Formation and evolution of vortex rings with weak to moderate swirl and their implications for enhancing vortex ring circulation

Abstract

The formation of swirling vortex rings and their early time evolution, resulting from the controlled discharge of an incompressible fluid into a stationary equivalent fluid
bulk, is explored both numerically and experimentally for swirl number S ∈ [0, 1]. For the numerical work, two practically realisable inlet conditions are investigated
with swirl simultaneously superposed onto a linear momentum discharge; the corresponding circulation based Reynolds number is 7500. The results reveal that, for S > 1/2, the addition of swirl promotes the breakdown of the leading primary vortex ring structure, giving rise to the striking feature of significant negative vorticity, or opposite sign vorticity (OSV), generation in the region surrounding the primary vortex ring core, whose strength scales with S2. Through a non-linear interaction with the vortex breakdown, the radius of the primary toroidal vortex core is rapidly
increased; consequently, the self-induced propagation velocity of the leading ring decreases with S and vortex stretching along the circular primary vortex core increases counteracting viscous diffusion effects. The latter governs the evolution of the peak vorticity intensity and the swirl velocity magnitude in the primary ring core, the circulation growth rate of this ring, as well as the vorticity intensity of the trailing jet and hence its stability. This combination of effects leads to an increased dimensionless kinetic energy for the primary ring with increasing S and results in an almost linearly decreasing circulation based formation number, F. In a rigorous complementary experimental investigation, OSV is observed by introducing swirl using a rotating pipe, varying the time period before the piston stroke to achieve the desired swirl strength at a Reynolds number of 1000. Rotating pipe is found to
generate a secondary flow altering the inlet condition. Nevertheless, it is observed, using short periods of pipe rotation and higher angular speed, that it is possible to
generate a swirling vortex ring with less OSV production and all the related effects discussed above. The relation between F and the radius of the vortex ring is investigated through manipulation of ring radius growth, achieved through its interaction with a preceding vortex ring. Reducing radius growth, facilitates an increase of the circulation of the vortex ring, which in turn affects its F value.