Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-18T01:09:18.968Z Has data issue: false hasContentIssue false
  • English
  • Français

Modelling silo clogging with non-local granular rheology

Published online by Cambridge University Press:  06 April 2022

Sachith Dunatunga Open the ORCID record for Sachith Dunatunga [Opens in a new window]  and
Ken Kamrin Open the ORCID record for Ken Kamrin [Opens in a new window]
Sachith Dunatunga
Affiliation:
Department of Mechanical Engineering, MIT, 77 Massachusetts Ave, Cambridge, MA 02139, USA
Ken Kamrin*
Affiliation:
Department of Mechanical Engineering, MIT, 77 Massachusetts Ave, Cambridge, MA 02139, USA
*
†Email address for correspondence: kkamrin@mit.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Granular flow in a silo demonstrates multiple non-local rheological phenomena due to the finite size of grains. We solve the non-local granular fluidity continuum model in quasi-two-dimensional silo geometries and evaluate its ability to predict these non-local effects, including flow spreading and, importantly, clogging (arrest) when the opening is small enough. The model is augmented to include a free-separation criterion and is implemented numerically with an extension of the trans-phase granular flow solver described in Dunatunga & Kamrin (J. Fluid Mech., vol. 779, 2015, pp. 483–513), to produce full-field solutions. The implementation is validated against analytical results of the model in the inclined chute geometry, such as the solution for the critical thickness for flow arrest, and the velocity profile as a function of layer height. We then implement the model in the silo geometry and vary the apparent grain size. The model predicts a clogging criterion when the opening competes with the scale of the mean grain size, which agrees with previous experimental studies. For larger openings, the flow within the silo obtains a diffusive characteristic whose spread depends on the model's non-local amplitude and the mean grain size. The numerical tests are controlled for grid effects and a comparison study of coarse vs refined numerical simulations shows agreement in the pressure field, the shape of the arch in a clogged silo configuration and the velocity field in a flowing configuration.

