An Eulerian-Lagrangian approach for coupling CFD and population balance equation

Abstract : A new approach is proposed here to ensure a complete resolution of the population balance equation (PBE) coupled with the fluid flow equations, which splits the determination of the fluid flow on an Eulerian frame from the PBE resolution along the Lagrangian trajectories of a set of fluid parcels. Knowing the size distribution of the particles aggregates, the viscosity of the overall product can be determined and used for the flow estimation. The coupling of the two types of model is allowed thanks to an iterative procedure until the stability of the calculated viscosity field. The numerical scheme is here described as a proof of concept for a continuous isothermal aggregation process in a pipe with likely parameters. This method allows the description of the aggregation process, and especially the size distribution determination, for the entire domain using a size class method. It was observed notably a high difference of aggregation state for the product flowing near the axis of the pipe and near the wall due to the differences between the shear rate histories of the two parts of the domain. The reconstruction of the bulk output product exhibit that the product properties dispersion is in large part due to the differences of product histories. The versatility of the numerical scheme presented here allows investigating a wide range of transformation.