6. Numerical Methods for Dispersed Multiphase Flows

This article gives an overview of numerical methods for the calculation of dispersed multi-phase flows. At the beginning, a brief introduction is given on the different flow regimes observed for multi-phase flows in general. Then a characterisation and classification of dispersed multi-phase flows is introduced based on inter-particle spacing and volume fraction. As an introduction to the subject, the numerical methods used for single-phase flows are briefly described based on the turbulent scales being resolved by the numerical grid. Since even dispersed multi-phase flows are extremely complex, the hierarchy of the different numerical methods is highlighted ranging from macro-scale numerical simulations for an entire industrial process down to micro-scale simulations required for analysing particle scale phenomena. Due to constraints in computational power and storage availability, macro-scale simulations can only be done with a limited grid resolution and the assumption of particles being treated as point-masses. Consequently, all transport phenomena occurring on scales smaller than the grid cell and on the scale of the particle have to be considered through additional closures and models. Therefore, essential elements in this multi-scale problem are direct numerical simulations that fully resolve the particles and the flow around them. The different methods for such resolved simulations are briefly described. The major part of this article is focused on the modelling of dispersed multi-phase flows relying on the point-particle assumption. The multi-fluid method or Euler/Euler model is briefly described in order to demark its applicability and limitations. The hybrid Euler/Lagrange approach based on tracking a large number of point particles and its different variants are introduced in more detail, emphasising the two-way coupling approaches for unsteady flows. The importance of accurately modelling particle-scale phenomena is highlighted and an estimate for the significance of particle-wall and inter-particle collisions is given. Finally, three application examples are introduced, emphasising the potential of Euler/Lagrange simulations. For a particle-laden swirling flow the semi-unsteady approach is used for analysing unsteady particle roping phenomena. The simulations of particle suspension in a stirred vessel highlight the importance of inter-particle collisions even at relatively low volume fractions up to 5%. Finally, it is demonstrated that the Euler/Lagrange approach may also be used to study an industrial filtration process where it allows the prediction of particle deposits and filter cake formation. In this respect extensions are possible which provide more information on the internal filter cake structure.