The impact of static and dynamic roughness elements on flow separation

The use of static or dynamic roughness elements has been shown in the past to delay the separation of a laminar boundary layer from a solid surface. Here, we examine analytically the effect of such elements on the local and breakaway separation points, corresponding respectively to the position of zero skin friction and presence of a singularity in the roughness region, for flow over a hump embedded within the boundary layer. Two types of roughness elements are studied: the first is small and placed near the point of vanishing skin friction; the second is larger and extends downstream. The forced flow solution is found as a sum of Fourier modes, reflecting the fixed frequency forcing of the dynamic roughness. Solutions for both the static and dynamic roughness show that the presence of the roughness element is able to move the separation points downstream, given an appropriate choice of roughness frequency, height, position and width. This choice is found to be qualitatively similar to that observed for leading-edge separation. Furthermore, for a negative static roughness a small region of separated flow forms at high roughness depth, although there is a critical depth above which boundary-layer breakaway moves suddenly upstream