- 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

Nonsteady discharge of granular media from a silo driven by a pressurized gas

Z. Zou1,2, P. Ruyer1, P.-Y. Lagrée3, and P. Aussillous2,*

  • 1Institut de Radioprotection et de Sûreté Nucléaire (IRSN), PSN-RES, SEMIA, LSMA, Cadarache, St Paul-Lez-Durance, 13115, France
  • 2Aix-Marseille Université, CNRS, IUSTI, Marseille, 13013 France
  • 3Sorbonne Université, CNRS UMR7190, Institut Jean le Rond ∂' Alembert, F-75005 Paris, France

  • *pascale.aussillous@univ-amu.fr
PDF

Phys. Rev. Fluids 7, 064306 – Published 28 June, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.064306

Abstract

We studied experimentally and numerically the effect of an imposed gas pressure on the discharge flow of granular media from a cylindrical silo. This study is motivated by a nuclear safety related phenomenology of fuel fragments displaced from a fuel rod under several accidental conditions, the flow being potentially driven by pressurized fission gases within the rod. We imposed a moderate constant air pressure at the top of the granular column (≈3000 Pa) and we varied the size and type of the particles and the surrounding fluid where the discharge occurs, using air and water to test the role of the coolant fluid in the nuclear safety problem. The measured parameters are the particle mass flow rate, the volumetric flow rate of air, and the pressure along the silo. The particle and air flow rates are found to be nonsteady and to increase with time. To model these behaviors, we use a two-phase continuum model with a frictional rheology to describe particle-particle interactions, and we propose a simple quasisteady analytical model considering the air-pressure gradient at the orifice as an additional driving force to the gravity. We implemented numerically the two-phase continuum model in an axisymmetric configuration which reproduces the experimental results.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (33)

