Skip to main content
SpringerLink
Log in

Role of flying buttresses in the jamming of granular matter through multiple rectangular outlets

  • Original Paper
  • Published:
Granular Matter Aims and scope Submit manuscript

Abstract

We present a simulation study on the formation of particle arches supported by flying buttresses that arrest the flow of monodisperse spherical particles through two adjacent slots (rectangular outlets) in a three-dimensional (3D) anisometric flat-bottomed silo discharging under gravity. Most previous experimental and simulation studies on the jamming of a silo have focused on a single outlet, and have shown that the mean number of particles exiting the silo before it jams depends on the ratio of outlet size to particle diameter (\(R\)). In this paper, we look at the nature of jamming if there are two adjacent outlets and discover some new physical insights on how sand arches are mechanically supported and how they interact with each other. For a fixed slot width \(D_{o}\) and particle diameter \(d\), the distance separating the two openings \(D_{w}\) is varied. The distribution of \(N\) particles exiting the silo before both slots are jammed is obtained for each \(D_{w}\). From these distributions, we show that as \(D_{w}\) becomes less than approximately \(3d\), the particle arches on adjacent outlets start affecting each other, and mutually stable arches become harder to form. We show that in cases, where for a small orifice ratio \(R={D_o}/d\) a single outlet would have easily jammed, two adjacent outlets do not jam. We propose that this is due to the importance of stable particles resting on the base of the silo adjacent to the arches, which redistribute the load much like a flying buttress does in Gothic arches.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Abbreviations

\(d\) :

Particle diameter, L, m (\(\,\upmu \hbox {m}\))

\(D_{o}\) :

Outlet size, L, m (\(\,\upmu \hbox {m}\))

\(D_{w}\) :

Wire-width or distance between adjacent outlets, L, m (\(\,\upmu \hbox {m}\))

\(e\) :

Dimensionless coefficient of restitution

\(E\) :

Young’s modulus, \(\hbox {ML}^{-1}\, \hbox {T}^{-2}\), Pa (psi)

\(f_{D_{w,R}}(N)\) :

Normalized frequency distribution of avalanche size

\(N\) :

Avalanche size

\(\left\langle N \right\rangle \) :

Mean avalanche size

\(R\) :

Dimensionless outlet-to-particle size ratio

\(R^{*}\) :

Critial \(R\) above which no jamming

\(S\) :

Dimensionless wire-width-to-particle size ratio

\(S^{*}\) :

Critial \(S\) below which adjacent outlets interact

\(\mu \) :

Friction coefficient

\(\mu _r\) :

Rolling-friction coefficient

\(\nu \) :

Poisson’s ratio

\(\phi \) :

Density, \(\hbox {ML}^{-3}, \hbox {kg/m}^{3}\)

References

  1. Zuriguel, I., Pugnaloni, L.A., Garcimartín, A., et al.: Jamming during discharge of grains from a silo described as a percolating transition. Phys. Rev. E 68(3), 030301 (2003). doi:10.1103/PhysRevE.68.030301

    Article  ADS  Google Scholar 

  2. Liu, A.J., Nagel, S.R.: Nonlinear dynamics: jamming is not just cool anymore. Nature 396(6706), 21–22 (1998). doi:10.1038/23819

    Article  ADS  Google Scholar 

  3. Janda, A., Zuriguel, I., Garcimartín, A., et al.: Jamming and critical outlet size in the discharge of a two-dimensional silo. EPL 84(4), 44002 (2008). doi:10.1209/0295-5075/84/44002

    Article  ADS  Google Scholar 

  4. Mehta, A., Barker, G.C.: The dynamics of sand. Rep. Prog. Phys. 57(4), 383 (1994). doi:10.1088/0034-4885/57/4/002

    Article  ADS  Google Scholar 

  5. Mehta, A.: Granular Physics. Cambridge University Press, Cambridge (2007). ISBN 978-0521660785

    Book  MATH  Google Scholar 

  6. Mehta, A.: Spatial, dynamical and spatiotemporal heterogeneities in granular media. Soft Matter 6(13), 2875–2883 (2010). doi:10.1039/B926809J

    Article  ADS  Google Scholar 

  7. Duran, J., Rajchenbach, J., Clement, E.: Arching effect model for particle size segregation. Phys. Rev. Lett. 70(16), 2431–2434 (1993). doi:10.1103/PhysRevLett.70.2431

