Study on the evolution of non-modal disturbances in hypersonic boundary layer based on HLNS approach

Laminar-turbulent transition in hypersonic boundary layers is of fundamental importance in the design of aerospace vehicles. Subcritical transition, occurring upstream of the linear instability region, appears frequently in conventional wind-tunnel experiments. The subcritical transition is usually triggered by the evolution of non-modal disturbances and their subsequent secondary instability. In order to reveal the inherent mechanisms governing the impact of abrupt changes on hypersonic subcritical transition, a numerical framework describing the evolution of non-modal disturbances based on the harmonic linearized Navier-Stokes (HLNS) equation and its adjoint system is developed. The advantage of this framework is that the elliptic nature of the original system is retained, leading to the ability to deal with the rapid distortion of the non-modal disturbances (streaks) in the vicinity of the local abrupt changes. For a hypersonic blunt-plate boundary layer with an oncoming Mach number 5.96 and an angle of attack $ - 4^\circ $, the impact of the cavities with different depths on streak amplitude is studied. Numerical solutions indicate that streaks are enhanced by the cavities, which agrees with the experimental observations in quantity. Moreover, the enhancement effect peaks at a particular cavity depth.