On the windward boundary layer transition over a hypersonic blunt cone with global stability analyses and experiments

This paper investigates the effect of the angle-of-attack (AOA) on the windward boundary-layer stability over a blunt cone with a nose radius of 5 mm. We consider a free-stream Mach number of 6 and a unit Reynolds number of 4.0 × 10⁷ m⁻¹ and conduct both wind-tunnel experiments and stability analyses for AOAs ranging from 2°–10° at intervals of 2°. The results suggest that, as the AOA increases, the pressure gradient across the spanwise range becomes more pronounced, and the windward-side boundary layer becomes thinner. Using bi-global stability analysis, two unstable three-dimensional modes (varicose and sinuous) are identified in the windward boundary layer at various AOAs. The most unstable mode is the varicose V1 mode, in which the amplitude peak is initially close to the windward centerline and gradually shifts to the centerline downstream. Hence, the primary unstable disturbance exhibits a “V-like” distribution along the streamwise direction, which is likely to cause the V-shaped transition front observed in the wind-tunnel experiments. The eN method based on bi-global analysis is used to predict the transition location along the centerline on the windward region of the cone. The results indicate that, as the AOA increases, the transition location shifts forward, in line with our experimental results. Moreover, linear stability theory accurately predicts the eigenfunction and growth rate of the V1 mode obtained from bi-global analysis. This indicates that linear stability theory can be used to predict transitions in the windward boundary layer of a blunt cone at large AOAs under the conditions studied in this paper.