Bi-Global Stability Analysis of Hypersonic Streamwise Corner Flows

The stability of hypersonic flows along a streamwise corner is studied here with bi-global stability theory for freestream Mach numbers 4.5 and 6.0. The steady laminar base flows are obtained by solving the corresponding self-similar solution for the corner plane and are in good agreement with direct numerical simulation. The base flow exhibits a pronounced low-speed region at the corner due to a secondary flow toward the corner causing an outflow along the corner bisector. The strength of the secondary flow increases with Mach number showing significant difference from the incompressible case. Two series of instability modes, corresponding to the slow and fast acoustic waves, are obtained in the Reynolds number-wavenumber stability diagram. In particular, the slow modes have higher frequencies and are of the second Mack modes stretched in the spanwise direction similar to the flat-plate boundary layer case. The leading slow mode has the most considerable growth rate, thus dominating the instability away from the corner. The fast instability mode F-I-even discovered in this work is an unique feature to the streamwise corner flow. This mode dominates the instability of the corner flow with increasing Mach-number effect.