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

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Length of standing jumps along granular flows down smooth inclines

Ségolène Méjean*

François Guillard

Thierry Faug†

Itai Einav

  • University Grenoble-Alpes, Irstea, UR ETGR, F-38402 St-Martin-d'Hères, France and School of Civil Engineering, The University of Sydney, Sydney NSW 2006, Australia

  • School of Civil Engineering, The University of Sydney, Sydney NSW 2006, Australia

  • University Grenoble-Alpes, Irstea, UR ETGR, F-38402 St-Martin-d'Hères, France

  • School of Civil Engineering, The University of Sydney, Sydney NSW 2006, Australia

  • *segolene.mejean@irstea.fr
  • †thierry.faug@irstea.fr
PDF

Phys. Rev. Fluids 5, 034303 – Published 13 March, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.034303

Abstract

Granular jumps—the change in height and depth-averaged velocity during granular flows—occur during transitions from thin and fast flows (supercritical) to thick and slow flows (subcritical). The present paper describes discrete element method simulations inspired by recent laboratory experiments, which produce standing jumps in two-dimensional free-surface dry granular flows down a slope. Special attention is paid to characterizing and measuring the finite length of those standing granular jumps, as well as to deciphering their internal structure. By varying macroscopic quantities, such as slope angle and mass discharge, and microscopic properties, such as interparticle friction and grain diameter, a rich variety of granular jump patterns is observed. Hydraulic-like granular jumps with an internal waterlike roller are identified, in addition to diffuse laminar granular jumps and steep colliding granular jumps. Moreover, a recently established depth-averaged relation for the prediction of jump heights is fed with the measured jump length and fitted against the numerical simulations to examine the effective friction in the granular medium for each type of jump. The dominant component of the general friction law is found to be different when transitioning from one jump pattern to the others. This study demonstrates that the granular jump pattern, and particularly its geometry and internal structure, can offer a stringent test for addressing the dissipation mechanisms that govern the flowability of granular media.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (39)

