Numerical analysis of a single rising bubble using boundary-fitted coordinate system

Abstract

A numerical method is developed to simulate unsteady axisymmetric flow with a free surface. The method is based on a finite-volume solution of the equations on an orthogonal curvilinear coordinate system. A new iteration technique is used for the boundary condition of the free surface in order to stabilize the solution. The numerical method is applied to the simulation of unsteady motion of a single deformed bubble rising through a quiescent liquid. The numerical results show good quantitative agreement with those of experiments and calculations reported previously by other researchers. In the present study, the transient phenomena of an initially spherical bubble as it reaches the steady state are investigated. It is known experimentally that the rising bubble begins to show an unsteady three-dimensional (spiral or zigzag) motion beyond certain critical Reynolds and Weber numbers. Our numerical results suggest that the growth of axisymmetric shape oscillation causes three-dimensional motions of a rising bubble.