- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Dynamics of dense granular flows of small-and-large-grain mixtures in an ambient fluid

C. Meruane* and A. Tamburrino

O. Roche

  • Departamento de Ingeniería Civil, Universidad de Chile Blanco Encalada 2002, Casilla 228-3, Santiago, Chile

  • Clermont Université, Université Blaise Pascal, Laboratoire Magmas et Volcans, BP 10448, F-63000 Clermont-Ferrand, France; CNRS, UMR 6524; LMV, F-63038 Clermont-Ferrand, France; IRD, R 163, LMV, F-63038 Clermont-Ferrand, France

  • *cmeruane@ing.uchile.cl; Also at Laboratoire Magmas et Volcans, UMR Unversité Blaise Pascal, 5 rue Kessler, 63038 Clermont-Ferrand, France.
PDF

Phys. Rev. E 86, 026311 – Published 20 August, 2012

DOI: https://doi.org/10.1103/PhysRevE.86.026311

Abstract

Dense grain flows in nature consist of a mixture of solid constituents that are immersed in an ambient fluid. In order to obtain a good representation of these flows, the interaction mechanisms between the different constituents of the mixture should be considered. In this article, we study the dynamics of a dense granular flow composed of a binary mixture of small and large grains immersed in an ambient fluid. In this context, we extend the two-phase approach proposed by Meruane et al. [J. Fluid Mech. 648, 381 (2010)] to the case of flowing dense binary mixtures of solid particles, by including in the momentum equations a constitutive relation that describes the interaction mechanisms between the solid constituents in a dense regime. These coupled equations are solved numerically and validated by comparing the numerical results with experimental measurements of the front speed of gravitational granular flows resulting from the collapse, in ambient air or water, of two-dimensional granular columns that consisted of mixtures of small and large spherical particles of equal mass density. Our results suggest that the model equations include the essential features that describe the dynamics of grains flows of binary mixtures in an ambient fluid. In particular, it is shown that segregation of small and large grains can increase the front speed because of the volumetric expansion of the flow. This increase in flow speed is damped by the interaction forces with the ambient fluid, and this behavior is more pronounced in water than in air.

View figure in article

Article Text

References (41)

  1. C. Ancey, J. Non-Newtonian Fluid Mech. 142, 4 (2007).
  2. J. Ottino and D. Khakhar, Annu. Rev. Fluid Mech. 32, 55 (2000).
  3. B. Zanuttigh and A. Lamberti, Rev. Geophys. 45, RG3006 (2007).
  4. C. Campbell, Powder Techno. 162, 208 (2006).
  5. S. B. Savage and C. K. K. Lun, J. Fluid Mech. 189, 311 (1988).
  6. T. Takahashi, Debris Flow (IAHR Monograph, A.A. Balkema Publishers, Rotterdam, 1991).
  7. V. Dolgunin and A. Ukolov, Powder Technol. 83, 95 (1995).
  8. J. M. N. T. Gray and V. A. Chugunov, J. Fluid Mech. 569, 365 (2006).
  9. B. Zanuttigh and P. Ghilardi, J. Hydrology 391, 175 (2010).
  10. N. Thomas, Phys. Rev. E 62, 961 (2000).
  11. O. Pouliquen, J. Delour, and S. B. Savage, Nature (London) 386, 816 (1997).
  12. H. A. Makse, S. Havlin, P. R. King, and E. Stanley, Nature (London) 386, 379 (1997).
  13. C. Meruane, A. Tamburrino, and O. Roche, J. Fluid Mech. 648, 381 (2010).
  14. O. Pouliquen and J. Vallance, Chaos 9, 621 (1999).
  15. J. Vallance and S. B. Savage, in IUTAM Symposium on Segregation in Granular Materials, edited by A. Rosato and D. Blackmore (Kluwer Academic, Dordrecht, The Netherlands, 2000), pp. 31–51.
  16. N. Burtally, P. J. King, and M. R. Swift, Science 295, 1877 (2002).
  17. P. Biswas, P. Sanchez, M. R. Swift, and P. J. King, Phys. Rev. E 68, 050301 (2003).
  18. O. Roche, M. Gilbertson, J. Phillips, and R. Sparks, Earth Planet. Sci. Lett. 240, 401 (2005).
  19. J. Phillips, A. Hogg, R. Kerswell, and N. Thomas, Earth Planet. Sci. Lett. 246, 466 (2006).
  20. E. Linares-Guerrero, C. Goujon, and R. Zenit, J. Fluid Mech. 593, 475 (2007).
  21. L. Staron and E. Lajeunesse, Geophys. Res. Lett. 36, L12402 (2009).
  22. C. Truesdell, Rand. Lincei 22, 33 (1957).
  23. C. Truesdell, Rational Thermodynamics (Springer-Verlag, Berlin, 1984).
  24. J. Gray and A. Thornton, Proc. R. Soc. A 461, 1447 (2005).
  25. A. Thornton, J. Gray, and A. Hogg, J. Fluid Mech. 550, 1 (2006).
  26. J. M. N. T. Gray and C. Ancey, J. Fluid Mech. 629, 387 (2009).
  27. R. Di Felice, Chem. Eng. Sci. 50, 1213 (1995).
  28. W. Rodi, Turbulence Models and Their Application in Q Hydraulics—A State-of-the-Art Review (IAHR Monograph, A.A. Balkema Publishers, Delft, 1983).
  29. C. Crowe, R. Troutt, and J. Chung, Annu. Rev. Fluid. Mech. 28, 11 (1996).
  30. C. Campbell, Annu. Rev. Fluid Mech. 22, 57 (1990).
  31. I. Goldhirsch, Annu. Rev. Fluid Mech. 35, 267 (2003).
  32. M. Goodman and S. Cowin, J. Fluid Mech. 45, 321 (1971).
  33. O. Pouliquen and Y. Forterre, J. Fluid Mech. 453, 133 (2002).
  34. J. Gray, C. Tai, and S. Noelle, J. Fluid Mech. 23, 161 (2003).
  35. E. Larrieu, L. Staron, and E. Hinch, J. Fluid Mech. 554, 259 (2006).
  36. Y. Forterre and O. Pouliquen, Annu. Rev. Fluid Mech. 40, 1 (2008).
  37. R. German, Particle Packing Characteristics (Metal Powder Industries Federation, Princeton, NJ, 1989).
  38. R. Fedors and R. Landel, Powder Technol. 23, 225 (1979).
  39. R. Rutgers, Nature (London) 193, 465 (1962).
  40. I. Ippolito, L. Samsom, S. Bourles, and J. Hulin, Eur. Phys. J. E 3, 227 (2000).
  41. S. Patankar, Numerical Heat Transfer and Fluid Flow (Hemisphere, Taylor and Francis, New York, 1980).

Outline

Information

Phys. Rev. E 86, 026311– Published 20 August, 2012
  • Received 1 March 2012

©2012 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation