowwith
good precision, and it is reliable to be used for the present numerical study of CFJ. 
afairlygoodprecision,anditisreliabletobeusedforthepresentnumericalstudyofCFJ.