Numerical Simulation of Bubbly Flow by Vortex in Cell Method

The Vortex in Cell (VIC) method for bubbly flow, proposed in the authors' prior study, is improved to promote the numerical accuracy and efficiency. The improvements are concerned with a discretization method using staggered grids, a correction method for vorticity and a single-stage calculation method for the convection of vortex element. To enlarge the applicability of the VIC method, vortex elements without core structure are employed. The improved VIC method is applied to simulate a bubble plume. In a tank containing water, small air bubbles are released from the base of the tank. The bubbles rise due to the buoyant force, inducing the water flow around them. The simulation for the plume at the starting period highlights that the rising bubbles induce vortex rings at their top and that a bubble cluster appears owing to the entrainment of the bubbles into the vortex rings. The rising velocity for the top of the bubbles is proportional to the square-root for the flowrate of the released bubbles, being consistent with existing theoretical and numerical investigations. The simulation also demonstrates that the developed bubble plume having some characteristics of a jet is successfully captured.