Quantitative Analysis of Accuracy of Voidage Computations in CFD-DEM Simulations

Abstract

CFD-DEM (Computational Fluid Dynamics – Discrete Element Modelling) is a two-phase flow numerical modelling technique, where the Eulerian method is used for the fluid and the Lagrangian method for the particles. The two phases are coupled by a fluid-particle interaction force (i.e. drag force) which is computed using a correlation. In a two-phase flow, one critical parameter is the voidage (or void fraction), which is defined as the ratio of the volume occupied by the fluid to the total volume. In a CFD-DEM simulation the local voidage is computed by calculating the volume of particles in a given fluid cell. For spherical particles, this computation is difficult when a particle is on the boundary of fluid cells. In this case, it is usual to compute the volume of a particle in a fluid cell approximately. One such approximation divides the volume of a particle into each cell in the same ratio as an equivalent cube of width equal to the particle diameter. Whilst this approach is computationally straight forward, the approximation introduces an error in the voidage computation. Here we estimate the error by comparing the approximate volume calculation with an exact (numerical) computation of the volume of a particle in a fluid cell. The results show that the error varies with the position of the particle relative to the cell boundary. A new approach is suggested which limits the error to less than 2.5 %, without significantly increasing the computational complexity.