Stability analysis of streamwise vortices over a blunt inclined cone under a hypersonic flight condition

Abstract

We studied the stability of leeward streamwise vortices over a hypersonic inclined blunt cone under a flight condition by solving the two-dimensional spatial eigenvalue problem (BiGlobal) and plane-marching parabolized stability equations (PSE3D). The stability analyses were performed based on the laminar flow obtained by direct numerical simulation. Due to the azimuthal pressure gradient and large bluntness, a pair of large-scale inward vortices dominate in the vicinity of the leeward ray. Such vortical structures are different from previous studies, where outward vortices are most prominent. Two types of unstable modes are identified, namely, “inner mode” with low phase velocities and “outer mode” with high phase velocities. The inner modes are unstable in a wide frequency range compared to the outer modes, differing from previous studies where inner modes are deemed to lie in a much lower frequency range compared to the outer modes. Moreover, the inner modes, with supersonic phase velocities, are found to be able to radiate weak acoustics outside the vortices. Mack mode, belonging to the outer-mode instability, is most amplified that it is likely responsible for the breakdown of the vortices. BiGlobal and PSE3D results show good agreement regarding the downstream developments of the Mack mode and inner modes and yet exhibit remarkable discrepancies in tracing the evolution of the outer modes, highlighting the necessity of considering the non-parallel effects when studying the stability of streamwise vortices.