Granular Flow in a Tumbler Under Variable g-Levels

The Froude number $\omega^2 r/g$, where $\omega$ is the rotational speed, $r$ the radius of the tumbler and $g$ the gravitational acceleration, is frequently used to characterize a granular flow. Although $g$ appears in the Froude number, little is understood about how its variation affects the nature of granular flow. Experiments were performed with $0.5mm$ glass beads in a half-full, quasi-two dimensional 45mm radius tumbler at high $g$-levels. The tumbler was mounted in a large centrifuge to provide high g-levels. At a particular tumbler rotational speed, the dynamic angle of repose decreases as the $g$-level increases from 1$g$ to 25$g$. However, the data at all g-levels collapses so that the angle of repose is independent of the $g$-level when plottet as a function of the Froude number. Furthermore, the shape of the surface of the flowing layer depends only on the Froude number, not directly on $g$. Thus, the Froude number appears to characterize the nature of the flowing layer in a tumbler when both $\omega$ and $g$ are varied.