Instability of Supersonic Radiation Mode in Hypersonic Boundary Layers

The supersonic mode in hypersonic flows is studied numerically. The radiation characteristics of this mode in a Ma=6 flat-plate boundary layer with cooled walls are focused on. The linear stability analysis and a marching investigation using a parabolized stability equations approach are performed. Unlike the traditional bounded freestream boundary condition, a more physical boundary condition was proposed based on the group velocity direction of the supersonic mode. Two classes of the supersonic modes, the radiation mode and the incoming mode, are distinguished according to their different group velocities in wall-normal direction. The radiation mode is more unstable than the incoming one, for which it is the dominant instability. It is also found that both the stable and unstable radiation modes can radiate slow acoustic waves into the freestream, and no coalescence occurs between the radiation mode and the wave of the slow acoustic spectrum. This process can only be predicted by the linear stability theory with the new boundary condition. The slow acoustic wave has no effect on the supersonic radiation mode.