(62b) Effective Drag Model for Euler-Lagrange Simulations of Gas-Fluidized Beds

Euler-Lagrange simulations, where the locally averaged equations of motion for the fluid phase are solved in an Eulerian framework (often denoted as CFD of the gas phase) and the particles are tracked in a Lagrangian fashion (using the Discrete Element Method, i.e., DEM), are widely used to investigate gas-solid flow behavior in fluidized beds. These flows manifest dynamic meso-scale structures that span a wide range of spatial and temporal scales. These structures can be resolved by CFD-DEM simulations in small computational domains. However, the computational cost to resolve them in simulations of flows in large industrial units is prohibitive, where coarse-grained (CG) simulation approaches such as CFD-DPM (discrete parcel method) and MP-PIC (multi-phase particle-in-cell) are more viable [1,2,3]. In these CG simulations, only a small number of representative particles (a.k.a. “parcels”) are simulated. It is now well established that the constitutive models (for quantities such as the fluid-particle drag force) that one employs in CG simulations should not be the same as those used in the highly resolved simulations [4-6]; instead, the constitutive models should reflect the effect of coarse-graining.

In the present study, we have performed highly resolved CFD-DEM simulations of gas-fluidization of particles in periodic domains at volume fractions typically observed in circulating fluidized beds and turbulent fluidized beds. By filtering CFD-DEM simulation results over coarse fluid grids, we formulate a correction for the effective drag to account for fluid (grid) coarsening. We then develop a systematic filtering methodology to perform particle coarsening, which is needed for simulations that track the motion of only a subset of particles (i.e., parcels); this additional correction accounts for the particle-phase fine structures, which is lost in a parcel-based simulation. An effective drag model accounting for both fluid and particle coarsening is then proposed. This model is assessed in a posteriori manner through coarse-grid CFD-DEM (only fluid coarsening) and CFD-DPM (fluid and particle coarsening) simulations in periodic domains. 

References

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3. P.J. O’Rourke, and D.M. Snider, “An improved collision damping time for MP-PIC calculations of dense particle flows with applications to polydisperse sedimenting beds and colliding particle jets”, Chem. Eng. Sci., 65, 6014 (2010). 
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