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 a 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 that comparable 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 a 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.

A systematic parametric study is presented on the modal global linear instability of Mach 6 boundary-layer flow over an inclined cone at 6 degree angle of attack under typical wind-tunnel conditions. The analysis is performed using the spatial BiGlobal theory. Results reveal two classes of global instabilities in the outboard region away from the leeward plane: high-frequency (hundreds of kHz) second mode instabilities and low-frequency (tens of kHz) crossflow instabilities. In the global eigenvalue spectra of the second mode instability, two distinct branches of significantly unstable modes are identified, namely an approximately continuous spectrum (branch S) and a few discrete points (branch D). The branch D modes peak at the windward centerline while branch S modes lie at a certain distance away from the windward meridian. The global stability characteristics of the crossflow instability over a conical configuration are uncovered for the first time. In the global eigenvalue spectra of the crossflow instability, many unstable modes emerge and form a complex pattern, with the most amplified frequency of around 30 kHz. The unstable crossflow modes are mainly distributed on the leeward side and wave angles obviously increase towards the leeward centerline. The peak growth rates are slightly smaller than those of second modes, and yet the most amplified frequency varies rather mildly along the streamwise direction so that they may achieve larger integrated growth rates than second modes do.