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Immersed granular collapse: from viscous to free-fall unsteady granular flows

Published online by Cambridge University Press:  09 February 2021

Laurent Lacaze Open the ORCID record for Laurent Lacaze [Opens in a new window] ,
Joris Bouteloup ,
Benjamin Fry  and
Edouard Izard
Laurent Lacaze*
Affiliation:
Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS, Toulouse31400, France
Joris Bouteloup
Affiliation:
Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS, Toulouse31400, France
Benjamin Fry
Affiliation:
Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS, Toulouse31400, France
Edouard Izard
Affiliation:
Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS, Toulouse31400, France
*
†Email address for correspondence: [email protected]
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Abstract

The collapse of a granular column in a liquid is investigated using numerical simulations. From previous experimental studies, it has been established that the dynamics of the collapse is mostly influenced by the Stokes number $St$, comparing grain inertia and viscous fluid dissipation, and the initial volume fraction of the granular column $\phi _i$. However, the full characterization of the collapse in the $(St,\phi _i)$ plane is still missing, restricting its modelling as a physical process for geophysical applications. Only numerical tools can allow the variation over the parameter space $(St,\phi _i)$ that is hardly reachable in experiments as well as a full description of the granular phase that plays a major role in dense granular flows. For this purpose, a dedicated numerical model is used including a discrete element method to resolve the granular phase. The specific objectives of the paper are then twofold: (i) the characterization of the dynamics of the collapse and its final deposit with respect to $(St,\phi _i)$ to complement available experimental data, and (ii) the description of the granular rheology according to these two dimensionless numbers including dilatancy effects. A simple predictive model stems from the obtained results, allowing one to explain the evolution of the final deposit with $(St,\phi _i)$.

