Multi-phase particle-in-cell coupled with population balance equation method for multi-scale computational fluid dynamics simulation

Abstract

A large variety of chemical processes including crystallization and polymerization, uses the mixing of micro-sized particulate phase and continuum phase. These multiphase particulate processes exhibit complex flow patterns that are not seen from gas and liquid fluids because the micro-scale changes influence meso-scale fluid dynamics and vice versa. For the simulation of the multiphysics phenomena seen in these processes, the multi-scale modeling is required to combine the different scale models in order to take into account resolutions of different scales. The simultaneous interpretation of computational fluid dynamics (CFD) and population balance equations (PBE) is the best multiscale modeling approach for predicting the correlation between the mesoscopic fluid flow and the microscopic particle distribution. However, this combination method of including the micro-scale PBE in the meso-scale CFD algorithm can be computationally highly inefficient when a high accuracy of the meso-scale phenomena is desired. In this setup, the meso- and micro- models are calculated concurrently but the multi-scale simulation exponentially increases the cost of the micro-scale calculation when the cost of the meso-scale calculation increases. Alternatively, in the particulate multi-scale modeling, the Lagrangian frame approach has been used to describe the micro-scale particle flow of individual particles without having to respect spatial dimensions. In this approach, there is no computational cost relationship between the meso-scale continuum and the micro-scale particulate transformations. However, the Lagrangian frame approach is computationally expensive because it individually calculates the motility of particles in the first place. This dissertation develops a novel numerical method called the ‘multiphase particle-in-cell coupled with population balance equation’ (MP-PIC-PBE) method, for simulating multi-scale and multiphase particulate flows. The method, an advanced version of the previously published MP-PIC method, is a numerical simulation procedure for predicting multi-scale fluid phenomena, combining the micro-scale particle size distribution and the meso-scale fluid dynamics. The homogeneous population balance equation is calculated for each discrete particle tracked in a Lagrangian frame after the MP-PIC numerical procedure is followed at each time instance. The particle information updated by the PBE is then reflected in the particulate phase, and the multiphase fluid dynamics is implicitly calculated. This new procedure allows the particulate phase to easily accommodate the particulate stresses using spatial gradients and allows the Lagrangian description to predict particle properties that are changed by the PBE. For validation, a crystallizer and a suspension polymerization reactor were simulated by the newly developed method and compared with a conventional method. The simulation result demonstrates that the developed approach has a lower computational cost and provides more detailed information such as mass, size, and age of particles.