Vibrational relaxation effects on acoustic disturbances in a hypersonic boundary layer over a cone

The effect of adding a vibrational mode to gas in hypersonic flow over a cone is studied through the use of direct numerical simulations (DNS) and stability analyses using the linear parabolized stability equations (PSE). A brief review of linear acoustic theory demonstrates the importance of energy capacity and energy transfer rate on a gas's ability to damp acoustic waves. After validating the computational fluid dynamics (CFD) solver for acoustic wave simulations, acoustic disturbances are introduced into a Mach 12 flow around a 7° half-angle, sharp-nosed cone. Results show good agreement between DNS and PSE on the predicted wall pressure disturbance amplification. The effects of acoustic damping are investigated, however, results for the current freestream conditions show that the vibrational temperature disturbance is largely driven by the mean flow, rather than acoustic damping effects. The current simulations are made possible using a recently developed low dissipation flux scheme for the finite volume method.