Limitations of quadrature-based moment methods for modeling inhomogeneous polydisperse fluidized powders

Computational fluid dynamics (CFD) is extensively used to investigate the behavior of dense fluidized suspensions. Often modelers assume that these are formed by few solid phases of particles with constant size. But real powders are continuously distributed over the particle size, and their distribution functions change continuously in time and space reflecting the physical and chemical phenomena occurring within the system. To account for this key feature, models have to include a population balance equation (PBE), which needs to be solved in place of or along with the customary fluid dynamic transport equations. The recently developed quadrature method of moments (QMOM) and direct quadrature method of moments (DQMOM) permit to solve PBEs in commercial CFD codes at relatively low computational cost. These methods, however, still need testing in the context of multiphase flows. Investigating a simple problem, namely the dynamics of two inert polydisperse fluidized suspensions initially segregated, we highlight an important limitation of these methods, which fail to properly model diffusion in real space. We explain where the problem originates and comment on a possible way to overcome it. To conclude the work, we discuss some simulations based on the original and revised formulations of the methods, describing how the code numerics affects the results.