Quadrature-Centered Averaging Scheme for Accurate and Continuous Void Fraction Calculation in Computational Fluid Dynamics–Discrete Element Method Simulations

Abstract

We propose a novel method to calculate the local void fraction in solid–fluid Euler–Lagrange models in an attempt to better predict the behavior of multiphase flows in complex computational fluid dynamics–discrete element method (CFD-DEM) simulations. This method is efficient, continuous in both time and space, and valid in structured and unstructured meshes. Cheap and common methods such as the particle centroid method (PCM) are commonly used to determine the void fraction. When particles are partially located in a cell, their volume contribution is not evaluated accurately, leading to inaccurate prediction of the void fraction and, consequently, inaccurate simulations. This also affects the stability of the simulation and introduces constraints on the elements’ sizes as well as the time steps for the CFD and DEM. There are several analytical approaches that accurately determine the void fraction, but these methods might not be always feasible due to their high computational cost as well as their inability to properly function on unstructured meshes. The proposed method aims at resolving these problems. We demonstrate the capacity of this method using its implementation in Lethe, an open-source CFD-DEM software.