Numerical simulations of bubbly flows.

Abstract

Dynamics of bubbly flows is studied by direct numerical simulations. The full Navier-Stokes equations are solved by a finite difference/front tracking technique that fully accounts for viscous, inertia, and surface tension effects, as well as deformability of the bubbles. Both two- and three-dimensional calculations are presented. Simulations of low Reynolds number, multi-bubble flows, in fully periodic domains show that the rise velocity of a freely evolving bubble cloud is higher than that of a regular array of bubbles with the same nondimensional numbers. Interactions of a few hundred two-dimensional bubbles at low Reynolds number suggests that the flow continuously evolves toward a state containing larger and larger scales. For moderate to high Reynolds numbers, simulations of up to 50 bubbles in two dimensions and 16 bubbles in three dimensions, in fully periodic domains, are presented. It is observed that, contrary to the low Reynolds number flows, the rise velocity of a freely evolving bubble cloud is smaller than that of the regular array counterpart. The variations of time-averaged statistics with the void fraction and the number of bubbles are investigated and it is shown that the rise velocity decreases with increase in void fraction. The dynamics of bubbly clouds in a shear flow is investigated and it is shown that the deformation of the bubbles has a major influence on the void distribution in the flow. While bubbles that do not deform migrate toward the downcoming flow, deformable bubbles migrate the other way. Preliminary investigations of polydispersed bubbly clouds in fully periodic domains show that while the transient evolution of flows with different initial conditions are not the same, the time-averaged statistics of the two flows are comparable. A brief account is given of the interactions of bubbles rising to an initially flat fluid surface, and the mechanism whereby the bubbles burst is explained.