Subsurface granular flow in rotating tumblers: a detailed computational study.

To better understand the subsurface velocity field and flowing layer structure, we have performed a detailed numerical study using the discrete element method for the flow of monodisperse particles in half-full three-dimensional (3D) and quasi-2D rotating tumblers. Consistent with prior measurements at the surface, a region of high speed flow with axial components of velocity occurs near each endwall in long tumblers. This region can be eliminated by computationally omitting the friction at the endwalls, confirming that a mass balance argument based on the slowing of particles immediately adjacent to the frictional endwalls explains this phenomenon. The high speed region with the associated axial flow near frictional endwalls persists through the depth of the flowing layer, though the regions of high velocity shift in position and the velocity is lower compared to the surface. The axial flow near the endwalls is localized and independent with the length of the tumbler for tumblers longer than one tumbler diameter, but these regions interact for shorter tumblers. In quasi-2D tumblers, the high speed regions near the endwalls merge resulting in a higher velocity than occurs in a long tumbler, but with a flowing layer that is not as deep. Velocity fluctuations are altered near the endwalls. Particle velocity fluctuations are greatest just below the surface and diminish through the depth of the flowing layer.