A hydrodynamic model for granular material flows including segregation effects

The simulation of granular flows including segregation effects in large industrial processes using particle methods is accurate, but very time-consuming. To overcome the long computation times a macroscopic model is a natural choice. Therefore, we couple a mixture theory based segregation model to a hydrodynamic model of Navier-Stokes-type, describing the flow behavior of the granular material. The granular flow model is a hybrid model derived from kinetic theory and a soil mechanical approach to cover the regime of fast dilute flow, as well as slow dense flow, where the density of the granular material is close to the maximum packing density. Originally, the segregation model has been formulated by Thornton and Gray for idealized avalanches. It is modified and adapted to be in the preferred form for the coupling. In the final coupled model the segregation process depends on the local state of the granular system. On the other hand, the granular system changes as differently mixed regions of the granular material differ i.e. in the packing density. For the modeling process the focus lies on dry granular material flows of two particle types differing only in size but can be easily extended to arbitrary granular mixtures of different particle size and density. To solve the coupled system a finite volume approach is used. To test the model the rotational mixing of small and large particles in a tumbler is simulated.