Clustering and flow around a sphere moving into a grain cloud.

ABSTRACT

A bidimensional simulation of a sphere moving at constant velocity into a cloud of smaller spherical grains far from any boundaries and without gravity is presented with a non-smooth contact dynamics method. A dense granular "cluster" zone builds progressively around the moving sphere until a stationary regime appears with a constant upstream cluster size. The key point is that the upstream cluster size increases with the initial solid fraction [Formula see text] but the cluster packing fraction takes an about constant value independent of [Formula see text]. Although the upstream cluster size around the moving sphere diverges when [Formula see text] approaches a critical value, the drag force exerted by the grains on the sphere does not. The detailed analysis of the local strain rate and local stress fields made in the non-parallel granular flow inside the cluster allows us to extract the local invariants of the two tensors dilation rate, shear rate, pressure and shear stress. Despite different spatial variations of these invariants, the local friction coefficient µ appears to depend only on the local inertial number I as well as the local solid fraction, which means that a local rheology does exist in the present non-parallel flow. The key point is that the spatial variations of I inside the cluster do not depend on the sphere velocity and explore only a small range around the value one.