Head-on collisions of vortex rings upon round cylinders

Abstract

Vortical structures and behaviour associated with vortex-ring collisions upon round cylinders with different cylinder-to-vortex-ring diameter ratios were studied using laser-induced fluorescence and time-resolved particle-image velocimetry techniques. Circular vortex rings of Reynolds number 4000 and three diameter ratios of $D/d=1$, 2 and 4 were considered in the present investigation. Results reveal that the collision behaviour is very different from that associated with flat surfaces, in which vortex disconnection and reconnection processes caused by the strong interactions between primary and secondary vortex rings produce small-scale vortex ringlets that eject away from the cylinders. For the cylinder with the largest diameter ratio used here, these vortex ringlets move towards each other along the collision axis, where they eventually collide to produce a vortex dipole that propagates upstream. However, as the diameter ratio decreases, these vortex ringlets are produced further away from the collision axis, which results in them ejecting away from the cylinder at increasingly larger angles relative to the collision axis. Trajectories of key vortex cores were extracted from the experimental results to demonstrate quantitatively the strong sensitivity of these vortical motions upon the diameter ratio. Furthermore, significant differences in the primary vortex-ring circulation along convex surfaces and straight edges after the collisions are observed. In particular, vortex flow models are presented here to better illustrate the highly three-dimensional flow dynamics of the collision behaviour, as well as highlighting the strong dependency of the secondary vortex-ring formation, vortex disconnection/reconnection processes, and ejection of the resulting vortex ringlets upon the diameter ratio. As such, these results are expected to shed more light on the more general scenario of vortex-ring collisions upon arbitrarily contoured solid boundaries.