Receptivity of a Hypersonic Flat-Plate Boundary Layer to Three-Dimensional Surface Roughness

Abstract

The laminar–turbulent transition of hypersonic boundary layers has a significant effect on drag calculation and aerothermal design of hypersonic vehicles. Recent research has shown that one possible explanation to roughnessinduced bypass transition is transient growth theory. However, it is not known how to generate the optimal disturbances computed by transient growth theory. Furthermore, there has not been any direct numerical simulation study on transient growth in hypersonic boundary layers. The objectives of this paper are to study the receptivity of a Mach 5.92 flow over a flat plate to three-dimensional surface roughness and the effect of spanwise wave number on the receptivity. Steady base flow is computed by solving compressible Navier–Stokes equationswith a combination of a fifth-order shock-fitting method and a second-order total variation diminishing scheme. In receptivity simulations, small surface roughness is introduced on the plate. The numerical results show that counterrotating streamwise vortices and transient growth are induced by surface roughness, however, transient growth is generally weak due to the small height of roughness. For the six cases considered, surface roughness with the spanwise wave number being 0.0101 has the strongest excitation of transient growth.