Introduction and Fundamentals of Modeling Approaches for Polydisperse Multiphase Flows

An overview of the basic formulation and conceptual ideas needed for modeling polydisperse multiphase systems is provided. Special emphasis is given to systems exhibiting polydispersity in more than one internal coordinate. Such systems are described by a multivariate population balance equation, governing a number density function, which can be solved using sectional or moment methods. When the particle velocity is treated as a fluctuating quantity, the corresponding number density function is the one-point velocity density function used in kinetic theory. For this special case, a generalized population balance equation is employed to describe polydispersity in the velocity and other internal coordinates (such as the particle size.) Here, due to their flexibility in treating inhomogeneous flows, we focus on quadrature-based moment methods and show how moment transport equations can be derived from the generalized population balance equation for polydisperse multiphase flows. An example application to the one-dimensional spray equation is used to illustrate the modeling concepts.