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

TL;DR

This study uses discrete element simulations to analyze gravity-driven granular flows confined by flat, frictional walls, revealing two flow regimes distinguished by flow angle and volume fraction behavior, with implications for flow scaling and structure.

Contribution

It introduces a detailed analysis of flow regimes and length scales in granular flows confined by sidewalls, highlighting the role of flow angle and wall effects in flow behavior.

Findings

Identified two distinct flow regimes based on flow angle and volume fraction.

Established scaling laws for flow properties involving system length scales.

Demonstrated differences in flow rate scaling between regimes.

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).