Transient Growth of A Mach 5.92 Flat-Plate Boundary Layer

Abstract

The laminar-turbulent transition of hypersonic boundary layers has a significant effect on drag calculation and aerothermal analysis of hypersonic vehicles. Surface roughness has been shown to have profound effects on boundary layer transition. Recent research has shown that one possible explanation to roughness induced bypass transition is the transient growth theory. However, there has been very few direct numerical simulation studies on transient growth in hypersonic boundary layers. This paper presents some results in on-going numerical simulation study on the transient growth of a Mach 5.92 flat-plate boundary layer to small three-dimensional surface roughness. The main objective is to study the effects of nonparallel flow and spanwise wave on transient growth. The freestream flow conditions are the same as those used in our previous study [1] . The responses of the boundary layer to surface roughness are computed by solving three-dimensional Navier-Stokes equations with a fifth-order shockfitting method and a Fourier collocation method. The numerical results show that no transient growth is observed when surface roughness is located in parallel flow region, which indirectly demonstrates that nonparallel flow effects enhance transient growth. It is also shown that surface roughness with a smaller spanwise wave number is more efficient in inducing disturbances with respect to energy norm.