An Euler–Lagrange model for simulating fine particle suspension in liquid flows

Abstract

This article presents a two-way coupled Euler–Lagrange model to simulate the suspension of fine particles in liquid flows. The goal is to develop a three-dimensional numerical model that is capable of replicating the detailed features of particle-laden turbulent flow. A two-phase fractional-step projection method is developed to ensure mixture incompressibility by solving a modified Poisson equation for pressure, which in turn affects the particle motion through the pressure gradient. An efficient particle-moving algorithm that exchanges particles between Eulerian meshes is developed that automatically retains the necessary particle information at each time step and does not require any Lagrangian particle tracking. A soft-sphere particle collision model is employed to avoid excessive particle overlap and to achieve the random closed packing limit for depositing particles. Since particles are all inherently localized in Eulerian meshes, efficient particle searches can be achieved when calculating particle–particle collision. This model is then used to simulate the gravitational settling of particles, and the results confirm the effect of mixture incompressibility and demonstrate that the model is capable of reaching the random closed packing limit. Numerical examples for the flow problems of particle-induced stratification are conducted, and the model is able to reveal the detailed features of particle-laden flows. Sensitivity on the grid resolution and deviations from the existing single-phase model results are also discussed.