Periodic, Unsteady Velocity Characteristics within Rotating Triangular Tumblers of Variable Fill Levels

Rotating tumblers are used in a wide variety of industrial applications from mixing and deburring to flow regulation and storage. Almost all model tumblers previously analyzed, both theoretically and experimentally, had circular cross sections that produced consistent flowing layer dimensions and steady state flow. In contrast, tumblers with triangular cross sections produced unsteady flow as a direct result of the dynamic dimensions of the flowing surface. Although unsteady, the flow produced in triangular tumblers is periodic every 120$^\circ$ of rotation after an initial start-up period. The mechanisms by which the flow characteristics vary as a triangular tumbler rotates and the number of tumbler walls in contact with the flowing layer change, is poorly understood. The primary objective of this work is to determine the effect of orientation, fill level, and tumbler size on flow velocities and flowing layer dimensions. High speed imaging with particle tracking velocimetry are used in experiments exploring the flow in the central region of the tumblers. Results indicate that fill level is the dominant feature on the velocity profile while tumbler size affects velocity amplitudes through the instantaneous dimension at each orientation. Normalization of various flow characteristics reveals a phase shift relation for velocity as a function of tumbler orientation as both fill level and tumbler dimension change.