Numerical study of drop formation by a vortex ring.

Abstract

The numerical simulations using a Front-Tracking/Finite difference method were performed to investigate the interface breakup and drop formation processes caused by the interaction of a vortex ring with an immiscible interface in zero-gravity. The investigation focuses on the critical Weber number for the interface breakup and the effects of viscosity and density ratios on the interaction. First, the propagation characteristics and flow structure of the vortex ring in the post-formation region were investigated to validate the numerical scheme and resolution of the numerical simulations. Second, Ohnesorge number effects in the interface breakup and drop formation processes were determined. The critical Weber number for the interface breakup increases as the Ohnesorge number increases, and this variation in the critical Weber number is attributed to the stabilizing effects of the viscosity. It was also found the critical Weber number for formation of one droplet is given by the correlation, <italic>We_c</italic>₁ = (9.8868 x 10<super>3</super>)<italic>Oh_b</italic> + 26.1. For cases at <italic>We_c</italic>₁, and at <italic> We_c</italic>₂ with large Ohnesorge number the interface breakup mechanism is buckling of the interface as the liquid column collapses on the lower layer. At higher Weber numbers instability of the liquid column develops that results in the formation of two or more droplets. Numerical results reveal that the correlation coefficient, the ratio of nozzle radius to the initial amplitude of the disturbance, ln&parl0;aN<de>zo</de> &parr0; , a function of Ohnesorge number which decreases as Ohnesorge number increases. The Weber, Ohnesorge numbers, and ln&parl0;aN<de>zo</de> &parr0; play crucial roles in determining the breakup length when the magnitude of Ohnesirge number is much less than one. Third, the viscosity and density ratios effects in the interface breakup and drop formation processes were investigated. The initial evolution of an interface and overall vorticity distribution are quite similar even for large variations in the viscosity ratio. The noticeable effects of the viscosity ratio are to change the first and the second breakup locations, the structure of the cylindrical column, and the time-dependent shape of the main droplet. The density difference inhibits the formation and growth of surface waves along the interface. As the density ratio decreases, the vortex ring forms a highly stretched and more persistent fluid column before the first breakup occurs. For the case having the density ratio is much less than one, the viscosity ratio effects over the observed small density ratio effects are also examined in a limited way. If the dispersed phase is more viscous than the continuous phase, the density ratio effects dominate over the viscosity ratio in the interface breakup and drop formation processes. In contrast, when the continuous phase is more viscous than the dispersed phase the viscosity ratio plays a more important role in determining the outcome of vortex ring interaction.