The direct simulation Monte Carlo method has been used to simulate 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 from dilute to dense (packed) flow regimes. In dense regions, however, the particle arrangement and collisions become correlated and molecular chaos assumptions inherent to kinetic theory or DSMC methodologies break down. The work presented herein describes a hybrid methodology, where dilute and moderately dense regions are simulated using the direct simulation Monte Carlo method and the dense (or packed) regions are simulated in a deterministic manner using a coarse-grained discrete element model. By modeling a particulate flow using representative particles, the computational expense is significantly reduced compared to discrete element modeling where all real particles are tracked. To extend the DSMC methodology to moderately dense particle flows, a radial distribution function that accounts for volume exclusion effects is incorporated into the collision frequency. In addition, scattering functions are derived for inelastic collisions between spherical particles in dilute flow regimes. The theoretical scattering is then validated via comparison to discrete element simulation. Coarse grained discrete element modeling is used in regions where the solids concentration exceeds a threshold value, typically 0.45. Coarse-grained DEM parcels represent many real particles, but the parcel size and dissipation coefficients are adjusted to account for over-packing and actual energy dissipation. The hybrid modeling approach is compared to high fidelity discrete element simulations for a 3-D fluidized bed. The hybrid method accurately predicts the bed expansion and bubbling characteristics at substantially reduced computational cost, as compared to discrete element simulations.
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