The leeward vortex transition over hypersonic yawed cones by e^N method based on global stability theory

An inclined cone with exists on a azimuthal pressure gradient on its surface, which drives the flow from the high-pressure region on the windward side to the low-pressure region on the leeward side. This results in the formation of large-scale flow vortex structures near the leeward centerline, which further destabilizing and triggering transitions. Linear global stability analyses were conducted by solving the two-dimensional eigenvalue problem (BiGlobal) and using plane-marching parabolized stability equations (PSE3D) to reveal the instabilities of streamwise vortices on the leeward side of the cones. Results showed that the Mack mode instability prevails in the upstream region for all cases. As the leeward base flow begins to distort significantly, the Mack mode weakens, while the intrinsic instability modes emerge and eventually take over. The downstream development of N factors for the unstable modes is obtained by PSE3D. According to the measured transition locations in experiments, the transition N factors are estimated to be less than 3 for the cases with a 2-deg angle of attack and approximately 6 for the case with a 4-deg angle of attack. The low N-factor at the transition location of the case with a 2-deg angle of attack implies that non-modal growth of disturbances may play a role in the transition process.