Effects of hump deflection angle on streamwise vortex instability over a yawed cone at Mach 6

Abstract

This paper investigates the influence of three-dimensional smooth humps with varying deflection angles (φ) on the linear stability of streamwise vortices over a yawed cone with a 7° half-angle at a 6° angle-of-attack, free-stream Mach number of 6, and unit Reynolds number of 1.0×107/m. The steady laminar flow is obtained using direct numerical simulations. The eN method based on global stability theory is used to predict the transition location of the streamwise vortices along the centerline on the leeward side of the cone. The results reveal that φ plays a significant role in the outward vortex generation location, with smaller values of φ effectively delaying the outward vortex generation. Moreover, there is a qualitative relationship between the instability of the streamwise vortices and the inward/outward vortex structure characteristics of the base flow over a yawed cone. Namely, the transition delay effect of the streamwise vortices is proportional to the delay in the generation location of the outward vortex, which provides insights into the control of the transition induced by streamwise vortices. In particular, the configuration based on a hump with φ=9° and a height of 0.57 times the local boundary layer thickness delays the transition by approximately 38.2% at the critical N-factor (Ntr=12.5) without significantly increasing the instability of the inner mode.