Transient behavior of granular materials as result of tumbler shape and orientation effects

Abstract

Granular flows are most often investigated at steady-state conditions. This allows time-averaged analysis to display results such as velocity profiles and convective accelerations within the thin flowing layer. Typically in rotating tumblers, constant rotation rates and circular shapes are used as they jointly produce a steady, uniform flowing layer at the free surface. Conversely, unsteady flowing layers can be generated through any combination of varying the rotation rate of a tumbler or using a non-circular cross-sectional shape to change the length of the flowing layer. The unsteady conditions, however, require the additional complexity of ensemble-averaged analysis of images in a sequence of multiple trials. The experiments of this paper examine the properties of unsteady flow produced by triangular-shaped rotating tumblers at constant rotation rates. The geometric shape naturally causes periodic changes in the flowing layer as a function of the instantaneous orientation of the triangle. Multiple experiments were conducted in which the parameters of tumbler dimension, particle size, fill level and rotation rate were varied in all combinations. The free surface properties of angle of repose and flowing layer length, position, and curvature are reported. Results show that the arithmetic difference between the angle of repose and the tumbler orientation has a functional relationship with the instantaneous flowing layer length in the form of a catenary indicating a minimization of energy in the granular flow. Furthermore, the oscillation of the flowing layer position appears to affect the free surface curvature in the upstream regions. This is likely due to the rapidly increasing and decreasing length of the free surface limiting the space where particles can enter or exit the flowing layer. Ultimately, the unsteady macroscopic properties of the free surface flowing layer in the triangular tumblers provide some indication of the complexities of granular velocity and acceleration that contribute to the mixing and segregation in this unique tumbler shape.