JFM classification

Granular media: Dry granular material Non-Newtonian Flows: Rheology Mathematical Foundations: Computational methods
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 940 , 10 June 2022 , A14
Check for updates
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Abe, K., Soga, K. & Bandara, S. 2014 Material point method for coupled hydromechanical problems. J. Geotech. Geoenviron. Engng 140 (3), 04013033.CrossRefGoogle Scholar
Andersen, S. & Andersen, L. 2009 Analysis of stress updates in the material-point method. In Proceedings of the Twenty Second Nordic Seminar on Computational Mechanics (ed. L. Damkilde, L. Andersen, A.S. Kristensen & E. Lund), pp. 129–134. Aalborg University. DCE Technical Memorandum.Google Scholar
Aranson, I.S. & Tsimring, L.S. 2001 Continuum description of avalanches in granular media. Phys. Rev. E 64 (2), 020301.CrossRefGoogle ScholarPubMed
Bandara, S. & Soga, K. 2015 Coupling of soil deformation and pore fluid flow using material point method. Comput. Geotech. 63, 199–214.CrossRefGoogle Scholar
Bardenhagen, S.G. 2002 Energy conservation error in the material point method for solid mechanics. J. Comput. Phys. 180, 383–403.CrossRefGoogle Scholar
Bardenhagen, S.G., Brackbill, J.U. & Sulsky, D. 2000 The material-point method for granular materials. Comput. Meth. Appl. Mech. Engng 187 (3–4), 529–541.CrossRefGoogle Scholar
Bardenhagen, S.G. & Kober, E.M. 2004 The generalized interpolation material point method. Comput. Model. Engng Sci. 5 (6), 477–495.Google Scholar
Bazant, M.Z. 2006 The spot model for random-packing dynamics. Mech. Mater. 38 (8–10), 717–731.CrossRefGoogle Scholar
Beverloo, W.A., Leniger, H.A. & van de Velde, J. 1961 The flow of granular solids through orifices. Chem. Engng Sci. 15 (3–4), 260–269.CrossRefGoogle Scholar
Buzzi, O., Pedroso, D.M. & Giacomini, A. 2008 Caveats on the implementation of the generalized material point method. Comput. Model. Engng Sci. 31 (2), 85–106.Google Scholar
Choi, J., Kudrolli, A. & Bazant, M.Z. 2005 Velocity profile of granular flows inside silos and hoppers. J. Phys.: Condens. Matter 17 (24), S2533–S2548.Google Scholar
da Cruz, F., Emam, S., Prochnow, M., Roux, J.-N. & Chevoir, F. 2005 Rheophysics of dense granular materials: discrete simulation of plane shear flows. Phys. Rev. E 72 (2), 021309.CrossRefGoogle ScholarPubMed
Dunatunga, S. & Kamrin, K. 2015 Continuum modelling and simulation of granular flows through their many phases. J. Fluid Mech. 779, 483–513.CrossRefGoogle Scholar
Dunatunga, S. & Kamrin, K. 2017 Continuum modeling of projectile impact and penetration in dry granular media. J. Mech. Phys. Solids 100, 45–60.CrossRefGoogle Scholar
Dunatunga, S.A. 2017 A framework for continuum simulation of granular flow. PhD thesis, Massachusetts Institute of Technology.Google Scholar
de Gennes, P. 1999 Granular matter: a tentative view. Rev. Mod. Phys. 71 (2), S374–S382.CrossRefGoogle Scholar
Gurtin, M.E., Fried, E. & Anand, L. 2010 The Mechanics and Thermodynamics of Continua. Cambridge University Press.CrossRefGoogle Scholar
Henann, D.L. & Kamrin, K. 2013 A predictive, size-dependent continuum model for dense granular flows. Proc. Natl Acad. Sci. USA 110 (17), 6730–6735.CrossRefGoogle ScholarPubMed
Henann, D.L. & Kamrin, K. 2014 Continuum thermomechanics of the nonlocal granular rheology. Intl J. Plasticity 60, 145–162.CrossRefGoogle Scholar
Hidalgo, R.C., Lozano, C., Zuriguel, I. & Garcimartín, A. 2013 Force analysis of clogging arches in a silo. Granul. Matt. 15 (6), 841–848.CrossRefGoogle Scholar
Holyoake, A.J. & McElwaine, J.N. 2012 High-speed granular chute flows. J. Fluid Mech. 710, 35–71.CrossRefGoogle Scholar
Jenike, A.W. 1964 Storage and flow of solids. Bulletin No. 123, Utah State University.Google Scholar
