Computational Study on the Aerodynamic Performance of Wind Turbine Airfoil Fitted with Coandă Jet

18 Pages·2015·3.3 MB·English

HindawiPublishingCorporation
JournalofRenewableEnergy
Volume2013,ArticleID839319,17pages
http://dx.doi.org/10.1155/2013/839319
Research Article
Computational Study on the Aerodynamic Performance of
s
Wind Turbine Airfoil Fitted with Coand Jet
H.Djojodihardjo,1,2M.F.AbdulHamid,2A.A.Jaafar,3S.Basri,3F.I.Romli,2
F.Mustapha,2A.S.MohdRafie,2andD.L.A.AbdulMajid2
1UniversitasAlAzharIndonesia,KebayoranBaru,Jakarta12110,Indonesia
2DepartmentofAerospaceEngineering,UniversitiPutraMalaysia,34400Serdang,Selangor,Malaysia
3FacultyofManufacturingEngineering,UniversityMalaysiaPahang,26300Kuantan,Pahang,Malaysia
CorrespondenceshouldbeaddressedtoH.Djojodihardjo;[e-mail]
Received16January2013;Accepted2April2013
AcademicEditor:Wei-HsinChen
Copyright©2013H.Djojodihardjoetal. This is an open access article distributed under the Creative Commons Attribution
License,whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalworkisproperly
cited.
Variousmethodsofflowcontrolforenhancedaerodynamicperformancehavebeendevelopedandappliedtoenhanceandcontrol
thebehaviorofaerodynamiccomponents.TheuseofCoanda˘effectfortheenhancementofcirculationandlifthasgainedrenewed
interest, in particular with the progress of CFD. The present work addresses the influence, effectiveness, and configuration of
Coanda˘-jetfittedaerodynamicsurfaceforimprovingliftand𝐿/𝐷,specificallyforS809airfoil,withaviewonitsincorporation
inthewindturbine.Asimpletwo-dimensionalCFDmodelingusing𝑘-𝜀turbulencemodelisutilizedtorevealthekeyelements
thatcouldexhibitthedesiredperformanceforaseriesofS809airfoilconfigurations.Parametricstudyperformedindicatesthat
theuseofCoanda˘-jetS809airfoilcanonlybeeffectiveincertainrangeoftrailingedgerounding-offradius,Coanda˘-jetthickness,
andmomentumjetsize.ThelocationoftheCoanda˘-jetwasfoundtobeeffectivewhenitisplacedclosetothetrailingedge.The
resultsarecomparedwithexperimentaldataforbenchmarking.Three-dimensionalconfigurationsaresynthesizedusingcertain
acceptableassumptions.Atrade-offstudyontheS809Coanda˘configuredairfoilisneededtojudgetheoptimumconfigurationof
Coanda˘-jetfittedWind-Turbinedesign.
1.Introduction to50×109MWh per year against the current total annual
world electricity consumption of about 15 × 109MWh. The
In line with the efforts to enhance the use of green energy global wind power capacity installed in the year 2004 was
technology for energy extraction, conversion, and propul- 6614MW,anincreaseintotalinstalledgeneratingcapacityof
sion, the fundamental principles and mechanisms that play nearly20%fromtheprecedingyear.
keyrolesinthesetechnologieshavebeenthefocusinmany Wind energy conversion research and development
currentresearcheffortsaswellasthepresentresearchwork, efforts have their origin on fluid physics, thermodynamics,
since these have the eventual potential of nationaldevelop- andmaterialsciences.Learningfromvariousinnovationsin-
mentsignificance.Sinceoneofthefirstattemptstogenerate troducedinaircrafttechnology,windenergytechnologycan
electricitybyusingthewindintheUnitedStatesbyCharles takeadvantageofflowcirculationmodificationandenhance-
Brushin1888[1],windenergyhasbeenutilizedforelectricity ment.
generation using large Wind turbines in many wind farms Flowcontrolforenhancedaerodynamicperformancehas
withpotentialwindenergyinlandaswellasoff-shore.Ithas takenadvantageofvarioustechniques,suchastheuseofjets
been estimated that roughly 10 million MW of energy are (continuous,synthetic,pulsed,etc.),compliantsurface,vor-
continuouslyavailableintheearth’swind[2].Thetechnical texcell,andthelike[3–16].Theseactivecontrolconceptscan
potential of onshore wind energy is very large, 20 × 109 dramaticallyalterthebehaviorofaerodynamiccomponents
2 JournalofRenewableEnergy
such as airfoils, wings, and bodies. Specifically, modified the rotor invariably stalls and experiences highly unsteady
circulation and enhanced circulation have been utilized for aerodynamic forces and moments. It is noted that over the
improvedaircraftandland-vehicleperformanceaswellasin pastseveralyears,therehasbeenanincreasedefforttoextend
novelair-vehiclesliftandpropulsionsystemconcept,dueto theusableoperatingrangeofstall-regulatedWindturbines.
their better energy conversion capabilities [17–23]. The po- Theconceptsofcirculationcontrolthroughtrailingedge(TE)
tentialbenefitsofflowcontrolincludeimprovedperformance blowing,orCoanda˘-jet,thencameintoview.
andmaneuverability,affordability,increasedrangeandpay- However, over the past decades, commonly used airfoil
load,andenvironmentalcompliance.Activeflowcontrolmay familiesforhorizontalaxisWindturbinessuchastheNACA
beappliedtodelayoradvancetransition,tosuppressoren- 44-,NACA23-,NACA63-,andNASALS(1)seriesairfoils
hanceturbulence,ortopreventorpromoteseparation,that suffer noticeable performance degradation from roughness
willresultindragreduction,liftenhancement,mixingaug- effects resulting from leading edge contamination [30].
