Transpiration Induced Shock Boundary-Layer Interactions

Steady and unsteady shock boundary-layer interactions are studied numerically by solving the two-dimensional time-dependent Navier-Stokes equations. To validate the numerical method, the steady interaction is compared with measurements and other numerical results reported in the literature. The numerical study of the steady interaction leads to a suitable method for transpiration boundary conditions. The method applies to unsteady flows as well. Using the validated numerical method, we show that an unsteady shock boundary-layer interaction can occur in a supersonic flow over a flat plate subjected to suction and blowing from the opposite side of the plate, even though the imposed transpiration is steady. Depending on the Mach number, the Reynolds number, the distance of the transpiration boundary to the lower wall, and the transpiration profile, the unsteadiness can be inviscid or viscous dominated. The viscous effect is characterized by the occurrence of self-excited vortex shedding. A criterion for the onset of vortex shedding for internal compressible flows is also proposed.