Input/output analysis of a Mach-6 cooled-wall hypersonic boundary layer using the One-Way Navier-Stokes (OWNS) Equations

Abstract

The dominant instability observed in adiabatic-wall flat-plate hypersonic boundary layers is the second Mack mode, which manifests itself as trapped acoustic waves between the wall and the relative sonic line. If the wall is highly cooled, not only is this mode destabilized, but an additional mode may emerge – the supersonic mode, which is characterized by an acoustic emission from the boundary layer. To investigate the input/output behavior of these boundary layers, we use the One-Way Navier-Stokes (OWNS) Equations, which efficiently approximate a rigorous parabolization of the equations by filtering out disturbances with upstream group velocity, resulting in memory and CPU savings compared to global methods on large grids. We investigate the mechanistic shift of the second mode in a 2D Mach-6 flat-plate boundary layer by examining how the optimal response varies with frequency and the wall temperature. Specifically, we tackle the global forced receptivity problem with highly-cooled-wall conditions by parametrically analyzing the optimal forcings and corresponding responses. We demonstrate that the optimal response shifts from the first to the second mode with increasing frequency, along with the excitation of the supersonic mode when the wall is sufficiently cooled. Although the aforementioned conclusions can also be ascertained from locally-parallel, linear stability theory (LST), we demonstrate that inter-modal interactions involving the supersonic mode locally affect the mode shapes that LST fails to capture. Furthermore, spatially transient or non-modal responses are observed in cases where LST predicts all modes to be stable.