Side-Wall Effects on the Global Stability of Swept and Unswept Supercritical Wings at Buffet Conditions

A fully three-dimensional (3D) RANS-based global stability analysis is performed in the turbulent transonic buffet regime to study the complex interaction between shock-oscillations, buffet cells and corner separations. The numerical setup is based on the experiments conducted at JAXA 0.8 m × 0.45 m high Reynolds number transonic wind tunnel on a two-dimensional (2D) Common Research Model profile extruded in the spanwise direction and flash mounted on lateral walls at both its extremities. Unswept and swept wings are considered and the effect of the angle of attack (AoA) is also investigated. Despite some differences on corner separation size and shock location, the RANS solutions are in reasonable good agreement with the experimental oil-flow visualizations. Global stability calculations show that when large recirculation regions appear on the side-walls, the cross-flow velocity components induced by the corner separations cause the convection of cellular structures towards the center of the wing, also for the unswept wing. For the swept configuration, the velocity induced by the outboard corner separation is directed against the cross-flow component of the swept wing, causing inboard and outboard traveling perturbations to coexist. In agreement with the dynamic mode decomposition analysis based on the experimental pressure sensitive paint, the unstable modes consisting of 2D inboard traveling shock-oscillation perturbations and 3D cellular packets near the corner separated region are characterized spatially and temporally. This work identifies the separated region as the origin of inboard traveling perturbations, potentially explaining the mechanisms also seen on the main wing of full-aircraft configurations at buffet conditions.