Mixture Model for Multiphase Flow

摘要

Numerical flow simulation utilising a full multiphase model is impractical for asuspension possessing wide distributions in the particle size or density. Various approximations are usually made to simplify the computational task. In the simplest approach, the suspension is repersented by a homogeneous single-phase system and the influence of the particles is taken into account in the values of the physical properties. The multiphase nature of the flow cannot, however, be avoided when the concentration gradients are large and the dispersed phases alter the hydrodynamic behavior of the mixture or when the distributions of the particles are studied. In many practical applications of multiphase flow, the mixture model is a sufficiently accurate approximation, with only a moderate increase in the computational effort compared to a single-phase simulation. This study concentrates on the derivation and closing of the model equations. The validity of the mixture model is also carefully analysed. Starting from the continuity and momentum equations written for each phase in a multiphase system, the field equations for the mixture are derived. The mixture equations largely resemble those for a single-phase flow but are represented in terms of the mixture density and velocity. However, an additional term in the mixture momentum equation arises to the continuous phase. The volume fraction for each dispersed phase is solved from a phase continuity equation. The mixture model applications reported in the literature are briefly summarised. The areas of application include gravity settling, rotational flows and turbulent flows. The multiphase models in three commerical codes, PHOENICS, FLUENT and CFX 4, are reviewed. The mixture model approach, in a simplified form, is implemented only in PHOENICS.