Volume-averaged Expression of Two-phase Flow

Abstract

In this paper, a two-phase flow with randomly distributed particles is considered. The Navier-Stokes equation is integrated over the control volume fixed to the absolute co-ordinates, and then an exact volume-averaged momentum equation is derived. We remove the difficulty of mathematical treatment due to the random particle distribution by using a smooth weight-function. By the above volume-averaged equation, we can explain some phenomena of two-phase flow. As an example, the apparent viscosity of the two-phase parallel flow, where the particle concentration is distributed arbitrarily in the plane perpendicular to the flow direction, is obtained theoretically and compared with the summarized experimental data.