A Coarse-Grained Two-Fluid Model for Gas-Solid Fluidized Beds

Abstract

Due to increasing computer power the numerical simulation of fluidized and moving beds has become feasible. However, while kinetic theory based CFD (Computational Fluid Dynamics) has become a valuable design tool for modeling pilot plant scale gassolid fluidized bed reactors, a fully resolved simulation of industrial scale reactor is still nearly unfeasible. It is, therefore, common to use sub-grid models to account for the effect of the small unresolved structures on large resolved scales when using coarse grids. It is generally agreed that the influence of these small scales on the drag force is a key parameter in the prediction of the hydrodynamics of fluidized beds. We present a sub-grid drag modification dealing with the influence of heterogeneous structures on the drag force. It is assumed that these structures appear as distinct clusters of particles within an interstitial dilute particle phase. The clusters and the dilute phase itself consist of homogeneously distributed particles enabling the application of a homogenous drag correlation to these structures. In contrast to the established sub-grid drag modification EMMS (Energy-Minimization Multi-Scale Method), the presented model distinguishes between resolved and unresolved clusters by computing the expectation value of the diameter of the unresolved clusters. This reveals a grid and slip velocity dependent drag modification, which recovers the homogenous drag law as the solids volume fraction approaches the maximum packing of frictional spheres. The presented model is validated on the one hand, in case of industrial scale bubbling and turbulent fluidized beds. On the other hand, the model is applied to the coarse grid simulation of a riser flow. The numerical results obtained on a coarse gird demonstrate that our model reveals fairly good agreement with experimental data of bed expansion and solids volume fraction distributions. Thus, the results proof that the presented drag modification is applicable to a wide range of particle diameters (Geldart A, B and D group particles) and different fluidization regimes.