Shallow granular flows down flat frictional channels: steady flows and longitudinal vortices

TL;DR

This paper investigates shallow granular flows down flat frictional channels using DEM simulations, revealing complex behaviors like convection and density inversion, and compares results with a viscoplastic rheological model.

Contribution

It provides the first detailed numerical analysis of granular flows on flat boundaries, highlighting flow regimes and validating a viscoplastic rheological model.

Findings

Identification of granular convection and density inversion at high angles.

Flow behavior can be modeled as over bumpy base with Bagnold profiles.

Transition between flow regimes shows a clear discontinuity in rheology.

Abstract

Granular flows down inclined channels with smooth boundaries are common in nature and in the industry. Nevertheless, the common setup of flat boundaries has comparatively been much less investigated than the bumpy boundaries one, which is used by most experimental and numerical studies to avoid sliding effects. Using DEM numerical simulations with side walls we recover quantitatively experimental results. At larger angles we predict a rich behavior, including granular convection and inverted density profiles suggesting a Rayleigh-B\'enard type of instability. In many aspects flows on a flat base can be seen as flows over an effective bumpy base made of the basal rolling layer, giving Bagnold-type profiles in the overburden over that layer. We have tested a simple viscoplastic rheological model (Nature 2006, vol 441, pp727-730) in average form. The transition between the unidirectional and the convective flows is then clearly apparent as a discontinuity in the constitutive relation.