Effect of base topography on dynamics and transition in a dense granular flow

Abstract

The effect of base roughness on the transition and dynamics of a dense granular flow down an inclined plane is examined using particle based simulations. Different types of base topographies, rough bases made of frozen particles in either random or hexagonally ordered configurations, as well as sinusoidal bases with height modulation in both the flow and the spanwise directions, are examined. The roughness (characteristic length of the base features scaled by the flowing particle diameter) is defined as the ratio of the base amplitude and particle diameter for sinusoidal bases, and the ratio of frozen and moving particle diameters for frozen-particle bases. There is a discontinuous transition from an ordered to a disordered flow at a critical base roughness for all base topographies studied here, indicating that it is a universal phenomenon independent of base topography. The transition roughness does depend on the base configuration and the height of the flow, but is independent of the contact model and is less than 1.5 times the flowing particle diameter for all of the bases considered here. The bulk rheology is independent of the base topography, and follows the Bagnold law for both the ordered and the disordered flows. The base topography does have a dramatic effect on the flow dynamics at the base. For flows over frozen-particle bases, there is ordering down to the base for ordered flows, and the granular temperature is comparable to that in the bulk. There is virtually no velocity slip at the base, and the mean angular velocity is equal to one-half of the vorticity down to the base. For flows over sinusoidal bases, there is significant slip at the base, and the mean angular velocity is approximately an order of magnitude higher than that in the bulk within a region of height approximately one particle diameter at the base. This large particle spin results in a disordered and highly energetic layer of approximately 5–10 particle diameters at the base, where the granular temperature is an order of magnitude higher than that in the bulk. Thus, this study reveals the paradoxical result that gentler base topographies result in large slip and large agitation at the base, whereas rougher topographies such as frozen-particle bases result in virtually no slip and no agitation at the base for both ordered and disordered flows.