A Two-Phase Fluid Model Based on the Linearized Constitutive Equations

Abstract

A two-fluid two-phase flow model is presented. The conservation equations for the two-phase mixture of fluids are derived from the theory of multiphase mixtures where the field equations for each phase are obtained by carrying out volume averaging of the macroscopic field equations of each phase over an arbitrary volume region in space. The model formulated in this manner is consistent with the theory of mixtures when the interfacial area is reduced to zero and it satisfies the coordinate frame invariance. The second law of thermodynamics for each phase is utilized to obtain restrictions on the constitutive assumption which includes the effects of temperature gradient, velocity gradients, density gradients, viscous drag, and virtual mass. The linearized and coordinate frame invariant constitutive equations are presented, and the forms of these equations are compared with the previous investigations. In all cases considered, the presented model gives superior results and reduces to simpler models currently available. To obtain these simple models requires, in many instances, questionable assumptions.