A new quadrature-based moment method for the mixing of inert polydisperse fluidized powders in commercial CFD codes

To describe the behavior of polydisperse multiphase systems in an Eulerian framework, we solved the population balance equation (PBE), letting it account only for particle size dependencies. To integrate the PBE within a commercial computational fluid dynamics code, we formulated and implemented a novel version of the quadrature method of moments (QMOM). This no longer assumes that the particles move with the same velocity, allowing the latter to be size-dependent. To verify and test the model, we simulated the mixing of inert polydisperse fluidized suspensions initially segregated, validating the results experimentally. Because the accuracy of QMOM increases with the number of moments tracked, we ran three classes of simulations, preserving the first four, six, and eight integer moments of the particle density function. We found that in some cases the numerics corrupts the higher-order moments and a corrective algorithm, designed to restore the validity of the moment set, has to be implemented.