Assessing the Validity of Monte Carlo Techniques for Simulating Particulate Flows

The direct simulation Monte Carlo (DSMC) method is well suited for simulating dilute granular gases, where collisions between particles are uncorrelated and molecular chaos assumptions are valid. In many industrial particulate processes, such as fluidized beds, the system spans dilute to dense flow regimes. In large-scale systems, it is computationally expensive to resolve the motion of individual particles in a deterministic way, as is done in discrete element methods. The direct simulation Monte Carlo method provides a powerful alternative to discrete element modeling because the particles are represented by computational parcels and collisions are computed stochastically based on kinetic theory arguments. Our simulation results show the DSMC method can predict similar phenomena as DEM with an order of magnitude reduction in computational cost. To date, the validity of the DSMC method has been evaluated for dilute particle flows. In dense regions, however, particle arrangement and collisions become correlated, and molecular chaos assumptions inherent to kinetic theory or DSMC methodologies break down. The work presented herein examines the validity of the DSMC method in moderately dense and dense flow regimes. To assess the validity of the DSMC method, simulations of homogeneous cooling systems are first compared to theoretical predictions. Such simulations assess the accuracy of the granular cooling rate as well as the ability to predict hydrodynamic instabilities. Simulations of quasi-1D shear flow are simulated and the resulting solids stress are compared to theory over a range of solids concentrations. We also test the DSMC method for a gas-solid flow in a fluidized bed and compare the simulation results to discrete element and multiphase particle-in-cell simulations.