Stability analysis and transition prediction of streamwise vortices over a yawed cone at Mach 6

Abstract

An investigation into the linear instability of streamwise vortices over a yawed blunt cone with a half-angle of 7° at 6° angle of attack, a free-stream Mach number of 6, and a Reynolds number of 1.0 × 107/m was performed. The steady laminar base flow obtained using direct numerical simulation (DNS) has a mushroom structure. Three classes of unstable modes (inner mode, outer mode, and Mack mode modified by the streamwise vortices) were identified using a two-dimensional spatial global stability analysis (bi-global). Among them, the inner mode and the modified Mack mode were discovered for the first time for such a configuration. Notably, the inner mode appears only over a short distance upstream of the cone, and its energy is mainly in the vicinity of the symmetry plane of the mushroom structure. By comparing with DNS results, it was shown that multiple instability modes can coexist physically during the transition in the leeward plane. In addition, the eN method based on global stability theory was used to predict the location of the transition along the centerline on the leeward side of the cone. It was found that the inner modes grow rapidly in the upstream region, while the outer mode near the stem of the mushroom structure dominates the transition in the downstream region. Further analysis suggests that the inner modes dominate the transition only in a noisy environment, whereas the traditional centerline modes dominate the transition in quiet free-stream conditions.