Advertisement

Inclined granular flow in a narrow chute

  • Sheng Zhang
  • Guanghui Yang
  • Ping Lin
  • Liangwen Chen
  • Lei YangEmail author
Regular Article
  • 45 Downloads

Abstract.

In this paper we presents a detailed description of granular flow down a flat, narrow chute using discrete element method simulations, with emphasis on the influence of sidewalls on the flow. The overall phase diagram is provided and it is found that there are four flow regimes (no flow, bulk flow, surface flow, and gas flow). The stop curve is very complicated and quite different from that in the case without sidewalls. The effective friction coefficient \( \mu_{{\rm w}}\) increases with pile height and a surface flow occurs when the inclination angle \( \theta\) exceeds a critical value. The profile of \( \mu_{{\rm w}}\) shows that the \( \mu (I)\) rheology is valid in boundary layers. Furthermore, \( \mu_{{\rm w}}\) increases with the velocity of particles and there is a saturation to a nonzero value in static heap. For small , the static heap vanishes and there is a bulk flow. A similarity between basal particles and sidewall particles indicates a universal role of the boundaries. In this bulk flow, there is a transition of the velocity profile with wall friction \( \mu_{{\rm ps}}\). When \( \mu_{{\rm ps}}\) is large, the velocity is linear and decreases with increasing height. With small \( \mu_{{\rm ps}}\), the velocity is nonlinear and the flow rate is roughly proportional to 3/2.

