Numerical Solutions of Population Balance Equations within Liquid/Gas–Liquid Flow Simulations

Numerical solvers based on population balance equations (PBE) coupled with flow equations are a promising approach to simulate liquid/gas–liquid dispersed flows which are very commonly observed in the nature and in industrial processes. Our aim is to discuss the challenges for the numerical solution of the coupled equation systems and to present detailed numerical recipes whose main ingredients are the method of classes, positivity-preserving linearization and the high-order FEM-AFC schemes, additional to our in-house flow solver software package FEATFLOW. We study liquid-liquid flows through a static mixer and dispersed phase systems in a flat bubble column with the accordingly developed computational tool. The suggested recipes were validated by comparing the numerical results against experimental data so that we present a novel approach to the numerical simulation of bubbly flows at moderate gas holdups, which involves highly accurate numerical techniques and is computationally efficient and robust.