Effects of favorable pressure gradient on turbulence structures and statistics of a flat-plate supersonic turbulent boundary layer

Abstract

A Mach 2.9 flat-plate supersonic turbulent boundary layer subject to a moderate favorable pressure gradient (FPG) induced by external expansion waves is investigated through direct numerical simulation and compared with a zero pressure gradient (ZPG) boundary layer. It is found that under FPG, the logarithmic region in the van Driest transformed velocity profile is lifted above the log law, while the wake region deviates below its ZPG counterpart. The near-wall streaks are elongated in the streamwise direction with wider spanwise spacing, which leads to an attenuated meandering effect compared to the ZPG case. Although small-scale motions in the outer layer are evidently suppressed, they survive mostly in the inner layer. On the other hand, large-scale motions tend to correlate further with the lifted fluid from upstream due to bulk dilatation. However, their relative locations within the boundary layer remain unchanged. Different responses of turbulence structures in the inner and the outer layer to FPG show that this two-layer feature within the boundary layer is mainly associated with the bulk dilatation rather than the wall curvatures. The profiles of turbulent kinetic energy (TKE) and turbulent Mach number also show a two-layer behavior, where the reduction in turbulence in the outer layer is more prominent than in the inner. Positive convection occurs from the buffer to the outer layer according to the TKE budget analysis, which compensates the production and resists the decrease in the turbulence level.