A New FEM/DEM Multiscale Model to Solve Immersed Granular Flows Based on Suspension Drops Simulations

Legat, Vincent [UCL] Constant, Matthieu [UCL] Lambrechts, Jonathan [UCL] Frédéric Dubois

his paper is devoted to the study of an hybrid multiscale model for flows mixing fluid and grains. The grains are solved at a fine scale using a Lagrangian approach with the Discrete Element Method. It provides the trajectories and the force applied on the grains with an accuracy that is needed to describe small scales phenomena happening in these flows. The dynamics of the fluid is deduced from a continuous representation of the mixture between grains and fluid at the coarse scale. We present an hybrid multiscale mode} for immersed granular flows using the Finite Element Method to solve the fluid phase and a non-smooth grains model to solve the contacts. This model will be validated on two-dimensional simulations of the uspension drops that refers to cluster of grains settling in a viscous fluid. The challenging point of this method stays in the coupling of the two different representation scales. Applying this model to the well-known problem of suspension drops provides validation and insight in this kind of methodology. All the features of a swarm of grains settling in a viscous fluid can be found to validate the model and its generality provides easily simulations at regimes where inertia is dominant compared to Stokeslet or Oseenlet simulations usually encountered in literature. Just after the drop begins to move, some grains escape from the closed envelop and form a tail that grows in time until it separates from the swarm. The tail contains grains from the rear of the swarm as well as grains from inside because of the recirculation that leads grains outside the closed envelop. The rate of grains leakage is linked to the falling velocity of the swarm, the radius of the swarm and the radius of the grains. At some time the centre of the swarm contains not enough grains and the tail breaks up. The fluid can go through the center of the swarm and it changes into an open torus that destabilises during expansion and contraction phases to form two (or more) secondary droplets.