Boundary-Layer Instabilities in Supersonic Expansion Corner Flows

Experiments show that a sudden expansion of supersonic flow may strongly stabilize or even relaminarize the boundary layer. Only few theoretical studies addressed this effect considering evolution of small disturbances in cases of Mach number less than 4, where the first mode is most unstable. This paper addresses stability of a hypersonic (Mach 6) flow over the planar expansion corners of 0 degrees (flat plate case), 5 degrees, and 10 degrees, where the Mack second mode is dominant. The linear analysis and direct numerical simulations of three-dimensional wave packets are performed to investigate details and understand mechanisms behind the stabilization effect. The theoretical and numerical results are compared demonstrating applicability of the linear stability theory to hypersonic expansion-corner configurations. No new modes of boundary layer are found over the expansion corners but the second Mack mode that is relevant to the flat plate boundary layer. Downstream the corner line, the second mode instability region shifts to lower frequencies due to an abrupt thickening of the boundary layer that causes the stabilization effect. The results of direct computations agree well with predictions of linear stability theory.