Linear stability of hypersonic flow over a parabolic leading edge

Abstract

The stability of the hypersonic flow over a parabolic leading edge is numerically investigated using linear stability analysis accounting for the existance of shock waves in comparison with direct numerical simulations. The linear stability analysis is performed using a global spectral collocation method accounting for the shock effects by using Rankine-Hugoniot shock conditions on the upper boundary. It is shown that in addition to the boundary layer first modes and higher modes(Mack modes), the linear stability of the hypersonic flow between a bow shock and a parabolic leading edge has a new family of modes, shock modes. The shock modes are important mainly in the shock layer. Due to the bow shock at the upper boundary, disturbance modes can communicate between the shock layer and the boundary layer. As a consequence, the evolution of boundary layer modes in the flow field may deviate from that in a flat plate boundary layer case. The stability characteristics of these modes are studied including the effects of frequency, Reynolds number, wave angle.