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Quantifying silo flow using MRI velocimetry for testing granular flow models

Luke Fullard*

Daniel J. Holland

Petrik Galvosas

Clive Davies

Pierre-Yves Lagrée and Stéphane Popinet

  • School of Fundamental Sciences, and Massey University, New Zealand

  • Department of Chemical and Process Engineering, University of Canterbury, New Zealand

  • School of Chemical and Physical Sciences, Victoria University, New Zealand

  • School of Food and Advanced Technology, Massey University, New Zealand

  • Institut Jean le Rond d'Alembert, CNRS UMR 7190 Sorbonne Université, Paris, France

  • *l.fullard@massey.ac.nz
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Phys. Rev. Fluids 4, 074302 – Published 3 July, 2019

DOI: https://doi.org/10.1103/PhysRevFluids.4.074302

Abstract

In this work we present experimental results of the gravity-driven discharge of poppy seeds from three-dimensionally (3D) printed silos. The velocity fields of the flowing poppy seeds are measured using magnetic resonance imaging (MRI) velocimetry techniques. Crucially, this approach allows the velocity field to be determined throughout the flow domain, unlike visual techniques such as particle image velocimetry and related methods where only the flow at or near the wall is accessible. We perform the experiment three times; with 3D-printed silos of cone half angles 30∘ and 50∘, respectively, and then repeat the 30∘ silo experiment but with a layer of poppy seeds glued to the silo wall to create a “rough wall” condition. In our experiments, we observe and quantify velocity fields for three well-known granular flow regimes; mass flow, funnel flow, and rat-holing. The results of the experiments are compared to equivalent output of numerical simulations. In this mathematical model, the well-known μ(I) friction law is used to define an effective granular viscosity, and the flow is solved using a standard Navier-Stokes type solver. While the results are generally encouraging, it is noted that some aspects of the model are lacking and should be improved; in particular, the rat-holing effect observed in one of the MRI experiments was not predicted by the model, nor was the exact volumetric flow rate from any of the silos. Suggestions for model improvement are discussed.

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References (64)

  1. B. Andreotti, Y. Forterre, and O. Pouliquen, Granular Media: Between Fluid and Solid (Cambridge University Press, Cambridge, 2013).
  2. R. M. Nedderman, Statics and Kinematics of Granular Materials (Cambridge University Press, Cambridge, 2005).
  3. K. K. Rao and P. R. Nott, An Introduction to Granular Flow (Cambridge University Press, New York, 2008), Vol. 10.
  4. M. C. Garcia, H. J. Feise, S. Strege, and A. Kwade, Segregation in heaps and silos: Comparison between experiment, simulation and continuum model, Powder Technol. 293, 26 (2016).
  5. T. Weinhart, C. Labra, S. Luding, and J. Y. Ooi, Influence of coarse-graining parameters on the analysis of dem simulations of silo flow, Powder Technol. 293, 138 (2016).
  6. D. Bertuola, S. Volpato, P. Canu, and A. C. Santomaso, Prediction of segregation in funnel and mass flow discharge, Chem. Eng. Sci. 150, 16 (2016).
  7. L. Staron, P.-Y. Lagrée, and S. Popinet, Continuum simulation of the discharge of the granular silo, Eur. Phys. J. E 37, 5 (2014).
  8. 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).
  9. S. Volpato, R. Artoni, and A. C. Santomaso, Numerical study on the behavior of funnel flow silos with and without inserts through a continuum hydrodynamic approach, Chem. Eng. Res. Des. 92, 256 (2014).
  10. Y. Wang and J. Y. Ooi, A study of granular flow in a conical hopper discharge using discrete and continuum approach, Procedia Eng. 102, 765 (2015).
  11. S. Dunatunga and K. Kamrin, Continuum modeling and simulation of granular flows through their many phases, J. Fluid Mech. 779, 483 (2015).
  12. L. A. Fullard, C. E. Davies, and G. C. Wake, Modelling powder mixing in mass flow discharge: A kinematic approach, Adv. Powder Technol. 24, 499 (2013).
  13. L. Fullard, E. Breard, C. Davies, P.-Y. Lagrée, S. Popinet, and G. Lube, Testing the μ (i) granular rheology against experimental silo data, in EPJ Web of Conferences (EDP Sciences, Les Ulis, 2017), Vol. 140, p. 11002.
  14. 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).
  15. L. A. Fullard, C. E. Davies, A. C. Neather, E. C. P. Breard, A. J. R. Godfrey, and G. Lube, Testing steady and transient velocity scalings in a silo, Adv. Powder Technol. 29, 310 (2018).
  16. L. A. Fullard, C. E. Davies, G. Lube, A. C. Neather, E. C. P. Breard, and B. J. Shepherd, The transient dynamics of dilation waves in granular phase transitions during silo discharge, Granul. Matter 19, 6 (2017).
  17. J. Choi, A. Kudrolli, and M. Z. Bazant, Velocity profile of granular flows inside silos and hoppers, J. Phys.: Condens. Matter 17, S2533 (2005).
  18. A. Janda, I. Zuriguel, A. Garcimartín, L. A. Pugnaloni, and D. Maza, Jamming and critical outlet size in the discharge of a two-dimensional silo, Europhys. Lett. 84, 44002 (2008).
  19. I. Sielamowicz, S. Blonski, and T. A. Kowalewski, Optical technique dpiv in measurements of granular material flows, part 1 of 3-plane hoppers, Chem. Eng. Sci. 60, 589 (2005).
  20. K. Endo, K. A. Reddy, and H. Katsuragi, Obstacle-shape effect in a two-dimensional granular silo flow field, Phys. Rev. Fluids 2, 094302 (2017).
  21. S. Waktola, A. Bieberle, F. Barthel, M. Bieberle, U. Hampel, K. Grudzień, and L. Babout, A new data-processing approach to study particle motion using ultrafast x-ray tomography scanner: Case study of gravitational mass flow, Exp. Fluids 59, 69 (2018).
  22. K. Grudzien, M. Niedostatkiewicz, J. Adrien, E. Maire, and L. Babout, Analysis of the bulk solid flow during gravitational silo emptying using X-ray and ECT tomography, Powder Technol. 224, 196 (2012).
  23. H.-Y. Xie and K. Shinohara, Measurement of solids velocity in a conical hopper by mass tracer particles, Chem. Eng. Sci. 54, 455 (1999).
  24. P. A. Langston, M. S. Nikitidis, U. Tüzün, D. M. Heyes, and N. M. Spyrou, Microstructural simulation and imaging of granular flows in two-and three-dimensional hoppers, Powder Technol. 94, 59 (1997).
  25. M. S. Nikitidis, U. Tüzün, and N. M. Spyrou, Determination of phase velocities in multi-phase flows in hoppers using dual photon gamma-ray tomography, Chem. Eng. Commun. 175, 3 (1999).
  26. M. S. Nikitidis, U. Tüzün, and N. M. Spyrou, Tomographic measurements of granular flows in gases and in liquids, KONA Powder Part. J. 12, 53 (1994).
  27. R. Stannarius, Magnetic resonance imaging of granular materials, Rev. Sci. Instrum. 88, 051806 (2017).
  28. A. Penn, T. Tsuji, D. O. Brunner, C. M. Boyce, K. P. Pruessmann, and C. R. Müller, Real-time probing of granular dynamics with magnetic resonance, Sci. Adv. 3, e1701879 (2017).
  29. C. M. Boyce, A. Penn, K. P. Prüssmann, and C. R. Müller, Magnetic resonance imaging of gas–solid fluidization with liquid bridging, AIChE J. 64, 2958 (2018).
  30. C. M. Boyce, N. P. Rice, A. Ozel, J. F. Davidson, A. J. Sederman, L. F. Gladden, S. Sundaresan, J. S. Dennis, and D. J. Holland, Magnetic resonance characterization of coupled gas and particle dynamics in a bubbling fluidized bed, Phys. Rev. Fluids 1, 074201 (2016).
  31. H. T. Fabich, A. J. Sederman, and D. J. Holland, Development of ultrafast ute imaging for granular systems, J. Magn. Reson. 273, 113 (2016).
  32. C. M. Boyce, A. Ozel, N. P. Rice, G. J. Rubinstein, D. J. Holland, and S. Sundaresan, Effective particle diameters for simulating fluidization of non-spherical particles: CFD-DEM models vs. MRI measurements, AIChE J. 63, 2555 (2017).
