Granular Matter

, 18:33 | Cite as

Analysis of the velocity field of granular hopper flow

  • F. G. R. MagalhãesEmail author
  • A. P. F. Atman
  • J. G. Moreira
  • H. J. Herrmann
Original Paper


We report the analysis of radial characteristics of the flow of granular material through a conical hopper. The discharge is simulated for various orifice sizes and hopper opening angles. Velocity profiles are measured along two radial lines from the hopper cone vertex: along the main axis of the cone and along its wall. An approximate power law dependence on the distance from the orifice is observed for both profiles, although differences between them can be noted. In order to quantify these differences, we propose a Local Mass Flow Index that is a promising tool in the direction of a more reliable classification of the flow regimes in hoppers.


Granular matter Discrete element method Velocity profile Hopper flow 



FGRM would like to thank Alessandro Leonardi for helpful discussions, as well as the whole Computational Physics Group at ETH Zürich for the hospitality and resources.

Compliance with ethical standards

Conflict of interest

This project was partially funded by Grant No. FP7-319968-FlowCCS of the European Research Council (ERC) Advanced Grant and Brazilian agencies CAPES, CNPq and Ciências sem Fronteiras. The authors declare that they have no conflict of interest.

Supplementary material

10035_2016_636_MOESM1_ESM.avi (14.1 mb)
Supplementary material 1 (avi 14487 KB)


