Boundary layer transition in high-speed flows due to roughness

Direct numerical simulation (DNS) is used to study the effect of individual (hemispherical) and distributed roughness on supersonic flat plate boundary layers. In both cases, roughness generates a shear layer and counter-rotating pairs of unsteady streamwise vortices. The vortices perturb the shear layer, resulting in trains of hairpin vortices and a highly unsteady flow. Mach 3.37 flow past a hemispherical bump is studied by varying the boundary layer thickness (k/δ = 2.54, 1.0, 0.25 & 0.125). Transition occurs in all cases, and the essential mechanism of transition appears to be similar. At smaller boundary layer thickness, multiple trains of hairpin vortices are observed immediately downstream of the roughness, while a single train of hairpin vortices is observed at larger δ. This behavior is explained by the influence of the boundary layer thickness on the separation vortices upstream of the roughness element. Mach 2.9 flow past distributed roughness results in a fully turbulent flow. Mean velocity profiles show spanwise inhomogeneity in the transitional region, with the flow becoming more homogenous downstream. Spanwise spectra initially exhibit only the wavelength of the roughness surface. Then, the energy at smaller wavelengths increases resulting in a broadband spectra downstream. Temporal spectra in the transitional region are characterized by the frequency of the unsteady vortices and a higher frequency corresponding to the shear layer breakdown. The magnitude of wall-pressure fluctuations is observed to be greater in the transitional region than in the turbulent region, where a good agreement with recent experiments is obtained.