Study on the linear instability of asymmetric streamwise vortices over a high-speed lifting body

The two-dimensional global stability analysis method (BiGlobal) was employed to investigate the instability characteristics of asymmetric streamwise vortex structures at the waist of a hypersonic transition research vehicle (HyTRV), with parameters set as model length 1 600 mm, 0° angle of attack, freestream Mach number 6, unit Reynolds number 1.0×10⁷/m, and static temperature 79 K. The laminar base flow field was obtained through direct numerical simulation by a high-order finite difference method under an isothermal wall condition (300 K). The results indicate that low-velocity fluids near the top of the upper surface and along the long axis of the lower surface converge at the waist, forming streamwise vortices. The pressure gradient disparity between the two sides leads to asymmetric development of these vortices, with the one on the lower side exhibiting more pronounced curling. Stability analysis reveals that the unstable modes of asymmetric streamwise vortices at the lifting body's waist can be categorized into inner modes, outer modes, and Mack modes, aligning with previous research findings. The inner modes are primarily influenced by spanwise velocity shear, whereas the outer modes are predominantly affected by normal velocity shear. The disturbance shape functions are primarily distributed on the side where the streamwise vortex exhibits stronger curling, which is different from the traditional symmetrical streamwise vortex. Utilizing the e^N method based on global stability analysis, it is concluded that the N factor of the Mack mode is higher in the upstream region. This suggests that the Mack mode is more likely to initiate transition in a noisy environment. Conversely, the N factor of the outer mode is more pronounced in the downstream region, indicating a higher potential for transition in a quiet environment.