Rodney O. Fox, "Chapter One - Quadrature-Based Moment Methods for Multiphase Chemically Reacting Flows", Advances in Chemical Engineering, Volume 52, 2018, Pages 1-50, https://doi.org/10.1016/bs.ache.2018.01.001.
Abstract: The numerical simulation of multiphase chemically reacting flows is very challenging due to their multiscale nature. In this chapter, the focus is on disperse multiphase flows with a continuous phase (gas or liquid) surrounding one or more disperse phases (e.g., particle, drops, or bubbles). In such flows, the disperse phase is usually characterized by a size, concentration, and/or temperature distribution that must be accounted for in the mathematical model. In this context, a population balance model (PBM) for the number density function is the most convenient way to account for polydispersity. In addition, the continuous phase is often turbulent, so mixing and chemical reactions in a turbulent flow must also be modeled. This can be done using probability density function (PDF) methods. In this chapter, computational methods for approximating solutions to PBM and PDF transport equations are reviewed in the context of computational fluid dynamic (CFD). In particular, quadrature-based moment methods (QBMM) have proven to be accurate and numerically efficient when combined with CFD simulations. Applications with increasing degrees of complexity in the flow physics are introduced to illustrate how QBMM are used to solve real problems in chemical engineering.
Keywords: Quadrature-based moment methods; Polydisperse multiphase flows; Computational fluid dynamics; Probability density function methods; Population balance models