Theoretical Analysis of CFD-DEM 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 solution relationship with computational cell size. In this paper, we investigate the theoretical relationship between the solution and computational cell size by tracing the effects of a change in cell size through the mathematical model. The porosity profile for 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 the standard deviation of bed porosity increases exponentially as the cell size is reduced, and the drag calculations are very sensitive to changes in the porosity standard deviation, resulting in an exponential change in expected drag 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 centred volume fraction method, as it reduces the porosity standard deviation. The sensitivity of five popular drag laws to changes in the porosity profile is presented, and the Ergun and Beetstra drag laws are shown to be the least sensitive to changes in the cell size.