Hostname: page-component-76fb5796d-x4r87 Total loading time: 0 Render date: 2024-04-27T01:01:43.736Z Has data issue: false hasContentIssue false
  • English
  • Français

Steady and unsteady fluidised granular flows down slopes

Published online by Cambridge University Press:  18 August 2017

D. E. Jessop Open the ORCID record for D. E. Jessop [Opens in a new window] ,
A. J. Hogg ,
M. A. Gilbertson  and
C. Schoof
D. E. Jessop*
Affiliation:
Laboratoire Magmas et Volcans, Université Clermont-Auvergne-CNRS-IRD, OPGC, 63178, Clermont-Ferrand, France Department of Earth, Ocean and Atmospheric Sciences, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
A. J. Hogg
Affiliation:
School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK
M. A. Gilbertson
Affiliation:
Department of Mechanical Engineering, University of Bristol, University Walk, Bristol BS8 1TR, UK
C. Schoof
Affiliation:
Department of Earth, Ocean and Atmospheric Sciences, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
*
†Email address for correspondence: d.jessop@opgc.fr
Get access Rights & Permissions [Opens in a new window]

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.

JFM classification

Multiphase and Particle-laden Flows: Fluidized beds Multiphase and Particle-laden Flows: Particle/fluid flow Multiphase and Particle-laden Flows: Multiphase flow
Type
Papers
Information
Journal of Fluid Mechanics , Volume 827 , 25 September 2017 , pp. 67 - 120
Check for updates
Copyright
© 2017 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adrian, R. J. 1991 Particle-imaging techniques for experimental fluid-mechanics. Annu. Rev. Fluid Mech. 23, 261–304.Google Scholar
Adrian, R. J. & Westerweel, J. 2010 Particle Image Velocimetry. Cambridge University Press.Google Scholar
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, 151–185.Google Scholar
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, 256–270.CrossRefGoogle Scholar
Berzi, D. 2014 Extended kinetic theory applied to dense, granular, simple shear flows. Acta Mechanica 225, 2191–2198.Google Scholar
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), 176–186.CrossRefGoogle Scholar
Botterill, J. S. M. & Abdul-Halim, B. H. 1979 The open-channel flow of fluidized solids. Powder Technol. 23 (1), 67–78.CrossRefGoogle Scholar
Botterill, J. S. M. & Bessant, D. J. 1973 The flow properties of fluidized solids. Powder Technol. 8 (5–6), 213–222.Google Scholar
Botterill, J. S. M. & Bessant, D. J. 1976 The flow properties of fluidized solids. Powder Technol. 14 (1), 131–137.Google Scholar
Botterill, J. S. M., van der Kolk, M., Elliott, D. E. & Mcguigan, S. 1972 The flow of fluidised solids. Powder Technol. 6 (6), 343–351.CrossRefGoogle Scholar
Campbell, C. S. 2006 Granular material flows – an overview. Powder Technol. 162 (3), 208–229.Google Scholar
Carnahan, N. & Starling, K. 1969 Equation of state for nonattracting rigid spheres. J. Chem. Phys. 51, 635–636.Google Scholar
Davidson, J. F. & Harrison, D. 1963 Fluidised Particles. Cambridge University Press.Google Scholar
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. 145–182. The Geological Society.Google Scholar
Eames, I. & Gilbertson, M. A. 2000 Aerated granular flow over a horizontal rigid surface. J. Fluid Mech. 424, 169–195.CrossRefGoogle Scholar
Epstein, N. & Young, M. J. 1962 Random loose packing of binary mixtures of spheres. Nature 196 (4857), 885–886.CrossRefGoogle Scholar
Ergun, S. 1952 Fluid flow through packed columns. Chem. Engng Prog. 48 (2), 89–94.Google Scholar
Foerster, S. F., Louge, M. Y., Chang, H. & Allia, K. 1994 Measurements of the collision properties of small spheres. Phys. Fluids 6 (3), 1108–1115.CrossRefGoogle Scholar
Formisani, B. 1991 Packing and fluidization properties of binary-mixtures of spherical particles. Powder Technol. 66 (3), 259–264.Google Scholar
Forterre, Y. & Pouliquen, O. 2008 Flows of dense granular media. Annu. Rev. Fluid Mech. 40 (1), 1–24.Google Scholar
Fullmer, W. D. & Hrenya, C. M. 2017 The clustering instability in rapid granular and gas-solid flows. Annu. Rev. Fluid Mech. 49, 485–510.CrossRefGoogle Scholar
Garzo, V. & Dufty, J. W. 1999 Dense fluid transport for inelastic hard spheres. Phys. Rev. E 59, 5895–5911.Google Scholar
GDR MiDi 2004 On dense granular flows. Eur. Phys. J. E 14 (4), 341–365.Google Scholar
Geldart, D. 1973 Types of gas fluidization. Powder Technol. 7 (5), 285–292.CrossRefGoogle Scholar
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), 747–759.Google Scholar
Goldhirsch, I. & Zanetti, G. 1993 Clustering instability in dissipative gases. Phys. Rev. Lett. 70, 1619–1622.Google Scholar
