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

Published online by Cambridge University Press:  11 April 2022

Patrick Richard Open the ORCID record for Patrick Richard [Opens in a new window] ,
Alexandre Valance Open the ORCID record for Alexandre Valance [Opens in a new window] ,
Renaud Delannay  and
Philippe Boltenhagen
Patrick Richard*
Affiliation:
Univ Gustave Eiffel, MAST-GPEM, F-44344 Bouguenais, France
Alexandre Valance
Affiliation:
IPR, Université de Rennes 1, CNRS UMR 6251, Campus Beaulieu, F-35042 Rennes, France
Renaud Delannay
Affiliation:
IPR, Université de Rennes 1, CNRS UMR 6251, Campus Beaulieu, F-35042 Rennes, France
Philippe Boltenhagen
Affiliation:
IPR, Université de Rennes 1, CNRS UMR 6251, Campus Beaulieu, F-35042 Rennes, France
*
†Email address for correspondence: patrick.richard@univ-eiffel.fr
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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).

JFM classification

Granular media: Dry granular material Granular media: Avalanches
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 940 , 10 June 2022 , A30
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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