https://ntrs.nasa.gov/search.jsp?R=20170004500 2019-04-05T17:02:50+00:00Z NASA/TM–2017–219602 CFD Study of NACA 0018 Airfoil with Flow Control ChristopherA.Eggert PurdueUniversity,WestLafayette,Indiana ChristopherL.Rumsey LangleyResearchCenter,Hampton,Virginia April 2017 NASASTIProgram...inProfile Sinceitsfounding,NASAhasbeendedicatedto • CONFERENCEPUBLICATION. theadvancementofaeronauticsandspace Collectedpapersfromscientificandtechnical science. TheNASAscientificandtechnical conferences,symposia,seminars,orother information(STI)programplaysakeypartin meetingssponsoredorco-sponsoredby helpingNASAmaintainthisimportantrole. NASA. TheNASASTIProgramoperatesunderthe • SPECIALPUBLICATION.Scientific, auspicesoftheAgencyChiefInformation technical,orhistoricalinformationfrom Officer. Itcollects,organizes,providesfor NASAprograms,projects,andmissions,often archiving,anddisseminatesNASA’sSTI. The concernedwithsubjectshavingsubstantial NASASTIProgramprovidesaccesstothe publicinterest. 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NASA/TM–2017–219602 CFD Study of NACA 0018 Airfoil with Flow Control ChristopherA.Eggert PurdueUniversity,WestLafayette,Indiana ChristopherL.Rumsey LangleyResearchCenter,Hampton,Virginia NationalAeronauticsand SpaceAdministration LangleyResearchCenter Hampton,Virginia23681-2199 April 2017 Acknowledgments TheauthorsacknowledgethehelpofDavidGreenblattandHannsMuller-VahloftheTechnion- Israel Institute of Technology, who conducted the experiment associated with this study. The experiment and subsequent collaboration was supported in part by the United States - Israel BinationalScienceFoundation. The use of trademarks or names of manufacturers in this report is for accurate reporting and does not constituteanofficialendorsement,eitherexpressedorimplied,ofsuchproductsormanufacturersbythe NationalAeronauticsandSpaceAdministration. Availablefrom: NASASTIProgram/MailStop148 NASALangleyResearchCenter Hampton,VA23681-2199 Fax: 757-864-6500 Abstract TheabilitiesoftwodifferentReynolds-AveragedNavier-Stokescodestopredicttheeffects ofanactiveflowcontroldeviceareevaluated. Theflowcontroldeviceconsistsofablowing slot located on the upper surface of an NACA 0018 airfoil, near the leading edge. A sec- ondblowingslotpresentontheairfoilnearmid-chordisnotevaluatedhere. Experimental results from a wind tunnel test show that a slot blowing with high momentum coefficient will increase the lift of the airfoil (compared to no blowing) and delay flow separation. A slotwithlowmomentumcoefficientwilldecreasetheliftandinduceseparationevenatlow angles of attack. Two codes, CFL3D and FUN3D, are used in two-dimensional compu- tations along with several different turbulence models. Two of these produced reasonable results for this flow, when run fully turbulent. A more advanced transition model failed to predictreasonableresults,butwarrantsfurtherstudyusingdifferentinputs. Includinginvis- cidupperandlowertunnelwallsinthesimulationswasfoundtobeimportantinobtaining pressure distributions and lift coefficients that best matched experimental data. A limited numberofthree-dimensionalcomputationswerealsoperformed. 1 Introduction Blowing slots have long been pursued as a means of controlling the forces generated by a wing, often by injecting momentum with the goal of reducing or eliminating separation. There are numerous uses for such a technology, such as for high-lift systems or low-drag control surfaces on aircraft. At Technion Israel Institute of Technology, Greenblatt [1] has recently been investigating the use of an unsteady low-speed wind tunnel to explore blowing effects for airfoils that are dynamically pitching. This type of problem represents a challenge for CFD, both because of the highly unsteady nature of the flow as well as becauseofknownlimitationsofReynolds-averagedNavier-Stokes(RANS)forcomputing separated flows. More advanced CFD methods such as large-eddy simulation (LES) are stillconsideredtooexpensiveforroutineuse. Theparticularexperimentthatprovidedthecomparisondata[2]forthisstudywasper- formedwiththeintentofimprovingtheperformanceofwindturbines. Onemajorchallenge in the design of wind turbines is the harmful