Energy dissipation and onset of instabilities in coarse-grained discrete element method on homogeneous cooling systems

Abstract

Recently, attention has been drawn to the CGDEM (coarse-grained discrete element method) as a valuable option to circumvent the cost of classic DEM (discrete element method) computations for large-scale industrial applications such as fluidized beds. It consists of increasing the particle size while decreasing their number, hence the benefit in the cost of the simulation. Various coarse-graining approaches have been reported in the literature, but only a few authors have suggested mechanisms to overcome the reduction of the collision frequency inherent to the coarse graining process. This study proposes a comparison between three solutions from the literature to this problem. Coarse grained numerical simulations are carried out on an elementary HCS (homogeneous cooling system) test case and confirm the existence of an inverse law for the drop in the collision frequency. If not compensated, missed contacts lead to an underprediction of the expected granular temperature decay rate, which can be quantitatively recovered using one of these approaches. As regular DEM simulations, the CGDEM also exhibits a propensity for the onset of instabilities, which are further discussed in the second part of this study. A dependency of the critical domain length associated with the onset of velocity vortices in HCS with respect to the coarse graining factor is predicted. It indicates that coarse grained simulations might be more stable than their DEM counterpart. This is qualitatively assessed by visualizing a locally averaged particle velocity field. A quantitative method based on the computation of the local granular temperature distribution allows validating these observations in most cases, by exhibiting a global shift toward lower variances. Repetitions are performed to estimate a characteristic time to instability, which is seen to be shorter for coarse grained simulations, although these show smaller discrepancies with Haff's law over longer times.