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

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) approximate to 40 degrees 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 resealed 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).

Automated summary

In this study, extensive simulations using the discrete element method were conducted to investigate the gravity-driven flows of cohesionless granular media over an erodible bed confined between two frictional sidewalls. The focus was on the role of the sidewalls, specifically the gap widths between them. Two distinct regimes were observed, with regime I corresponding to dense flows and regime II exhibiting a strong variation of the volume fraction through the depth. Various flow properties were rescaled using three relevant lengths identified in the system: the gap between sidewalls (W), the length characterizing the vertical variation of the volume fraction (l), and a characteristic length associated with the vertical variation of the streamwise velocity (h). The behavior of l and h differed between regime I and regime II, resulting in differing scaling of flow rate with respect to these lengths.