mentation, heat transfer enhancement, and flow induced Annualenergylossesduetoleadingedgeroughnessaregreat-
noise suppression [24], as appropriate. It could be men- estforstall-regulatedrotors.Thelossislargelyproportionalto
tioned that more recently plasma-based flow control has the reduction in maximum lift coefficient (𝑐𝑙,max) along the
alsobeenconsideredforwindturbineapplications[25–28]. blade.Highblade-roottwisthelpsreducethelossbykeeping
Sucheffortsmayinvolvethedesignof“smart”windturbine theblade’sangleofattackdistributionawayfromstallwhich
bladeswithintegratedsensor-actuator-controllermodulesto delays the onset of 𝑐𝑙,max. Roughness also degrades the
improvetheperformanceofwindturbines,byenhancingen- airfoil’slift-curveslopeandincreasestheprofiledrag,which
ergy capture, and reduction of aerodynamic loading and contributestofurtherlosses.Forstall-regulatedrotors,whose
noise by way of virtual aerodynamic shaping. These are angle of attack distribution increases with wind speed, the
beyondthescopeofthepresentwork. annual energy loss can be 20% to 30% where leading edge
Inthisconjunction,andwiththeprogressofCFD,theuse contaminationfrominsectsandairbornepollutantsiscom-
ofCoanda˘effecttoenhancelifthasattractedrenewedinterest mon. Variable-pitch toward stall would result in simi-
[4–7, 10–14, 17, 29]. Tangential jets that take advantage of lar roughness losses as fixed-pitch stall regulation, while
Coanda˘ effect to closely follow the contour of the body are variable-pitch toward feather would decrease the loss to
consideredtobesimpleandparticularlyeffectiveinthatthey around 10% at the expense of the rotor being susceptible
canentrainalargemassofsurroundingair.Thiscanleadto to power spikes in turbulent high winds. For variable-rpm
increasedcirculationinthecaseofairfoils,ordragreduction rotors operating at constant tip-speed ratio and angle of
(ordragincreaseifdesired)inthecaseofbluffbodiessuchas attackdistribution,thelossisminimalataround5%to10%.
anaircraftfuselage. Tominimizetheenergylossesduetoroughnesseffectsand
InthedesignofanovelWindturbineusingwiththelatest todevelopspecial-purposeairfoilsforhorizontalaxisWind
aerospace engineering technology, including aerodynamics, Turbine(HAWT’s),theNationalRenewableEnergyLabora-
new lightweight materials, and efficient energy extraction tory (NREL), formerly the Solar Energy Research Institute
technology, highly efficient aerodynamic surface came as a (SERI),andtheAirfoilsInc.beganajointairfoildevelopment
keyissue.Recenteffortsinthelastdecadehavealsoindicated effortin1984.Resultsofthisefforthaveproducedanewseries
that Coanda˘ effect has been given new and considerable ofairfoilswhichareconsideredmoreappropriateforHAWT
considerations for circulation control technique [17, 19, 20, applications.Thesebladesareprovidingsignificantincreases
29].Takingadvantageoftheserecentresults,thepresentwork inannualenergyproductionasaresultoflesssensitivityto
looksintotheefforttooptimizeaerodynamicperformanceof roughness effects, better lift-to-drag ratios, and, in the case
WindturbineandtocriticallyinvestigatetheuseofCoanda˘ ofstall-regulatedrotors,throughtheuseofmoresweptarea
effect. foragivengeneratorsize.Becauseoftheeconomicbenefits
The progress of high speed computers exemplified by providedbytheseairfoils,theyarerecommendedforretrofit
the availability of new generations of notebooks has made bladesandmostnewWindturbinedesigns[30].
possible the use of first-principles-based computational ap- Annual energy improvements from the NREL airfoil
proaches for the aerodynamic modeling of Wind turbine familiesareprojectedtobe23%to35%forstall-regulatedtur-
blades,tonameanexample.AspointedoutbyXuandSankar bines,8%to20%forvariable-pitchturbines,and8%to10%
[17], since these approaches are based on the laws of con- for variable-rpm turbines. Optimizing airfoil’s performance
servationofmass,momentum,andenergy,theycancapture characteristics for the appropriate Reynolds number and
much of the physics in great detail. These approaches are thickness provides additional performance enhancement in
particularly helpful at high wind speeds, where appreciable therangeof3%to5%[31].Becauseoftheeconomicbenefits
regionsofseparationarepresentandtheflowisunsteady. providedbytheseairfoils,theyarerecommendedforretrofit
In the design of circulation control technique, one may bladesandmostnewWindturbinedesigns[30].Inorderto
note the progress of stall-controlled and pitch-controlled obtain results that can be well assessed, especially with
turbinerotortechnologyfordealingwithpowerproduction reference to extensive research carried out as described in
at low and high wind conditions [30]. Of interest is the [17,19,20,29],theairfoilS809[31]isconsideredinthepresent
deployment of Wind turbines at larger range of sites not work.Forthispurpose,inthisparticularworkwefocusona
limitedtoarelativelysmallnumberofsiteswherefavorable particular problem, that is, the basic airflow idealization
conditions exist. At the other extreme, precautions should overatwo-dimensionalairfoilinsubsonicflow.Twospecific
be taken when the wind speeds become very high, when conditionsareconsidered.ThefirstisacleanS809airfoiland
JournalofRenewableEnergy 3
the second is the GTRI Dual Radius CCW airfoil that has velocitycontributedbytherotationoftheWindturbineblade
alreadybeeninvestigatedthoroughly,forbenchmarking.The (at a selected baseline radial position, say 0.7𝑅, with 𝑅 the
Coanda˘effectstudiesarecarriedoutonS809airfoil. radiusofthewindturbinerotor)andthefree-streamvelocity
oftheambientair.
2.ProblemFormulation
3.Objectives
Circulationcontrolwing(CCW)technologyisknowntobe
beneficialinincreasingtheboundcirculationandhencethe
To arrive at desired design configurations, one is lead to
sectional lift coefficient of airfoil. This technology has been
comeupwithdesiredlogicalcauseandeffectlawsaswellas
extensivelyinvestigatedbothexperimentallyandnumerically
tofindwaystocarryoutoptimizationschemes.Itiswithsuch
[3–22,29–32]overmanyyears.Circulationcontrolisimple-
objectivesinmindthatusingnumericalanalyses,parametric
mentedbytangentiallyblowingasmallhigh-velocityjetover
studies can be carried out and may offer some clues on
ahighlycurvedsurface,suchasaroundedTE.
