Numerical simulation of head-on collision of two coaxial vortex rings

Abstract

Past experimental and numerical studies show that when two identical circular vortex rings of moderate Reynolds number collide head-on, vortex ringlets are generated around the circumference of the primary vortex rings and propagated radially outward through self-induction. Here, we show that dissimilarity in vortex core sizes between two colliding rings, despite having the same circulation, can significantly affect the outcome of the collision. This finding may help to explain the asymmetry in vortex ringlets formation observed in some of the experimental studies, which could be due to imperfections in vortex ring generators. The study was carried out by using a lattice Boltzmann method for the Reynolds number range of 500 ≤ ReΓ ≤ 2000. Our simulations show that in the absence of azimuthal perturbations on primary vortex rings, dissimilar core sizes between the two rings leads to unequal induced velocity on each other and hence unequal rates of radial expansion. This scenario sets up a condition that enables the thicker-core vortex ring (slower moving) to ‘slip-over’ a thinner-core ring (faster moving). Thereafter, the rings contract radially due to mutual induction as they propagate away from each other in opposite direction. For a sufficiently low Reynolds number, the ‘slip-over’ process does not take place due to the combined effect of lower momentum of the approaching rings and a more dominate effect of viscosity. Under this circumstance, the two primarily vortex rings remain in constant proximity during the collision, and the ensuing cross diffusion of vorticity of opposite sign at the collision ‘plane’ eventually leads to the ‘demise’ of the vortex rings. However, in the presence of an azimuthal perturbation at a moderate Reynolds number, the attempted slip-over by a thicker-core vortex ring causes a realignment of their azimuthal perturbations. This leads to the reorientation of resulting vortex ringlets, which travel outward in directions that are inclined to the plane of collision. This inclination angle increases with initial core size ratio, with a near zero inclination angle for the case of identical vortex rings.