Numerical simulation of roughness effect on the stability of a hypersonic boundary layer

A new high-order cut-cell method is used to numerically simulate two dimensional roughness effects on modal growth in a hypersonic boundary layer. The steady base flow is simulated first by solving the compressible Navier-Stokes equations. Perturbations correspond to Mode S wave at 100 kHz and a wall normal velocity pulse with a continuous frequency spectrum up to 1 MHz are imposed onto the mean flow with roughness separately. A Fast Fourier Transform (FFT) is used to decompose the perturbation and to study the evolution of perturbations at different frequencies. The number of roughness elements in the boundary layer is changed for two test cases. Moreover, the effect of roughness height is studied in the Mode S simulation. It is found that when the roughness element is located at the synchronization point of a particular frequency (i.e. synchronization frequency), perturbations at frequencies higher than the synchronization frequency are damped. On the other hand, perturbations at frequencies lower than the synchronization frequency are amplified by the roughness. The same conclusion is drawn in cases where the roughness location is changed. The relation between roughness and the synchronization point is a candidate to explain roughness delayed transition seen experimentally. (C) 2014 Elsevier Ltd. All rights reserved.