Abstract
In this paper, we study the behavior of gas bubbles rising through a viscous liquid in a vertical square duct numerically. The level set formulation developed by Sussman et al. is successfully generalized for three-dimensional incompressible two-phase flows including large density and viscosity ratios as well as surface tension effect. Numerical simulations are carried out for gas-liquid flows with different ratios of density. It is shown that the effect of variation of the density ratio on the bubble shape and the flow field is extremely weak when the ratio is larger than 1:50. The simulations of flows with a single bubble in a duct are also carried out to investigate the influence of the duct walls on the flow field. It is clarified that the bubble shape and the rising velocity strongly depend upon the ratio of a duct width to an initial bubble radius, but that there is hardly the effect of the ratio on the rising velocity when it exceeds ten. Finally, we present a numerical result on the interaction of...
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