Receptivity of Crossflow Instabilities to a Periodic Roughness Array on a Swept Cylinder: Investigation of the Roughness Size Influence

Abstract

A direct numerical simulation of the flow around a micro-roughness array placed within the laminar boundary layer on a swept cylinder has been performed. Several dimensions of the roughness elements have been investigated. In any case, the quite large value (a few percent of the boundary layer thickness) of the roughness heigth prevents from getting linear receptivity phenomena and requires a computation which takes into account nonlinear effects. Both steady and unsteady instability waves are generated downstream of the roughness array, even if the roughness forcing is purely steady. The presence of the unsteady wave may be due to a pocket of absolute instability in the chordwise direction. The unsteady DNS wave fits perfectly with the traveling crossflow wave predicted by the linear stability theory. Its amplitude seems to be fixed by transient effects induced by the numerical initialization procedure. As this amplitude is quite high, this wave interacts nonlinearly with the steady wave, which thus does not match exactly with the linear steady crossflow wave. Therefore, the receptivity process cannot be precisely quantified. However, the results enlighten qualitatively the influence of both the roughness heigth and spanwise extent.