Skip to main content Accessibility help
×
Home

High-speed granular chute flows

  • Alex J. Holyoake (a1) and Jim N. McElwaine (a1)

Abstract

This paper reports experimental findings on the flow of sand down a steep chute. Nearly all granular flow models have a maximum value for the friction and therefore predict that flows on steep slopes will accelerate at a constant rate until the interaction with the ambient fluid becomes important. This prediction has not been tested by previous work, which has focused on relatively low slope angles where steady, fully developed flows occur after short distances. We test this by investigating flows over a much greater range of slope angles (30–50) and flow depths (4–130 particle diameters). We examine flows with two basal conditions, one flat and frictional, the other bumpy. The latter imposes a no-slip condition for slow, deep flows, but permits some degree of slip for high flow velocities. The data suggests that friction can be much larger than theories such as the rheology proposed by Jop, Forterre & Pouliquen (Nature, vol. 441, 2006) suggest and that there may be constant velocity states above the angle of vanishing . Although these flows do not vary in time, all but the flows on the bumpy base at low inclinations accelerate down the slope. A recirculation mechanism sustains flows with a maximum mass flux of , allowing observations to be made at multiple points for each flow for an indefinite period. Flows with Froude number in the range 0.1–25 and bulk inertial number 0.1–2.7 were observed in the dense regime, with surface velocities in the range 0.2–5.6 . Previous studies have focused on . We show that a numerical implementation of the rheology does not fully capture the accelerating dynamics or the transverse velocity profile on the bumpy base. We also observe the transverse separation of the flow into a dense core flanked by dilute regions and the formation of longitudinal vortices.

