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Supercritical shallow granular flow through a contraction: experiment, theory and simulation

Published online by Cambridge University Press:  26 April 2007

A. W. VREMAN ,
M. AL-TARAZI ,
J. A. M. KUIPERS ,
M. VAN SINT ANNALAND  and
O. BOKHOVE
A. W. VREMAN
Affiliation:
Department of Chemical Engineering, University of Twente, 7500 AE Enschede, The Netherlands Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands Vreman Research, Hengelo, The Netherlands
M. AL-TARAZI
Affiliation:
Department of Chemical Engineering, University of Twente, 7500 AE Enschede, The Netherlands
J. A. M. KUIPERS
Affiliation:
Department of Chemical Engineering, University of Twente, 7500 AE Enschede, The Netherlands
M. VAN SINT ANNALAND
Affiliation:
Department of Chemical Engineering, University of Twente, 7500 AE Enschede, The Netherlands
O. BOKHOVE*
Affiliation:
Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
*
†Author to whom correspondence should be addressed: [email protected]
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Abstract

Supercritical granular flow through a linear contraction on a smooth inclined plane is investigated by means of experiments, theoretical analysis and numerical simulations. The experiments have been performed with three size classes of spherical glass beads, and poppy seeds (non-spherical). Flow states and flow regimes are categorized in the phase space spanned by the supercritical Froude number and the minimum width of the contraction. A theoretical explanation is given for the formation of steady reservoirs in the contraction observed in experiments using glass beads and water. For this purpose, the classical, one-dimensional shallow-water theory is extended to include frictional and porosity effects. The occurrence of the experimentally observed flow states and regimes can be understood by introducing integrals of acceleration. The flow state with a steady reservoir arises because friction forces in the reservoir are much smaller than in other parts of the flow. Three-dimensional discrete-particle simulations quantitatively agree with the measured granular flow data, and the crucial part of the theoretical frictional analysis is clearly confirmed. The simulations of the flow further reveal that porosity and frictional effects interact in a complicated way. Finally, the numerical database is employed to investigate the rheology in a priori tests for several constitutive models of frictional effects.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 578 , 10 May 2007 , pp. 233 - 269
Copyright
Copyright © Cambridge University Press 2007

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References

REFRENCES

Akers, B. 2005 Shallow water flow through a contraction. Report Geophysical Fluid Dynamics Fellowship Program, Woods Hole Oceanographic Institution. http://gfd.whoi.edu/proceedings.htmlGoogle Scholar
Akers, B. & Bokhove, O. 2006 Hydraulic flow through a contraction: multiple steady states. In preparation.Google Scholar
Al-Tarazi, M., Bokhove, O., Kuipers, J. A. M., vanSint Annaland, M. Sint Annaland, M. & Vreman, A. W. 2006 Reservoir formation in shallow granular flows through a contraction. Mathematical Communications, Department of Applied Mathematics. ISSN 0169-2690, http://eprints.eemcs.utwente.nlGoogle Scholar
Augenstein, D. A. & Hogg, R. 1978 An experimental sTUdy of the flow of dry powders over inclined surfaces. Powder Technol. 19, 205–215.Google 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
Baines, P. G. & Whitehead, J. A. 2003 On multiple states in single-layer flows. Phys. Fluids 15, 398–407.Google Scholar
Brennen, C. E., Sieck, K. & Palaski, J. 1983 Hydraulic jumps in granular material flow. Powder Technol. 35, 31–37.Google Scholar
Campbell, C. S. & Brennen, C. E. 1985 Computer simulations of granular shear flows. J. Fluid Mech. 151, 167–188.Google Scholar
Campbell, C. S., Brennen, C. E. & Sabersky, R. H. 1985 Flow regimes in inclined open-channel flows of granular materials. Powder Technol. 41, 77–82.Google Scholar
Cundall, P. A. & Strack, O. D. L. 1979 A discrete numerical model for granular assemblies. Geótechnique 29, 47.Google Scholar
GDR MiDi 2004 On dense granular flows. Eur. Phys. J. E 14, 341–365.Google Scholar
Goldhirsch, I. 2003 Rapid granular flows. Annu. Rev. Fluid Mech. 35, 267–293.Google Scholar
Goldschmidt, M. J. V., Beetstra, R. & Kuipers, J. A. M. 2004 Hydrodynamic modelling of dense gas-fluidised beds: comparison and validation of three-dimensional discrete particle and continuum models. Powder Technol. 142, 23–47.Google Scholar
Gray, J. M. N. T., Tai, Y.-C. & Noelle, S. 2003 Shock waves, dead zones and particle-free regions in rapid granular free-surface flows. jfm 491, 161–181.Google Scholar
Haff, P. K. 1983 Granular flow as a fluid mechanical phenomenon. jfm 134, 401–430.Google Scholar
Hakonardottir, K. M. & Hogg, A. J. 2005 Oblique shocks in rapid granular flows. Phys. Fluids 17, 077101.Google Scholar
vander Hoef, M. A. der Hoef, M. A., Ye, M., vanSint Annaland, M. Sint Annaland, M., AndrewsIV, A. T. IV, A. T., Sundaresan, S. & Kuipers, J. A. M. 2006 Multi-scale modelling of gas-fluidized beds. Adv. Chem. Engng 31, 65.Google Scholar
Hui, K., Haff, P. K., Ungar, J. R. & Jackson, R. C. 1984 Boundary conditions for high-shear grain flows. J. Fluid Mech. 145, 223–233.Google Scholar
Jackson, R. 1986 Some features of the flow of granular materials and aerated granular materials. J. Rheology 30, 907–930.Google Scholar
Johnson, P. C., Nott, P. & Jackson, R. C. 1990 Frictional-collisional equations of motion for particulate flows and their application to chutes. J. Fluid Mech. 210, 501–535.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 flow field. jfm 140, 223–256.Google Scholar
Louge, M. Y. & Keast, S. C. 2001 On dense granular flows down flat frictional inclines. Phys. Fluids 13, 1213–1233.Google Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.Google Scholar
Pouliquen, O. 1999 Scaling laws in granular flows down a rough inclined plane'. Physics of fluids 11, 542–548.Google Scholar
Pouliquen, O. & Forterre, Y. 2002 Friction law for dense granular flows: application to the motion of a mass down a rough inclined plane. jfm 453, 133–151.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
Savage, S. B. & Hutter, K. 1991 The dynamics of avalanches of granular materials from initiation to run-out. Part I: Analysis. Acta Mechanica 86, 201–223.Google Scholar
Schmincke, H. -U. 2000 Vulkanismus. Wissenschaftliche Buchgesellschaft Darmstadt.Google Scholar
Silbert, L. E., Landry, J. W. & Crest, G. S. 2003 Granular flow down a rough inclined plane: transition between thin and thick piles. Phys. Fluids 15, 1–10.Google Scholar
Shapiro, A. H. 1953 The Dynamics and Thermodynamics of Compressible Fluid Flow.Google Scholar