The formation of stationary cross flow 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 cross flow 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.