Dynamics of a vortex ring impinging on a concave hemicylindrical shell

The dynamics of a single vortex ring impinging on the concave hemicylindrical shell with different radii at Re = 1500 are explored experimentally. Five different ratios of hemicylindrical cavity radii to vortex ring are studied: D_m/D_e = 15, 10, 5, 2, 1. Planar laser-induced fluorescence and two-dimensional particle image velocimetry techniques are adopted for flow measurements, and the finite-time Lyapunov exponent field based on the Lagrangian framework is employed to identify the Lagrangian coherent structures of the vortex dynamics. The experimental results indicate that for D_m/D_e = 15, 10 conditions, the impinging dynamics of the vortex ring are similar to the vortex ring interacting with a flat plate. The subvortex cluster consisting of secondary vortex rings and tertiary vortex rings, dominates the motion of the induced vortex rings after the primary vortex ring impinges with concave surfaces. For D_m/D_e = 5, 2 conditions, the collision of the vortex ring on the concave surfaces is quite different. The concave surface effectively constrains the primary vortex ring after impinging it. The concave secondary vortex ring rotates earlier than the straight-edged secondary vortex ring. Eventually, the straight-edged secondary vortex ring is lifted in the straight-edged direction, moving diagonally towards the collision axis, away from the solid wall. Subvortex rings in the final dominant flow field change from the tertiary to the secondary as the model radius decreases. As the diameter decreases to D_m/D_e = 1, the primary vortex ring deforms farther in the straight-edged direction. After the straight-edged secondary vortex ring is formed, it moves vertically away from the wall. Finally, a dynamic model is proposed to illustrate the effects of cylindrical cavity radii on the vortex-ring impingement.