  1. 1.
    Duran, J.: Sands, Powders, and Grains, vol. 12. Springer, New York (2000)CrossRefGoogle Scholar
  2. 2.
    Campbell, C.S.: Granular material flows—an overview. Powder Technol. 162(3), 208–229 (2006)CrossRefGoogle Scholar
  3. 3.
    Herrmann, H.J.: Grains of understanding. Phys. World 10(11), 31–34 (1997)CrossRefGoogle Scholar
  4. 4.
    Cleary, P.W., Sawley, M.L.: DEM modelling of industrial granular flows: 3D case studies and the effect of particle shape on hopper discharge. Appl. Math. Model. 26(2), 89–111 (2002)CrossRefzbMATHGoogle Scholar
  5. 5.
    Zuriguel, I.: Clogging of granular materials in bottlenecks. Pap. Phys. 6, 060014 (2014)CrossRefGoogle Scholar
  6. 6.
    Janda, A., Zuriguel, I., Garcimartín, A., Pugnaloni, L.A., Maza, D.: Jamming and critical outlet size in the discharge of a two-dimensional silo. Europhys. Lett. 84(4), 44002 (2008)ADSCrossRefGoogle Scholar
  7. 7.
    Magalhães, C.F.M., Atman, A.P.F., Combe, G., Moreira, J.G.: Jamming transition in a two-dimensional open granular pile with rolling resistance. Pap. Phys. 6, 060007 (2014)CrossRefGoogle Scholar
  8. 8.
    Ristow, G., Herrmann, H.J.: Density patterns in two-dimensional hoppers. Phys. Rev. E 50, R5(R) (1994)Google Scholar
  9. 9.
    Artega, P., Tüzün, U.: Flow of binary mixtures of equal-density granules in hoppers-size segregation, flowing density and discharge rates. Chem. Eng. Sci. 45(1), 205–223 (1990)CrossRefGoogle Scholar
  10. 10.
    Magalhães, C.F.M., Moreira, J.G., Atman, A.P.F.: Segregation in arch formation. Eur. Phys. J. E Soft Matter Biol. Phys. 35(5), 1–5 (2012)CrossRefGoogle Scholar
  11. 11.
    Ristow, G.H., Herrmann, H.J.: Forces on the walls and stagnation zones in a hopper filled with granular material. Phys. A Stat. Mech. Appl. 213(4), 474–481 (1995)CrossRefGoogle Scholar
  12. 12.
    Goda, T.T., Ebert, F.: Three-dimensional discrete element simulations in hoppers and silos. Powder Technol. 158(1), 58–68 (2005)CrossRefGoogle Scholar
  13. 13.
    Gutiérrez, G., Colonnello, C., Boltenhagen, P., Darias, R., Peralta-Fabi, J.R., Brau, F., Clément, E.: Silo collapse under granular discharge. Phys. Rev. Lett. 114, 018001 (2015)ADSCrossRefGoogle Scholar
  14. 14.
    Jenike, A.W.: Gravity flow of bulk solids. Bulletin No. 108, Utah State University (1961)Google Scholar
  15. 15.
    Johanson, J.R., Jenike, A.W.: Stress and velocity fields in gravity flow of bulk solids. Bull. Univ. Utah 53(21) (1962)Google Scholar
  16. 16.
    Jenike, A.W.: Quantitative design of mass-flow bins. Powder Technol. 1(4), 237–244 (1967)CrossRefGoogle Scholar
  17. 17.
    Nguyen, T.V., Brennen, C.E., Sabersky, R.H.: Funnel flow in hoppers. J. Appl. Mech. 47(4), 729–735 (1980)ADSCrossRefGoogle Scholar
  18. 18.
    González-Montellano, C., Gallego, E., Ramírez-Gómez, A., Ayuga, F.: Three dimensional discrete element models for simulating the filling and emptying of silos: analysis of numerical results. Comput. Chem. Eng. 40, 22–32 (2012)CrossRefGoogle Scholar
  19. 19.
    Medina, A., Cordova, J.A., Luna, E., Trevino, C.: Velocity field measurements in granular gravity flow in a near 2d silo. Phys. Lett. A 250(1), 111–116 (1998)ADSCrossRefGoogle Scholar
  20. 20.
    Kondic, L.: Simulations of two dimensional hopper flow. Granul. Matter 16(2), 235–242 (2014)CrossRefGoogle Scholar
  21. 21.
    Baran, O., Kondic, L.: On velocity profiles and stresses in sheared and vibrated granular systems under variable gravity. Phys. Fluids (1994-present) 18(12), 121509 (2006)ADSCrossRefzbMATHGoogle Scholar
  22. 22.
    Ketterhagen, W.R., Curtis, J.S., Wassgren, C.R., Hancock, B.C.: Predicting the flow mode from hoppers using the discrete element method. Powder Technol. 195(1), 1–10 (2009)CrossRefGoogle Scholar
  23. 23.
    Nedderman, R.M.: The measurement of the velocity profile in a granular material discharging from a conical hopper. Chem. Eng. Sci. 43(7), 1507–1516 (1988)CrossRefGoogle Scholar
  24. 24.
    Sielamowicz, I., Czech, M.: Analysis of the radial flow assumption in a converging model silo. Biosyst. Eng. 106(4), 412–422 (2010)CrossRefGoogle Scholar
  25. 25.
    Pöschel, T., Schwager, T.: Computational Granular Dynamics. Springer, Berlin (2005)Google Scholar
  26. 26.
    Brilliantov, N.V., Spahn, F., Hertzsch, J.-M., Pöschel, T.: Model for collisions in granular gases. Phys. Rev. E 53(5), 5382 (1996)ADSCrossRefGoogle Scholar
  27. 27.
    Cundall, P.A., Strack, O.D.L.: A discrete numerical model for granular assemblies. Geotechnique 29(1), 47–65 (1979)CrossRefGoogle Scholar
  28. 28.
    Luding, S.: Molecular dynamics simulations of granular materials. In: Hinrichsen, H., Wolf, D.E. (eds.) The Physics of Granular Media, pp 297–324. (2004). doi: 10.1002/352760362X.ch13
  29. 29.
    Schäfer, J., Dippel, S., Wolf, D.E.: Force schemes in simulations of granular materials. J. Phys. I 6(1), 5–20 (1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • F. G. R. Magalhães
    • 1
    • 2
    • 3
    Email author
  • A. P. F. Atman
    • 4
    • 5
  • J. G. Moreira
    • 1
  • H. J. Herrmann
    • 2
    • 5
    • 6
  1. 1.Departamento de FísicaUniversidade Federal de Minas GeraisBelo HorizonteBrazil
  2. 2.Computational Physics, IfBETH ZürichZurichSwitzerland
  3. 3.Instituto de Ciências ExatasUniversidade Federal de ViçosaRio ParanaíbaBrazil
  4. 4.Departamento de Física e MatemáticaCentro Federal de Educação Tecnológica de Minas GeraisBelo HorizonteBrazil
  5. 5.Instituto Nacional de Ciência e Tecnologia Sistemas ComplexosBelo HorizonteBrazil
  6. 6.Departamento de FísicaUniversidade Federal do CearáFortalezaBrazil

Personalised recommendations