Simulation of a batch crystallizer using a multi-scale approach in time and space

Abstract

The simulation of a crystallizer leads to a challenging problem with very different time and length scales. After checking a simple 0-D approach in time, and a brute-force coupling process describing the complete problem in space and time, the multi-scale methodology developed in this work combines three-dimensional Computational Fluid Dynamics simulations on a short time-scale (to describe hydrodynamic features) with zero-dimensional simulations relying on a Population Balance Model over long time-scales to compute the evolution of all important particle properties (volume fraction, particle size distribution, slip velocities, mass transfer coefficients). The flow field in the crystallizer is almost homogeneous, apart for a stagnation zone below the impeller leading to an increased solid-phase volume fraction but smaller crystals. The diffusive mass transfer coefficient evolves in a non-monotonic way. A proper prediction of dynamically changing local supersaturations requires a closer coupling between the two simulation steps in the multi-scale framework.