effect of unsteady loads on the blades. This type of active flow control could be used to reduce these unsteady loads by increasing or reducingtheliftgeneratedastheturbinebladecycles,aswellasbyreducingoreliminating dynamicstall. This experiment has several characteristics that often challenge CFD codes. First, the Reynoldsnumberswererelativelylow(lessthan400,000basedonairfoilchord). Suchlow Reynolds numbers means that the flow is transitional. Transitional flows generally pose problemsforstandardturbulencemodels,whichareintendedforfullyturbulentsituations. The experiment also experiences three-dimensional effects where the airfoil intersects the tunnel sidewalls. Because the tunnel width-to-chord ratio is relatively low (approximately 1.75), these three-dimensional effects likely occur over a significant fraction of the model at high angles of attack; and 2-D computations would be questionable at such conditions. Finally, the upper and lower wind tunnel walls are only 1.44c above and below the airfoil. The wall presence is therefore likely very influential on the flowfield near the airfoil. For 1 CFD, this in and of itself is not a big problem, but it does require the generation of a new gridforeveryangleofattack. Andfordynamicstallinvestigations,anoversetordeforming gridwouldberequired. Inthisstudy,weinvestigatetheeffectofcode,turbulencemodel,andgridontwocases withblowingfromtheleadingedgeslot(inadditiontothebaselinecaseofnoblowing). We alsoinvestigatetheinfluenceofthewindtunnelwallsandtherelativeimportanceofthree- dimensionality. Althoughtheexperimentwasprimarilyconcernedwithdynamicstall[2,3], here we focus the CFD study primarily on the effect of flow control (steady blowing) at steady-stateconditionsandatanglesofattackmostlybelowornearstall. 2 Geometry and Flow Characteristics The wind tunnel experiment from which the results were obtained tested an NACA 0018 airfoilmodelwithtwoblowingslotscutintotheuppersurface,locatedat5and50%ofthe chord (see figure 1(a)). These slots point at a 20 degree angle toward the trailing edge of theairfoil. Theairfoilmodelhadspanb = 0.610mandchordlengthc = 0.347m,andwas placed in a wind tunnel with dimensions 0.610 m wide × 1.004 m high (see figure 1(b)). In the experiments chosen for comparison, Re = 250,000 and freestream M = 0.03265 c (U = 11.1m/s). ∞ There were 40 pressure taps along the upper and lower surfaces of the model to pro- videtheexperimentalpressurecoefficientC values,whichwerethenusedtocalculatethe p experimentalvaluesoftheliftcoefficientC . L The geometry used in the CFD trials varied slightly from the experimental geometry. The slot height of the as-designed model was originally specified as 1 mm. However, the model, once manufactured, had a slot height of 1.2 mm. In this study, because there was nocomputer-aideddesign(CAD)representationfortheas-builtslots,theoriginalspecified slot height of 1 mm was used in the construction of all grids. However, the momentum coefficientC ,definedby µ hU2 j C = (1) µ (1/2)cU2 ∞ whichisameasureoftheeffectofblowing,waskeptconsistentbetweenCFDandexperi- ment. Previousexperiments[4]showedthatwhenh << c,themeasuredresultsofblowing dependonlyonC ,andarenotsensitivetochangesinh. InEq.(1),histheslotheight,U µ j isthejetblowingvelocity,cistheairfoilchord,andU isthefreestreamvelocity. ∞ 3 CFD Codes and Turbulence Models TwoNASACFDcodeswereusedinthisstudy: CFL3DandFUN3D.Bothcodessolvethe RANSequations. CFL3D [5] is a structured-grid upwind multi-zone CFD code that solves the general- ized thin-layer or full Navier-Stokes equations. In the current study, the full viscous terms areusedforallcomputations. CFL3Dcanusepoint-matched,patched,oroversetgridsand employs local time-step scaling, grid sequencing and multigrid to accelerate convergence 2 tosteadystate. CFL3Disacell-centeredfinite-volumemethod. Itusesthird-orderupwind- biased spatial differencing on the convective and pressure terms, and second-order differ- encing on the viscous terms; it is globally second-order accurate. Roe’s flux difference- splitting method [6] is used to obtain fluxes at the cell faces. The solution is advanced in