Reynolds number effect of a vortex ring impinging on a concave hemi-cylindrical shell

Experimental investigations were conducted on a single vortex ring impinging on a concave hemi-cylindrical shell with Dm/De = 2 at different Reynolds numbers. Vortex rings with five different Reynolds numbers were generated for experimental studies, i.e., Re = 750, 1500, 3000, 5000, and 7000. The planar laser-induced fluorescence visualizations and two-dimensional particle image velocimetry measurements were used in the experiment. The vorticity field based on the Eulerian framework and the finite-time Lyapunov exponent (FTLE) field based on the Lagrangian framework were used to identify the dynamic processes of vortex rings, respectively. The results show that as the vortex rings impinge on concave surfaces from Re = 750 to Re = 7000, the extension of the main vortex ring in the straight-edged direction is larger than that in the concave direction, and the instability of the vortex ring is promoted. While the Reynolds number is increasing, the vortex ring deformation becomes larger, and the overall vortex ring cross section becomes smaller, leading to a larger attenuation of the vortex ring rotation. Calculations performed by the FTLE field were used to derive the Lagrangian coherent structure to analyze the boundaries of the vortex ring motion process, clearly observe the shape of the secondary vortex connecting segments, and verify the speculation by the vortex ring trajectory identification results. Finally, a dynamic model of vortex rings impinging a concave surface was proposed, and the inference of the experimental process was explained by the model.