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

Journal of Fluid Mechanics - Tập 940 - 2022
Patrick Richard1, Alexandre Valance2, Renaud Delannay2, P. Boltenhagen2
1MAST-GPEM - Granulats et Procédés d'Elaboration des Matériaux (Allée des Ponts et Chaussées Route de Bouaye 44344 Bouguenais Cedex - France)
2IPR - Institut de Physique de Rennes (Bâtiment 11A , B, C, E – 10B 263 av. Général Leclerc 35042 Rennes cedex FRANCE - France)

Tóm tắt

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).

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Journal of Fluid Mechanics

Tập 940

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