Direct numerical simulations of first-mode oblique breakdown in a supersonic boundary layer under wall transpiration

Abstract

Complete first-mode oblique breakdowns under wall transpirations in a Mach 2 flat-plate boundary layer are investigated by direct numerical simulations. The parameters of oblique waves are determined by linear stability analysis, while air transpiration is modeled by a wall-injection boundary condition. Wall transpiration with various blowing ratios is imposed at two distinct streamwise regions to assess its effects. When wall transpiration is located in the linear and early nonlinear region, the transition shifts upstream with increasing blowing ratios. This promotion effect arises from the destabilization of the oblique mode, steady vortex mode and higher-harmonic modes. Wall transpiration also leads to reduced skin friction and heat transfer in the transpiration and downstream turbulent regions. Through integral analysis, the impacts of transpiration on the generation mechanisms of skin friction and heat transfer are gained. The reduced skin friction and heat transfer in the transpiration region are mainly attributed to the amplified negative contributions from mean convection. In the turbulent region, the reduction of skin friction can be attributed to the heightened negative contributions from mean convection and the diminished positive contributions from turbulent convection. Concurrently, heat transfer experiences a decrease as a consequence of reduced positive contributions from spatial development and augmented negative contributions from mean convection. When wall transpiration is located in the late nonlinear region, its impacts resemble those observed when transpiration is located in the linear and early nonlinear region. However, the transition-promoting effect weakens, and the heat-transfer reduction effect becomes more pronounced.