Vortex ring and bubble interaction: Effects of bubble size on vorticity dynamics and bubble dynamics

Abstract

Bubbly turbulent flows involve complex interactions between bubbles and vortices, in which their size ratio plays a critical role. The present work investigates an idealization, namely, the interaction of a single air bubble with a (water) vortex ring, with the focus being on the effects of the bubble-to-vortex core size ratio (Db/Dc,o) on the bubble and ring dynamics (Db = bubble diameter and Dc,o = initial vortex core diameter). The interaction is studied for size ratio, Db/Dc,o, of 0.6–1.7, over a large Weber number range from 10 to 500 [We=0.87ρ(Γ/πDc,o)2/(σ/Db), Γ = circulation]. On the bubble dynamics side, in the initial stages of the interaction after the bubble's capture by the ring, the bubble's radial equilibrium position, its azimuthal elongation, and breakup pattern are influenced by both Db/Dc,o and We. However, at longer times, the results show that the We alone decides the broken bubbles to Db ratio and scales as We−0.13, which can be contrasted with the scaling of We−0.6 in isotropic turbulence [R. Shinnar, J. Fluid Mech. 10, 259–275 (1961)]. On the ring dynamics side, increasing Db/Dc,o leads to larger deformation of the vortex ring core at low We, and these effects are significant above a critical Db/Dc,o of about 1.2. Under these conditions, the vortex core can fragment, leading to large reductions in the ring's measured convection speed and axial enstrophy, both of which follow a similar scaling, (Db/Dc,o)2/We; the reduction in enstrophy being reminiscent of bubbly turbulent flows. These results and scalings should help us to better understand and model bubble–turbulence interactions.