NUMERICAL INVESTIGATION OF THE SEPARATED FLOW OVER A SMOOTHLY CONTOURED RAMP

Abstract

Large Eddy Simulation (LES) and ReynoldsaveragedNavier-Stokes(RANS)calculationshave been used to predict the development, separation, reattachmentand downstreamrecovery of the flow over a smoothlycontouredramp. The statisticallytwo-dimensionalupstreamflow separatesalong the ramp surfaceand then reattaches downstreamon a flat section. A canonicalflatplate turbulent boundary layer at a momentum thicknessReynolds number1100, and having a boundarylayer thickness , is introduced four ramplengthsupstreamof theonsetof curvature. Subgrid-scale(SGS)stressesin theLES are closedusingthedynamiceddyviscositymodelof Germanoet al. (1991). RANS calculationsof the steady-statesolutionareperformedusingtwo leading models: Spalart-Allmaras(Spalart-Allmaras 1994) and (Durbin 1991). Mean flow predictionsobtainedusingall the modelsagreewell with theexperimentalmeasurements of Songet al. (2000). Boundarylayer detachment occursalong the curved section( ) with reattachmentat roughly . Theprimary turbulent shearstresssharplyincreasesin theseparated region andLES predictionsof theshearstressdevelopmentareaccurate.RANS estimationsof the shearstressarebelow thedatain theseparatedregion,thoughreasonablefurtherdownstream. INTRODUCTION AND OBJECTIVES Separatedboundary layers are a challenging subsetof flows that may be generallyclassified as ‘non-equilibrium’. Non-equilibriumboundary currentaddress:Centerfor Simulationof AdvancedRockets,Universityof Illinois, Urbana,Illinois 61801,USA layersarethe norm, ratherthanthe exception,in engineeringapplications.Theimportanceof additional lengthscalesto describingtheflow and/ora significantimbalancebetweenproductionanddissipationaretwo featureswhich characterizethese flows. An adverse pressuregradient boundary layer approachingseparationdevelops an inflection point, the height of which is an additional importantlengthscale.Turbulentstresses, for example,develop large peaksaroundthe inflection point andboundarylayerrecovery following reattachmentshouldbeexpectedto besensiti ve to this lengthscale. Theseandotherfeaturesof separatedflowssubstantiallychallengepredicti ve methods.The vast majority of engineeringpredictionsare obtained from solutionsof the Reynolds-averagedNavierStokes (RANS) equations.In flows not far from equilibrium, the boundaryconditionsthat define largescalestructuresremainnearlyunchangedand theleadingRANSmodelsaretypically adequate. In separatedflows, however, RANS models often yield mixed results (e.g., see Apsley and Leschziner1999),providing onerationalefor use of techniquessuch as Large Eddy Simulation (LES). In LES,thelarge,energy-containingscales of motion areresolved on the meshandonly the small, subgridscalesare modeled. LES predictionsarelesssensiti veto modelingerrorsthantheir RANS counterparts. This featureshouldbeanadvantagein predictionof flows far from thecalibration rangeof RANS modelsand in regimeswith multiple perturbations(e.g., in pressuregradient, streamlinecurvature,roughness, etc.). Assessment of simulation techniquesfor predicting separatedboundarylayersis complicated by the fact that thereis relatively strongcoupling betweenthefreestreamandboundarylayer. Thisin turnincreasesthesensiti vity of theflow to parametersnotdirectlyconnectedto theturbulencemodel andmay not allow oneto easily isolatethe cause of discrepancies betweennumericalsimulationand experiment.Therefore,it is usefulin any studydirectedtowardsrefinedevaluationof techniquesand modelsthatcarefulevaluationof abaselinecasebe established. Oneof the overall aimsin this work is prediction of theeffectof Reynoldsnumberonseparated boundarylayers(seealsoSongandEaton2001in thisvolume).In thepresentcontributiontheflow at moderateReynoldsnumberis predictedusingLES andRANS in orderto assesstheaccuracy of each techniqueaswell asto investigatesomeof theunderlyingcharacteristicsof theflow. Theparticular flow underconsiderationis the statistically twodimensional boundarylayerwhichseparates overa smoothlycontouredramp(Figure1). Thelocation of boundarylayer detachment is not fixed by the geometryandtheflow providesa reasonablywelldefinedplatformfor investigatingtheprocessesof reattachment and downstreamrecovery. Experimentalmeasurements from Songet al. (2000)are usedto evaluatethepredictions.