Formation and evolution of vortex rings with weak to moderate swirl

The formation of swirling vortex rings and their early time evolution, resulting from the controlled discharge of an incompressible, Newtonian fluid into a stationary equivalent fluid bulk, is explored for weak to moderate swirl number S ? [0, 1]. 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 obtained 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 azimuthal vorticity generation in the region surrounding the primary vortex ring core, whose strength scales with S-2. Through a nonlinear 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 the primary 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.

Automated summary

The controlled discharge of fluid with swirl promotes the breakdown of the leading vortex ring structure, resulting in significant negative azimuthal vorticity generation. The interaction between vortex breakdown and swirl increases the radius of the primary vortex core, decreases the self-induced propagation velocity of the leading ring, and increases vortex stretching along the circular primary vortex core. These effects lead to an increased dimensionless kinetic energy for the primary ring and a decrease in the circulation based formation number, F.