timewithanimplicitapproximatefactorizationmethod. Foreachlooselycouplediteration, themeanflowequationsareadvancedintimewiththeeddy-viscosityfixed;thentheturbu- lencemodelisadvancedintimewiththemeanflowsolutionfixed. Severalturbulencemod- elsareavailableinthecode,includingtheone-equationmodelofSpalart-Allmaras[7](SA), the two-equation shear stress transport (SST) model of Menter [8], and the four-equation γ-Re SST transition model of Langtry-Menter [9]. These models are not described here; θ seetheTurbulenceModelingResourcewebsite[10]ortheoriginalreferencesforcomplete descriptions. FUN3D [11,12] is a finite-volume solver in which the flow variables are stored at the verticesornodesofthemesh. FUN3Dsolvestheequationsonmixedelementgrids,includ- ingtetrahedra,pyramids,prismsandhexahedra. Thecodealsohasatwo-dimensionalpath for triangular and quadrilateral grids. At interfaces between neighboring control volumes, theinviscidfluxesarecomputedusinganapproximateRiemannsolverbasedonthevalues oneithersideoftheinterface. SeveralconvectivefluxschemesareavailableinFUN3D.The mostcommonschemeforsubsonicandtransonicflowsisRoe’sfluxdifferencesplitting,[6] whichisusedinthecurrentstudy. Forsecond-orderaccuracy,interfacevaluesareobtained byextrapolationofthecontrolvolumecentroidalvalues,basedongradientscomputedatthe meshverticesusinganunweightedleast-squarestechnique. Severalreconstructionlimiters are available in FUN3D, but none were used in this study. The solution at each time-step is updated with a backwards Euler time-integration scheme. At each time step, the linear system of equations is approximately solved with either a multi-color point-implicit pro- cedure or an implicit-line relaxation scheme [13]. Local time-step scaling is employed to accelerateconvergencetosteadystate. ThesameturbulencemodelsmentionedforCFL3D (SA,SST,andγ-Re )arealsoavailableinFUN3D. θ 4 Grid Characteristics and CFD Boundary Conditions Aseriesofgridswasusedtoidentifytheeffectivenessofeachcodeandturbulencemodel. All grids were produced in Pointwise(cid:13)R, a commercial grid generator capable of creating bothstructuredandunstructuredgrids. First,a2-D,structured,free-airgridwasusedwithbothcodes(CFL3DandFUN3D)to verifythattheyproducedsimilarresults. Thisgridwasalsousedtoperformaninitialgrid sensitivitystudy,theresultsofwhichwereconsultedduringthecreationofotherstructured andunstructuredgridsintheseries. Theseinitialstructuredgridsusedasharptrailingedge on the airfoil. The finest grid size had 687,093 grid points (per plane), or 684,032 grid cells, and 1073 grid points on the airfoil surface, with minimum spacing of 2.88×10−6c of the first grid point off the wall and farfield extent of 144c (chord length c was 0.347 m). Eachsuccessivelycoarserlevelwascreatedbyremovingeveryothergridpointineach coordinatedirectionfromthenextfinergrid. Theminimumwallspacingofthefinestgrid ensuredthatthe∆y+ spacingofthefirstgridpointoffthewallwaslessthan1forallgrid levels. Insidetheairfoilslots,thewallsweretreatedinviscidly,soinviscidwallspacingwas 3 used (approximately in the range of 0.0001c−0.001c). A view of the structured free-air grid is shown in figure 2(a) and (b). Adiabatic no slip boundary conditions were applied ontheairfoil,exceptwithintheslots,whosesidewallsweretreatedasslipsurfaces. When blowingwasused,densityandvelocitywerespecifiedatthelowerwalloftheslot’splenum, whilepressurewasextractedfromtheinteriorofthedomain(densitywassettofreestream, andvelocitywassetinaniterativefashiontoachievethecorrectaveragevelocitynearthe slot exit). When blowing was not used, the lower wall of the slot’s plenum was treated as a slip surface. At the outer boundary of the grid, a farfield Riemann-invariant boundary conditionwasemployed. A series of 2-D structured grids incorporating inviscid upper and lower tunnel walls wasthencreatedtoidentifytheeffectthatthewalls’presencehadontheliftcoefficientand pressuredistributionalongtheairfoil. Adifferentgridwascreatedforeachangleofattack investigated (see, for example, figure 2(c)). These grids also used a sharp trailing edge on the airfoil. The grid used here was based on the finest grid level from the free-air grid convergence study. Its size was 407,523 grid points (per plane), with 