Numerical simulation of fully-developed compressible flows over wavy surfaces

Rough surfaces are common on high-speed vehicles, for example on heat shields, but compressibility is not usually taken into account in the flow modelling other than through the mean density. In the present study, supersonic fully-developed turbulent rough wall channel flows are simulated using direct numerical simulation to investigate whether strong compressibility effects significantly alter the mean flow and turbulence properties across the channel. The simulations were run for three different Mach numbers M = 0.3, 1.5 and 3.0 over a range of wall amplitude-to-wavelength ratios from 0.01 to 0.08, corresponding to transitionally and fully rough cases respectively. The velocity deficit values are found to decrease with increasing Mach number. It is also found that at Mach 3.0 significant differences occur in the mean flow and turbulence statistics throughout the channel and not just in a roughness sublayer. These differences are found to be due to the presence of strong shock waves created by the peaks of the roughness elements.

► DNS of supersonic turbulent flow over wavy surfaces.
► Roughness effect reduces with increasing Mach number.
► Shock-wave formation from surfaces peaks at Mach 3.0.
► Shock-waves significantly alter the mean properties and turbulent statistics.