Sphere–wall collisions: vortex dynamics and stability

Abstract

For moderate Reynolds numbers, a sphere colliding with a wall in the normal direction will lead to a trailing recirculating wake, threading over the sphere after impact and developing into a complex vortex-ring system as it interacts with vorticity generated at the wall. The primary vortex ring, consisting of the vorticity from the wake of the sphere prior to impact, persists and convects, relatively slowly, outwards away from the sphere owing to the motion induced from its image. The outward motion is arrested only a short distance from the axis because of the strong interaction with the secondary vorticity. In this paper, the structure and evolution of this combined vortex system, consisting of a strong compact primary vortex ring surrounded by and interacting with the secondary vorticity, is quantified through a combined experimental and numerical study. The Reynolds-number range investigated is (100 < Re < 2000). At Reynolds numbers higher than about 1000, a non-axisymmetric instability develops, leading to rapid distortion of the ring system. The growth of the instability does not continue indefinitely, because of the dissipative nature of the flow system; it appears to reach a peak when the wake vorticity first forms a clean primary vortex ring. A comparison of the wavelength, growth rate and perturbation fields predicted from both linear stability theory and direct simulations, together with theoretical predictions, indicates that the dominant physical mechanism for the observed non-axisymmetric instability is centrifugal in nature. The maximum growth occurs at the edge of the primary vortex core, where the vorticity changes sign. Notably, this is a physical mechanism different from that proposed previously to explain the development of the three-dimensional flow of an isolated vortex ring striking a wall.