Numerical Simulation of the Interaction between a Shock and the Boundary Layer on a Flat Plate in Motion
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rical Simulation of the Interaction between a Shock and the Boundary Layer on a Flat Plate in Motion I. V. Egorova,b, I. M. Ilyukhina,b,*, and V. Ya. Neilanda aZhukovski
Central Aerohydrodynamic Institute (TsAGI), ul. Zhukovskogo 1, Zhukovsky, Moscow region, 140180 Russia bMoscow Institute of Physics and Technology, Institutski per. 9, Dolgoprudny, Moscow region, 141701 Russia
*e-mail: [email protected] Received February 29, 2020; revised March 12, 2020; accepted March 12, 2020
Abstract—The results of numerical simulation of the interaction between a shock and the laminar boundary layer on a flat plate in motion in supersonic perfect-gas flow at Mach number М∞ = 3 are considered. The shock is preassigned using the Rankine—Hugoniot boundary conditions, which corresponds to a shock wave produced by a wedge with a given semi-vertex angle in an inviscid gas flow. The simulation is based on the numerical solution of the time-dependent, two-dimensional Navier— Stokes equations by time marching to steady state. The numerical results are verified by means of comparing the results for separation flow past a flat plate at rest with experimental data. The numerical data are used to investigate the effect of the plate velocity of the separation flow structure and the basic laws governing the problem. It is shown that the motion of the plate downstream diminishes the separation zone length, whereas the opposite motion leads to its increase.
Keywords: laminar boundary layer, numerical simulation, shock wave, flat plate in motion, NavierStokes equations, Stokes equations DOI: 10.1134/S0015462820050055
The shock/boundary layer interaction is a widespread phenomenon in supersonic flows. Local boundary layer separation due to this interaction can have a considerable effect on the aerodynamic heating and flow stability [1]. The asymptotic theory of the free interaction for supersonic laminar boundary layers in the two-dimensional formulation [2–4] describes the separation induced by an adverse pressure gradient over a wall at rest. In particular, this gradient can be due to the incidence of a shock on the boundary layer. The disturbance thus produced is transferred upstream along the subsonic region of the boundary layer deflecting streamlines. This, in turn, changes the external inviscid flow pattern via the formation of compression waves. At the point on the wall, where friction is zero, the boundary layer starts to separate. In accordance with the asymptotic theory, the scale of the separation vicinity is proportional to Re−3/8 , where s Res is the Reynolds number based on the spacing between the leading edge of the plate and the separation point. The shock is reflected from the separated boundary layer as a fan of expansion waves. Within the boundary layer, the separation point is followed by a recirculation zone, where the pressure is near-constant. In the vicinity of the reattachment point a compression wave fan and a shock can be observable. In practice, situations, in which a shock wave can move both downstream an
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