Numerical simulation of flow over rough surfaces, including effects of shock waves

The finite-difference boundary layer method of Christoph and Pletcher for flow over rough surfaces is extended to include the effect of shock waves off roughness elements. The equivalent sand-grain roughness height is not needed, but rather the actual roughness height and spacing is used. A turbulence model that contains very little empiricism but yet is capable of accounting for roughness height, spacing, and geometry is presented. Computations are presented for smooth and rough wall profiles and skin friction data obtained at AFWAL in the Mach 6 facility. Agreement is quite good, especially in light of the fact that in no way was the turbulence modeling adjusted during these comparisons.