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), 23–47.CrossRefGoogle Scholar
Haff, P. K. 1983 Grain flow as a fluid-mechanical phenomenon. J. Fluid Mech. 134, 401–430.Google Scholar
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, 233–254.Google Scholar
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), 47–70.Google Scholar
Hogg, A. J. & Woods, A. W. 2001 The transition from inertia to bottom-drag-dominated motion of turbulent gravity currents. J. Fluid Mech. 449, 201–224.Google Scholar
Ishida, M., Hatano, H. & Shirai, T. 1980 The flow of solid particles in an aerated inclined channel. Powder Technol. 27 (1), 7–12.CrossRefGoogle Scholar
Jackson, R. 2000 The Dynamics of Fluidised Particles. Cambridge University Press.Google Scholar
Jaeger, H. M. & Nagel, S. R. 1992 Physics of granular states. Science 255 (5051), 1523–1531.Google Scholar
Jenkins, J. T. 2007 Dense inclined flows of inelastic spheres. Granul. Matt. 10, 47–52.Google Scholar
Jenkins, J. T. & Berzi, D. 2010 Dense inclined flows of inelastic spheres: tests of an extension of kinetic theory. Granul. Matt. 12, 151–158.Google Scholar
Jenkins, J. T. & Berzi, D. 2012 Kinetic theory applied to inclinded flows. Granul. Matt. 14, 79–84.Google Scholar
Jenkins, J. T. & Savage, S. B. 1983 A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles. J. Fluid Mech. 130, 187–202.CrossRefGoogle Scholar
Jenkins, J. T. & Zhang, C. 2002 Kinetic theory for identical, frictional, nearly elastic spheres. Phys. Fluids 14 (3), 1228–1235.Google Scholar
Johnson, P. C. & Jackson, R. 1987 Frictional-collisional constitutive relations for granular materials, with application to plane shearing. J. Fluid Mech. 176, 67–93.Google Scholar
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, 501–535.Google Scholar
Kharaz, A. H., Gorham, D. A. & Salman, A. D. 2001 An experimental study of the elastic rebound of spheres. Powder Technol. 120 (3), 281–291.Google Scholar
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, 229–263.Google Scholar
Kumaran, V. 2014 Dense shallow granular flows. J. Fluid Mech. 756, 555–599.CrossRefGoogle Scholar
Li, T., Grace, J. & Bi, X. 2010 Study of wall boundary condition in numerical simulations of bubbling fluidized beds. Powder Technol. 203 (3), 447–457.Google Scholar
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, 223–256.CrossRefGoogle Scholar
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), 285–289.CrossRefGoogle Scholar
Menon, N. & Durian, D. 1997 Particle motions in a gas-fluidized bed of sand. Phys. Rev. Lett. 79 (18), 3407–3410.Google Scholar
Meunier, P. & Leweke, T. 2003 Analysis and treatment of errors due to high velocity gradients in particle image velocimetry. Exp. Fluids 35 (5), 408–421.Google Scholar
Nedderman, R. M. 1992 Statics and Kinematics of Granular Materials. Cambridge University Press.Google Scholar
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, 125–144.Google Scholar
Ogawa, S., Umemura, A. & Oshima, N. 1980 On the equations of fully-fluidized granular materials. Z. Angew. Math. Phys. 31 (4), 483–493.Google Scholar
Oger, L. & Savage, S. B. 2013 Airslide flows. Part 2 – flow modeling and comparison with experiments. Chem. Engng Sci. 91, 22–34.CrossRefGoogle Scholar
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.Google Scholar
Rowe, P. N. & Masson, H. 1981 Interaction of bubbles with probes in gas-fluidized beds. T. I. Chem. Eng.-Lond. 59 (3), 177–185.Google Scholar
Savage, S. B. 1992 Instabilities of unbounded uniform granular shear flow. J. Fluid Mech. 241, 109–123.Google Scholar
Savage, S. B. & Oger, L. 2013 Airslide flows, Part 1 – experiments, review and extension. Chem. Engng Sci. 91, 35–43.Google Scholar
Scmid, P. J. & Kytomaa, H. K. 1994 Transient and asymptotic stability of granular shear flow. J. Fluid Mech. 264, 255–275.Google Scholar
Singh, B., Callcott, T. G. & Rigby, G. R. 1978 Flow of fluidized solids and other fluids in open channels. Powder Technol. 20 (1), 99–113.Google Scholar
Toomey, R. D. & Johnstone, H. F. 1952 Gaseous fluidization of solid particles. Chem. Engng Prog. 48 (5), 220–226.Google Scholar
Torquato, S. 1995 Nearest-neighbour statistics for packing of hard spheres and disks. Phys. Rev. E 51, 3170–3182.Google Scholar
Tsimring, L. S., Ramaswamy, R. & Sherman, P. 1999 Dynamics of a shallow fluidized bed. Phys. Rev. E 60 (6), 7126–7130.Google Scholar
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.Google Scholar
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, 427–460.CrossRefGoogle Scholar