relevantparameterswhichmaybeutilizedinamultivariable
Thiscausestheboundarylayerandthejetsheettoremain
optimization (and to a larger scale, multidisciplinary opti-
attached along the curved surface due to the Coanda˘ effect
mization). The present work will investigate the influence,
(i.e., a balance of the radial pressure gradient and centrif-
effectiveness,andconfigurationofCoanda˘-jetfittedaerody-
ugal forces) causing the jet to turn without separation. The
namicsurface,inparticularS809airfoil,forimprovingitslift
rearstagnationpointlocationmovestowardthelowerairfoil
augmentation and L/D, with a view on its incorporation in
surface,producingadditionalincreaseincirculationaround
thedesignofwindturbine.Inaddition,parametricstudyis
the entire airfoil. The outer irrotational flow is also turned
carried out for obtaining optimum configuration of the
substantially,leadingtohighvalueofliftcoefficientcompa-
Coanda˘effectliftenhancedairfoil.Thecomprehensiveresults
rabletothatachievablefromconventionalhighliftsystems,
asaddressedintheobjectiveoftheworkwillbeassessedto
as illustrated in Figure1(b) [4]. Tongchitpakdee et al. [19,
establishkeyfindingsthatwillcontributetothephysicalbasis
20]observedthatearlyCirculationControlledWingdesigns
of Coanda˘-jet for lift enhancement in aerodynamic lifting
typically had a large-radius rounded TE to maximize the
surfaces, and an analysis based on physical considerations
lift benefit. These designs, however, also result in high drag
will be carried out with reference to their application in
penalty when the jet is turned off. One way to reduce this
propeller(orhelicopterrotor)andwindturbinebladeconfig-
dragistomakethelowersurfaceoftheTEaflatsurface,while
urationfordesignpurposes.Thefeasibilityandpracticability
keepingtheuppersurfacehighlycurved.Thiscurvatureon
ofCoanda˘configuredairfoilforwindturbineapplicationsare
theuppersurfaceproducesalargejetturningangle,leading
assessed.
tohighlift.Inthisconjunction,theabilityofcirculationcon-
trol technology to produce large values of lift advantageous
4.ComputationalModelingandSalient
forWindturbinedesignsinceanyincreaseinthemagnitude
of the lift force (while keeping drag small and L/D high) FeaturesofCFDComputationalScheme
will immediately contribute to a corresponding increase in
inducedthrustandtorquewillbetakenintoconsideration. 4.1. Governing Equations: Reynolds-Averaged Navier Stokes.
Numerical simulation carried out by Tongchitpakdee Two-dimensionalincompressibleReynolds-averagedNavier-
et al. [19, 20] looked into two approaches of introducing Stokes(RANS)equationwillbeutilizedtoperformtheanaly-
Coanda˘-jet,thatis,attheappropriatelychosenpointinthe sisandtoobtainnumericalsolutionsonacomputationalgrid
vicinity of the trailing as well as leading edge. A leading surrounding a reference airfoil. The governing equation is
edgeblowingjetwasfoundtobehelpfulinincreasingpower givenby(steadystateandignoringbodyforces)
generationatleadingedgeseparationcases,whileaTEblow-
𝜕𝑢
ingmayproducetheoppositeeffect. 𝜌𝑢 𝑖
Withsuchbackground,thepresentworkisaimedatthe ⏟⏟⏟⏟⏟⏟𝑗⏟𝜕⏟⏟𝑥⏟⏟⏟𝑗⏟
search for favorable Coanda˘-jet lift enhanced configuration
Changeinmeanmomentumoffluidelement
forwindturbinedesigns,focusingontwo-dimensionalsub-
sonicflow,byperformingmeticulousanalysisandnumerical ⏞⏞⏞⏞⏞V⏞⏞⏞i⏞s⏞c⏞⏞o⏞⏞u⏞s⏞s⏞⏞t⏞r⏞e⏞⏞s⏞s⏞⏞⏞⏞⏞⏞
simulation using commercially available CFD code. Results = 𝜕 [[ −𝑝𝛿 +𝜇(𝜕𝑢𝑖 + 𝜕𝑢𝑗)− 𝜌𝑢󸀠𝑢󸀠 ]],
obtainedfromrecentresearcheswillbeutilizedfordirecting 𝜕𝑥 [ ⏟⏟⏟⏟⏟⏟⏟⏟𝑖𝑗⏟ 𝜕𝑥 𝜕𝑥 ⏟⏟⏟⏟⏟𝑖⏟⏟⏟𝑗⏟ ]
𝑗 𝑗 𝑖
the search as well as for validation. For example, best lift [Normalstress Reynoldsstress]
enhancing configuration [19], that is, lower part of the TE
𝜕𝑢
surfacetobeflat,willbeincorporatedinthepresentnumer- 𝑖 =0.
icalinvestigation.Casestudiesperformedhereusebaseline 𝜕𝑥𝑖
chord dimension of 1m airfoil chord length. Two values of (1)
free-streamvelocitiesareinvestigated,thatis,5.77m/secand
14.6m/sec,correspondingtoReynoldsnumberof3.95×105 Computationalfluiddynamicscodeswillbeusedtoana-
6
and 10 , which should fall within the typical situations for lyze the flow around two-dimensional airfoil. Various CFD
large wind turbines. The free-stream velocity in the present codes are available and are alternatively utilized. Careful
two-dimensional study is taken to be equal to the resultant reviewandanalysisoftheapplicationofthefirstprinciplein
4 JournalofRenewableEnergy
Inboard: circulation control
wing/thrust deflector
(a)
Possible leading edge blowing
Tangential blowing over rounded
trailing edge surface
Pressure/centrifugal
force balance
𝐶
𝐿 Slot
Δ𝐶 /𝐶 >80
𝐿 𝜇
Circulation control
Boundary layer control
Jet sheet
(b)
Figure1:(a)Circulationcontrolwing/uppersurfaceblowingSTOLaircraftconfiguration,from[4];(b)Coanda˘-jettangentialblowingover
TEsurfaceforliftenhancement,from[5].
the numerical computationare carried out prior to the uti- finenessshouldbechosentoobtainefficientsolution,which
lizationofcommerciallyavailableCFDcodesforthepresent isacombinationofcomputationalspeedandaccuracy.The
study.Forvalidationofthecomputationalprocedure,resort secondistheturbulencemodeling,whichisbasedonphysical
ismadetoappropriateinviscidcase,andonlineaerodynamic modeling of real flow. Associated with turbulence model-
codesareutilized.Foratwo-dimensionalgeometrythemesh ing, the wall boundaries are the most common boundaries
generator partitions the subdomains into triangular or encountered in fluid flow problems. Turbulent flows are
quadrilateralmeshelements[33].Careshouldbeexercisedin significantlyaffectedbythepresenceofwalls.Thesuccessful
thechoiceandgenerationofthecomputationalgrid,which prediction of wall bounded turbulent flows relies on the
will be elaborated subsequently. The comprehensive results accuracy with which the flow in the near-wall region is
as addressed in the objective of the work are assessed to represented. Experiments have shown that the near-wall
establishkeyfindingsthatwillcontributetothephysicalbasis region can be subdivided into several layers, characterized
of Coanda˘-jet for lift enhancement in aerodynamic lifting bythevalueof𝑦+,whichincludetheviscoussublayerwhere
surfaces. An analysis based on physical considerations is thelaminarpropertyisdominant,thefullyturbulentregion
carriedoutwithreferencetoitsapplicationinwindturbine whichconsistsoftheturbulentlogarithmiclayerforarange
bladeconfigurationfordesignpurposes. of𝑦+values,andtheouterlayer,asschematicallyexhibitedin
The basis of the computational approach in the present Figure2(b). The no-slip condition at stationary walls forces
work is the two-dimensional incompressible Reynolds- themeanvelocitycomponentstoazeromagnitudeandcan
averaged Navier-Stokes (RANS) equation (1) and its imple- alsosignificantlyaffecttheturbulencequantities.Ifthegrid
mentation into the CFD equation. When pursuing further distribution is fine enough so as to satisfy the no-slip con-
the numerical solution of dynamic fluid flow using CFD dition,near-walltreatmentisnotnecessary[34–42].