1073 grid points on theairfoilsurfaceandminimumspacingof2.88×10−6cofthefirstgridpointoffthewall. Thetunnelwallsextendedfrom5.76cinfrontoftheairfoilquarterchordto5.76cbehindit. Normalgridspacingatthetunnelwalls(treatedinviscidly)wasapproximatelyintherange of0.01c−0.06c. Insidetheairfoilslots,thewallswereagaintreatedinviscidly. Forthese grids, the boundary conditions on the airfoil surface and within its slots were the same as before. Theupperandlowertunnelwallsweretreatedasslipsurfaces. Attunnelinflow,the total pressure and total temperature were specified according to adiabatic relations using M = 0.03265: p /p = 1.00075, T /T = 1.00021, and Riemann invariants were t ref t ref extrapolatedfromtheinteriorofthedomain. Attunneloutflow,staticpressurewasspecified asp/p = 1.0,andallotherquantitieswereextrapolatedfromtheinterior. ref A series of 2-D unstructured grids (with triangular elements) incorporating inviscid upperandlowertunnelwallswasalsocreated. Adifferentgridwascreatedforeachangle of attack investigated (see, for example, figure 2(d)). To explore the influence of airfoil trailingedgeshape,thesegridsalsousedablunttrailingedgeontheairfoil,approximately correspondingtotheactualbluntnessofthewindtunnelmodel(about0.0035cthickness). Althoughdetails arenotprovided inthisreport, theinfluence ofthemodeled trailingedge thickness was found to be insignificant in terms of the results of interest (surface pressure coefficients and lift coefficients) for this study. These grids contained 384,732 grid points (inthe2-Dplane),andused2141gridpointsontheairfoilsurfaceandminimumspacingof 2.88×10−6cofthefirstgridpointoffthewall. Tunnelwallextentwassomewhatdifferent from the structured tunnel grids, with the downstream end extending to 8.64c. Normal grid spacing at the tunnel walls (treated inviscidly) was approximately 0.007c. Boundary conditions for these grids were the same as for the structured tunnel grids, except that the side walls inside the airfoil slots were treated viscously (the grids had finer spacing and the boundary conditions were adiabatic no-slip). This viscous slot treatment was done to overcomeaproblemrunningFUN3Dwithsomeoftheturbulencemodels. Afewrunswerealsoperformedin3-D.Forthese,the2-D,structured,tunnelgridwas extruded in the spanwise (y) direction a distance of y = 0.305 m, representing the tunnel halfwidth. Gridsspacingwasclusteredneary = 0,representingthetunnelsidewall. See figure2(e). The grids used in this study each included the contracting portion of the blowing slots 4 between the slot plenums and the actual slot exit, as shown in figure 2(b). Therefore, the boundary condition at the plenum exit was set as a subsonic inflow when the slot was blowing. The inflow velocity at this boundary was adjusted so that the jet velocity U j (velocity at the slot exit line) matched the correct value for the chosen case. The target jet velocitieswerefoundbyrewritingEq.(1)as (cid:115) (1/2)C cU2 U = µ ∞ (2) j h then solving Eq. (2) for U using each value of C included in the study. The target jet j µ velocity is equal to 32.693 m/s when C = 5%, and 11.325 m/s when C = 0.6%. When µ µ nondimensionalized with the reference speed of sound, these two velocities are 0.096155 and0.03331,respectively. To ensure that the jet velocity matched the target velocities for each value of C , an µ iterativeprocesswasusedinwhichtheaveragevelocityoftheCFDsolutionacrosstheslot exitlinewasfound,thenadjustmentsweremadetotheplenuminflowboundarycondition until the desired average jet velocity was attained (see figure 3). The inflow boundary conditionrequiredwasapproximatelythesameregardlessofwhethertheinteriorslotwalls weretreatedinviscidlyorviscously. 5 Results The results include grid sensitivity studies (both grid density as well as comparison of re- sults with structured and unstructured grids). Comparisons are made using different codes and different turbulence models. Efforts to model or capture transitional effects are de- scribed, and the effects of including the tunnel upper and lower walls are documented. Mostcomputationsare2-D,butseveral3-Dtrialswerealsoexplored(i.e.,includingtunnel sidewalls). 