The current understanding of the effects of thermochemical nonequilibrium on hypersonic boundary-layer instability still contains uncertainties, and there has been little research into the effects of surface ablation, or two-dimensional roughness, on hypersonic boundary-layer instability. The objective of this work is to study the effects of thermochemical nonequilibrium on hypersonic boundary-layer instability. More specifically, two separate nonequilibrium flow configurations are studied: 1) flows with graphite surface ablation, and 2) flows with isolated two-dimensional surface roughness. These two flow types are studied numerically and theoretically, using direct numerical simulation and linear stability theory, respectively.

To study surface ablation, a new high-order shock-fitting method with thermochemical nonequilibrium and finite-rate chemistry boundary conditions for graphite ablation is developed and validated. The method is suitable for direct numerical simulation of boundary-layer transition in a hypersonic real-gas flow with graphite ablation. The new method is validated by comparison with three computational data sets and one set of experimental data. Also, a thermochemical nonequilibrium linear stability theory solver with a gas phase model that includes multiple carbon species, as well as a linearized surface graphite ablation model, is developed and validated. It is validated with previously published linear stability analysis and direct numerical simulation results. A high-order method for discretizing the linear stability equations is used which can easily include high-order boundary conditions. The developed codes are then used to study hypersonic boundary-layer instability for a 7 deg half angle blunt cone at Mach 15.99 and the Reentry F experiment at 100~kft. Multiple simulations are run with the same geometry and freestream conditions to help separate real gas, blowing, and carbon species effects on hypersonic boundary-layer instability. For the case at Mach 15.99, a directly simulated 525~kHz second-mode wave was found to be significantly unstable for the real-gas simulation, while in the ideal-gas simulations, no significant flow instability is seen. An N factor comparison also shows that real-gas effects significantly destabilize the flow when compared to an ideal gas. Blowing is destabilizing for the real gas simulation and has a negligible effect for the ideal gas simulation due to the different locations of instability onset. Notably, carbon species resulting from ablation are shown to slightly stabilize the flow for both cases. For the Reentry F flow conditions, inclusion of the ablating nose cone was shown to increase the region of second mode growth near the nose cone. Away from the nose cone, the second mode was relatively unaffected.

Experimental and numerical results have shown that two-dimensional surface roughness can stabilize a hypersonic boundary layer dominated by second-mode instability. It is sought to understand how this physical phenomenon extends from an airflow under a perfect gas assumption to that of a flow in thermochemical nonequilibrium. To these ends, a new high-order shock-fitting method that includes thermochemical nonequilibrium and a cut-cell method, to handle complex geometries unsuitable for structured body-fitted grids, is presented. The new method is designed specifically for direct numerical simulation of hypersonic boundary-layer transition in a hypersonic real-gas flow with arbitrary shaped surface roughness. The new method is validated and shown to perform comparably to a high-order method with a body-fitted grid. For a Mach 10 flow over a flat plate, a two-dimensional roughness element was found to stabilize the second mode when placed downstream of the synchronization location. This result is consistent with previous results for perfect-gas flows. For a Mach 15 flow over a flat plate, a two-dimensional surface roughness element stabilizes the second-mode instability more effectively in a thermochemical nonequilibrium flow, than in a corresponding perfect gas flow.