Compressibility effects on roughness-induced boundary layer transition

Direct numerical simulation (DNS) is used to investigate the effect of compressibility on roughness-induced boundary layer transition. Computations are performed both in the low- and the high-speed regime (up to free-stream Mach number M∞ = 4) for an isolated three-dimensional cubic element submerged in the boundary layer, by considering variations in the roughness height k and in the roughness Reynolds number Rek, formed with flow properties evaluated at the edge of the roughness element. In agreement with previous experimental observations at low speed, unsteady release of hairpin vortices past the disturbing element is observed at sufficiently high Rek for all Mach numbers, which eventually results in the breakdown to turbulence. A similar vortex organization is found for all flow cases which experience transition, regardless of the Mach number, the main effect of roughness consisting in the generation of streamwise and wall-normal vorticity, with the formation of an unstable detached shear-layer on the top of the element. A suitable criterion for roughness-induced transition is identified and a modified roughness Reynolds number, based on the kinematic viscosity at the wall, is proposed to scale out the effect of compressibility.