  1. Y. Forterre and O. Pouliquen, Flows of dense granular media, Annu. Rev. Fluid Mech. 40, (2007).
  2. H. M. Jaeger, S. R. Nagel, and R. P. Behringer, Granular solids, liquids, and gases, Rev. Mod. Phys. 68, 1259 (1996).
  3. GDR Midi, On dense granular flows, Eur. Phys. J. E 14, 341 (2004).
  4. J. Boudet, Y. Amarouchene, B. Bonnier, and H. Kellay, The granular jump, J. Fluid Mech. 572, 413 (2007).
  5. C. G. Johnson and J. M. N. T. Gray, Granular jets and hydraulic jumps on an inclined plane, J. Fluid Mech. 675, 87 (2011).
  6. T. Faug, Depth-averaged analytic solutions for free-surface granular flows impacting rigid walls down inclines, Phys. Rev. E 92, 062310 (2015).
  7. S. P. Pudasaini and C. Kröner, Shock waves in rapid flows of dense granular materials: Theoretical predictions and experimental results, Phys. Rev. E 78, 041308 (2008).
  8. S. Viroulet, J. L. Baker, A. N. Edwards, C. G. Johnson, C. Gjaltema, P. Clavel, and J. M. N. T. Gray, Multiple solutions for granular flow over a smooth two-dimensional bump, J. Fluid Mech. 815, 77 (2017).
  9. C. Brennen, K. Sieck, and J. Paslaski, Hydraulic jumps in granular material flow, Powder Technol. 35, 31 (1983).
  10. C. Campbell, C. Brennen, and R. Sabersky, Flow regimes in inclined open-channel flows of granular materials, Powder Technol. 41, 77 (1985).
  11. H. Morrison and O. Richmond, Application of spencer's ideal soil model to granular materials flow, J. Appl. Mech. 43, 49 (1976).
  12. H. Xiao, J. Hruska, J. M. Ottino, R. M. Lueptow, and P. B. Umbanhowar, Unsteady flows and inhomogeneous packing in damp granular heap flows, Phys. Rev. E 98, 032906 (2018).
  13. Y.-C. Tai, and Y.-C. Lin, A focused view of the behavior of granular flows down a confined inclined chute into the horizontal run-out zone, Phys. Fluids 20, 123302 (2008).
  14. J. M. N. T. Gray, Y.-C. Tai, and S. Noelle, Shock waves, dead zones and particle-free regions in rapid granular free-surface flows, J. Fluid Mech. 491, 161 (2003).
  15. S. B. Savage, Gravity flow of cohesionless granular materials in chutes and channels, J. Fluid Mech. 92, 53 (1979).
  16. T. Faug, P. Childs, E. Wyburn, and I. Einav, Standing jumps in shallow granular flows down smooth inclines, Phys. Fluids 27, 073304 (2015).
  17. T. Faug, Jumps and bores in bulky frictional granular flows, in Powders and Grains 2013: Proceedings of the 7th International Conference on Micromechanics of Granular Media, Vol. 1542 (AIP Publishing, Sydney, 2013), pp. 642–645.
  18. S. Méjean, T. Faug, and I. Einav, A general relation for standing normal jumps in both hydraulic and dry granular flows, J. Fluid Mech. 816, 331 (2017).
  19. F. da Cruz, S. Emam, M. Prochnow, J.-N. Roux, and F. Chevoir, Rheophysics of dense granular materials: Discrete simulation of plane shear flows, Phys. Rev. E 72, 021309 (2005).
  20. P. Jop, Y. Forterre, and O. Pouliquen, A constitutive law for dense granular flows, Nature 441, 727 (2006).
  21. V. Smilauer, A. Gladky, J. Kozicki, C. Modenese, and J. Stronsky, Yade, using and programming, in Yade Documentation, 1st ed. edited by V. Smilauer (The Yade Project, Prague, 2010).
  22. S. Méjean, T. Faug, and I. Einav, Discrete element method simulations of standing jumps in granular flows down inclines, in EPJ Web of Conferences, Vol. 140 (EDP Sciences, 2017), p. 03026.
  23. C. Goldenberg and I. Goldhirsch, Continuum Mechanics for Small Systems and Fine Resolutions (American Scientific, Stevenson Ranch, CA, 2006).
  24. I. Goldhirsch, Stress, stress asymmetry and couple stress: From discrete particles to continuous fields, Granul. Matter 12, 239 (2010).
  25. T. Weinhart, R. Hartkamp, A. R. Thornton, and S. Luding, Coarse-grained local and objective continuum description of three-dimensional granular flows down an inclined surface, Phys. Fluids 25, 070605 (2013).
  26. L. B. Lucy, A numerical approach to the testing of the fission hypothesis, Astron. J. 82, 1013 (1977).
  27. W. G. Hoover and C. G. Hoover, Smooth-particle phase stability with generalized density-dependent potentials, Phys. Rev. E 73, 016702 (2006).
  28. P. Rognon, T. Miller, and I. Einav, A circulation-based method for detecting vortices in granular materials, Granul. Matter 17, 177 (2015).
  29. A. Savitzky and M. J. Golay, Smoothing and differentiation of data by simplified least squares procedures, Anal. Chem. 36, 1627 (1964).
  30. J. M. N. T. Gray and X. Cui, Weak, strong and detached oblique shocks in gravity-driven granular free-surface flows, J. Fluid Mech. 579, 113 (2007).
  31. N. Brodu, P. Richard, and R. Delannay, Shallow granular flows down flat frictional channels: Steady flows and longitudinal vortices, Phys. Rev. E 87, 022202 (2013).
  32. H. Chanson, Development of the bélanger equation and backwater equation by Jean-Baptiste Bélanger (1828), J. Hydraul. Eng. 135, 159 (2009).
  33. S. B. Savage and K. Hutter, The motion of a finite mass of granular material down a rough incline, J. Fluid Mech. 199, 177 (1989).
  34. A. Fall, G. Ovarlez, D. Hautemayou, C. Mézière, J.-N. Roux, and F. Chevoir, Dry granular flows: Rheological measurements of the μ(i)-rheology, J. Rheol. 59, 1065 (2015).
  35. O. Pouliquen, Scaling laws in granular flows down rough inclined planes, Phys. Fluids 11, 542 (1999).
  36. R. Artoni and P. Richard, Average balance equations, scale dependence, and energy cascade for granular materials, Phys. Rev. E 91, 032202 (2015).
  37. M. Lätzel, S. Luding, and H. J. Herrmann, Macroscopic material properties from quasi-static, microscopic simulations of a two-dimensional shear-cell, Granul. Matter 2, 123 (2000).
  38. A. Thornton, T. Weinhart, V. Ogarko, and S. Luding, Multi-scale methods for multi-component granular materials, Comput. Methods Mater. Sci. 13, 197 (2013).
  39. T. Weinhart, A. R. Thornton, S. Luding, and O. Bokhove, From discrete particles to continuum fields near a boundary, Granul. Matter 14, 289 (2012).

Outline

Information

Phys. Rev. Fluids 5, 034303– Published 13 March, 2020
  • Received 13 September 2018
  • Accepted 11 February 2020
Crossmark - Check for updates button

©2020 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation