Direct numerical simulations of laminar-turbulent transition in hypersonic flows over flat plate

Abstract eng:
In this paper w we simulate 3D wave trains geenerated by a peeriodic suction-blowing actuatoor working at a fixed frequenccy. These disturbaances brake doown within the computationall domain that aallows for sim mulations of thee early stage oof LTT. DNS aare performed by solving the 3D Navier-Stokes equations for uunsteady comprressible flows oof viscous perfeect gas using thhe in-house solvver “HSFlow” (High Speed Flow solver). The probblem of laminnar-turbulent ttransition (LTT T) in hypersoonic flows oveer bodies is onne of the mainn tasks of higghspeed aerodyynamics. LTT leads to a subsstantial increaase of the surfaace heating annd aerodynamiic drag of hypeersonic vehiclles as well as afffects the efficciency of proppulsion system m and controll surfaces. To solve this prroblem it is neeeded to clariify physical mecchanisms causing transitionn to turbulennce. In the caase of low fr free-stream disturbances tyypical for fligght conditions, thhe LTT includdes the three main m stages [1]]: receptivity tto external dissturbances; groowth of unstabble modes (such as first and seecond Mack m modes, cross fllow instabilityy and Görtler vortices); v nonllinear breakdoown of disturbaances leading to the fully turbuulent flow reggime. A holisticc computationn of the all LT TT stages is poossible only uusing direct nuumerical simullations (DNS)), where the fuull unsteady threee-dimensionaal (3D) Navieer–Stokes equuations are sollved without any restrictioon on the meaan (unperturbed laminar) flow w and disturbaance amplituddes. In additioon, as opposed to physical experiments, DNS gives full f informatioon about 3D distturbance fieldd, which enablles to identifyy and study in detail differennt LTT mechaanisms. The m modern methoods of parallel coomputations and a rapid devvelopments off multi-processsor supercom mputers makee it feasible too conduct such numerical expperiments for hypersonic booundary layerss for simple coonfigurations such as a flat pplate and a coone at zero anggle of attack [2]. In this ppaper we coonsider a plaat plate at tthe freestream m Mach num mber 5.373 aand unit Reyynolds numbber Re! ,1 " 17.9 #106 m $1 . Theese flow param meters are releevant to the Hyyper-X model tested in the N NASA LaRC 20-Inch Machh 6 Air Tunnel [3]. The earllier stability and numericaal studies in these conditiions were peerformed for the 5.5 degrree compression corner in 2D [4, 5] and 3D D cases [6, 7]. In this papeer we simulatte 3D wave trrains generateed by a perioddic suction-blowiing actuator w working at a ffixed frequenccy. These distturbances brakke down withhin the compuutational domaain that allows foor simulationss of the early stage of LTT T. DNS are peerformed by soolving the 3D D Navier-Stokees equations ffor unsteady com mpressible flow ws of viscous pperfect gas using the in-houuse solver “HS SFlow” (High Speed Flow solver). # ny #151 noddes, where thee number of nnodes in verticcal Computatiions are perfoormed on an orthogonal o griid with 6001# direction ny varies from 126 1 to 376 throough the compputational dom main dependinng on the bow shock locationn. It is clustered near the surfa face so that 555% of nodes aare within thee boundary layyer with the ssmallest cell y-size y of %y " 0.0001 . In thhe spanwise direection the gridd is equidistannt with the stepp size of %z " 0.0013 . Nearr the outflow bboundary the size of 160 grrid cells is graduually increasedd from %x " 00.0005 to %x " 0.1 . This paart of computaational domainn acts as “buff ffer” zone wheere the unsteady disturbances ddissipates via nnumerical visccosity. The soolution in this zone z is inaccuurate and is ignnored during thhe analysis below w. The grid coontains 251×106 nodes in tootal.

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