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A two-phase two-layer model for fluidized granular flows with dilatancy effects

Published online by Cambridge University Press:  19 July 2016

François Bouchut ,
Enrique D. Fernández-Nieto ,
Anne Mangeney  and
Gladys Narbona-Reina
François Bouchut*
Affiliation:
Université Paris-Est, Laboratoire d’Analyse et de Mathématiques Appliquées (UMR 8050)CNRS, UPEM, UPEC, F-77454, Marne-la-Vallée, France
Enrique D. Fernández-Nieto
Affiliation:
Departamento de Matemática Aplicada I, Universidad de Sevilla. E.T.S. Arquitectura. Avda, Reina Mercedes, s/n. 41012 Sevilla, Spain
Anne Mangeney
Affiliation:
Université Paris Diderot, Sorbone Paris Cité, Institut de Physique du Globe de Paris, Equipe de Sismologie, 1 rue Jussieu, 75005 Paris, France ANGE team, INRIA, CETMEF, Lab. J.-Louis Lions, Paris, France
Gladys Narbona-Reina
Affiliation:
Departamento de Matemática Aplicada I, Universidad de Sevilla. E.T.S. Arquitectura. Avda, Reina Mercedes, s/n. 41012 Sevilla, Spain
*
†Email address for correspondence: francois.bouchut@u-pem.fr
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Abstract

We propose a two-phase two-thin-layer model for fluidized debris flows that takes into account dilatancy effects, based on the closure relation proposed by Roux & Radjai (Physics of Dry Granular Media, 1998, Springer, pp. 229–236). This relation implies that the occurrence of dilation or contraction of the granular material depends on whether the solid volume fraction is respectively higher or lower than a critical value. When dilation occurs, the fluid is sucked into the granular material, the pore pressure decreases and the friction force on the granular phase increases. On the contrary, in the case of contraction, the fluid is expelled from the mixture, the pore pressure increases and the friction force diminishes. To account for this transfer of fluid into and out of the mixture, a two-layer model is proposed with a fluid layer on top of the two-phase mixture layer. Mass and momentum conservation are satisfied for the two phases, and mass and momentum are transferred between the two layers. A thin-layer approximation is used to derive average equations, with accurate asymptotic expansions. Special attention is paid to the drag friction terms that are responsible for the transfer of momentum between the two phases and for the appearance of an excess pore pressure with respect to the hydrostatic pressure. For an appropriate form of dilatancy law we obtain a depth-averaged model with a dissipative energy balance in accordance with the corresponding three-dimensional initial system.

JFM classification

Multiphase and Particle-laden Flows: Fluidized beds Granular media: Granular media
Type
Papers
Information
Journal of Fluid Mechanics , Volume 801 , 25 August 2016 , pp. 166 - 221
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© 2016 Cambridge University Press 

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