Analysis of vortex ring collisions using Lattice Boltzmann Method

Abstract

Vortical structures appear in a wide range of flow scenarios, including wall-bounded turbulence, boundary layer separation behind bluff bodies, and large-scale phenomena such as hurricanes. Understanding these structures is crucial for gaining insights into the overall flow behaviour. Among them, vortex rings are unique flow features characterized by vorticity concentrated around a closed circular loop. Due to the mutually induced velocity along the ring, they self propagate in a straight line. Coaxial vortex ring collisions, a topic widely studied in the literature, exhibit different mechanisms of vortex stretching and dissipation across varying Reynolds numbers. However, these cases represent idealized configurations that differ significantly from realistic flow scenarios, where vortex collisions often occur under arbitrary orientations. In the present work, we numerically investigate non-coaxial vortex ring interactions using the Lattice Boltzmann method, wherein the axes of the colliding rings are offset by a finite distance. We examine the influence of varying this offset for different Reynolds numbers. For small axial offsets, the collision plane of the rings tilts proportionally to the offset distance. In contrast, for larger offsets (of the order of ring radius), vortex stretching occurs predominantly on one side of the ring while the other side undergoes reconnection, forming secondary vortex rings. This behaviour reveals a novel breakup mechanism. Furthermore, we extend our numerical study to explore vortex ring interactions with V-shaped walls. Due to the acute angle of these walls, the rings exhibit enhanced curling, maintaining sufficient vorticity to generate secondary and even tertiary vortex rings. These complex dynamics are successfully captured in our simulations, demonstrating the capability of the numerical model to reproduce intricate reconnection processes and multiple ring formations.