Numerical simulation of transpiration cooling for a high-speed boundary layer undergoing transition to turbulence

Cooling the surface of high-speed vehicles by injection of coolant into the flow stream aims to reduce the overall weight and cost of thermal protection systems. Here, the transpiration-based cooling method is studied for a Mach number M∞ = 5 with coolant injected through a porous layer composed of a staggered arrangement of spheres. Disturbances are introduced into the boundary layer upstream of the porous layer to study in detail the flow regime in which the boundary layer is transitional, including cases where transition is triggered either downstream or directly over the sample. The present work evaluates the effects of transition location, Reynolds number at injection location, and blowing ratio on the cooling performance downstream of the porous sample with heat fluxes that are comparable in magnitude to those seen in laboratory experiments. Flow within the porous layer is found to be unsteady, with a non-negligible streamwise pressure gradient introduced by shock and expansion waves at the leading and trailing edge of the porous sample. For cases where transition occurs just downstream of the sample, the lowest pressure/blowing ratio case results in more cooling immediately after the porous layer, but cooling performance worsens farther downstream. Higher blowing ratio cases show higher effectiveness for a longer distance downstream, despite the transition location moving upstream. For cases where transition occurs over the porous sample, the cooling effect is more consistent, with the heat flux decreasing monotonically with increasing pressure/blowing ratio. The results not only show a strong dependence on transition location, but also that opposite trends in cooling performance are possible when transition occurs just downstream of the injection.