Jop, P., Forterre, Y. & Pouliquen, O. 2005 Crucial role of sidewalls in granular surface flows: consequences for the rheology. J. Fluid Mech. 541, 167–192.CrossRefGoogle Scholar
Jop, P., Forterre, Y. & Pouliquen, O. 2006 A constitutive law for dense granular flows. Nature 441 (7094), 727–30.CrossRefGoogle ScholarPubMed
Kamrin, K. 2010 Nonlinear elasto-plastic model for dense granular flow. Intl J. Plasticity 26 (2), 167–188.CrossRefGoogle Scholar
Kamrin, K. 2019 Non-locality in granular flow: phenomenology and modeling approaches. Front. Phys. 7, 116.CrossRefGoogle Scholar
Kamrin, K. 2020 Quantitative rheological model for granular materials: the importance of particle size. In Handbook of Materials Modeling: Applications: Current and Emerging Materials (ed. W. Andreoni & S. Yip), pp. 153–176. Springer.CrossRefGoogle Scholar
Kamrin, K. & Bazant, M.Z. 2007 Stochastic flow rule for granular materials. Phys. Rev. E 75 (4), 041301.CrossRefGoogle ScholarPubMed
Kamrin, K. & Henann, D.L. 2015 Nonlocal modeling of granular flows down inclines. Soft Matt. 11, 179–185.CrossRefGoogle ScholarPubMed
Kamrin, K. & Koval, G. 2012 Nonlocal constitutive relation for steady granular flow. Phys. Rev. Lett. 108 (17), 178301+.CrossRefGoogle ScholarPubMed
Kamrin, K. & Koval, G. 2014 Effect of particle surface friction on nonlocal constitutive behavior of flowing granular media. Comput. Part. Mech. 1 (2), 169–176.CrossRefGoogle Scholar
Liu, D. & Henann, D.L. 2018 Size-dependence of the flow threshold in dense granular materials. Soft Matt. 14 (25), 5294–5305.CrossRefGoogle ScholarPubMed
Mankoc, C., Janda, A., Arevalo, R., Pastor, J.M., Zuriguel, I., Garcimartín, A. & Maza, D. 2007 The flow rate of granular materials through an orifice. Granul. Matt. 9 (6), 407–414.CrossRefGoogle Scholar
Martin, A., Dubois, F., Monerie, Y. & Radjai, F. 2009 Jamming and flow statistics in a silo geometry. AIP Conf. Proc. 1145 (1), 653–656.CrossRefGoogle Scholar
Mast, C.M. 2013 Modeling landslide-induced flow interactions with structures using the material point method. PhD thesis, University of Washington.Google Scholar
Mast, C.M., Arduino, P., Mackenzie-Helnwein, P. & Miller, G.R. 2015 Simulating granular column collapse using the material point method. Acta Geotech. 10, 101–116.CrossRefGoogle Scholar
Medina, A., Cordova, J.A., Luna, E. & Trevino, C. 1998 Velocity field measurements in granular gravity flow in a near 2D silo. Phys. Lett. A 250 (1–3), 111–116.CrossRefGoogle Scholar
MiDi, G.D.R. 2004 On dense granular flows. Eur. Phys. J. E 14 (4), 341–65.CrossRefGoogle Scholar
Mowlavi, S. & Kamrin, K. 2021 Interplay between hysteresis and nonlocality during onset and arrest of flow in granular materials. Soft Matt. 17, 7359–7375.CrossRefGoogle ScholarPubMed
Mullins, W.W. 1972 Stochastic theory of particle flow under gravity. J. Appl. Phys. 43 (2), 665–678.CrossRefGoogle Scholar
Nedderman, R.M. & Tüzün, U. 1979 A kinematic model for the flow of granular materials. Powder Technol. 22 (2), 243–253.CrossRefGoogle Scholar
Pongó, T., Stiga, V., Török, J., Lévay, S., Szabó, B., Stannarius, R., Hidalgo, R.C. & Börzsönyi, T. 2021 Flow in an hourglass: particle friction and stiffness matter. New J. Phys. 23 (2), 023001.CrossRefGoogle Scholar
Pouliquen, O. 1999 Scaling laws in granular flows down rough inclined planes. Phys. Fluids 11 (3), 542–548.CrossRefGoogle Scholar
Rycroft, C.H., Bazant, M.Z., Grest, G.S. & Landry, J.W. 2006 Dynamics of random packings in granular flow. Phys. Rev. E 73 (5 Pt 1), 051306.CrossRefGoogle ScholarPubMed
Sadeghirad, A., Brannon, R.M. & Burghardt, J. 2011 A convected particle domain interpolation technique to extend applicability of the material point method for problems involving massive deformations. Intl J. Numer. Meth. Engng 86 (12), 1435–1456.CrossRefGoogle Scholar
