Virtual Force Term Based on the Velocity Distribution Surrounding a Spherical Particle Settling in a Simple Shear Flow

Abstract

Recently, the inside-out property of the interaction term in the two-fluid model equation was revealed, and the mathematical expression for the virtual force term, which compensates the gap between the correct interaction term and the conventional interaction term, was given. In this work, analytical solutions are given for the velocity field surrounding a spherical solid particle settling in a simple shear flow. The convection term in the Navier-Stokes equation was neglected. The virtual force term is calculated on the basis of the analytical solutions. The horizontal and vertical components of the virtual force term are 2.5 times the product of the viscosity, the velocity gradient, and the holdup gradient. These terms should be considered in the two-fluid model equation to simulate the dispersed multiphase flow with spatial distributions of velocity and holdup.