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Fluidized Beds

Due to computational limitations a detailed simulation of poly-disperse reactive industrial scale reactors is still unfeasible. It is, therefore, common to use coarse grids and average particle properties to reduce the demand on computational resources. Such a procedure inevitably neglects on the one hand small (unresolved) scales. In the literature, numerous approaches have been put forth to account for these scales. However, these „coarse-grained“ models differ by more than two orders of magnitude. Moreover, they even disagree in their functional dependencies. While all of them depend on the average gas void fraction, some of them take into account the relative velocity between the solid phase and fluid (dashed lines) and others additionally consider the effect of filter width. For example, figure 1a outlines the differences for two different filtered sub-grid drag modifications. The filtered correlations deduced from highly resolved simulations of a bubbling fluidized bed of Geldart B type particles show a completely different behavior to filtered correlations determined from periodic box simulations. Nevertheless, this differences can be avoided by using different markers characterizing the filtered correlations. The figure clearly reveals that using the kinetic energy of the sub-filter scale velocity fluctuations yields nearly indistinguishable filtered correlations, which is in contrast to the filtered slip velocity.

We further applied these next generation sub-grid models to the coarse grid simulation of a poly-disperse industrial fluidized bed in combination with the Lagrangian-Eulerian hybrid model, Here, the local distribution of the different particle diameters, which is required for the gas-solid drag force, is obtained by tracking statistically representative particle trajectories for each particle diameter class. Figure 2 demonstrates that the hybrid model yields fairly good agreement with experimental data of the particle size distribution.

Future modeling efforts will concentrate on the numerical analysis of fluidized bed – cyclone assemblies as well as the numerical prediction of sheeting/chunks.

Fig. 1: left: variation of the fractional correction with filtered solids volume fraction for different slip velocities; right: variation of the fractional correction with the kinetic energy of the meso-scale velocity fluctuations for different volume fractions.

Fig. 2: Particle size distribution of the raw gas of the cyclone

(Simon Schneiderbauer)