Numerical study of supersonic boundary-layer modal stability for a slightly rarefied gas using Navier-Stokes approach

In this paper, a systematic study on the supersonic boundary-layer modal stability for a slightly rarefied gas is conducted by considering velocity slip and temperature jump effects in the Navier-Stokes (NS) equations. The effects of slip boundary on the first- and second-mode instability at different conditions are presented in detail. The laminar flow is obtained by solving the NS equations along with no-slip and slip boundary conditions, which shows that the slip boundary causes the boundary layer becoming thinner and the supersonic region near the wall becoming narrower. The perturbation slip boundary conditions at the wall and their influence on the stability are carefully discussed. The tangential momentum accommodation coefficient and the thermal accommodation coefficient are set equal or unequal for a broad range to study the combined or leading effects of velocity slip and temperature jump, respectively. It is found that velocity slip significantly stabilizes the second-mode disturbances while largely destabilizes the first-mode perturbations. On the contrary, the temperature jump apparently enhances the second-mode instability, while it has little influence on the first mode. When velocity slip and temperature jump are both present, the first mode is more destabilized, while a competitive effect acts on the second mode. Additional results show that the neutral stability curves for the second and third modes as well as the synchronization between fast and slow modes are delayed further downstream due to velocity slip. These findings are shown consistently regardless of the wall cooling for both supersonic and hypersonic flows.

Automated summary

This study systematically investigates the supersonic boundary-layer modal stability of a slightly rarefied gas, considering the effects of velocity slip and temperature jump. The results show that velocity slip stabilizes second-mode disturbances but destabilizes first-mode perturbations, while temperature jump enhances second-mode instability but has little effect on the first mode. The presence of both velocity slip and temperature jump leads to increased destabilization of the first mode and competitive effects on the second mode. Velocity slip delays neutral stability curves for higher modes and synchronization between fast and slow modes downstream, regardless of wall cooling.