  1. G. H. L. Hagen, Über den Druck und die Bewegung des trocknen Sandes, Bericht über die zur Bekanntmachung geeigneten Verhandlungen der Königlich Preussischen Akademie der Wissenschaften zu Berlin, 35–42 (1852).
  2. B. P. Tighe and M. Sperl, Pressure and motion of dry sand: translation of Hagen's paper from 1852, Granul. Matter 9, 141 (2007).
  3. S. M. Rubio-Largo, A. Janda, D. Maza, I. Zuriguel, and R. C. Hidalgo, Disentangling the Free-Fall Arch Paradox in Silo Discharge, Phys. Rev. Lett. 114, 238002 (2015).
  4. P.-Y. Lagrée, L. Staron, and S. Popinet, The granular column collapse as a continuum: validity of a two-dimensional navier-stokes model with a μ(I)-rheology, J. Fluid Mech. 686, 378 (2011).
  5. L. Staron, P.-Y. Lagrée, and S. Popinet, Continuum simulation of the discharge of the granular silo, Eur. Phys. J. E 37, 5 (2014).
  6. S. Dunatunga and K. Kamrin, Continuum modelling and simulation of granular flows through their many phases, J. Fluid Mech. 779, 483 (2015).
  7. G. Daviet and F. Bertails-Descoubes, Nonsmooth simulation of dense granular flows with pressure-dependent yield stress, J. Non-Newtonian Fluid Mech. 234, 15 (2016).
  8. Y. Zhou, P. Y. Lagrée, S. Popinet, P. Ruyer, and P. Aussillous, Experiments on, and discrete and continuum simulations of, the discharge of granular media from silos with a lateral orifice, J. Fluid Mech. 829, 459 (2017).
  9. G. D. R. MIDI, On dense granular flows, Eur. Phys. J. E 14, 341 (2004).
  10. P. Jop, Y. Forterre, and O. Pouliquen, A constitutive law for dense granular flows, Nature (London) 441, 727 (2006).
  11. Y. Forterre and O. Pouliquen, Flows of dense granular media, Annu. Rev. Fluid Mech. 40, 1 (2008).
  12. W. A. Beverloo, H. A. Leniger, and J. Van de Velde, The flow of granular solids through orifices, Chem. Eng. Sci. 15, 260 (1961).
  13. A. Janda, I. Zuriguel, and D. Maza, Flow Rate of Particles through Apertures Obtained from Self-Similar Density and Velocity Profiles, Phys. Rev. Lett. 108, 248001 (2012).
  14. R. M. Nedderman, U. Tūzūn, and R. B. Thorpe, The effect of interstitial air pressure gradients on the discharge from bins, Powder Technol. 35, 69 (1983).
  15. J. A. H. de Jong, Vertical air-controlled particle flow from a bunker through circular orifices, Powder Technol. 3, 279 (1969).
  16. J. A. H. de Jong and Q. E. J. J. M. Hoelen, Cocurrent gas and particle flow during pneumatic discharge from a bunker through an orifice, Powder Technol. 12, 201 (1975).
  17. B. J. Crewdson, A. L. Ormond, and R. M. Nedderman, Air-impeded discharge of fine particles from a hopper, Powder Technol. 16, 197 (1977).
  18. R. A. Altenkirch and R. Eichhorn, Effect of fluid drag on low Reynolds number discharge of solids from a circular orifice, AIChE J. 27, 593 (1981).
  19. S.-S. Hsiau, C.-C. Hsu, and J. Smid, The discharge of fine silica sands in a silo, Phys. Fluids 22, 043306 (2010).
  20. Y. Zhou, P.-Y. Lagrée, S. Popinet, P. Ruyer, and P. Aussillous, Gas-assisted discharge flow of granular media from silos, Phys. Rev. Fluids 4, 124305 (2019).
  21. J. L. Lage, The fundamental theory of flow through permeable media from Darcy to turbulence, in Transport Phenomena in Porous Media, edited by D. B. Ingham and I. Pop (Pergamon, Oxford, 1998), pp. 1–30.
  22. M. Benyamine, M. Djermane, B. Dalloz-Dubrujeaud, and P. Aussillous, Discharge flow of a bidisperse granular media from a silo, Phys. Rev. E 90, 032201 (2014).
  23. Y. Zhou, P. Ruyer, and P. Aussillous, Discharge flow of a bidisperse granular media from a silo: Discrete particle simulations, Phys. Rev. E 92, 062204 (2015).
  24. Z. Zou, P. Ruyer, P.-Y. Lagrée, and P. Aussillous, Discharge of a silo through a lateral orifice: Role of the bottom inclination versus friction, Phys. Rev. E 102, 052902 (2020).
  25. Z. Gu and H. Wang, Gravity waves over porous bottoms, Coastal Eng. 15, 497 (1991).
  26. K. R. Hall, G. M. Smith, and D. J. Turcke, Comparison of oscillatory and stationary flow through porous media, Coastal Eng. 24, 217 (1995).
  27. K. R. Rajagopal, On a hierarchy of approximate models for flows of incompressible fluids through porous solids, Math. Models Methods Appl. Sci. 17, 215 (2007).
  28. T. Zhu, C. Waluga, B. Wohlmuth, and M. Manhart, A study of the time constant in unsteady porous media flow using direct numerical simulation, Transp. Porous Media 104, 161 (2014).
  29. R. J. Lowe, U. Shavit, J. L. Falter, Je. R. Koseff, and S. G. Monismith, Modeling flow in coral communities with and without waves: A synthesis of porous media and canopy flow approaches, Limnol. Oceanogr. 53, 2668 (2008).
  30. L. Staron, P.-Y. Lagrée, and S. Popinet, The granular silo as a continuum plastic flow: The hour-glass vs the clepsydra, Phys. Fluids 24, 103301 (2012).
  31. http://basilisk.fr.
  32. http://basilisk.fr/src/poisson.h.
  33. R. O. Uñac, A. M. Vidales, O. A. Benegas, and I. Ippolito, Experimental study of discharge rate fluctuations in a silo with different hopper geometries, Powder Technol. 225, 214 (2012).

Outline

Information

Phys. Rev. Fluids 7, 064306– Published 28 June, 2022
  • Received 21 October 2021
  • Accepted 6 May 2022
Crossmark - Check for updates button

©2022 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation