Interaction of a vortex ring with a single bubble: bubble and vorticity dynamics

Abstract

The interaction of a single bubble with a single vortex ring in water has been studied experimentally. Measurements of both the bubble dynamics and vorticity dynamics have been done to help understand the two-way coupled problem. The circulation strength of the vortex ring (${\it\Gamma}$) has been systematically varied, while keeping the bubble diameter ($D_{b}$) constant, with the bubble volume to vortex core volume ratio ($V_{R}$) also kept fixed at about 0.1. The other important parameter in the problem is a Weber number based on the vortex ring strength $(\mathit{We}=0.87{\it\rho}({\it\Gamma}/2{\rm\pi}a)^{2}/({\it\sigma}/D_{b});a=\text{vortex core radius},{\it\sigma}=\text{surface tension})$, which is varied over a large range, $\mathit{We}=3{-}406$. The interaction between the bubble and ring for each of the $\mathit{We}$ cases broadly falls into four stages. Stage I is before capture of the bubble by the ring where the bubble is drawn into the low-pressure vortex core, while in stage II the bubble is stretched in the azimuthal direction within the ring and gradually broken up into a number of smaller bubbles. Following this, in stage III the bubble break-up is complete and the resulting smaller bubbles slowly move around the core, and finally in stage IV the bubbles escape. Apart from the effect of the ring on the bubble, the bubble is also shown to significantly affect the vortex ring, especially at low $\mathit{We}$ ($\mathit{We}\sim 3$). In these low-$\mathit{We}$ cases, the convection speed drops significantly compared to the base case without a bubble, while the core appears to fragment with a resultant large decrease in enstrophy by about 50 %. In the higher-$\mathit{We}$ cases ($\mathit{We}>100$), there are some differences in convection speed and enstrophy, but the effects are relatively small. The most dramatic effects of the bubble on the ring are found for thicker core rings at low $\mathit{We}$ ($\mathit{We}\sim 3$) with the vortex ring almost stopping after interacting with the bubble, and the core fragmenting into two parts. The present idealized experiments exhibit many phenomena also seen in bubbly turbulent flows such as reduction in enstrophy, suppression of structures, enhancement of energy at small scales and reduction in energy at large scales. These similarities suggest that results from the present experiments can be helpful in better understanding interactions of bubbles with eddies in turbulent flows.