Theoretical Analysis of Computational Fluid Dynamics–Discrete Element Method Mathematical Model Solution Change With Varying Computational Cell Size

Successful verification and validation is crucial to build confidence in the application of coupled computational fluid dynamics–discrete element method (CFD–DEM). Model verification includes ensuring a mesh-independent solution, which poses a major difficulty in CFD–DEM due to the complicated relationship between solution and computational cell size. In this paper, we investigate the production of numerical error in the CFD–DEM coupling procedure with computational grid refinement. The porosity distribution output from simulations of fixed-particle beds is determined to be Gaussian, and the average and standard deviation of the representative distribution are reported against cell size. We find that the standard deviation of bed porosity increases exponentially as the cell size is reduced. The average drag calculated from each drag law is very sensitive to changes in the porosity standard deviation. When combined together, these effects result in an exponential change in expected drag force when the cell size is small relative to the particle diameter. The divided volume fraction method of porosity calculation is shown to be superior to the centered volume fraction (CVF) method. The sensitivity of five popular drag laws to changes in the porosity distribution is presented, and the Ergun and Beetstra drag laws are shown to be the least sensitive to changes in the cell size. A cell size greater than three average particle diameters is recommended to prevent errors in the simulation results. A grid refinement study (GRS) is used to quantify numerical error.