High-speed boundary layer transition induced by a discrete roughness element

The effect of a hemispherical bump on a Mach 3.37 laminar boundary layer is studied using DNS for three conditions with $k/\delta=$ 2.54, 0.25 and 0.125, where $k$ is the roughness height. The simulation parameters are based on the experiment by Danehy {\it et. al.} (AIAA-2009-394). The flow downstream of the roughness is transitional for all the three conditions accompanied by a rise in skin friction and heat transfer. Upon interaction with the roughness element, the boundary layer separates to form a series of spanwise vortices upstream and a shear layer. These vortices wrap around the roughness to yield a system of streamwise vortices downstream. Perturbation of the shear layer due to the vortices results in the formation of hairpin-shaped vortices further downstream of the roughness. While hairpin vortices were observed in both the center plane and off-symmetry planes on either side for the smallest $\delta$ case, they were observed only in the center plane for the other cases.