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Non-local continuum modelling of steady, dense granular heap flows

Published online by Cambridge University Press:  13 October 2017

Daren Liu  and
David L. Henann Open the ORCID record for David L. Henann [Opens in a new window]
Daren Liu
Affiliation:
School of Engineering, Brown University, Providence, RI 02906, USA
David L. Henann*
Affiliation:
School of Engineering, Brown University, Providence, RI 02906, USA
*
†Email address for correspondence: david_henann@brown.edu
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Abstract

Dense granular heap flows are common in nature, such as during avalanches and landslides, as well as in industrial flows. In granular heap flows, rapid flow is localized near the free surface with the thickness of the rapidly flowing layer dependent on the overall flow rate. In the region deep beneath the surface, exponentially decaying creeping flow dominates with characteristic decay length depending only on the geometry and not the overall flow rate. Existing continuum models for dense granular flow based upon local constitutive equations are not able to simultaneously predict both of these experimentally observed features – failing to even predict the existence of creeping flow beneath the surface. In this work, we apply a scale-dependent continuum approach – the non-local granular fluidity model – to steady, dense granular flows on a heap between two smooth, frictional side walls. We show that the model captures the salient features of both the flow-rate-dependent, rapidly flowing surface layer and the flow-rate-independent, slowly creeping bulk under steady flow conditions.

JFM classification

Mathematical Foundations: Computational methods Granular media: Granular media Non-Newtonian Flows: Rheology
Type
Papers
Information
Journal of Fluid Mechanics , Volume 831 , 25 November 2017 , pp. 212 - 227
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Copyright
© 2017 Cambridge University Press 

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