Boundary conditions for a two pressure two-phase flow model

Abstract

New closures for two pressure two-phase flow in the context of unstable fluid mixing have been proposed recently by the authors. Here we examine the physical basis for the models, the nature of the boundary conditions at the edges of the mixing layer, and an algorithm for the numerical solution of the two-phase flow equations. Physically, the closures describe chunk mix, in which the flow is dominated by coherent structures of size comparable to the mixing zone thickness. The closed form solution previously introduced for the incompressible limit is reviewed and extended. Sufficient boundary conditions for the compressible equations are found from drag and buoyancy laws proposed by others, with coefficients fit to two sets of independent experiments. These laws complete the closure of the two-phase flow equations. A postulate of stationary center of mass, previously introduced at a numerical level, is here related to a weak notion of self similarity and is solved analytically for the ratio of the growth rates of the two sides of the mixing zone in the self similar case.