Time- and Volume-Averaged Conservation Equations for Multiphase Flow. Part 1. System without Internal Solid Structures.

摘要

A set of rigorously derived conservation equations of mass, momentum, and energy for multiphase systems without internal solid structures via time-volume averaging of point, instantaneous conservation equations is presented. These equations are differential-integral equations in which the area integrals account for the interfacial transport of mass, momentum, and energy. The equations from volume averaging contain averages of the product of the dependent variables which must be expressed in terms of the products of their averages. In nonturbulent flows, this is achieved by expressing the 'point' variable as the sum of its intrinsic volume average and a spatial deviation. In turbulent flows for which further time-averaging is required, the 'point' variable is then decomposed into a low-frequency component and a high-frequency component. Time averaging following volume averaging preserves the identity of the dynamic phases. Under certain simplifying conditions, the proposed set of rigorously derived conservation equations reduces closely to various forms that are currently 'accepted' for two-phase flow analysis. This set of conservation equations serves as a reference point for modeling multiphase flow and provides theoretical guidance and physical insight that may be useful to develop correlations for quantifying interfacial transport of mass, momentum, and energy.