On artificial density treatment for the pressure Poisson equation in the DEM-CFD simulations

Abstract

The discrete element method (DEM) coupled with computational fluid dynamics (CFD) is regarded to be a standard approach in a numerical calculation of gas-solid flow. When the DEM-CFD method is applied to the simulation of industrial systems, we cannot shy away from the modeling of arbitrary shape wall boundaries. Very recently, we have developed an innovative wall boundary model in the DEM-CFD simulations, where the signed distance function (SDF) and the immersed boundary method (IBM) are used for the wall boundary in the DEM and CFD. The SDF makes it possible to create an arbitrary shape wall boundary based on the scalar field. The IBM can be used for the wall boundary model by reflecting the number of the SDF points on the local volume fraction in CFD grid. Thus, the arbitrary shape wall boundary can be easily created in the DEM-CFD method by combining the SDF with the IBM. On the other hand, the authors' group has pointed out the necessity of the density scale technique in CFD. In the density scale technique, the density scale coefficient is considered in the calculation of the pressure Poisson equation. When the SDF/IBM is applied to CFD without density scaling technique, an unnatural fluid flow might occur through the wall boundary object. The effect of the density scaling coefficient on a gas-solid flow has not been examined so far. From this background, the influence of the density scale coefficient on a gas-solid flow is investigated in the present study. Through this study, introduction of the density scaling technique is designated to be crucial when the IBM is used for the wall boundary in the DEM-CFD simulation. The density scaling coefficient is shown to be decided not by theory but by experience, and the value should become 100 to 1000 in a typical gas-solid flow system. Besides, it is illustrated that the calculation cost is not influenced by the value of the density scale coefficient in the DEM-CFD simulations.