Recirculation cells for granular flow in cylindrical rotating tumblers

Convection of monodisperse particles in a highly filled rotating cylinder

We investigate the occurrence of spontaneous convection in a coaxial cylinder highly filled with monodisperse spheres. To analyze the flow field noninvasively, initial pulses consisting of colored particles are placed at equal intervals. By analyzing the spatiotemporal distribution of these pulses, we obtained axial velocity profiles for both the surface and subsurface regions. Our advection-diffusion equations with steady advection terms incorporate experimentally obtained axial velocity profiles in the surface layer, while the rest of the components are estimated using azimuthal symmetry and volume conservation. The validity of our model is confirmed by comparing experimental data with numerical solutions for both the spatiotemporal distribution and cross-sectional profile of the colored particles.

Mechanisms for recirculation cells in granular flows in rotating cylindrical rough tumblers

Friction at the endwalls of partially filled horizontal rotating tumblers induces curvature and axial drift of particle trajectories in the surface flowing layer. Here we describe the results of a detailed discrete element method study of the dry granular flow of monodisperse particles in three-dimensional cylindrical tumblers with endwalls and cylindrical wall that can be either smooth or rough. Endwall roughness induces more curved particle trajectories, while a smooth cylindrical wall enhances drift near the endwall. This drift induces recirculation cells near the endwall. The use of mixed roughness (cylindrical wall and endwalls having different roughness) shows the influence of each wall on the drift and curvature of particle trajectories as well as the modification of the free surface topography. The effects act in opposite directions and have variable magnitude along the length of the tumbler such that their sum determines both direction of net drift and the recirculation cells. Near the endwalls, the dominant effect is always the endwall effect, and the axial drift for surface particles is toward the endwalls. For long enough tumblers, a counter-rotating cell occurs adjacent to each of the endwall cells having a surface drift toward the center because the cylindrical wall effect is dominant there. These cells are not dynamically coupled with the two endwall cells. The competition between the drifts induced by the endwalls and the cylindrical wall determines the width and drift amplitude for both types of cells.