Global stability analyses of Mack mode on the windward face of a hypersonic yawed cone

In this study, the influence of isolated three-dimensional (3D) humps on the linear evolution of streamwise vortex unstable modes over a yawed cone is investigated numerically. The yawed cone has a 7° half-angle at a 6° angle-of-attack, the freestream Mach number (Ma) is 6, and the unit Reynolds number is 1.0×107 m–1. The induced disturbance at the numerical inlet is obtained using the two-dimensional global stability theory (biglobal stability theory). The clear linear-evolution process and the growth rate curve of a single-frequency disturbance wave along the axial direction are obtained using well-designed direct numerical simulations. The numerical results show that the evolutionary paths of the inner and outer modes are related to the inward and outward vortices inside the mushroom structure of the leeward ray, respectively. However, a small part of the outer mode energy can also propagate downstream along the inward vortex. Moreover, the introduction of an inner mode at the inlet can not only excite the unstable inner mode but also trigger the unstable outer mode downstream after the amplitude of the inner mode is attenuated. At the same time, a clear mode transformation process among the outer modes is also observed inside the streamwise vortex-induced boundary layer. By comparing the results of the linear evolution of the disturbance over a smooth wall, it is found that the induced hump can enhance the inner mode instability, resulting in a hysteresis phenomenon of the outer mode amplification interval, which is in good agreement with the results of the spatial biglobal analysis in our previous work. Additionally, the induced hump can also delay the mode transformation process and does not induce new mode transformation mechanisms.

The effects of a smooth hump on the modal linear evolution of streamwise vortices over a yawed cone at Mach 6 from direct numerical simulations

Li,

Zhang,

Chen

et al. 2024

Nonmodal linear stability analysis of hypersonic flow over an inclined cone

Liu,

Chen,

Wan

et al. 2024

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.

Experimental study on influences of steps on hypersonic boundary layer transition at different angles-of-attack

Xu,

Ye,

et al. 2024

The influences of the forward-facing step (FFS) and backward-facing step (BFS) on the 7° half-angle conical boundary layer instability and transition are investigated at different angles-of-attack (AoAs) in a hypersonic quiet wind tunnel using the Nano-tracer-based Planar Laser Scattering techniques, Temperature-Sensitive Paints, and high-frequency pressure sensors. The results show that the FFS stabilizes the second mode instability but strongly destabilizes the crossflow instability. Conversely, the BFS destabilizes both the second mode and crossflow instabilities, yet its impact on crossflow instability is weaker compared to that of an FFS with an identical height. At a small AoA (AoA < 3° in this paper), the boundary layer transition is dominated by the second mode instability. For sharp cones, the transition is delayed on the windward side but promoted on the leeward side, resulting in a monotonically inclined transition front. In contrast, blunt cones exhibit localized depressions in the transition front on the leeward side. At large AoA, the transition process is dominated by the crossflow instability, resulting in heat flux stripes on the leeward side, making the transition front distribution more complex. Therefore, at small AoAs, the promotion effect of the BFS on the conical boundary layer transition is stronger than that of the FFS with the same height. Moreover, the FFS with a small height even exhibits a suppressive effect on the transition. However, as the AoA increases, low-frequency instability modes, such as crossflow instability, gradually become dominant. Consequently, the promoting effect of the FFS surpasses that of the BFS.