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

In this paper, we employ the global stability analysis method (BiGlobal) to investigate the instability characteristics of asymmetric streamwise vortices at the waist of a high-speed transition research vehicle (HyTRV). The laminar base flow is obtained through direct numerical simulation. The incoming flow has a Mach number of 6, a unit Reynolds number of 1.0 × 10⁷/m, and a static temperature of 79 K. The model is 1600 mm in length, set at an angle of attack of 0° with an isothermal wall temperature of 300 K. The base flow 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.