An implicit bounding formulation for the volume fraction equation in multiphase flows

Abstract

The solution of the volume fraction equations in multiphase flows has to satisfy geometric conservation, that is, the volume fraction fields at each control volume sum to 1. Enforcing this constraint on the volume fraction fields is critical for all multiphase flow applications especially for cases involving mass transfer. This article reviews some of the techniques used to enforce geometric conservation when solving the volume fraction equations for general multiphase flows, including free surface flows. An implicit method is then introduced and applied to a number of multiphase and free surface flow problems. It is compared to the current explicit approaches and its effectiveness in enforcing the geometric conservation demonstrated.