Nonmodal linear stability analysis of hypersonic flow over an inclined cone

Abstract

Nonmodal linear stability analysis results are presented for hypersonic flow over a cone at 6° angle of attack complementing earlier modal stability analysis. Based on the parallel flow assumption, singular value decomposition is applied to obtain the optimal linear combination of global crossflow modes. The optimal disturbance exhibits significant transient growth in the initial short distance and progressively follows the path of the most unstable mode downstream. The largest transient energy gain is observed for disturbances at around 40 kHz close to the most amplified modal frequency and tends to increase with the Reynolds number. The optimal disturbance initially exhibits two amplitude peaks in the azimuthal direction, one lying in the leeward region where the unstable crossflow modes reside and the other in the windward region where the adjoint modes exist. As the optimal disturbance travels downstream, the second amplitude peak rapidly shifts toward the leeward side and reaches the optimal energy gain when it eventually merges with the first amplitude peak. The evolution process of the optimal disturbance indicates that the optimal disturbance might have exploited the locally crossflow instability through traveling from the windward side to the leeward side.