Samadani, A., Pradhan, A. & Kudrolli, A. 1999 Size segregation of granular matter in silo discharges. Phys. Rev. E 60 (6), 7203.CrossRefGoogle ScholarPubMed
Sheldon, H.G. & Durian, D.J. 2010 Granular discharge and clogging for tilted hoppers. Granul. Matt. 12 (6), 579–585.CrossRefGoogle Scholar
Silbert, L.E., Landry, J.W. & Grest, G.S. 2003 Granular flow down a rough inclined plane: transition between thin and thick piles. Phys. Fluids 15 (1), 1–10.CrossRefGoogle Scholar
Staron, L., Lagrée, P.-Y. & Popinet, S. 2012 The granular silo as a continuum plastic flow: the hour-glass vs the clepsydra. Phys. Fluids 24 (10), 103301.CrossRefGoogle Scholar
Staron, L., Lagrée, P.-Y. & Popinet, S. 2014 Continuum simulation of the discharge of the granular silo: a validation test for the $\mu$(I) visco-plastic flow law. Eur. Phys. J. E 37 (1), 5.CrossRefGoogle ScholarPubMed
Sulsky, D., Chen, Z. & Schreyer, H.L. 1994 A particle method for history-dependent materials. Comput. Meth. Appl. Mech. Engng 118 (1–2), 179–196.CrossRefGoogle Scholar
Thomas, C. & Durian, D. 2013 Geometry dependence of the clogging transition in tilted hoppers. Phys. Rev. E 87, 052201.CrossRefGoogle ScholarPubMed
Thomas, C. & Durian, D. 2016 Intermittency and velocity fluctuations in hopper flows prone to clogging. Phys. Rev. E 94, 022901.CrossRefGoogle Scholar
To, K., Lai, P.-Y. & Pak, H.K. 2001 Jamming of granular flow in a two-dimensional hopper. Phys. Rev. Lett. 86, 71–74.CrossRefGoogle Scholar
Tüzün, U. & Nedderman, R.M. 1979 Experimental evidence supporting kinematic modelling of the flow of granular media in the absence of air drag. Powder Technol. 24 (2), 257–266.CrossRefGoogle Scholar
Weinhart, T., Labra, C., Luding, S. & Ooi, J.Y. 2016 Influence of coarse-graining parameters on the analysis of dem simulations of silo flow. Powder Technol. 293, 138–148.CrossRefGoogle Scholar
Wiȩckowski, Z. 1999 A particle-in-cell solution to the silo discharging problem. Intl J. Numer. Meth. Engng 1225 (February 1998), 1203–1225.3.0.CO;2-C>CrossRefGoogle Scholar
Wiȩckowski, Z. 2001 Analysis of granular flow by the material point method. In European Conference on Computational Mechanics, Cracow, Poland.Google Scholar
Wiȩckowski, Z. 2003 Modelling of silo discharge and filling problems by the material point method. Task Quarterly 4 (4), 701–721.Google Scholar
Wiȩckowski, Z. & Kowalska-Kubsik, I. 2011 Non-local approach in modelling of granular flow by the material point method. In Computer Methods in Mechanics, Warsaw, Poland.Google Scholar
Yue, Y., Smith, B., Chen, P.Y., Chantharayukhonthorn, M., Kamrin, K. & Grinspun, E. 2018 Hybrid grains: adaptive coupling of discrete and continuum simulations of granular media. ACM Trans. Graph. 37 (6), 283.CrossRefGoogle Scholar
Zuriguel, I., Garcimartín, A., Maza, D., Pugnaloni, L.A. & Pastor, J.M. 2005 Jamming during the discharge of granular matter from a silo. Phys. Rev. E 71, 051303.CrossRefGoogle ScholarPubMed
Zuriguel, I., Maza, D., Janda, A., Hidalgo, R.C. & Garcimartín, A. 2019 Velocity fluctuations inside two and three dimensional silos. Granul. Matt. 21 (3), 47.CrossRefGoogle Scholar
Zuriguel, I., et al. 2014 Clogging transition of many-particle systems flowing through bottlenecks. Sci. Rep. 4 (1), 7324.CrossRefGoogle ScholarPubMed
Zuriguel, I., Pugnaloni, L., Garcimartín, A. & Maza, D. 2003 Jamming during the discharge of grains from a silo described as a percolating transition. Phys. Rev. E 68, 030301.CrossRefGoogle ScholarPubMed

Dunatunga and Kamrin supplementary movie

See pdf file for movie cation

Download Dunatunga and Kamrin supplementary movie(Video)
Video 4.4 MB
Supplementary material: PDF

Dunatunga and Kamrin supplementary material

Caption for movie

Download Dunatunga and Kamrin supplementary material(PDF)
PDF 10.3 KB