    Article  ADS  Google Scholar 

  8. O’Hern, C.S., Langer, S.A., Liu, A.J., et al.: Force distributions near jamming and glass transitions. Phys. Rev. Lett. 86(1), 111–114 (2001). doi:10.1103/PhysRevLett.86.111

    Article  ADS  Google Scholar 

  9. Nowak, E.R., Knight, J.B., Ben-Naim, E., et al.: Density fluctuations in vibrated granular materials. Phys. Rev. E 57(2), 1971–1982 (1998). doi:10.1103/PhysRevE.57.1971

    Article  ADS  Google Scholar 

  10. Pugnaloni, L.A., Valluzzi, M.G., Valluzzi, L.G.: Arching in tapped deposits of hard disks. Phys. Rev. E 73(5), 051302 (2006). doi:10.1103/PhysRevE.73.051302

    Article  ADS  Google Scholar 

  11. Dorobolo, S., Vandewalle, N.: Electrical investigations of granular arches. Phys. A Stat. Mech. Appl. 311(3–4), 307–312 (2002). doi:10.1016/S0378-4371(02)00746-X

    Article  Google Scholar 

  12. To, K., Lai, P.Y., Pak, H.K.: Jamming of granular flow in a two-dimensional hopper. Phys. Rev. Lett. 86(1), 71–74 (2001). doi:10.1103/PhysRevLett.86.71

    Article  ADS  Google Scholar 

  13. To, K., Lai, P.K., Pak, H.K.: Flow and jam of granular particles in a two-dimensional hopper. Phys. A Stat. Mech. Appl. 315(1–2), 174–180 (2002). doi:10.1016/S0378-4371(02)01237-2

    Article  Google Scholar 

  14. To, K., Lai, P.Y.: Jamming pattern in a two-dimensional hopper. Phys. Rev. E 66(1), 011308 (2002). doi:10.1103/PhysRevE.66.011308

    Article  ADS  Google Scholar 

  15. Zuriguel, I., Garcimartín, A., Diego, M., et al.: Jamming during discharge of granular matter from a silo. Phys. Rev. E 71(5), 051303 (2005). doi:10.1103/PhysRevE.71.051303

    Article  ADS  Google Scholar 

  16. Arevalo, R., Maza, D., Pugnaloni, L.A.: Identification of arches in two-dimensional granular packings. Phys. Rev. E 74(2), 021303 (2006). doi:10.1103/PhysRevE.74.021303

    Article  ADS  Google Scholar 

  17. Saraf, S., Franklin, S.V.: Power-law flow statistics in anisometric (wedge) hoppers. Phys. Rev. E 83(3), 030301 (2011). doi:10.1103/PhysRevE.83.030301

    Article  ADS  Google Scholar 

  18. Pournin, L., Ramaioli, M., Folly, P., et al.: About the influence of friction and polydispersity one the jamming behavior of bead assemblies. Eur. Phys. J. E 23(2), 229–235 (2007). doi:10.1140/epje/i2007-10176-5

    Article  Google Scholar 

  19. Tsukahara, M., Pournin, L., Liebling, T.M.: Simple probabilistic modeling of granular jamming and validation using DEM. AIP Conf. Proc. 1145, 507–510 (2009). doi:10.1063/1.3179973

    Article  ADS  Google Scholar 

  20. Magalhaes, C.F.M., Moreira, J.G., Atman, A.P.F.: Segregation in arch formation. Eur. Phys. J. E 35, 38 (2012). doi:10.1140/epje/i2012-12038-5

    Article  Google Scholar 

  21. Chevoir, F., Gaulard, F., Roussel, N.: Flow and jamming of granular mixtures through obstacles. EPL 79(1), 14001 (2007). doi:10.1209/0295-5075/79/14001

    Article  ADS  Google Scholar 

  22. Mondal, S., Sharma, M.M., Chanpura, R.A., et al.: Numerical simulations of sand-screen performance in standalone applications. SPE Drill Compl. 26(4), 472–483 (2011). doi:10.2118/134326-PA

    Google Scholar 

  23. Mondal, S., Sharma, M.M., Hodge, R.M., et al.: A new method for the design and selection of premium/woven sand screens. SPE Drill Compl. 27(3), 407–416 (2012). doi:10.2118/146656-PA

