Effects of surface roughness on a separating turbulent boundary layer

Separating turbulent boundary layers over smooth and rough flat plates are studied by large-eddy simulations. A suction-blowing velocity distribution imposed at the top boundary of the computation domain produces an adverse-to-favourable pressure gradient and creates a closed separation bubble. The Reynolds number based on the momentum thickness and the free-stream velocity before the pressure gradient begins is 2500. Virtual sand grain roughness in the fully rough regime is modelled by an immersed boundary method. Compared with a smooth-wall case, streamline detachment occurs earlier and the separation region is substantially larger for the rough-wall case, due to the momentum deficit caused by the roughness. The adverse pressure gradient decreases the form drag, so that the point where the wall stress vanishes does not coincide with the detachment of the flow from the surface. A thin reversed-flow region is formed below the roughness crest; the presence of recirculation regions behind each roughness element also affects the intermittency of the near-wall flow, so that upstream of the detachment point the flow can be reversed half of the time, but its average velocity can still be positive. The separated shear layer exhibits higher turbulent kinetic energy (TKE) in the rough-wall case, the growth of the TKE there begins earlier relative to the separation point, and the peak TKE occurs close to the separation point. The momentum deficit caused by the roughness, again, plays a critical role in these changes.