Free surface vortex and associated air entrainment during liquid drainage using two outlets

Plughole vortex dynamics and the corresponding air entrainment is of paramount importance in various process industries. The present study experimentally investigates plughole vortex induced air entrainment during the drainage of water through two closely spaced outlets from a tank. The discharge from the two outlet tubes has been modulated and the different stages of air entrainment including formation of air lamella, periodic slug bubble pinch-off, and transition into the stable annular flow are observed. The transition between the slug bubble pinch-off and the stable annular flow has been modelled by balancing the local dynamic pressure of the fluid and the Laplacian pressure jump across the gas-liquid interface. The balance yields the ratio of critical height, $H_c$ and radius of the stable air neck, $r_m$ as $H_c/r_m\approx 30.68{\mathrm{Bo}}^{-0.904}{\left(f\left(D,r_e\right)\right)}^{-0.210}$, with the Bond number, $\mathrm{Bo}=\Delta \rho g{D}^2/\sigma$ and the geometric parameter, $f\left(D,r_e\right)={\left(1-\frac{{2r}_e}{D}\right)}^2$.