High-speed confined granular flows down inclines revisited

TL;DR

This paper revisits high-speed confined granular flows down inclines, providing detailed profiles and transition characterizations, and introduces a universal friction function analogous to the Froude number.

Contribution

It offers new detailed flow profiles, characterizes flow regime transitions, and proposes a universal friction function based on a Froude number for these flows.

Findings

Vertical and transverse profiles of flow properties provided.

Flow regime transitions characterized by packing fraction and vorticity.

A universal friction function analogous to the $ppa(I)$ rheology proposed.

Abstract

Recent numerical work has shown that high-speed confined granular flows down inclines exhibit a rich variety of flow patterns, including dense unidirectional flows, flows with longitudinal vortices and supported flows characterized by a dense core surrounded by a dilute hot granular gas (Brodu et al, JFM 2015). Here, we revisit the results obtained by Brodu et al. (JFM, 2015) and present new features characterizing these flows. In particular, we provide vertical and transverse profiles for the packing fraction, velocity and granular temperature.We also characterize carefully the transition between the different flow regimes and show that the packing fraction and the vorticity can be successfully used to describe these transitions. Additionally, we emphasize that the effective friction at the basal and side walls can be described by a unique function of a dimensionless number which is the analog of a Froude number: $Fr=V/\sqrt{gH\cos \theta}$ where $V$ is the particle velocity at the walls, $\theta$ is the inclination angle and $H$ the particle holdup (defined as the depth-integrated particle volume fraction). This universal function bears some similarities with the $\mu(I)$ rheological curve derived for dense granular flows.