Skip to main content

On the role of the ambient fluid on gravitational granular flow dynamics

  • C. MERUANE (a1) (a2), A. TAMBURRINO (a1) and O. ROCHE (a2)

The effects of the ambient fluid on granular flow dynamics are poorly understood and commonly ignored in analyses. In this article, we characterize and quantify these effects by combining theoretical and experimental analyses. Starting with the mixture theory, we derive a set of two-phase continuum equations for studying a compressible granular flow composed of homogenous solid particles and a Newtonian ambient fluid. The role of the ambient fluid is then investigated by studying the collapse and spreading of two-dimensional granular columns in air or water, for different solid particle sizes and column aspect (height to length) ratios, in which the front speed is used to describe the flow. The combined analysis of experimental measurements and numerical solutions shows that the dynamics of the solid phase cannot be explained if the hydrodynamic fluid pressure and the drag interactions are not included in the analysis. For instance, hydrodynamic fluid pressure can hold the reduced weight of the solids, thus inducing a transition from dense-compacted to dense-suspended granular flows, whereas drag forces counteract the solids movement, especially within the near-wall viscous layer. We conclude that in order to obtain a realistic representation of gravitational granular flow dynamics, the ambient fluid cannot be neglected.

Corresponding author
Email address for correspondence:
Hide All
Ancey, C. 2007 Plasticity and geophysical flows: a review. J. Non-Newtonian Fluid Mech. 142, 435.
Anderson, T. B. & Jackson, R. 1967 A fluid mechanical description of fluidized beds: equations of motion. Ind. Engng Chem. Fundam. 6, 527539.
Bagnold, R. A. 1954 Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear. Proc. R. Soc. Lond. Ser. A 225, 4963.
Balmforth, N. J. & Kerswell, R. R. 2005 Granular collapse in two dimensions. J. Fluid Mech. 538, 399428.
Bedford, A. 1983 Recent advances: theories of immiscible and structured mixtures. Intl J. Engng Sci. 21, 863960.
Boussinesq, J. 1877 Théorie de l'écoulement tourbillant. Mem. Présentés par Divers Savants Acad. Sci. Inst. Fr. 23, 4650.
Campbell, C. 1990 Rapid granular flows. Annu. Rev. Fluid Mech. 22, 5792.
Campbell, C. 2006 Granular material flows: an overview. Powder Technol. 162, 208229.
Cassar, C., Nicolas, M. & Pouliquen, O. 2005 Submarine granular flows down inclined planes. Phys. Fluids 17, 103301.
Crowe, C. T. 2000 On models for turbulence modulation in fluid-particle flows. Intl J. Multiphase Flow 26, 719727.
Crowe, C. T., Troutt, R. & Chung, J. N. 1996 Numerical models for two-phase turbulent flows. Annu. Rev. Fluid. Mech. 28, 1143.
Dallavalle, J. M. 1948 Micromeritics: The Technology of Fine Particles, 2nd ed. Pitman.
Di Felice, R. 1994 The voidage function for fluid–particle interaction systems. Intl J. Multiphase Flow 20, 153159.
Di Felice, R. 1995 Hydrodynamics of liquid fluidisation. Chem. Engng Sci. 50, 12131245.
Drew, D. A. 1983 Mathematical modelling of two-phase flow. Annu. Rev. Fluid Mech. 15, 261291.
Elghobashi, S. & Truesdell, G. C. 1993 On the two-way interaction between homogeneous turbulence and dispersed solid particles. II. Turbulence modification. Phys. Fluids 5, 17901801.
Forterre, Y. & Pouliquen, O. 2008 Flows of dense granular media. Annu. Rev. Fluid Mech. 40, 124.
Goldhirsch, I. 2003 Rapid granular flows. Annu. Rev. Fluid Mech. 35, 267293.