    Google Scholar 

  24. Kloss, C., Goniva, C.: LIGGGHTS-A new open source discrete element simulation software. In: Proceedings of Fifth International Conference on Discrete Element Methods, London. pp. 25–26, ISBN 978-0-9551179-8-5 (2010)

  25. Kloss, C., Goniva, C., Hager, A., et al.: Models, algorithms and validation for opensource DEM and CFD-DEM. Progr. Comput. Fluid Dyn. Int. J. 12(2–3), 140–152 (2012). doi:10.1504/PCFD.2012.047457. (LIGGGHTS and CFDEM are available online at http://www.cfdem.com)

  26. Plimpton, S.J.: Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117(1), 1–19 (1995). doi:10.1006/jcph.1995.1039

    Article  ADS  MATH  Google Scholar 

  27. Brilliantov, N.V., Spahn, F., Hertzsch, J.M., et al.: Model for collisions in granular gases. Phys. Rev. E 53(5), 5382–5392 (1996). doi:10.1103/PhysRevE.53.5382

    Article  ADS  Google Scholar 

  28. Silbert, L.E., Ertas, D., Grest, G.S., et al.: Granular flow down an inclined plane: bagnold scaling and rheology. Phys. Rev. E 64(5), 051302 (2001). doi:10.1103/PhysRevE.64.051302

    Article  ADS  Google Scholar 

  29. Zhang, H.P., Makse, H.A.: Jamming transition in emulsions and granular materials. Phys. Rev. E 72(1), 011301 (2005). doi:10.1103/PhysRevE.72.011301

    Article  ADS  Google Scholar 

  30. Ai, J., Chen, J.F., Rotter, J.M., et al.: Assessment of rolling resistance models in discrete element simulations. Powder Technol. 206(3), 269–282 (2011). doi:10.1016/j.powtec.2010.09.030

    Article  Google Scholar 

  31. Renzo, A.D., DiMaio, F.P.: Comparison of contact-force models for the simulation of collisions in DEM-based granular flow codes. Chem. Eng. Sci. 59(3), 525–541 (2004). doi:10.1016/j.ces.2003.09.037

    Article  Google Scholar 

  32. Luding, S., Duran, J., Clement, E., Rajchenbach, J.: Computer simulations and experiments of dry granular media: polydisperse disks in a vertical pipe. In: Proceedings of 5th World Congress of, Chemical Engineering, vol. 5, pp. 325–330 (1996)

  33. Luding, S., Duran, J., Clement, E., Rajchenbach, J.: Simulations of dense granular flow: dynamic arches and spin organization. J. Phys. I France 6, 823–836 (1996). doi:10.1051/jp1:1996244

    Article  Google Scholar 

  34. Salpietra, M. Physics of stone arches [http://www.pbs.org/wgbh/nova/physics/arch-physics.html]

  35. Ignis, [http://commons.wikimedia.org/wiki/File:Flying_buttress_Notre_Dame_de_Strasbourg_Strasbourg_FRA_001.jpg]

  36. Mark, R.: Structural experimentation in gothic architecture. Am. Sci. 66(5), 542–550 (1978). http://www.jstor.org/stable/27848848

    Google Scholar 

  37. Vivanco, F., Rica, S., Melo, F.: Dynamical arching in two dimensional granular flow. Granul. Matter 14, 563–576 (2012). doi:10.1007/s10035-012-0359-7

    Google Scholar 

  38. Hidalgo, R.C., Lozano, C., Zuriguel, I., Garcimartin, A.: Force analysis of clogging arches in a silo. Granul. Matter 15, 841–848 (2013). doi:10.1007/s10035-013-0451-7

    Article  Google Scholar 

Download references

Acknowledgments

We wish to acknowledge the Texas Advanced Computing Center (TACC) at the University of Texas at Austin for providing HPC resources for this research.

Author information

Authors and Affiliations

  1. Department of Petroleum and Geosystems Engineering, University of Texas at Austin, Austin, TX, 78712, USA

    Somnath Mondal & Mukul M. Sharma

Authors
  1. Somnath Mondal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mukul M. Sharma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Somnath Mondal.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mondal, S., Sharma, M.M. Role of flying buttresses in the jamming of granular matter through multiple rectangular outlets. Granular Matter 16, 125–132 (2014). https://doi.org/10.1007/s10035-013-0461-5

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10035-013-0461-5

Keywords

Search

Navigation