Graphical abstract

Keywords

Flowing Matter: Granular Materials 

References

  1. 1.
    R.A. Bagnold, Proc. R. Soc. London Ser. A. Math. Phys. Sci. 225, 49 (1954)ADSGoogle Scholar
  2. 2.
    L.E. Silbert et al., Phys. Rev. E 64, 051302 (2001)ADSCrossRefGoogle Scholar
  3. 3.
    S. Ogawa, A. Umemura, N. Oshima, Z. Angew. Math. Phys. 31, 483 (1980)CrossRefGoogle Scholar
  4. 4.
    J.T. Jenkins, S.B. Savage, J. Fluid Mech. 130, 187 (1983)ADSCrossRefGoogle Scholar
  5. 5.
    M.W. Richman, Acta Mech. 75, 227 (1988)CrossRefGoogle Scholar
  6. 6.
    P. Jop, Y. Forterre, O. Pouliquen, J. Fluid Mech. 541, 167 (2005)ADSCrossRefGoogle Scholar
  7. 7.
    K. Hui et al., J. Fluid Mech. 145, 223 (1984)ADSCrossRefGoogle Scholar
  8. 8.
    J.T. Jenkins, M.W. Richman, J. Fluid Mech. 171, 53 (1986)ADSCrossRefGoogle Scholar
  9. 9.
    M.Y. Louge, S.C. Keast, Phys. Fluids 13, 1213 (2001)ADSCrossRefGoogle Scholar
  10. 10.
    G.D.R. MiDi, Eur. Phys. J. E 14, 341 (2004)CrossRefGoogle Scholar
  11. 11.
    D.M. Hanes, O.R. Walton, Powder Technol. 109, 133 (2000)CrossRefGoogle Scholar
  12. 12.
    L.E. Silbert et al., Phys. Fluids 14, 2637 (2002)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    R. Delannay et al., Nat. Mater. 6, 99 (2007)ADSCrossRefGoogle Scholar
  14. 14.
    J. Rajchenbach, Phys. Rev. Lett. 90, 144302 (2003)ADSCrossRefGoogle Scholar
  15. 15.
    T. Borzsonyi, R.E. Ecke, Phys. Rev. E 74, 061301 (2006)ADSCrossRefGoogle Scholar
  16. 16.
    W.T. Bi et al., Phys. Fluids 18, 123302 (2006)ADSCrossRefGoogle Scholar
  17. 17.
    A.J. Holyoake, J.N. McElwaine, J. Fluid Mech. 710, 35 (2012)ADSCrossRefGoogle Scholar
  18. 18.
    O. Pouliquen, Phys. Fluids 11, 542 (1999)ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    P.C. Johnson, P. Nott, R. Jackson, J. Fluid Mech. 210, 501 (1990)ADSCrossRefGoogle Scholar
  20. 20.
    O.R. Walton, Mech. Mater. 16, 239 (1993)ADSCrossRefGoogle Scholar
  21. 21.
    C.S. Campbell, C.E. Brennen, J. Appl. Mech. Trans. ASME 52, 172 (1985)ADSCrossRefGoogle Scholar
  22. 22.
    N. Brodu, P. Richard, R. Delannay, Phys. Rev. E 87, 022202 (2013)ADSCrossRefGoogle Scholar
  23. 23.
    N. Brodu et al., J. Fluid Mech. 769, 218 (2015)ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    N. Taberlet et al., Phys. Rev. Lett. 91, 064301 (2003)ADSCrossRefGoogle Scholar
  25. 25.
    N. Taberlet, P. Richard, R. Delannay, Comput. Math. Appl. 55, 230 (2008)CrossRefGoogle Scholar
  26. 26.
    P. Richard et al., Phys. Rev. Lett. 101, 248002 (2008)ADSCrossRefGoogle Scholar
  27. 27.
    D. Gollin, D. Berzi, E.T. Bowman, Granular Matter 19, 56 (2017)CrossRefGoogle Scholar
  28. 28.
    R.D. Mindlin, J. Appl. Mech. 16, 259 (1949)MathSciNetGoogle Scholar
  29. 29.
    Y. Tian et al., Comput. Chem. Eng. 104, 231 (2017) (Suppl. C)CrossRefGoogle Scholar
  30. 30.
    V.J.-L. Ralaiarisoa et al., EPJ Web of Conferences 140, 03081 (2017)CrossRefGoogle Scholar
  31. 31.
    T. Weinhart et al., Granular Matter 14, 531 (2012)CrossRefGoogle Scholar
  32. 32.
    G. Yang, Influence of Inclined Angles on the Stability of Inclined Granular Flows Down Rough Bottoms, in Proceedings of the 7th International Conference on Discrete Element Methods, edited by X. Li, Y. Feng, G. Mustoe (Springer Singapore, Singapore, 2017) pp. 647--657Google Scholar
  33. 33.
    T.S. Komatsu et al., Phys. Rev. Lett. 86, 1757 (2001)ADSCrossRefGoogle Scholar
  34. 34.
    D. Bonamy, F. Daviaud, L. Laurent, Phys. Fluids 14, 1666 (2002)ADSCrossRefGoogle Scholar
  35. 35.
    N. Taberlet et al., Phys. Rev. Lett. 91, 264301 (2003)ADSCrossRefGoogle Scholar
  36. 36.
    Y. Forterre, O. Pouliquen, J. Fluid Mech. 486, 21 (2003)ADSMathSciNetCrossRefGoogle Scholar
  37. 37.
    A.V. Orpe, D.V. Khakhar, J. Fluid Mech. 571, 1 (2007)ADSMathSciNetCrossRefGoogle Scholar
  38. 38.
    C. Jérome et al., J. Stat. Mech.: Theor. Exp. 2008, P03009 (2008)Google Scholar
  39. 39.
    L. Sarno, Experimental Investigation on the Effects of the Fixed Boundaries in Channelized Dry Granular Flows (Rock Mechanics and Rock Engineering, 2017)Google Scholar
  40. 40.
    L. Sarno et al., Phys. Fluids 26, 103303 (2014)ADSCrossRefGoogle Scholar
  41. 41.
    L. Sarno et al., Adv. Water Resour. 100, 183 (2017)ADSCrossRefGoogle Scholar
  42. 42.
    W. Losert et al., Phys. Rev. Lett. 85, 1428 (2000)ADSCrossRefGoogle Scholar
  43. 43.
    D.M. Mueth, Phys. Rev. E 67, 011304 (2003)ADSCrossRefGoogle Scholar
  44. 44.
    P.K. Haff, J. Rheol. 30, 931 (1986)ADSCrossRefGoogle Scholar
  45. 45.
    E. Azanza, F. Chevoir, P. Moucheront, J. Fluid Mech. 400, 199 (1999)ADSCrossRefGoogle Scholar
  46. 46.
    R. Artoni, P. Richard, Phys. Rev. Lett. 115, 158001 (2015)ADSCrossRefGoogle Scholar
  47. 47.
    R. Artoni et al., Phys. Rev. Lett. 108, 238002 (2012)ADSCrossRefGoogle Scholar
  48. 48.
    V. Kumaran, S. Bharathraj, Phys. Fluids 25, 070604 (2013)ADSCrossRefGoogle Scholar
  49. 49.
    H. Ahn, C. Brennen, Channel flows of granular materials and their rheological implications, in Particulate Two-Phase Flow, edited by M.C. Roco (Butterworth-Heinemann, 1993) pp. 210--243Google Scholar
  50. 50.
    H. Ahn, C.E. Brennen, R.H. Sabersky, J. Appl. Mech. Trans. ASME 59, 109 (1992)ADSCrossRefGoogle Scholar
  51. 51.
    T.G. Drake, J. Fluid Mech. 225, 121 (1991)ADSMathSciNetCrossRefGoogle Scholar
  52. 52.
    S. Courrech du Pont et al., Phys. Rev. Lett. 94, 048003 (2005)ADSCrossRefGoogle Scholar
  53. 53.
    R.M. Nedderman, C. Laohakul, Powder Technol. 25, 91 (1980)CrossRefGoogle Scholar
  54. 54.
    P. Richard et al., Phys. Rev. Lett. 101, 248002 (2008)ADSCrossRefGoogle Scholar
  55. 55.
    Y. Khidas et al., Eur. Phys. J. E 10, 387 (2003)CrossRefGoogle Scholar
  56. 56.
    T.G. Drake, J. Geophys. Res.: Solid Earth Planets 95, 8681 (1990)CrossRefGoogle Scholar
  57. 57.
    Y. Forterre, O. Pouliquen, Phys. Rev. Lett. 86, 5886 (2001)ADSCrossRefGoogle Scholar
  58. 58.
    W.T. Bi et al., J. Phys.: Condens. Matter 17, S2457 (2005)Google Scholar

Copyright information

© EDP Sciences, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Sheng Zhang
    • 1
  • Guanghui Yang
    • 1
  • Ping Lin
    • 1
  • Liangwen Chen
    • 1
  • Lei Yang
    • 1
    Email author
  1. 1.Institute of Modern PhysicsLanzhouChina

Personalised recommendations