  33. H. T. Fabich, A. J. Sederman, and D. J. Holland, Study of bubble dynamics in gas-solid fluidized beds using ultrashort echo time (UTE) magnetic resonance imaging (MRI), Chem. Eng. Sci. 172, 476 (2017).
  34. H. T. Fabich, T. I. Brox, D. Clarke, J. D. Seymour, S. L. Codd, P. Galvosas, J. Brown, A. J. Sederman, and D. J. Holland, Measurements of the velocity distribution for granular flow in a couette cell, Phys. Rev. E 98, 062901 (2018).
  35. T. Kawaguchi, MRI measurement of granular flows and fluid-particle flows, Adv. Powder Technol. 21, 235 (2010).
  36. M. Gentzler and G. I. Tardos, Measurement of velocity and density profiles in discharging conical hoppers by NMR imaging, Chem. Eng. Sci. 64, 4463 (2009).
  37. Z. H. Gu, P. C. Arnold, and A. G. McLean, Prediction of the flowrate of bulk solids from mass flow bins with conical hoppers, Powder Technol. 72, 157 (1992).
  38. P. Jop, Y. Forterre, and O. Pouliquen, A constitutive law for dense granular flows, Nature 441, 727 (2006).
  39. 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).
  40. P. B. Kowalczuk and J. Drzymala, Physical meaning of the sauter mean diameter of spherical particulate matter, Part. Sci. Technol. 34, 645 (2016).
  41. K. To, Jamming transition in two-dimensional hoppers and silos, Phys. Rev. E 71, 060301(R) (2005).
  42. N. Gui, X. Yang, J. Tu, and S. Jiang, Effects of rocking frequency and amplitude on particle discharge in rocking bed: A DEM study, Powder Technol. 292, 31 (2016).
  43. A. McLean, The use of standpipes for increasing limiting gravitational flowrate from mass flow bins, KONA Powder Part. J. 11, 139 (1993).
  44. C. Mankoc, A. Janda, R. Arevalo, J. M. Pastor, I. Zuriguel, A. Garcimartín, and D. Maza, The flow rate of granular materials through an orifice, Granul. Matter 9, 407 (2007).
  45. W. A. Beverloo, H. A. Leniger, and J. Van de Velde, The flow of granular solids through orifices, Chem. Eng. Sci. 15, 260 (1961).
  46. P. T. Callaghan, Translational Dynamics and Magnetic Resonance, 1st ed. (Oxford University Press, Oxford, 2011).
  47. S. Popinet, Gerris: A tree-based adaptive solver for the incompressible euler equations in complex geometries, J. Comput. Phys. 190, 572 (2003).
  48. R. Artoni, A. C. Santomaso, M. Go, and P. Canu, Scaling Laws for the Slip Velocity in Dense Granular Flows, Phys. Rev. Lett. 108, 238002 (2012).
  49. R. Artoni and A. Santomaso, Effective wall slip in chutes and channels: Experiments and discrete element simulations, Granul. Matter 16, 377 (2014).
  50. T. Barker, D. G. Schaeffer, M. Shearer, and J. M. N. T. Gray, Well-posed continuum equations for granular flow with compressibility and μ(I)-rheology, Proc. R. Soc. A 473, 20160846 (2017).
  51. L. Fullard and C. Davies, Minimising the spread of residence-time distribution for flat and heaped powders in a wedge-shaped planar hopper, Particuology 30, 102 (2017).
  52. K. E. Fickie, R. Mehrabi, and R. Jackson, Density variations in a granular material flowing from a wedge-shaped hopper, AIChE J. 35, 853 (1989).
  53. R. L. Brown, Minimum energy theorem for flow of dry granules through apertures, Nature 191, 458 (1961).
  54. M. Benyamine, P. Aussillous, and B. Dalloz-Dubrujeaud, Discharge flow of a granular media from a silo: Effect of the packing fraction and of the hopper angle, in EPJ Web of Conferences (EDP Sciences, Les Ulis, 2017), Vol. 140, p. 03043.
  55. D. L. Henann and K. Kamrin, A predictive, size-dependent continuum model for dense granular flows, Proc. Natl. Acad. Sci. USA 110, 6730 (2013).
  56. G. D. R. MiDi, On dense granular flows, Eur. Phys. J. E 14, 341 (2004).
  57. P. Jop, Y. Forterre, and O. Pouliquen, Crucial role of sidewalls in granular surface flows: Consequences for the rheology, J. Fluid Mech. 541, 167 (2005).
  58. E. Azéma, N. Estrada, I. Preechawuttipong, J.-Y. Delenne, and F. Radjai, Systematic description of the effect of particle shape on the strength properties of granular media, in EPJ Web of Conferences (EDP Sciences, Les Ulis, 2017), Vol. 140, p. 06026.
  59. S. Zhao and X. Zhou, Effects of particle asphericity on the macro-and micro-mechanical behaviors of granular assemblies, Granul. Matter 19, 38 (2017).
  60. T. Börzsönyi, E. Somfai, B. Szabó, S. Wegner, A. Ashour, and R. Stannarius, Elongated grains in a hopper, in EPJ Web of Conferences (EDP Sciences, Les Ulis, 2017), Vol. 140, p. 06017.
  61. E. Goldberg, C. M. Carlevaro, and L. A. Pugnaloni, Effect of grain shape on the jamming of two-dimensional silos, in EPJ Web of Conferences (EDP Sciences, Les Ulis, 2017), Vol. 140, p. 06009.
  62. 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).
  63. T. Barker, D. G. Schaeffer, P. Bohorquez, and J. M. N. T. Gray, Well-posed and ill-posed behavior of the μ(I)-rheology for granular flow, J. Fluid Mech. 779, 794 (2015).
  64. J. Heyman, R. Delannay, H. Tabuteau, and A. Valance, Compressibility regularizes the μ(I)-rheology for dense granular flows, J. Fluid Mech. 830, 553 (2017).

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Phys. Rev. Fluids 4, 074302– Published 3 July, 2019
  • Received 6 March 2019
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