JFM classification

Granular media: Granular media Multiphase and Particle-laden Flows: Particle/fluid flow Non-Newtonian Flows: Rheology
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 912 , 10 April 2021 , A15
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Balmforth, N.J. & Kerswell, R.R. 2005 Granular collapse in two dimensions. J. Fluid Mech. 538, 399–428.CrossRefGoogle Scholar
Baran, O., Ertaş, D., Halsey, T.C., Grest, G.S. & Lechman, J.B. 2006 Velocity correlations in dense gravity-driven granular chute flow. Phys. Rev. E 74 (5), 051302.CrossRefGoogle ScholarPubMed
Barker, T. & Gray, J.M.N.T. 2017 Partial regularisation of the incompressible $\mu ({I})$-rheology for granular flow. J. Fluid Mech. 828, 5–32.CrossRefGoogle Scholar
Baumgarten, A.S. & Kamrin, K. 2019 A general fluid–sediment mixture model and constitutive theory validated in many flow regimes. J. Fluid Mech. 861, 721–764.CrossRefGoogle Scholar
Bougouin, A. & Lacaze, L. 2018 Granular collapse in a fluid: different flow regimes for an initially dense-packing. Phys. Rev. Fluids 3 (6), 064305.CrossRefGoogle Scholar
Cabrera, M. & Estrada, N. 2019 Granular column collapse: analysis of grain-size effects. Phys. Rev. E 99 (1), 012905.CrossRefGoogle ScholarPubMed
Cassar, C., Nicolas, M. & Pouliquen, O. 2005 Submarine granular flows down inclined planes. Phys. Fluids 17 (10), 103301.CrossRefGoogle Scholar
Charru, F., Bouteloup, J., Bonometti, T. & Lacaze, L. 2016 Sediment transport and bedforms: a numerical study of two-phase viscous shear flow. Meccanica 51 (12), 3055–3065.CrossRefGoogle Scholar
Courrech du Pont, S., Gondret, P., Perrin, B. & Rabaud, M. 2003 Granular avalanches in fluids. Phys. Rev. Lett. 90 (4), 044301.CrossRefGoogle ScholarPubMed
Crosta, G.B., Imposimato, S. & Roddeman, D. 2009 Numerical modeling of 2-D granular step collapse on erodible and nonerodible surface. J. Geophys. Res. 114 (F3).Google Scholar
Da Cruz, F., Emam, S., Prochnow, M., Roux, J.-N. & Chevoir, F. 2005 Rheophysics of dense granular materials: discrete simulation of plane shear flows. Phys. Rev. E 72 (2), 021309.CrossRefGoogle ScholarPubMed
Daerr, A. & Douady, S. 1999 Sensitivity of granular surface flows to preparation. Europhys. Lett. 47 (3), 324.CrossRefGoogle Scholar
Degaetano, M., Lacaze, L. & Phillips, J.C. 2013 The influence of localised size reorganisation on short-duration bidispersed granular flows. Eur. Phys. J. E 36 (4), 36.CrossRefGoogle ScholarPubMed
GDR, MiDi 2004 On dense granular flows. Eur. Phys. J. E 14 (4), 341–365.Google Scholar
Girolami, L., Hergault, V., Vinay, G. & Wachs, A. 2012 A three-dimensional discrete-grain model for the simulation of dam-break rectangular collapses: comparison between numerical results and experiments. Granul. Matt. 14 (3), 381–392.CrossRefGoogle Scholar
Goldhirsch, I. & Goldenberg, C. 2002 On the microscopic foundations of elasticity. Eur. Phys. J. E 9 (3), 245–251.CrossRefGoogle ScholarPubMed
Gondret, P., Lance, M. & Petit, L. 2002 Bouncing motion of spherical particles in fluids. Phys. Fluids 14 (2), 643–652.CrossRefGoogle Scholar
Guazzelli, E. & Pouliquen, O. 2018 Rheology of dense granular suspensions. J. Fluid Mech. 852, P1.CrossRefGoogle Scholar
Ionescu, I.R., Mangeney, A., Bouchut, F. & Roche, O. 2015 Viscoplastic modeling of granular column collapse with pressure-dependent rheology. J. Non-Newtonian Fluid Mech. 219, 1–18.CrossRefGoogle Scholar
Izard, E., Bonometti, T. & Lacaze, L. 2014 Modelling the dynamics of a sphere approaching and bouncing on a wall in a viscous fluid. J. Fluid Mech. 747, 422–446.CrossRefGoogle Scholar
Jackson, R. 2000 The Dynamics of Fluidized Particles. Cambridge University Press.Google Scholar
Jing, L., Yang, G.C., Kwok, C.Y. & Sobral, Y.D. 2018 Dynamics and scaling laws of underwater granular collapse with varying aspect ratios. Phys. Rev. E 98 (4), 042901.CrossRefGoogle Scholar
Jing, L., Yang, G.C., Kwok, C.Y. & Sobral, Y.D. 2019 Flow regimes and dynamic similarity of immersed granular collapse: a CFD-DEM investigation. Powder Technol. 345, 532–543.CrossRefGoogle Scholar
Jop, P., Forterre, Y. & Pouliquen, O. 2006 A constitutive law for dense granular flows. Nature 441 (7094), 727–730.CrossRefGoogle ScholarPubMed
Lacaze, L. & Kerswell, R.R. 2009 Axisymmetric granular collapse: a transient 3D flow test of viscoplasticity. Phys. Rev. Lett. 102 (10), 108305.CrossRefGoogle ScholarPubMed
Lacaze, L., Phillips, J.C. & Kerswell, R.R. 2008 Planar collapse of a granular column: experiments and discrete element simulations. Phys. Fluids 20 (6), 063302.CrossRefGoogle Scholar
Lagrée, P.-Y., Staron, L. & Popinet, S. 2011 The granular column collapse as a continuum: validity of a two-dimensional Navier–Stokes model with a $\mu$ (i)-rheology. J. Fluid Mech. 686, 378–408.CrossRefGoogle Scholar
Lajeunesse, E., Mangeney-Castelnau, A. & Vilotte, J.-P. 2004 Spreading of a granular mass on a horizontal plane. Phys. Fluids 16 (7), 2371–2381.CrossRefGoogle Scholar
Lajeunesse, E., Monnier, J.B. & Homsy, G.M. 2005 Granular slumping on a horizontal surface. Phys. Fluids 17 (10), 103302.CrossRefGoogle Scholar
Lube, G., Huppert, H.E., Sparks, R.S.J. & Freundt, A. 2005 Collapses of two-dimensional granular columns. Phys. Rev. E 72 (4), 041301.CrossRefGoogle ScholarPubMed
Lube, G., Huppert, H.E., Sparks, R.S.J. & Hallworth, M.A. 2004 Axisymmetric collapses of granular columns. J. Fluid Mech. 508, 175–199.CrossRefGoogle Scholar
Mangeney, A., Roche, O., Hungr, O., Mangold, N., Faccanoni, G. & Lucas, A. 2010 Erosion and mobility in granular collapse over sloping beds. J. Geophys. Res. 115, F03040.CrossRefGoogle Scholar
Mangeney-Castelnau, A., Bouchut, F., Vilotte, J.-P., Lajeunesse, E., Aubertin, A. & Pirulli, M. 2005 On the use of saint venant equations to simulate the spreading of a granular mass. J. Geophys. Res. 110, B09103.Google Scholar
Maurin, R., Chauchat, J., Chareyre, B. & Frey, P. 2015 A minimal coupled fluid-discrete element model for bedload transport. Phys. Fluids 27 (11), 113302.CrossRefGoogle Scholar
Pähtz, T. & Durán, O. 2018 Universal friction law at granular solid-gas transition explains scaling of sediment transport load with excess fluid shear stress. Phys. Rev. Fluids 3 (10), 104302.CrossRefGoogle Scholar
Pailha, M. & Pouliquen, O. 2009 A two-phase flow description of the initiation of underwater granular avalanches. J. Fluid Mech. 633, 115–135.CrossRefGoogle Scholar
Phillips, J.C., Hogg, A.J., Kerswell, R.R. & Thomas, N.H. 2006 Enhanced mobility of granular mixtures of fine and coarse particles. Earth Planet. Sci. Lett. 246 (3-4), 466–480.CrossRefGoogle Scholar
Richardson, J.F. & Zaki, W.N. 1954 The sedimentation of a suspension of uniform spheres under conditions of viscous flow. Chem. Engng Sci. 3 (2), 65–73.CrossRefGoogle Scholar
Roche, O., Attali, M., Mangeney, A. & Lucas, A. 2011 On the run-out distance of geophysical gravitational flows: insight from fluidized granular collapse experiments. Earth Planet. Sci. Lett. 311 (3–4), 375–385.CrossRefGoogle Scholar
Rondon, L., Pouliquen, O. & Aussillous, P. 2011 Granular collapse in a fluid: role of the initial volume fraction. Phys. Fluids 23 (7), 073301.CrossRefGoogle Scholar
Roux, S. & Radjai, F. 1998 Texture-dependent rigid-plastic behavior. In Physics of Dry Granular Media (ed. H.J. Herrmann, J.-P. Hovi & S. Luding), pp. 229–236. Springer.CrossRefGoogle Scholar
Staron, L. & Hinch, E.J. 2005 Study of the collapse of granular columns using two-dimensional discrete-grain simulation. J. Fluid Mech. 545, 1–27.CrossRefGoogle Scholar
Staron, L. & Hinch, E.J. 2007 The spreading of a granular mass: role of grain properties and initial conditions. Granul. Matt. 9 (3–4), 205–217.CrossRefGoogle Scholar
Topin, V., Monerie, Y., Perales, F. & Radjai, F. 2012 Collapse dynamics and runout of dense granular materials in a fluid. Phys. Rev. Lett. 109 (18), 188001.CrossRefGoogle Scholar
Trulsson, M., Andreotti, B. & Claudin, P. 2012 Transition from the viscous to inertial regime in dense suspensions. Phys. Rev. Lett. 109 (11), 118305.CrossRefGoogle ScholarPubMed
Weinhart, T., Thornton, A.R., Luding, S. & Bokhove, O. 2012 Closure relations for shallow granular flows from particle simulations. Granul. Matt. 14 (4), 531–552.CrossRefGoogle Scholar
Zenit, R. 2005 Computer simulations of the collapse of a granular column. Phys. Fluids 17 (3), 031703.CrossRefGoogle Scholar
Zhang, D.Z. & Prosperetti, A. 1997 Momentum and energy equations for disperse two-phase flows and their closure for dilute suspensions. Intl J. Multiphase Flow 23 (3), 425–453.CrossRefGoogle Scholar
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