Copyright

Corresponding author

Email address for correspondence: a.j.holyoake@damtp.cam.ac.uk

References

Hide All
1. Ahn, H., Brennen, C. E. & Sabersky, R. H. 1991 Measurements of velocity, velocity fluctuation, density, and stresses in chute flows of granular materials. J. Appl. Mech. 58 (792), 12.
2. Ahn, H., Brennen, C. E. & Sabersky, R. H. 1992 Analysis of the fully developed chute flow of granular materials. J. Appl. Mech. 59, 109.
3. Ancey, C., Coussot, P. & Evesque, P. 1999 A theoretical framework for granular suspensions in a steady simple shear flow. J. Rheol. 43, 1673.
4. Baran, O., Ertaş, D., Halsey, T. C., Grest, G. S. & Lechman, J. B. 2006 Velocity correlations in dense gravity-driven granular chute flow. Phys. Rev. E 74 (5), 051302.
5. Börzsönyi, T. & Ecke, R. E. 2006 Rapid granular flows on a rough incline: phase diagram, gas transition, and effects of air drag. Phys. Rev. E 74 (6), 061301.
6. Börzsönyi, T., Ecke, R. E. & McElwaine, J. N. 2009 Patterns in flowing sand: understanding the physics of granular flow. Phys. Rev. Lett. 103 (17), 178302.
7. Delannay, R., Louge, M., Richard, P., Taberlet, N. & Valance, A. 2007 Towards a theoretical picture of dense granular flows down inclines. Nat. Mater. 6 (2), 99108.
8. Ertaş, D., Grest, G. S., Halsey, T. C., Levine, D. & Silbert, L. E. 2001 Gravity-driven dense granular flows. Europhys. Lett. 56, 214.
9. Forterre, Y. 2006 Kapiza waves as a test for three-dimensional granular flow rheology. J. Fluid Mech. 563, 123132.
10. Forterre, Y. & Pouliquen, O. 2001 Longitudinal vortices in granular flows. Phys. Rev. Lett. 86 (26), 58865889.
11. Forterre, Y. & Pouliquen, O. 2003 Long-surface-wave instability in dense granular flows. J. Fluid Mech. 486, 2150.
12. Forterre, Y. & Pouliquen, O. 2008 Flows of dense granular media. Annu. Rev. Fluid Mech. 40 (1), 124.
13. Goldhirsch, I. 2003 Rapid granular flows. Annu. Rev. Fluid Mech. 35, 267293.
14. Gray, J., Wieland, M. & Hutter, K. 1985 Gravity-driven free surface flow of granular avalanches over complex basal topography. Proc. R. Soc. Lond. Ser. A: Math. Phys. Engng Sci. 455, 1841.
15. Jackson, R. 1983 Some mathematical and physical aspects of continuum models for the motion of granular materials. In Theory of Dispersed Multiphase Flow (ed. Meyer, R. ). MRC Seminar, May 1982 , Academic Press.
16. Janssen, H. A. 1895 Tests on grain pressure silos. Z. Verein. Deutsch. Ing. 39 (35), 10451049.
17. Jenkins, J. & Berzi, D. 2010 Dense inclined flows of inelastic spheres: tests of an extension of kinetic theory. Granul. Matt. 12, 151158.
18. Jenkins, J. T. & Richman, M. W. 1985 Kinetic theory for plane flows of a dense gas of identical, rough, inelastic, circular disks. Phys. Fluids 28, 3485.
19. Jop, P., Forterre, Y. & Pouliquen, O. 2005 Crucial role of sidewalls in granular surface flows: consequences for the rheology. J. Fluid Mech. 541, 167192.
20. Jop, P., Forterre, Y. & Pouliquen, O. 2006 A constitutive law for dense granular flows. Nature 441.
21. Louge, M. Y. & Keast, S. C. 2001 On dense granular flows down flat frictional inclines. Phys. Fluids 13, 1213.
22. McNamara, S. & Young, W. R. 1994 Inelastic collapse in two dimensions. Phys. Rev. E 50, 2831.
23. MiDi, G. D. R. 2004 On dense granular flows. Eur. Phys. J. E: Soft Matter Biol. Phys. 14 (4), 341365.
24. Mitarai, N. & Nakanishi, H. 2005 Bagnold scaling, density plateau, and kinetic theory analysis of dense granular flow. Phys. Rev. Lett. 94, 128001.
25. Nedderman, R. M., Tuzun, U., Savage, S. B. & Houlsby, G. T. 1982 The flow of granular materials–i: discharge rates from hoppers. Chem. Engng Sci. 37 (11), 15971609.
26. Patton, J. S., Brennen, C. E. & Sabersky, R. H. 1987 Shear flows of rapidly flowing granular materials. J. Appl. Mech. 54, 801.
27. Pouliquen, O. 1999 Scaling laws in granular flows down rough inclined planes. Phys. Fluids 11, 542.
28. Pouliquen, O., Cassar, C., Jop, P., Forterre, Y. & Nicolas, M. 2006 Flow of dense granular material: towards simple constitutive laws. J. Stat. Mech.: Theory Exp. 2006, P07020.
29. Savage, S. B. 1979 Gravity flow of cohesionless granular materials in chutes and channels. J. Fluid Mech. 92 (1), 5396.
30. Savage, S. B. 1984 The mechanics of rapid granular flows. Adv. Appl. Mech. 24, 289366.
31. Savage, S. B. & Hutter, K. 1989 The motion of a finite mass of granular material down a rough incline. J. Fluid Mech. 199, 177215.
32. Silbert, L. E., Ertaş, 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 (5), 51302.
33. Sveen, J. K. & Dalziel, S. B. 2005 A dynamic masking technique for combined measurements of PIV and synthetic schlieren applied to internal gravity waves. Meas. Sci. Technol. 16, 19541960.
34. Taberlet, N., Richard, P., Jenkins, J. T. & Delannay, R. 2007 Density inversion in rapid granular flows: the supported regime. Eur. Phys. J. E 22 (1), 1724.
35. 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 (26), 264301.
36. White, D. J. 2003 PSD measurement using the single particle optical sizing (SPOS) method. Géotechnique 53 (3), 317326.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Related content

Powered by UNSILO

High-speed granular chute flows

  • Alex J. Holyoake (a1) and Jim N. McElwaine (a1)

Metrics

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.