techniques, in order to arrive at accurate solution, at least
two aspects should be given careful attention, with due 4.2.TurbulenceModelingConsiderations. Turbulencemodel-
considerationofcomputationaluncertainties.Thefirstisthe inginCFDisveryessentialinthechoiceofgridfinenessand
gridgeneration,andthesecondistheturbulencemodeling obtainingthecorrectsimulationofparticularflowfield.For
of the particular flow. The first is based on computational thispurpose,onehastochooseaparticularmodeloutofa
algorithmincludingthechoiceofappropriategrid;thegrid hostofavailableturbulencemodelsdevelopedtodate.Oneof
JournalofRenewableEnergy 5
0.05 ismodeledbyusingtheKomolgorov-Prandtlexpressionfor
turbulentviscosity
𝑘2
0.04 𝜇𝜏 =𝜌C𝜇 𝜀 , (2)
whereC𝜇isamodelconstant.Inexpression(2)𝜇𝜏wasbased
0.03 ontheeddyviscosityassumptionintroducedforconvenience
𝑐
ht/ of further analysis by Boussinesq [41] to draw analogy
g
ei betweenthemomentumtransfercausedbyturbulenteddies
H
0.02 andtheviscosityinlaminarflow.
The dimensionless distance in the boundary layer, sub-
layer scaled, representing the viscous sublayer length scale,
0.01 plays significant role in capturing relevant physical turbu-
lencephenomenaneartheairfoilsurfacecommensuratewith
the grids utilized in the numerical computation. In this
regards,theflowfieldinthevicinityoftheairfoilsurfaceis
0
0.8 1 1.2 1.4 1.6 1.8 2 usuallycharacterizedbythelawofthewall,whichattempts
𝑈/𝑈∞ toidentifyintricaterelationshipsbetweenvariousturbulence
SA 𝑘-𝜀 model scaling in various sublayers. For example, the wall
functions approach (wall functions were applied at the first
SST Experimental
node from the wall) utilized by k-𝜀 turbulence model uses
Figure 2: Typical 𝑦+ values in the turbulent boundary layer and empiricallawstomodelthenear-wallregion[35]tocircum-
velocityprofilesinwallunitsforsubsonicflowoverflatplate,M= vent the inability of the k-𝜀 model to predict a logarithmic
0.2,Re=1×106,mediumgrid;nozzlepressureratio=1.4.(Source: velocityprofilenearawall.Thelawofthewallischaracterized
Menter[23],SalimandCheah[45],andEconomonandMilholenII
byadimensionlessdistancefromthewalldefinedas
[46]).
𝑢 𝑦
𝑦+ = 𝜏 .
(3)
𝜐
Subject to local Reynolds number considerations, the wall
theseturbulencemodelsthatisconsideredtobeappropriate 𝑦+ is often used in CFD to choose the mesh fineness
anduserfriendlyisthek-𝜀turbulencemodel,withoutdisre- requirements in the numerical computation of a particular
gardingothermodelsthatmaybesuitableforthepurposeof flow.
thepresentwork. Basedonpreliminaryattemptstochoosetheappropriate
The k-epsilon turbulence model was first proposed by turbulence model which yields desirable results, in the
HarlowandNakayama[34]andfurtherdevelopedbyJones presentwork,k-𝜀turbulencemodelischosen[34,35].Inthe
and Launder [40]. Continuing extensive research has been framework of eddy viscosity based turbulence models, the
carriedouttounderstandthenatureofturbulence,andthis flow of a turbulent incompressible fluid is governed by the
theoryhasbeenfurtherelaboratedandmanyothertheories Reynolds-averaged Navier-Stokes (RANS) equation (1) for
havealsobeenintroducedsuchaselaboratedin[43],which thevelocityuandpressurep.
seem to be satisfactory for only certain classes of cases. Forpracticalimplementationpurposes,itisworthwhile
TheturbulentviscositymodelsbasedonReynolds-averaged tointroduceanauxiliaryparameter𝛾 = 𝜀/𝑘tolinearizethe
Navier-Stokes(RANS)equations(1)arecommonlyemployed equations of the k-𝜀 turbulence model using the following
inCFDcodesduetotheirrelativeaffordability[44].However, equivalentrepresentation:
sincethechoiceofturbulencemodelandassociatedphysical
𝜕𝑘 ]
phenomena addressed are relevant in modeling and com- 𝜕𝑡 +∇⋅(𝑘𝑢− 𝜎𝑇∇𝑘)+𝛾𝑘=𝑃𝑘, (4a)
putersimulationoftheflowsituationneartheairfoilsurface 𝑘
consideredhere,acloserlookatturbulencemodelsutilized
𝜕𝜀 ]
bytheCFDcodechosenwillbemade.Althoughthepractical 𝜕𝑡 +∇⋅(𝜀𝑢− 𝜎𝑇∇𝜀)+𝐶2𝛾𝑘=𝛾𝐶1𝑃𝑘. (4b)
implementationofturbulencemodel,especially,forthenear- 𝑘
walltreatment,hasbeensomesomewhatofamystery[35], The corresponding linearization parameter is given by 𝛾 =
the numerical implementation of turbulence models has a C𝜇(𝑘/]𝑇).Hencethestandardk-𝜀turbulencemodelisbased
decisive influence on the quality of simulation results. In
particular,apositivity-preservingdiscretizationofthetrou- on the assumption that ]𝑇 = C𝜇(𝑘2/𝜀), where k is the
blesome convective terms is an important prerequisite for turbulent kinetic energy and 𝜀 is the dissipation rate. 𝑃𝑘 =
the robustness of the numerical algorithm [35]. The k-𝜀 (]𝑇/2)|∇𝑢+∇𝑢𝑇|2 and 𝜀 are responsible for the production
modelintroducestwoadditionaltransportequationsandtwo anddissipationofturbulentkineticenergy,respectively.The
dependentvariables:theturbulentkineticenergy,𝑘,andthe default values of the involved empirical constants are C𝜇 =
dissipation rate of turbulence energy, 𝜀. Turbulent viscosity 0.09,𝐶1 =1.44,𝐶2 =1.92,𝜎𝑘 =1.0,and 𝜎𝜀 =1.3.
6 JournalofRenewableEnergy
FollowingiterativeprocedureelaboratedbyKuzminetal. the wall (airfoil) surface, practically the meshing layer of
[35],withprescribedhomogenousNeumannboundarycon- width y is removed from the computational domain, thus
ditionandimpermeablewall,itremainstoprescribethewall reducing the total number of grids involved, and hence
shear stress as well as the boundary conditions for 𝑘 and 𝜀 reducing the computational time. Kuzmin et al. [35] have
on the wall. The equations of the k-𝜀 model are invalid in introducedawallfunctionthatisabletocontrolthe𝑦+value
thevicinityofthewall,wheretheReynoldsnumberisrather suchthattheydistancewillnotfallintotheviscoussublayer,
low and viscous effects are dominant. Therefore, analytical whichcouldjeopardizethewallfunctionassumptionmade.
solutions of the boundary layer equations are commonly The smallest distance of 𝑦+ that can be defined, following
employedtobridgethegapbetweentheno-slipboundaries GrotjansandMenter[47],correspondstothepointwherethe
and the region of turbulent flow. The friction velocity 𝑢𝜏 is logarithmiclayermeetstheviscoussublayer.
assumedtosatisfythenonlinearequation The distance y is automatically computed iteratively by
solving𝑦+ =(1/𝑘)log𝑦++𝛽=(1/0.41)log𝑦++5.2,sothat
|𝑢| 1
= log𝑦++𝛽 (5) 𝑦+ = (𝑢𝜏𝑦)/𝜐 = 𝜌𝑢𝜏(𝑦/𝜇), where 𝑢𝜏 = 𝜌C𝜇(𝑘2/𝜀) (which
𝑢 𝜅
𝜏 hasbeenfurtherderivedbyKuzminetal.[35]tobeequivalent
valid in the logarithmic layer, where the local Reynolds to𝑢𝜏 = C1𝜇/4√𝑘)isthefrictionvelocityandisequalto11.06.
number This corresponds to the distance from the wall where the
𝑢 𝑦 logarithmiclayermeetstheviscoussublayer.Hence,thevalue
𝑦+ = 𝜏 (6) of𝑦,asrepresentedbythechoiceofthecomputationalgrid
]
size, can never become smaller than half of the height of
]isintherange11.06≤ 𝑦+ ≤300.Theempiricalconstant𝛽 the boundary mesh cell [48], as illustrated in Figure3(a).
equals 5.2 for smooth walls. Note that the above derivation This means that 𝑦+ can become higher than 11.06 if the
resultsintheboundaryvalueoftheturbulenteddyviscosity meshisrelativelycoarse.Thek-𝜀variablesarenotspecified
]𝑇tobeproportionalto].Indeed, a priory, but during the computation using CFD software,
k-𝜀variablevaluesareimplicitlysettoobtainacceptable𝑦+
𝑘2
] =𝐶 =𝜅𝑢 𝑦=𝜅𝑦+], (7) valuesthatproviderelativelyrapidconvergenceandaccuracy
𝑇 𝜇 𝜀 𝜏 ∗ (asvalidatedwithappropriatedata).
Therefore, care is exercised in the choice of grids in the
where 𝑦∗+ = |𝑢|/𝑢𝜏. Based on such information, the search vicinityoftheairfoil,toobtainacertainacceptableerrortol-
forappropriategridfines,inadditiontotheoutcomeofgrid
erance(whichmayalsobeattributabletonumericalerrorand
finenessratiostudy,isalsoguidedbyplausiblecomparisonof
uncertainties). The plausibility of the numerical results will
thevalidationofCFDcomputationalresultsofthetestairfoil
be judged by comparisonto other established results in the
withexperimentalvalues.HeretheCFDcodeutilizedusing
literature (numerical or experimental) for specific cases. In
𝑦+ value of 11 and as suggested in [35] was found to yield
thepresentstudy,itwasfoundthattheturbulenceintensity
satisfactoryresultsasindicatedthere.Figure2belowshows
of5%andlengthscaleof0.01myieldresultsthatagreewith
theinfluenceof𝑦+ inrepresentingtheboundarylayernear
benchmarkingdata.ItisnotedthatHowelletal.[49]alsouse
thewall.
thisvalueandturbulenceintensityof1%intheirnumerical
Various studies [23, 35, 42, 47] have indicated that
studyonVAWT.
integrating of the k-𝜀 type models through the near-wall
regionandapplyingtheno-slipconditionyieldunsatisfactory
results.Therefore,takingintoaccounttheneedforeffective 5.ComputationalSet-UpandValidation
choice of grid mesh compatible with the turbulence model,
adoptedusingthecommercialCFDcode,aparametricstudy 5.1.ComputationalGrid. Inthepresentwork,thegridswere
iscarriedoutontwoairfoilswhereeitherexperimentaldata constructed following free mesh parameter grid generation
or computational results are available, to validate the com- usinganalgebraicgridgeneratorandvariedfromextremely
putationalprocedure,turbulencemodelandgridsizechosen coarseuptoextremelyfinegrids.However,fortheS809airfoil
and establish their plausibility for further application in case, near the surface of the airfoil, boundary layer based
the present work. The idea is to place the first computa- meshingiscarriedoutthroughout.Gridsensitivitystudyon
tionalnodesoutsidetheviscoussublayerandmakesuitable the lift force per unit span for clean airfoil at zero angle of
assumptionsabouthowthenear-wallvelocityprofilebehaves, attackisplottedinFigure4.
in order to obtain the wall shear stress. Hence, the wall Figure4showsthattheliftanddragarevirtuallyinsen-
functionscanbeusedtoprovidenear-wallboundarycondi- sitive of the size of the grid generated. The grid sensitivity
tionsforthemomentumandturbulencetransportequations, studyhasledtoacceptablegridsizesintherangeoffineup
rather than conditions at the wall itself, so that the viscous toextrafinegridsize,sincewithinthisrangetheliftaswell
sublayerdoesnothavetoberesolvedandtheneedforavery asthedragforcesdonotchangeappreciably.Theassociated
finemeshiscircumvented.ThewallfunctionsinCOMSOL rangeoffreemeshparameters(rangingfromextrafinetofine
[48] are chosen such that the computational domain is meshinggridsize)isdefinedinTable1.
assumedtostartatadistanceyfromthewall(seeFigure3). Inordertocontrolthe𝑦+value(setat11.06,ontheairfoil
By applying the wall function at the nodes of the first surface),themaximumelementsizewassetat0.005,whileat
meshinglayerofthecomputationalgridatadistanceyfrom theTErounding-offsurfacethemaximumelementsizewas
JournalofRenewableEnergy 7
𝑈/𝑈𝜏 Buffer layer Fully turbulent region
Viscous
or or
sublayer blending region log-law region
1.2(1.2𝑦)
1.2𝑦
𝑦
ln(𝑈𝜏(𝑦)/(cid:13))
(a) (b)
Figure3:Forwallfunctions,thecomputationaldomainstartsadistanceyfromthewall.(a)GridgenerationfollowedfromCOMSOL4.2
User’sGuide;(b)thestructureofturbulenceboundarylayer,adaptedfromMenter[23].
m) 11.4 m) 2.02
N/ 11.3 N/ 2
Lift force per unit span ( 1111111100001......2119876 0.0002 0.00005 Drag force per unit span ( 11111....1.99998.986428 0.0002 0.00005
Extra... Coarser Coarse Normal Fine Finer Extra... Extra... Coarser Coarse Normal Fine Finer Extra...
(a) (b)
Figure4:GridsensitivitystudyforcleanS809airfoilatzerodegreeangleofattack;(a)liftforceperunitspan;(b)dragforceperunitspan.
Table1:Therangeoffreemeshparameters. Table2:Computationalgridmeshinglayerproperties.
Parameter Range Parameter Range
Maximumelementsize 0.156–0.42 Numberofmeshlayersintheboundarylayers 8
Minimumelementsize 0.018–0.12 Boundarylayermeshexpansionfactor 1.2
Maximumelementgrowthrate 1.08–1.13 Thicknessoffirstmeshlayer 0.00005–0.0002
Resolutionofcurvature 0.25–0.3 Thicknessadjustmentfactor 1
Resolutionofnarrowregions 1
setat0.001.AttheCoanda˘-jetoutlet,thesurfaceisdivided 0.0002m, commensurate with the curvature on the airfoil
into a minimum of 10 grid meshes. To obtain acceptable surface.Havingchosenthethicknessoftheelementsofthe
computationalresultsusingCFDcode,appropriateboundary first meshing layer adjacent to the airfoil surface, the fol-
layer mesh properties should be carefully chosen and the lowingconsecutivelayerswereexpandedwithanexpansion
thinboundarylayersalongtheno-slipboundariesshouldbe factorof1.2,foreightconsecutivelayers.Anotheroptioncan
resolvedintomeshlayerscommensuratewiththegridfine- be taken to allow thickness adjustment of the first meshing
ness.Aboundarylayermeshisaquadrilateralmesh(2Dflow) layer, by choosing the thickness adjustment factor [48]; for
withdenseelementdistributioninthenormaldirectionalong thepresentstudy,thethicknessadjustmentfactorofonewas
specificboundariestoresolvethethinboundarylayersalong chosen.
theno-slipboundaries.Theboundarylayerpropertieschosen Thegridgeneratorissufficientlygeneralsothatonecan
aredefinedinTable2. easilyvarythejetslotlocationandsize.Gridspacingandclus-
Alongwiththerequirementofthe𝑦+valuetocapturethe teringcanhavesignificanteffectsonWindturbineloadand
salientturbulentflowfieldsublayers,arangeofvaluesofthe performancepredictions[49].Theouterboundaryisplaced
grid dimension could be chosen to represent the thickness farawayfromthebladesurface,atleastatsixchordlengths
of the first meshing sublayers. In the present example the (6C) from the airfoil surface, to avoid significant influ-
grid dimension was chosen to be between 0.00005m and ence from outer boundary into the interior domain and to
8 JournalofRenewableEnergy
6C
6C 6C
6C
Boundary
layer mesh
Figure5:Computationalgridaroundatypicalairfoil,shownhereforS809Coanda˘configuredairfoil.
allow the disturbances to leave the domain [20]. The com- bejustifiedintheresultspresentedinFigure5.Itshouldbe
putationaldomainandthegridinthevicinityoftheairfoil noted,however,thatFigure5indicatesthatwithhigherangle
surfaceandCoanda˘-jetslotareexhibitedinFigure5. ofattack,far-fieldboundariesshouldbeplacedfurtheraway
fromtheairfoil.
5.2. Initial and Boundary Conditions. In general, the initial
conditions are set to be equal to the properties of the free- 5.3.BaselineValidation. Priortoitsutilization,variousbase-
stream flow condition [19]. The flow properties everywhere line cases have been tried out, with favorable results. As a
insidetheflowfieldareassumedtobeuniformandsettothe caseinpoint,forbenchmarkingpurposesthecodehasbeen
free-streamvalues.Thefollowinginitialvaluesareused: appliedtocalculatethelift-slopecharacteristicsofS809airfoil
(cleanconfiguration,withoutCoanda˘)andGTRICCWDual
𝑢=𝑢 , V=V , 𝜌=𝜌 , 𝑝=𝑝 ,
∞ ∞ ∞ ∞ Radius airfoil (with Coanda˘) and compared to the results
(8)
𝑇=𝑇 . obtained by Somers [50], as shown in Figure6, and Englar
∞
et al. [5], as shown in Figure7, respectively. The results as
Theouterboundaryisplacedfarawayfromthebladesur- shown in both Figures demonstrated the plausibility of the
face,ataminimumof6chords(6C).Nonreflectingboundary presentnumericalcomputationalscheme.
conditionsareappliedattheouterboundariesofthecompu- Computational results exhibited in Figure6 served to
tational domain. The jet is set to be tangential to the blade validatethecomputationalprocedureassociatedwiththeuse
surface at the Coanda˘-jet nozzle location. The jet velocity of CFD code in the numerical simulation and as a baseline
profileisspecifiedtobeuniformatthejetexit.Ontheairfoil in furthering the computational study of Coanda˘-jet in the
surface,exceptatthejetexit,no-slipboundaryconditionsare presentstudy.Figure6comparesthepresentcomputational
applied.Togainbenefits,thejetvelocityisheredesignedto simulation using k-𝜀 turbulence model and Kuzmin’s [35]
belargerthanthepotentialflowvelocityatthevicinityofthe wall function (the associated 𝑦+ value is 11.06) with the
outeredgeoftheboundarylayer.Inaddition,thethicknessof experimental data of Somers [50]. The numerical results
theCoanda˘-jetisdesignedtobelessthanthelocalboundary above simulated similar experimental conditions of Somers
layerthickness. for clean S809 airfoil (with wall boundary conditions and
Outer boundary conditions are chosen to minimize without Coanda˘-jet). It also shows that the lift and drag
blockage effect, that is, significant discrepancies with free coefficientsatzeroangleofattackareincloseagreementwith
flightsituations,whethertheoreticallyornumericallysimu- theexperimentaldata.
latedorexperimental.Walleffectsblockagechangesstream- Similar numerical simulation was carried out for GTRI
linecurvatureinteractionboundarylayersandtheseshould Dual Radius CCW airfoil with leading edge blowing and
be minimized. The best measure is by carrying out com- comparedtotheexperimentaldata(inFigure7)fromEnglar
putational experiments with reasonable outer boundaries et al. [5] with the same boundary conditions and jet con-
of the computational grid and validating with both outer figuration using k-𝜀 turbulence model and Kuzmin’s wall
potentialflowresultsandnumericalparametricstudies.This function[35].Ofsignificantinterestarethegridsize,thewall
rationale has shown that, for the case considered, an outer function,and𝑦+valueutilizedfornumericalsimulation.The
gridboundarydistancetothecomputationaldomaincenter- associated𝑦valueforthecellsadjacenttotheairfoilsurface
lineofsixchordsproducesresultswithhighaccuracy,ascan wasdesignedtobenomorethan0.0002minordertosatisfy
JournalofRenewableEnergy 9
0.05
1.2
0.045
1.1
1 0.04
0.9 nt 0.035
ent 0.8 cie 0.03
ci 0.7 ffi
coeffi 00..65 g coe 00.0.0225
Lift 00..43 S809 Dra 0.015
0.01
0.2
0.1 0.005
0 0
−0.1−1 0 1 2 3 4 5 6 7 8 9 10 −1 0 1 2 3 4 5 6 7 8 9 10
Angle of attack Angle of attack
Experiment, in closed conduit Experiment, in closed conduit
COMSOL𝑘-𝜀, in closed conduit COMSOL𝑘-𝜀, in closed conduit
COMSOL𝑘-𝜀, in infinite medium COMSOL𝑘-𝜀, in infinite medium
(a) (b)
Figure6:ComparisonforvalidationofS809airfoilofCFDcomputationalresultsusingCOMSOLk-𝜀turbulencemodelandexperimental
valuesfromSomers[50]atRe=1E6;(a)liftcoefficient;(b)dragcoefficient.
5 appropriateCFDnumericalprocedures.Simplifiedtheoreti-
calanalysisiscarriedoutpriortothemodelingandnumerical
4
nt computation,whilefurthertheoreticalanalysiswillbecarried
e
ffici 3 outinevaluatingthecomputationalresults.
e
co 2
ft
Li 1 GTRI Dual Radius CCW 6.ResultsandDiscussions
0
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 6.1.DesignConsiderationsforCoanda˘ConfiguredAirfoil. For
Momentum jet the purpose of assessing the influence and the effectiveness
oftheCoanda˘enhancedL/Dandliftaugmentationonwind
Experiment, in closed conduit
turbine blade, a generic two-dimensional study is carried
COMSOL𝑘-𝜀, in closed conduit
out. The problem at issue is how the Coanda˘-jet can be
COMSOL𝑘-𝜀, in infinite medium
introduced at the TE of the airfoil, bearing in mind that
Figure 7: Comparison of lift-curve slope for GTRI Dual Radius such design may recover any losses due to the possible
CCWairfoilwithLEblowingonCFDcomputationusingCOMSOL inception of flow separation there. In addition, for effective
k-𝜀turbulencemodelandexperimentalvaluesfromEnglaretal.[5] Coanda˘-jetperformance,acurvatureshouldbeintroduced.
atRe=395,000.
Furthermore,thethicknessoftheCoanda˘-jetasintroduced
ontheairfoilsurfacecouldhaveaverycriticaleffectonthe
intended lift enhancement function. For best effect, the
lower surface near the TE should be flat, as suggested by
the𝑦+valuerequirements,whichwerechosentobe11.06.The
Tongchitpakdee et al. [19, 20]. The design of the Coanda˘-
resultsexhibitedinFigure7forthiscaseisalsoencouraging
configuredTEshouldalsoconsidertheoff-designconditions.
duetothecloseagreementbetweenthepresentcomputation
With all these considerations, a configuration suggested is
andtheexperimentaldata.
exhibitedinFigure8.
The results exhibited in both examples above serve to
indicate that the computational procedure and choice of
turbulencemodelseemtobesatisfactoryforthepresentcom- 6.2.ComputationalResultsforS809Airfoil. Next,wewould
putationalstudyandcouldlendsupporttofurtheruseofthe liketoinvestigatetheinfluenceofspecificallydesignedairfoil
approachinthenumericalparametricstudy. geometryforWindturbineapplication,andforthispurpose
Allcomputationsinthepresentstudywereperformedon atypicalS809,incleanandCoanda˘-jetequippedconfigura-
alaptopcomputerwitha2.10GHzIntelCoreDuoprocessor, tions. S809 airfoil represents one of a new series of airfoils
4GBofRAM,and32-bitoperatingsystem.Typicalcompu- whicharespecificallydesignedforHAWTapplications[20].
tation time for the computation of the flow characteristics Forthepresentstudy,thenumericalsimulationwascarried
around a two dimensional airfoil is in the order of 4 hours out at two free-stream velocities. These are 5.77m/s (corre-
witharound300,000degreesoffreedombyusingstationary spondingtoRe=3.95×105)and14.6m/sec(correspondingto
segregatedsolverink-𝜀turbulentmodelanalysis.Withsuch Re=1×106),whichrepresentlowandhighfree-streamcases,
computationalenvironment,whichinconsequencelimitsthe respectively,whilethechord-lengthismaintainedatc=1m,
computational grids, the present work will seek and adopt and density at 𝜌 = 1.225kg/m3. The baseline for assessing
10 JournalofRenewableEnergy
beenappliedtotheproductionaircrafts.Manyoftheroad-
TE jet thickness blocks have been associated with the engine bleed require-
mentsandcruisepenaltiesassociatedwithblownbluntTEs.
In addition, there is a tradeoff between the use of a larger
Parallel Tangent line radius Coanda˘ configured airfoil for maximum lift and the
useofasmallerradiusoneforminimumcruisedrag.
Distance from LE TE radius In contrast to the needs of TE rounding-off radius,
performancedegradationassociatedwithitalwaysstandsas
an issue due to the drag penalty when the jet is in the off
Figure8:TEconstructionoftheCoanda˘configuredairfoil(thejet mode. To overcome such drawback, the TE radii should be
flowistangentialtotheroundedcircularsector). specificallyandcarefullydesigned.Forthatpurpose,simula-
tionsatseveralTEradius(from10mmto50mm)havebeen
performed,atafixedCoanda˘-jetmomentumcoefficient𝐶𝜇
(𝐶𝜇 = 0.003, considered just enough to fit with the Wind
theadvantagesofCoanda˘-jetfromparametricstudyonS809 turbine application), and at a constant free-stream velocity
airfoil is the computational result for the clean airfoil. The of 𝑉∞ = 14.6m/sec (Re = 1 × 106), to investigate the effect
computationalresultforthisbaselinecasehasbeenvalidated of TE radius on the aerodynamic characteristics of Coanda˘
bycomparisonofthecomputationalvalueforthesameS809 configuredairfoils.ResultsexhibitedinFigure10showthata
airfoiltotheexperimentalresultsbasedonwind-tunneltest. higher𝐿/𝐷canbeachievedwithasmallerTEradius(30mm)
Itshouldbenotedthattheflowfieldboundariesaredifferent andthatthe𝐿/𝐷isdecreasingastheTEradiusisincreased
fromthoseutilizedfortheparametricstudy. from 30mm to 50mm. The effect of TE radius on the lift
Thetwo-dimensionalnumericalsimulationstudyforthe augmentationissignificant,asexhibitedbythedashedlinein
S809 airfoil is carried out in logical and progressive steps. Figure10.However,whentheTEradiusisincreasedbeyond
First,thenumericalcomputationisperformedontheclean certain value (in Figure10, ≫35mm), the TE rounding-off
S809 airfoil, then on the Coanda˘ configured S809 airfoil seemstobeineffective,evendetrimental.
withoutthejet(i.e.,afterappropriatemodificationduetoTE
Moving the location of the Coanda˘-jet forward implies
rounding-off and back-step geometry), and then finally on
theincreaseoftheTEradius.Consequently,thecamberofthe
Coanda˘configuredS809airfoilinitsoperationalconfigura-
airfoilwillalsobechanged.Thisinturnwillproducechanges
tion.
intheangleofattackoftheairfoilcomparedtothebaseline
To address three-dimensional wind turbine configura-
case. Therefore, although the present study looks into the
tions,particularlyfortheoptimumdesignofahorizontalaxis
influenceofmodifyingTEradius,whileholdingotherairfoil
Windturbine(HAWT),logicaladaptationshouldbemade,
geometrical parameters constant, the zero angle of attack
takingintoaccountthefactthatdifferentairfoilprofilesmay
conditionisatbestpossibleonlyasfirstapproximation.The
beemployedatvariousradialsections.Certainassumptions
robustness of the computational procedure adopted in the
havetobemadeinordertoprojecttwo-dimensionalsimu-
presentcomputationalset-upmaybeabletotakeintoaccount
lation results to the three-dimensional case, which may be
all these changes. Such a case is indeed revealed in Figures
necessarytoevaluatetheequivalentBetzlimit.
10(c)and10(d)wherebytheinfluenceofallthechangesofthe
geometricalvariablesaccompanyingthepresentparametric
6.2.1.TheInfluenceofCoanda˘-JetontheFlowofftheTE. The study should have been incorporated in the computational
flowfieldinthevicinityoftheTEforbothconfigurationsis scheme which is focused on the TE radius changes and
showninFigures9(a)and9(b).Carefulinspectionofthese produceschangesinLandDcontributedalsobythechanges
figuresmayleadtotheidentificationofthegeometryofthe intheangleofattack.Additionally,thesefiguresshowthatthe
flowthatcouldcontributetoincreasedlift,insimilarfashion changes in lift is much larger than the changes in drag, as
asthatcontributedbyflap,jetflap,orGurneyflap.Figure9(b) exhibitedinFigures10(c)and10(d).
typifiestheflowfieldaroundCoanda˘configuredS809airfoil Variation of the Coanda˘-jet thickness from 0.5mm to
without Coanda˘-jet (only with its back-step configuration), 3.0mm at a fixed 𝐶𝜇 (𝐶𝜇 = 0.005) and at a constant free-
whichisusedheretogetinsighttotheactionoftheCoanda˘- stream velocity of 𝑉∞ = 14.6m/sec (Re = 1 × 106) is per-
jet.
formedtoinvestigatetheeffectofCoanda˘-jetthickness(also
calledjetslotthickness)ontheaerodynamiccharacteristics
6.2.2. Parametric Study Results for Coanda˘ Configured S809 of Coanda˘ configured airfoils. From Figure11, it is found
Airfoil. TheTEradiusplaysanimportantroleintheCoanda˘ thatahigherL/DcanbeachievedwithasmallerCoanda˘-jet
configureddesignairfoil,sinceitmaypositivelyornegatively thickness (1.0mm) and that the L/D is decreased rapidly as
influencethedownstreamflowbehavior.Tongchitpakdeeet theCoanda˘-jetthicknessisincreasedfrom1.5mmto3.0mm.
al.[19,20]hadclaimedthatthelowersurfaceattheTEofthe A similar behavior is observed for the lift augmentation as
applied Coanda˘-jet should be flat in order to minimize the exhibitedbythedashedlineinFigure11.However,generating
drag when the jet is turned off. Also, as reported earlier by asmallerjetrequireshigherpressurethanalargeroneatthe
AbramsonandRogers[51,52]inthelate1980s,inspiteofthe same momentum coefficient. Since higher lift with as low
abilitytogeneratemoreliftthetechniquehasnotingeneral mass flow rate as possible is preferred, a thin jet is more