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

Abstract

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.