Goodman, M. & Cowin, S. 1971 Two problems in the gravity flow of granular materials. J. Fluid Mech. 45, 321339.
Hutter, K., Wang, Y. & Pudasaini, S. 2005 The Savage–Hutter avalanche model: how far can it be pushed? Phil. Trans. R. Soc. A 363, 1507 – 1528.
Iverson, R. 1997 The physics of debris flows. Rev. Geophys. 35, 245296.
Iverson, R. & Denlinger, R. 2001 Flow of variably fluidized granular masses across three-dimensional terrain. 1. Coulomb mixture theory. J. Geophys. Res. 106, 537552.
Jackson, R. 2000 The Dynamics of Fluidized Particles. Cambridge University Press.
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.
Johnson, P. C. & Jackson, R. 1987 Frictional–collisional constitutive relations for granular materials, with application to plane shearing. J. Fluid Mech. 176, 6793.
Joseph, D. & Lundgren, T. 1990 Ensemble averaged and mixture theory equations for incompressible fluid–particle suspensions. Intl J. Multiphase Flow 16, 3542.
Kármán, T. von 1940 The engineer grapples with nonlinear problems. Bull. Am. Math. Soc. 46, 615683.
Lajeunesse, E., Monnier, J. & Homsy, G. 2005 Granular slumping on a horizontal surface. Phys. Fluids 17, 103302.
Larrieu, E., Staron, L. & Hinch, E. 2006 Raining into shallow water as a description of the collapse of a column of grains. J. Fluid Mech. 554, 259270.
Lube, G., Huppert, H., Sparks, R. & Freundt, A. 2005 Collapses of two-dimensional granular columns. Phys. Rev. E 72, 041301.
Lun, C. K. K., Savage, B. & Jeffrey, D. J. 1984 Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flow field. J. Fluid Mech. 140, 223256.
MiDi, GDR 2004 On dense granular flows. Eur. Phys. J. E 14, 341365.
Morland, L. W. 1992 Flow of viscous fluids through a porous deformable matrix. Surv. Geophys. 13, 209268.
Morland, L. & Sellers, S. 2001 Multiphase mixtures and singular surfaces. Intl J. Non-Linear Mech. 36, 131146.
Passman, S. L., Nunziato, J. W. & Walsh, E. K. 1984 A Theory of Multiphase Mixtures. Appendix 5C, Rational thermodynamics (ed. Truesdell, C.), pp. 286325. Springer.
Patankar, S.V. 1980 Numerical Heat Transfer and Fluid Flow. Hemisphere.
Pitman, B. & Le, L. 2005 A two-fluid model for avalanche and debris flows. Phil. Trans. R. Soc. A 363, 15731601.
Pope, S. 2000 Turbulent Flows. Cambridge University Press.
Reynolds, O. 1895 On the dynamical theory of turbulent incompressible viscous fluids and the determination of the criterion. Phil. Trans. R. Soc. A 186, 121161.
Rodi, W. 1983 Turbulence Models and Their Application in Hydraulics: A State-Of-The-Art Review. IAHR.
Savage, S. B. 1983 Mechanical of granular materials: new models and constitutive relations. In Granular Flows Down Rough Inclines: Review and Extension (ed. Jenkins, J. T. and Satake, M.), pp. 261282. Elsevier.
Staron, L. & Hinch, E. J. 2005 Study of the collapse of granular columns using two-dimensional discrete-grain simulation. J. Fluid Mech. 545, 127.
Stewart, H. B. & Wendroff, B. 1984 Two-phase flow: models and methods. J. Comput. Phys. 56, 363409.
Sundaresan, S. 2003 Instabilities in fluidized beds. Annu. Rev. Fluid Mech. 35, 6388.
Truesdell, C. 1957 Sulle basi della thermomecanica. Rand Lincei, Ser. 8, 3338.
Truesdell, C. 1984 Rational Thermodynamics. Springer.
Wang, Y. & Hutter, K. 2001 Geomorphological fluid mechanics. In Granular Material Theories Revisited (ed. Balmforth, N. J. and Provenzale, A.), pp. 79107. Springer.
Ystrom, J. 2001 On two-fluid equations for dispersed incompressible two-phase flow. Comput. Visual. Sci. 4, 125135.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed