Vortex ring formation from the interaction of a cavitation bubble with a confined air bubble: experiments and a timing criterion

Abstract

We study vortex ring formation arising from the interaction between a cavitation bubble and a confined air bubble in a cylindrical blind hole, using high-speed shadowgraphy imaging. As the cavitation bubble grows above the hole, it drives a downward flow that compresses the air bubble at the base. The air bubble subsequently expands, expelling the overlying liquid column upward as a coherent slug; impact of this slug on the far boundary of the collapsing cavitation bubble produces a vortex ring. Parametric experiments across the dimensionless stand-off distance $\mathcal{H}=h/R_{\max }$ and the air bubble fill fraction $\mathcal{B}=(d_{\text{hole}}-d_{\text{top}})/d_{\text{hole}}$ identify three regimes: (i) liquid column impact during collapse, producing a vortex ring ($\mathcal{H}\lesssim 0.5$, $\mathcal{B}\lesssim 0.5$); (ii) late impact near the end of collapse (large $\mathcal{H}$); and (iii) direct air bubble impact after bypassing the liquid column (large $\mathcal{B}$), with neither (ii) nor (iii) producing a ring. Two one-dimensional models, based on the Rayleigh-Plesset equation and isentropic air bubble expansion, predict the liquid column impact location and its speed $U_{\text{lc}}$, respectively. A dimensionless timing parameter $\hat{I}=(h+R_{\max })/(U_{\text{lc}}\cdot t_{\text{cav}}/2)$, comparing the liquid column travel time to the cavitation collapse half-period, distinguishes the three regimes: ring formation occurs for $1\lesssim \hat{I}\lesssim 1.5$. The ring propagates from the hole at an initial speed of $5$ m/s, decelerating quadratically, and breaks apart via azimuthal instabilities at $Re\approx 4500$.

22 pages, 13 figures