5.1 StructuredGridSensitivityStudies A grid sensitivity study was performed on the 2-D, structured, free-air grid. The original “fine”grid(684,032cells)wascoarsenedbyremovingeveryothergridpointtoproducea “medium” grid (171,008 cells), then coarsened again to produce a “coarse” grid (42,752 cells). For the purposes of the grid sensitivity study, the case was run at several angles of attackwithoutblowing. Liftcoefficientresultsareplottedinfigure4. Theresultsindicated littleinfluenceofgriddensityonliftcoefficients overtheangleofattackrangeofinterest, sothemediumgridwasselectedforuseinobtainingfurther“free-air”results. Notice in figure 4 that the experiment yielded an unusual lift curve shape. Rather than an approximately linear progression of lift with angle of attack over the lower angles, the experimentalresultsexhibitedanonlinearincreaseinliftbetweenapproximately5and10 degrees. This is believed to be due to the presence of a laminar bubble near the airfoil’s uppersurfaceleadingedge,whichcausesadditionalflowaccelerationaroundit. Aswillbe describedfurtherbelow,theCFDwasnotabletocapturethiseffect. 5 5.2 CodeComparison Several test cases were run in both CFL3D and FUN3D to identify whether the two codes wouldproducesimilarresultsforthiscase. Theanglesofattackusedwere0,5,8,10,and 12 degrees. A sample of these results can be found in figure 5. These results show that onthesamesufficientlyrefinedgridforthiscase,CFL3DandFUN3Dproducepractically identicalsolutions. 5.3 TurbulenceModelComparison Next,threeturbulencemodelswereexaminedusingthesametestcases. Theresultsofthese runs can be found in figures 6 and 7. The SA and SST models displayed similar behavior of relatively linear lift curve slope (failing to predict the nonlinear change in the lift curve slopebetween5and10degreesangleofattack). However,theirpressuredistributionswere reasonableandconsistentwitheachotherandwiththeexperiment. The γ-Re turbulence model was used to attempt to capture the nonlinear lift curve θ behavior. C results at α = 5◦ appeared to be promising. The model yielded delay of L transitiontoturbulenceontheuppersurface,resultinginaseriesofsmallrecirculatingre- gionsontheuppersurface,whichwereproductsofaverylargeregionofseparatedlaminar flow. Exampleplotsshowingtheextentoftheseregionscanbeseeninfigure7(b),(d),and (f). However,theexperimentshowedthatlaminarseparationbubblereattachmentoccurred prior to 0.07 m along the chord in all cases for which the forward inactive slot on the up- per surface tripped the flow to turbulent [2]. Such large separated regions from the γ-Re θ modelindicateditsfailuretocapturethetrippingeffectofthisslot. The cause of the failure of the γ-Re model has not been determined, but one poten- θ tial cause is the natural decay of freestream turbulence intensity inherent in the model. Turbulence intensity was specified to be 0.05%, based on information provided by the ex- perimenters. A large portion of that intensity might have decayed over the length of the grid, so that the level near the airfoil was too low for the model to accurately predict tran- sition. Future efforts should focus on either adjusting the freestream turbulent boundary conditions or disallowing their decay; also, time-accurate computations may be required withthismodeltofindtheaverageofanyinherentunsteadinessduetolaminarseparation. However,thismodelwasnotpursuedfurtherinthecurrentstudy. 5.4 ForcedTransitionStudy To investigate the effects that transition location might have on the flow solutions, several test cases were run in which the transition location was specified in conjunction with the SAmodel. Theultimategoaloftheseparticularrunswastodetermineiftransitionlocation could alter the solution enough to produce the behavior in the lift curve slope similar to thatseenintheexperimentaldata. Transitioneffectswereoneofthefirstsuspectedcauses ofthebehavior,sinceCFDisgenerallyunreliableatpredictingtransitioncharacteristicsat low Reynolds numbers such as the one in this problem. Seven transition locations on the uppersurfaceoftheairfoilweretested,rangingfromapproximately5%(thelocationofthe blowing slot) to 25% of chord length. Results from these tests can be found in figures 8 and9. 6