Euler-Lagrange Modeling of the Hydrodynamics of Dense Multiphase Flows

The large-scale hydrodynamic behavior of relatively dense dispersed multiphase flows, such as encountered in fluidized beds, bubbly flows, and liquid sprays, can be predicted efficiently by use of Euler-Lagrange models. In these models, grid-averaged equations for the continuous-phase flow field are solved, where the grid size is larger than the discrete phase size, while the discrete phase is explicitly tracked and experiencing forces in a Lagrangian fashion. In this chapter, we provide a summary of our own efforts in this field, including details which we deem necessary for a novice to be aware of. We start with a theoretical introduction to Euler-Lagrange models, emphasizing the importance of the availability of high-quality correlations for the interphase momentum transfer and the outcome of binary interactions between members of the discrete phase. Then, in three topical sections, we discuss implementations of the methods which are used intensely in our group: the computational fluid dynamics/discrete element method (CFD-DEM), discrete bubble method (DBM), and direct simulation Monte Carlo (DSMC). CFD-DEM is most suitable for solid particles moving in a gas. The interplay between hydrodynamic flow and dissipative collisions between these particles leads to inhomogeneities at meso- and larger scale. DBM applies to bubbly flows, where the additional complication of coalescence and splitting of bubbles needs to be taken into account accurately. DSMC is suitable for not-too-dense systems of particles or droplets in a gas (dispersed volume fraction less than 10%). Collisions between the discrete phase elements are detected stochastically from the local number density, relative velocities, and sizes of neighboring dispersed elements, leading to a considerable saving of computer time. We end with an outlook into directions of research which would lead to an even more comprehensive use of Euler-Lagrange models in the future.