Numerical simulation of a spatially developing accelerating boundary layer over roughness

Abstract

The direct numerical simulation of an accelerating boundary layer over a rough wall has been carried out to investigate the coupling between the effects of roughness and strong free-stream acceleration. While the favourable pressure gradient is sufficient to achieve quasi-laminarization on a smooth wall, the flow reversion is prevented on a rough wall, and a higher friction coefficient, a faster increase of turbulence intensity compared to the free-stream velocity and more isotropic turbulence near the wall are observed. The logarithmic region of the mean-velocity profile presents an initial decrease in slope as in the smooth case, but soon recovers, as the fully rough regime is reached and a new overlap region is established. A strong coupling between the roughness and acceleration effects develops as roughness leads to more responsive turbulence and prevents the strong acceleration from stabilizing the turbulence, and the acceleration intensifies the velocity scale of the wake field (i.e. the near-wall spatial heterogeneity of the time-averaged velocity distribution). The combined effect is a ‘rougher’ surface as the flow accelerates. In addition, the link between the local values of the free stream and the near-wall velocity depends on the flow history; this explains the different flow responses observed in previous studies, in terms of friction coefficient, turbulent kinetic energy and Reynolds-stress anisotropy. This study elucidates the near-wall flow dynamics, which may be used to explain other non-canonical flows over rough walls.