Receptivity to surface roughness near a swept leading edge

The formation of stationary crossflow vortices in a three-dimensional boundary layer due to surface roughness located near the leading edge of a swept wing is investigated using numerical solutions of the compressible Navier–Stokes equations. The numerical solutions are used to evaluate the accuracy of theoretical receptivity predictions which are based on the parallel-flow approximation. By reformulating the receptivity theory to include the effect of surface curvature, it is shown that convex surface curvature enhances receptivity. Comparisons of the parallel-flow predictions with Navier–Stokes solutions demonstrate that non-parallel effects strongly reduce the initial amplitude of stationary crossflow vortices. The curvature and non-parallel effects tend to counteract one another; but, for the cases considered here, the non-parallel effect dominates leading to significant over-prediction of receptivity by parallel-flow receptivity theory. We conclude from these results that receptivity theories must account for non-parallel effects in order to accurately predict the amplitude of stationary crossflow instability waves near the leading edge of a swept wing.