Development of effective drag model for discrete-parcel approach

Euler-Lagrange simulations of fluidized beds, where the locally-averaged equations of motion for the fluid phase are solved in an Eulerian framework (often denoted simply as CFD of the gas phase) and the particles are tracked in a Lagrangian fashion by solving Newton’s equations, have found widespread application in the study of fluidization [1-3]. Particle-particle contact is handled either as hard-sphere collisions or through a soft-sphere model, commonly known as the discrete element method (DEM) [4]. Many research groups are currently investigating the effects of cohesion and size distribution of fluidization characteristics via CFD-DEM simulations [for example, see ref. 2, 3]. It is impractical to simulate via CFD-DEM the gas-particle flows in the industrial-scale fluidized beds containing billions particles. This consideration has led to the development of coarse-grained simulation approaches such as CFD-DPM (discrete parcel method) and MP-PIC (multi-phase particle-in-cell) where only a small number of representative particles (a.k.a. “parcels”) are simulated [5,6,7]. It is now well established that the constitutive models (for quantities such as fluid-particle drag force) that one employs in coarse CFD-DPM or MP-PIC simulations should not the same as those used in the more-highly resolved CFD-DEM simulations [8-10]; instead, the constitutive models should reflect the effect of coarse graining.

In the present study, we have performed CFD-DEM simulations of gas-fluidization of particles in periodic domains at volume fractions typically observed in circulating fluidized beds and turbulent fluidized beds. We then asked how one should systematically coarse-grain these results to deduce the effective drag model for coarse CFD-DPM or MP-PIC simulations. We demonstrate that the effective drag coefficient decreases upon coarsening the fluid grid and that the same is true when switching from DEM to DPM where only a small number of representative particles are simulated.

We will also present some results on the effect of inter-particle cohesion and particle size distribution on the flow.