Direct numerical simulation of supersonic boundary layer transition induced by gap-type roughness

Abstract The transition of the supersonic boundary layer induced by roughness is a highly intricate process. Gaining a profound understanding of the transition phenomena and mechanisms is crucial for accurate prediction and control. In this study, to delve into the flow mechanisms of a transition in a supersonic boundary layer induced by the medium gap-type roughness, direct numerical simulation is employed to capture and analyze the transition process. Research indicates that as the flow over the flat plate passes the gap, the spanwise convergence effect leads to the formation of both upper and lower counter-rotating vortex pairs. As the flow progresses, these counter-rotating vortex pairs in the central region exhibit attenuation, with streamwise vortices developing on both sides. At a certain downstream distance, the boundary layer becomes unstable, triggering the formation of streamwise vortex legs. These streamwise vortex legs undergo further evolution, transforming into hairpin vortices and leg-buffer vortices. The formation of the central low-speed zone downstream of the roughness element is mainly attributed to the lift-up effect of the low-speed flow propelled by the central counter-rotating vortex pairs. The low-speed streaks on both sides are primarily influenced by the streamwise vortices. Through a meticulous analysis of the turbulent kinetic energy distribution and its generation mechanisms during the transition phase, this study infers that the primary sources of turbulent kinetic energy are the hairpin vortices, leg-buffer vortices, and their consequent secondary vortices. Combined with modal analysis, the study further elucidates the generation and breakdown of hairpin and leg-buffer vortices.