Surface-Weighted Gaussian-Moment Method for Polydisperse Multiphase Flow Prediction

Abstract

Polydisperse multiphase flows are characterized as particle-laden flows, for which the flows of interest are comprised of small particles of different sizes. These flows are computationally difficult to model as the number of particles increases. As such, many methods have been developed over the years in order to build simplified models. One such technique, higher-order moment closure methods, provide an expanded set of partial differential equations (PDEs) describing the evolution of statistical properties of the particle phase. Moment-based methods rely on modelling the statistical moments of the studied flow, such as the average particle velocity and provides equations describing the evolution of these moments. This thesis introduces the fundamentals of kinetic theory and moment methods, provides an extension to a previously proposed three-dimensional polydisperse Gaussian-moment model (PGM). The previous PGM, while showing promising preliminary results, has been improved by the implementation of surface-weighted particle statistics. Namely this new model exactly recovers the steady-state solution for particles settling in Stokes flow. Finally, this thesis describes the numerical methods used in obtaining one-dimensional and three-dimensional results of the PGM. Several simple flow problems are solved and analysed to demonstrate the predictive capabilities of the new model.