The receptivity of a laminar boundary-layer flow to small-amplitude wall roughness is investigated on an ONERA-D swept aerofoil by introducing a dedicated transfer function from small-amplitude wall displacements to full-state velocity perturbations. The singular value decomposition of this operator for a given spanwise wavenumber provides optimal wall roughness and flow responses that maximise an input–output gain. At the most receptive spanwise wavenumber, the optimal response is a cross-flow mode associated with an optimal roughness located close to the attachment line and presenting a wavy shape with a wavevector nearly orthogonal to the external streamlines. The method therefore allows direct identification of the location and structure (chordwise and spanwise wavenumbers) of the most receptive roughness. For various given wall roughness shapes and locations (periodic or compact in the chordwise and/or spanwise directions), an approximation of the response based on the dominant optimal response is shown to accurately match the total response downstream of the roughness. The method therefore allows a straightforward computation of the response of the flow to any given small-amplitude roughness.

In this study, a series of numerical experiments are performed on supersonic/hypersonic flows over an adiabatic flat plate with transitionally and fully rough surfaces. The Mach numbers simulated are 4, 5, 6, and 7; the flight heights considered are 20, 24, 28, 32, and 36 km. First, a modified roughness correction is proposed and validated with the measured data for low-speed flat-plate cases. It is verified that for the equivalent sand grain heights in the intermediate and fully rough regimes, there is a good agreement with the semi-empirical formula available in the open literature. Then, this roughness correction is applied to high-speed flow regime to investigate the effects of flight heights and Mach numbers on drag for rough-wall flat-plate cases. It is found that within the roughness measured in real flight, the roughness height change has little effect on drag compared to the variations of both flight heights and Mach numbers. The drag coefficient derivation between rough-wall and smooth-wall conditions, achieves the maximum value of 0.79% for the 60 cases selected.