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A theoretical analysis of free-surface flows of saturated granular–liquid mixtures

Published online by Cambridge University Press:  11 July 2008

D. BERZI  and
J. T. JENKINS
D. BERZI
Affiliation:
Department of Environmental, Hydraulic, Infrastructures and Surveying Engineering, Politecnico di Milano, Milan 20133, Italy
J. T. JENKINS
Affiliation:
Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 14853, USA
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Abstract

A simple two-phase model for steady fully developed flows of particles and water over erodible inclined beds is developed for situations in which the water and particles have the same depth. The rheology of the particles is based on recent numerical simulations and physical experiments, the rheology of the fluid is based on an eddy viscosity, and the interaction between the particles and the fluid is through drag and buoyancy. Numerical solutions of the resulting differential equations and boundary conditions provide velocity profiles of the fluid and particles, the concentration profile of the particles, and the depth of the flow at a given angle of inclination of the bed. Simple approximations permit analytical expressions for the flow velocities and the depth of flow to be obtained that agree with the numerical solutions and those measured in experiments.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 608 , 10 August 2008 , pp. 393 - 410
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Aranson, I. S. & Tsimring, L. S. 2002 Continuum description of partially fluidized granular flows. Phys. Rev. E 65, 061303.Google Scholar
Armanini, A., Capart, H., Fraccarollo, L. & Larcher, M. 2005 Rheological stratification in experimental free–surface flows of granular–liquid mixtures. J. Fluid Mech. 532, 269–319.CrossRefGoogle Scholar
Bagnold, R. A. 1954 Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear. Proc. R. Soc. Lond. A 225, 49–63.Google Scholar
Bingham, E. C. 1922 Fluidity and Plasticity. McGraw-Hill.Google Scholar
Brufau, P., Garcia-Navarro, P., Ghilardi, P., Natale, L. & Savi, F. 2000 1-d mathematical modelling of debris flow. J. Hydraul. Res. 38 (6), 435–446.CrossRefGoogle Scholar
Cassar, C., Nicolas, M. & Pouliquen, O. 2005 Submarine granular flows down inclined planes. Phys. Fluids 17, 103301.Google Scholar
Chen, C. L. & Ling, C. H. 1998 Rheological equations in asymptotic regimes of granular flow. J. Engng Mech. 124 (3), 301–310.Google Scholar
Courrech du Pont, S., Gondret, P., Perrin, B. & Rabaud, M. 2003 Granular avalanches in fluids. Phys. Rev. Lett. 90, 044301.CrossRefGoogle ScholarPubMed
Coussot, P. 1994 Steady, laminar flow of concentrated mud suspensions in open channel. J. Hydraul. Res. 32 (4), 535–559.Google Scholar
da Cruz, F., Sacha, E., Prochnow, M., Roux, J. & Chevoir, F. 2005 Rheophysics of dense granular materials: discrete simulation of plane shear flows. Phys. Rev. E 72, 021309.Google ScholarPubMed
Dallavalle, J. 1943 Micromeritics. Pitman.CrossRefGoogle Scholar
GDR MiDi 2004 On dense granular flows. Eur. Phys. J. E 14, 341–365.Google Scholar
Iverson, R. M. 1997 The physics of debris flows. Rev. Geophys. 35 (3), 245–296.CrossRefGoogle Scholar
Jenkins, J. T. 2006 Dense shearing flows of inelastic disks. Phys. Fluids 18, 103307.CrossRefGoogle Scholar
Jenkins, J. T. 2007 Dense inclined flows of inelastic spheres. Gran. Matter 10, 47–52.CrossRefGoogle Scholar
Jenkins, J. T. & Hanes, D. M. 1998 Collisional sheet flows of sediment driven by a turbulent fluid. J. Fluid Mech. 370, 29–52.CrossRefGoogle Scholar
Jop, P., Forterre, Y. & Pouliquen, O. 2005 Crucial role of sidewalls in granular surface flows: consequences for the rheology. J. Fluid Mech. 541, 167–192.CrossRefGoogle Scholar
Komatsu, T. S., Inagaki, S., Nakagawa, N. & Nasuno, S. 2001 Creep motion in a granular pile exhibiting steady surface flow. Phys. Rev. Lett. 86, 1757–1760.Google Scholar
Kumaran, V. 2006 The constitutive relation for the granular flow of rough particles and its application to the flow down an incline plane. J Fluid Mech. 561, 1–42.Google Scholar
Larcher, M., Fraccarollo, L., Armanini, A. & Capart, H. 2007 Set of measurement data from flume experiments on steady, uniform debris flows. J. Hydraul. Res. 45 (extra).CrossRefGoogle Scholar
Louge, M. Y. 2003 Model for dense granular flows down bumpy inclines. Phys. Rev. E 67, 061303.Google Scholar
de Marsily, G. 1981 Quantitative Hydrogeology: Groundwater Hydrology for Engineers. Academic.Google Scholar
Mills, P., Tixier, M. & Loggia, D. 1999 Model for stationary dense granular flow along an inclined wall. Europhys. Lett. 45 (6), 733–738.Google Scholar
Mills, P., Tixier, M. & Loggia, D. 2000 Influence of roughness and dilatancy for dense granular flow along an inclined wall. Eur. Phys. J. E 1, 5–8.Google Scholar
Mitarai, N. & Nakanishi, H. 2005 Bagnold scaling, density plateau, and kinetic theory analysis of dense granular flow. Phys. Rev. Lett. 94, 128001.CrossRefGoogle ScholarPubMed
Mitarai, N. & Nakanishi, H. 2007 Velocity correlations in dense granular shear flows: effects on energy dissipation and normal stress. Phys. Rev. E 75, 031305.Google Scholar
Pouliquen, O. 1999 Scaling laws in granular flows down rough inclined planes. Phys. Fluids 11 (3), 542–548.Google Scholar
Richardson, J. F. & Zaki, W. N. 1954 Sedimentation and fluidization. Trans. Inst. Chem. Engrs 32, 35–53.Google Scholar
Savage, S. B. & Hutter, K. 1989 The motion of a finite mass of granular material down a rough incline. J. Fluid Mech. 199, 177–215.Google Scholar
Silbert, L. E., Ertas, D., Grest, G. S., Halsey, T. C., Levine, D. & Plimpton, S. J. 2001 Granular flow down an inclined plane: Bagnold scaling and rheology. Phys. Rev. E 64, 51302.Google ScholarPubMed
Spinewine, B., Capart, H., Larcher, M. & Zech, Y. 2003 Three-dimensional Voronoï imaging methods for the measurement of near-wall particulate flows. Exps. Fluids 34, 227–241.Google Scholar
Taberlet, N., Richard, P., Valance, A., Losert, W., Pasini, J. M., Jenkins, J. T. & Delannay, R. 2003 Superstable granular heap in a thin channel. Phys. Rev. Lett. 91, 264301.Google Scholar
Takahashi, T. 1991 Debris Flow. IAHR Monograph Series. Balkema.Google Scholar