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Steady and unsteady fluidised granular flows down slopes

  • D. E. Jessop (a1) (a2), A. J. Hogg (a3), M. A. Gilbertson (a4) and C. Schoof (a2)

Abstract

Fluidisation is the process by which the weight of a bed of particles is supported by a gas flow passing through it from below. When fluidised materials flow down an incline, the dynamics of the motion differs from their non-fluidised counterparts because the granular agitation is no longer required to support the weight of the flowing layer. Instead, the weight is borne by the imposed gas flow and this leads to a greatly increased flow mobility. In this paper, a framework is developed to model this two-phase motion by incorporating a kinetic theory description for the particulate stresses generated by the flow. In addition to calculating numerical solutions for fully developed flows, it is shown that for sufficiently thick flows there is often a local balance between the production and dissipation of the granular temperature. This phenomenon permits an asymptotic reduction of the full governing equations and the identification of a simple state in which the volume fraction of the flow is uniform. The results of the model are compared with new experimental measurements of the internal velocity profiles of steady granular flows down slopes. The distance covered with time by unsteady granular flows down slopes and along horizontal surfaces and their shapes are also measured and compared with theoretical predictions developed for flows that are thin relative to their streamwise extent. For the horizontal flows, it was found that resistance from the sidewalls was required in addition to basal resistance to capture accurately the unsteady evolution of the front position and the depth of the current and for situations in which sidewall drag dominates, similarity solutions are found for the experimentally measured motion.

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Corresponding author

Email address for correspondence: d.jessop@opgc.fr

References

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Adrian, R. J. 1991 Particle-imaging techniques for experimental fluid-mechanics. Annu. Rev. Fluid Mech. 23, 261304.
Adrian, R. J. & Westerweel, J. 2010 Particle Image Velocimetry. Cambridge University Press.
Agrawal, K., Loezos, P. N., Syamlal, M. & Sundaresan, S. 2001 The role of meso-scale structures in rapid gas-solid flows. J. Fluid Mech. 445, 151185.
Altantzis, C., Bates, R. B. & Ghoniem, A. F. 2015 3D Eulerian modeling of thin rectangular gas-solid fluidized beds: estimation of the specularity coefficient and its effects on bubbling dynamics and circulation times. Powder Technol. 270A, 256270.
Berzi, D. 2014 Extended kinetic theory applied to dense, granular, simple shear flows. Acta Mechanica 225, 21912198.
Bokkers, G. A., van Sint Annaland, M. & Kuipers, J. A. M. 2004 Mixing and segregation in a bidisperse gas-solid fluidised bed: a numerical and experimental study. Powder Technol. 140 (3), 176186.
Botterill, J. S. M. & Abdul-Halim, B. H. 1979 The open-channel flow of fluidized solids. Powder Technol. 23 (1), 6778.
Botterill, J. S. M. & Bessant, D. J. 1973 The flow properties of fluidized solids. Powder Technol. 8 (5–6), 213222.
Botterill, J. S. M. & Bessant, D. J. 1976 The flow properties of fluidized solids. Powder Technol. 14 (1), 131137.
Botterill, J. S. M., van der Kolk, M., Elliott, D. E. & Mcguigan, S. 1972 The flow of fluidised solids. Powder Technol. 6 (6), 343351.
Campbell, C. S. 2006 Granular material flows – an overview. Powder Technol. 162 (3), 208229.
Carnahan, N. & Starling, K. 1969 Equation of state for nonattracting rigid spheres. J. Chem. Phys. 51, 635636.
Davidson, J. F. & Harrison, D. 1963 Fluidised Particles. Cambridge University Press.
Druitt, T. H. 1998 Pyroclastic density currents. In The Physics of Explosive Volcanic Eruptions (ed. Gilbert, J. S. & Sparks, R. S. J.), vol. 145, pp. 145182. The Geological Society.
Eames, I. & Gilbertson, M. A. 2000 Aerated granular flow over a horizontal rigid surface. J. Fluid Mech. 424, 169195.
Epstein, N. & Young, M. J. 1962 Random loose packing of binary mixtures of spheres. Nature 196 (4857), 885886.
Ergun, S. 1952 Fluid flow through packed columns. Chem. Engng Prog. 48 (2), 8994.
Foerster, S. F., Louge, M. Y., Chang, H. & Allia, K. 1994 Measurements of the collision properties of small spheres. Phys. Fluids 6 (3), 11081115.
Formisani, B. 1991 Packing and fluidization properties of binary-mixtures of spherical particles. Powder Technol. 66 (3), 259264.
Forterre, Y. & Pouliquen, O. 2008 Flows of dense granular media. Annu. Rev. Fluid Mech. 40 (1), 124.
Fullmer, W. D. & Hrenya, C. M. 2017 The clustering instability in rapid granular and gas-solid flows. Annu. Rev. Fluid Mech. 49, 485510.
Garzo, V. & Dufty, J. W. 1999 Dense fluid transport for inelastic hard spheres. Phys. Rev. E 59, 58955911.
GDR MiDi 2004 On dense granular flows. Eur. Phys. J. E 14 (4), 341365.
Geldart, D. 1973 Types of gas fluidization. Powder Technol. 7 (5), 285292.
Girolami, L., Roche, O., Druitt, T. H. & Corpetti, T. 2010 Particle velocity fields and depositional processes in laboratory ash flows, with implications for the sedimentation of dense pyroclastic flows. Bull. Volcanol. 72 (6), 747759.
Goldhirsch, I. & Zanetti, G. 1993 Clustering instability in dissipative gases. Phys. Rev. Lett. 70, 16191622.
Goldschmidt, M. J. V., Beetstra, R. & Kuipers, J. A. M. 2004 Hydrodynamic modelling of dense gas-fluidised beds: comparison and validation of 3D discrete particle and continuum models. Powder Technol. 142 (1), 2347.
Haff, P. K. 1983 Grain flow as a fluid-mechanical phenomenon. J. Fluid Mech. 134, 401430.
van der Hoef, M. A., Beetstra, R. & Kuipers, J. A. M. 2005 Lattice-Boltzmann simulations of low-Reynolds-number flow past mono- and bi-disperse arrays of spheres: results for the permeability and drag force. J. Fluid Mech. 528, 233254.
van der Hoef, M. A., van Sint Annaland, M., Deen, N. G. & Kuipers, J. A. M. 2008 Numerical simulation of dense gas-solid fluidized beds: a multiscale modeling strategy. Annu. Rev. Fluid Mech. 40 (1), 4770.
Hogg, A. J. & Woods, A. W. 2001 The transition from inertia to bottom-drag-dominated motion of turbulent gravity currents. J. Fluid Mech. 449, 201224.
Ishida, M., Hatano, H. & Shirai, T. 1980 The flow of solid particles in an aerated inclined channel. Powder Technol. 27 (1), 712.
Jackson, R. 2000 The Dynamics of Fluidised Particles. Cambridge University Press.
Jaeger, H. M. & Nagel, S. R. 1992 Physics of granular states. Science 255 (5051), 15231531.
Jenkins, J. T. 2007 Dense inclined flows of inelastic spheres. Granul. Matt. 10, 4752.
Jenkins, J. T. & Berzi, D. 2010 Dense inclined flows of inelastic spheres: tests of an extension of kinetic theory. Granul. Matt. 12, 151158.
Jenkins, J. T. & Berzi, D. 2012 Kinetic theory applied to inclinded flows. Granul. Matt. 14, 7984.
Jenkins, J. T. & Savage, S. B. 1983 A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles. J. Fluid Mech. 130, 187202.
Jenkins, J. T. & Zhang, C. 2002 Kinetic theory for identical, frictional, nearly elastic spheres. Phys. Fluids 14 (3), 12281235.
Johnson, P. C. & Jackson, R. 1987 Frictional-collisional constitutive relations for granular materials, with application to plane shearing. J. Fluid Mech. 176, 6793.
Johnson, P. C., Nott, P. & Jackson, R. 1990 Frictional-collisional equations of motion for particulate flows and their application to chutes. J. Fluid Mech. 210, 501535.
Kharaz, A. H., Gorham, D. A. & Salman, A. D. 2001 An experimental study of the elastic rebound of spheres. Powder Technol. 120 (3), 281291.
Koch, D. L. & Sangani, A. S. 1999 Particle pressure and marginal stability limits for a homogeneous monodisperse gas-fluidized bed: kinetic theory and numerical simulations. J. Fluid Mech. 400, 229263.
Kumaran, V. 2014 Dense shallow granular flows. J. Fluid Mech. 756, 555599.
Li, T., Grace, J. & Bi, X. 2010 Study of wall boundary condition in numerical simulations of bubbling fluidized beds. Powder Technol. 203 (3), 447457.
Lun, C. K. K., Savage, S. B., Jeffrey, D. J. & Chepurniy, N. 1984 Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flowfield. J. Fluid Mech. 140, 223256.
Meinhart, C. D., Wereley, S. T. & Santiago, J. G. 2000 A PIV algorithm for estimating time-averaged velocity fields. Trans. ASME J. Fluids Engng 122 (2), 285289.
Menon, N. & Durian, D. 1997 Particle motions in a gas-fluidized bed of sand. Phys. Rev. Lett. 79 (18), 34073410.
Meunier, P. & Leweke, T. 2003 Analysis and treatment of errors due to high velocity gradients in particle image velocimetry. Exp. Fluids 35 (5), 408421.
Nedderman, R. M. 1992 Statics and Kinematics of Granular Materials. Cambridge University Press.
Nott, P. & Jackson, R. 1992 Frictional-collisional equations of motion for granular materials and their application to flow in aerated chutes. J. Fluid Mech. 241, 125144.
Ogawa, S., Umemura, A. & Oshima, N. 1980 On the equations of fully-fluidized granular materials. Z. Angew. Math. Phys. 31 (4), 483493.
Oger, L. & Savage, S. B. 2013 Airslide flows. Part 2 – flow modeling and comparison with experiments. Chem. Engng Sci. 91, 2234.
Roche, O., Gilbertson, M. A., Phillips, J. C. & Sparks, R. S. J. 2004 Experimental study of gas-fluidized granular flows with implications for pyroclastic flow emplacement. J. Geophys. Res. 109 (B10), B10201.
Rowe, P. N. & Masson, H. 1981 Interaction of bubbles with probes in gas-fluidized beds. T. I. Chem. Eng.-Lond. 59 (3), 177185.
Savage, S. B. 1992 Instabilities of unbounded uniform granular shear flow. J. Fluid Mech. 241, 109123.
Savage, S. B. & Oger, L. 2013 Airslide flows, Part 1 – experiments, review and extension. Chem. Engng Sci. 91, 3543.
Scmid, P. J. & Kytomaa, H. K. 1994 Transient and asymptotic stability of granular shear flow. J. Fluid Mech. 264, 255275.
Singh, B., Callcott, T. G. & Rigby, G. R. 1978 Flow of fluidized solids and other fluids in open channels. Powder Technol. 20 (1), 99113.
Toomey, R. D. & Johnstone, H. F. 1952 Gaseous fluidization of solid particles. Chem. Engng Prog. 48 (5), 220226.
Torquato, S. 1995 Nearest-neighbour statistics for packing of hard spheres and disks. Phys. Rev. E 51, 31703182.
Tsimring, L. S., Ramaswamy, R. & Sherman, P. 1999 Dynamics of a shallow fluidized bed. Phys. Rev. E 60 (6), 71267130.
Vescovi, D., Berzi, D., Richard, P. & Brodu, N. 2014 Plane shear flows of frictionless spheres: kinetic theory and 3D soft-sphere discrete element method simulations. Phys. Fluids 26, 053305.
Woodhouse, M. J., Hogg, A. J. & Sellar, A. A. 2010 Rapid granular flows down inclined planar chutes. Part 1. steady flows, multiple solutions and existence domains. J. Fluid Mech. 652, 427460.
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