Interaction between an elliptic vortex ring and a bubble: effect of capture angle

Abstract

The rich interaction of multiple bubbles with multiple vortical structures makes the study of bubbly turbulent flows quite challenging. An idealisation of this problem would be the interaction between a single bubble and an elliptic vortex ring, the latter of which can be considered a representative vortical structure. The elliptic vortex ring is characterised by its initial aspect ratio $AR_0$, defined as the ratio of the semi-minor to semi-major axes of the ellipse, with $AR_0=1$ corresponding to a circular vortex ring. In the first part, we focus on the interaction between the elliptic vortex ring ($AR_0 = 0.6$) and a bubble, where we explore the effects of the capture angle ($\theta _C$) on the different quantities relevant to the ring as well as the bubble, using simultaneous side and top-view high-speed visualisations; $\theta _C$ is defined as the angle subtended by the bubble with the instantaneous major axis of the elliptic vortex ring at bubble capture. We study the effect of $\theta _C$ on the reduction in the ring’s convection speed $\Delta U^*$ and the number of daughter bubbles $N_b$, computed at a later stage of the interaction. For this part of the study, the Weber number $We=\rho U_0^2 D_b/\sigma$, defined as the ratio of the ring’s inertial effects to surface tension effects, is fixed at $We=11$. We find that bubble capture at lower capture angles ($\theta _C \approx 0^\circ$) corresponding to the high-curvature part of the elliptic vortex ring is found to be more probable compared to that at higher capture angles ($\theta _C \approx 90^\circ$). Further, a lower capture angle ($\theta _C \approx 0^\circ$) leads to a larger number of daughter bubbles $N_b$ and a slightly higher reduction in ring speed $\Delta U^*$. In the second part, we study the effect of $AR_0$ by contrasting the elliptic ring ($AR_0 = 0.6$) with a circular ring ($AR_0 = 1$) over a range of Weber numbers, in which the parameters of interest are the ring’s speed and the number of daughter bubbles. We observe that the elliptic vortex ring produces fewer daughter bubbles than the circular ring, with the difference increasing at larger ring strengths corresponding to higher Weber numbers. At higher We, the elliptic ring deviates from the $N_b \propto We^{0.42}$ scaling, which holds for the circular ring. The current study thus helps to gain a better insight into the complex problem of bubbly turbulent flows.