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Investigation of the mobile granular layer in bedload transport by laminar shearing flows

Published online by Cambridge University Press:  13 November 2013

Pascale Aussillous*
Affiliation:
Aix-Marseille Université, CNRS, IUSTI UMR 7343, 13013 Marseille, France
Julien Chauchat
Affiliation:
Grenoble-INP/UJF-Grenoble 1/CNRS, LEGI UMR 5519, Grenoble, F-38041, France
Mickael Pailha
Affiliation:
Université de Savoie, POLYTECH Annecy-Chambéry, LOCIE - UMR5271, 73376 Le Bourget du Lac, France
Marc Médale
Affiliation:
Aix-Marseille Université, CNRS, IUSTI UMR 7343, 13013 Marseille, France
Élisabeth Guazzelli
Affiliation:
Aix-Marseille Université, CNRS, IUSTI UMR 7343, 13013 Marseille, France
*
Email address for correspondence: [email protected]

Abstract

The mobile layer of a granular bed composed of spherical particles is experimentally investigated in a laminar rectangular channel flow. Both particle and fluid velocity profiles are obtained using particle image velocimetry for different index-matched combinations of particles and fluid and for a wide range of fluid flow rates above incipient motion. A full three-dimensional investigation of the flow field inside the mobile layer is also provided. These experimental observations are compared to the predictions of a two-phase continuum model having a frictional rheology to describe particle–particle interactions. Different rheological constitutive laws having increasing degrees of sophistication are tested and discussed.

Type
Papers
Copyright
©2013 Cambridge University Press 

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References

Andreotti, B., Forterre, Y. & Pouliquen, O. 2013 Granular Media: Between Fluid and Solid. Cambridge University Press.Google Scholar
Bagnold, R. A. 1954 Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear. Proc. R. Soc. A 225, 4963.Google Scholar
Bagnold, R. A. 1956 The flow of cohesionless grains in fluids. Phil. Trans. R. Soc. A 249, 235297.Google Scholar
Boyer, F., Guazzelli, É. & Pouliquen, O. 2011 Unifying suspension and granular rheology. Phys. Rev. Lett. 107, 188301.CrossRefGoogle ScholarPubMed
Brinkman, H. C. 1947 A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Appl. Sci. Res. A 1, 2734.CrossRefGoogle Scholar
Cassar, C., Nicolas, M. & Pouliquen, O. 2005 Submarine granular flows down inclined planes. Phys. Fluids 17, 103301.CrossRefGoogle Scholar
Chauchat, J. & Médale, M. 2010 A three-dimensional numerical model for incompressible two-phase flow of a granular bed submitted to a laminar shearing flow. Comput. Meth. Appl. Mech. Engng 199, 439449.Google Scholar
Chauchat, J. & Médale, M. 2014 A three-dimensional model for dense granular flows based on the $\mu (I)$ rheology. J. Comput. Phys. 256, 696712.Google Scholar
Charru, F., Mouilleron-Arnould, H. & Eiff, O. 2004 Erosion and deposition of particles on a bed sheared by a viscous flow. J. Fluid Mech. 519, 5580.Google Scholar
Derksen, J. 2011 Simulations of granular bed erosion due to laminar shear flow near the critical Shields number. Phys. Fluids 23, 113303.Google Scholar
Dijksman, J. A., Rietz, F., Lõrincz, K. A., Van Hecke, M. & Losert, W. 2012 Refractive index matched scanning of dense granular materials. Rev. Sci. Instrum. 83, 011301.Google Scholar
Forterre, Y. & Pouliquen, O. 2008 Flows of dense granular media. Annu. Rev. Fluid Mech. 40, 124.CrossRefGoogle Scholar
Goharzadeh, A., Khalili, A. & Jørgensen, B. B. 2005 Transition layer thickness at a fluid–porous interface. Phys. Fluids 17, 057102.Google Scholar
Jackson, R. 1997 Locally averaged equations of motion for a mixture of identical spherical particles and a Newtonian fluid. Chem. Engng Sci. 52, 24572469.Google Scholar
Jackson, R. 2000 The Dynamics of Fluidized Particles. Cambridge University Press.Google Scholar
Lajeunesse, E., Malverti, L., Lancien, P., Armstrong, L., Metivier, F., Coleman, S., Smith, C. E., Davies, T., Cantelli, A. & Parker, G. 2010 Fluvial and submarine morphodynamics of laminar and near-laminar flows: a synthesis. Sedimentology 57, 126.Google Scholar
Lobkovsky, A. E., Orpe, A. V., Molloy, R., Kudrolli, A. & Rothman, D. H. 2008 Erosion of a granular bed driven by laminar fluid flow. J. Fluid Mech. 605, 4758.Google Scholar
Loiseleux, T., Gondret, P., Rabaud, M. & Doppler, D. 2005 Onset of erosion and avalanches for an inclined granular bed sheared by a continuous laminar flow. Phys. Fluids 17, 103304.Google Scholar
Malverti, L., Lajeunesse, E. & Métivier, F. 2008 Small is beautiful: upscaling from microscale laminar to natural turbulent rivers. J. Geophys. Res. 113, F04004.Google Scholar
Meunier, P. & Leweke, T. 2003 Analysis and minimization of errors due to high gradients in particle image velocimetry. Exp. Fluids 35, 408421.CrossRefGoogle Scholar
Mouilleron, H., Charru, F. & Eiff, O. 2009 Inside the moving layer of a sheared granular bed. J. Fluid Mech. 628, 229239.Google Scholar
Nicolas, X., Luijkx, J.-M. & Platten, J.-K. 2000 Linear stability of mixed convection flows in horizontal rectangular channels of finite transversal extension heated from below. Intl J. Heat Mass Transfer 43, 589610.Google Scholar
Ouriemi, M., Aussillous, P. & Guazzelli, É. 2009 Sediment dynamics. Part 1. Bed-load transport by laminar shearing flows. J. Fluid Mech. 636, 295319.CrossRefGoogle Scholar
Ouriemi, M., Aussillous, P., Médale, M., Peysson, Y. & Guazzelli, É. 2007 Determination of the critical Shields number for particle erosion in laminar flow. Phys. Fluids 19, 061706.CrossRefGoogle Scholar
Pailha, M. & Pouliquen, O. 2009 A two-phase flow description of the initiation of underwater granular avalanches. J. Fluid Mech. 633, 115135.CrossRefGoogle Scholar
Van der Hoef, M. A., Beetstra, R. & Kuipers, J. A. M. 2005 Lattice–Boltzmann simulations of low-Reynolds-number flow past mono- and bidisperse arrays of spheres: results for the permeability and drag force. J. Fluid Mech. 528, 233254.Google Scholar
Van Rijn, L. C. 1984 Sediment transport, Part I: bed load transport. J. Hydraul. Engng 110, 14311456.Google Scholar

Aussillous et al. supplementary movie

Typical movie of the bed test section for run 15.

Download Aussillous et al. supplementary movie(Video)
Video 9.2 MB

Aussillous et al. supplementary movie

Particle + fingerprint (◦, red) and solely fingerprint (∗, blue ) velocity profiles and particle volume fraction (+, green) for run 2 after 35.5s (velocity scale = 0.025mm.s−1.pixel−1, length scale = 0.029 mm.pixel−1, particle-volume-fraction scale = 0.001 pixel−1)

Download Aussillous et al. supplementary movie(Video)
Video 4.3 MB

Aussillous et al. supplementary movie

Particle + fingerprint (◦, red) and solely fingerprint (∗, blue) velocity profiles for run 16 after 115.5 s (velocity scale = 0.025 mm.s−1.pixel−1, length scale = 0.046 mm.pixel−1)

Download Aussillous et al. supplementary movie(Video)
Video 7.2 MB
Supplementary material: File

Aussillous et al. supplementary material

Data

Download Aussillous et al. supplementary material(File)
File 1.3 MB