Improved γ-Re_θ-A_r Model for Predicting Distributed Roughness-Induced Transition

The surface roughness during ablation significantly affects the hypersonic boundary-layer transition and heat transfer. In this study, an equation of transport for the roughness amplification factor A_r is introduced based on the improved baseline hypersonic γ-Re_θ transition model by considering the effects of surface roughness. The roughness amplification factor A_r is convected into the flow field to represent the disturbance induced by the surface roughness. It defines a region of influence of the surface roughness to locally modify the transition model and track changes in the momentum thickness to locally modify the criteria for the onset of transition. Moreover, the boundary condition of the wall is amended for the specific rate of turbulence dissipation to model the effects of roughness in the fully turbulent zone. The improved model can accurately predict the location of transition in roughness under different hypersonic flows.