Granular surface flows confined between flat, frictional walls. Part 1. Kinematics

Abstract

We report and analyse the results of extensive discrete element method simulations of three-dimensional gravity driven flows of cohesionless granular media over an erodible bed, the whole being confined between two flat and frictional sidewalls. We focus on the role of sidewalls by performing simulations for different gap widths ( $W$ ) between the two confining sidewalls: from $5$ to $30$ grain sizes ( $d$ ). Our results indicate the existence of two distinct regimes: regime I for flow angles smaller than the critical angle $\theta_c\approx 40^\circ$ and regime II at flow angles larger than $\theta_c$ . Regime I corresponds to dense flows whereas flows belonging to regime II exhibit a strong variation of the volume fraction through the depth. Three relevant lengths are identified in the system: $W$ the gap between sidewalls, $l$ the length characterizing the vertical variation of the volume fraction and $h$ a characteristic length associated with the vertical variation of the streamwise velocity. Using these lengths we can rescale the profiles of various flow properties (e.g. streamwise velocity, granular temperature, particle rotation…). In regime II, in contrast to regime I, $l$ and $h$ have a similar behaviour. As a consequence, the rescaled profiles in regime II only involve $h$ (or equivalently $l$ ) and $W$ . Other dissimilarities exist between regimes I and II. In particular, the scaling of the flow rate with $h$ (at fixed $W$ ) differs in the two regimes, although they display a similar scaling with $W$ (at fixed flow angle).

Modelling the wall friction coefficient for a simple shear granular flow in view of the degradation mechanism

“…The current power exponent in the shear zone is greater than the values, 0.5 to 0.625, reported from a simulated confined shear flow but losing the constant exponent in the creeping regime is a shared feature (Richard et al. 2020, 2022). Further, it is worth noting that our power exponent falls in the range of 0.5–1.0 measured in the flowing layer of a quasi-two-dimensional narrow rotating drum flow (Orpe & Khakhar 2007) and below the exact 1.0 predicted for pure collisional flows in simple shear (Jenkins & Savage 1983; Campbell 1990).…”