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Computational Particle Mechanics

, Volume 6, Issue 1, pp 55–84 | Cite as

Grains3D, a flexible DEM approach for particles of arbitrary convex shape—Part III: extension to non-convex particles modelled as glued convex particles

  • Andriarimina Daniel Rakotonirina
  • Jean-Yves Delenne
  • Farhang Radjai
  • Anthony WachsEmail author
Article
  • 95 Downloads

Abstract

Large-scale numerical simulation using the discrete element method (DEM) contributes to improving our understanding of granular flow dynamics involved in many industrial processes and geophysical flows. In industry, it leads to an enhanced design and an overall optimization of the corresponding equipment and process. Most of the DEM simulations in the literature have been performed using spherical particles. A limited number of studies dealt with non-spherical particles, even less with non-convex particles. Even convex bodies do not always represent the real shape of certain particles. In fact, more complex-shaped particles are found in many industrial applications, for example, catalytic pellets in chemical reactors or crushed glass debris in recycling processes. In Grains3D-Part I (Wachs et al. in Powder Technol 224:374–389, 2012), we addressed the problem of convex shape in granular simulations, while in Grains3D-Part II (Rakotonirina and Wachs in Powder Technol 324:18–35, 2018), we suggested a simple though efficient parallel strategy to compute systems with up to a few hundreds of millions of particles. The aim of the present study is to extend even further the modelling capabilities of Grains3D towards non-convex shapes, as a tool to examine the flow dynamics of granular media made of non-convex particles. Our strategy is based on decomposing a non-convex-shaped particle into a set of convex bodies, called elementary components. We call our method glued or clumped convex method, as an extension of the popular glued sphere method. Essentially, a non-convex particle is constructed as a cluster of convex particles, called elementary components. At the level of these elementary components of a glued convex particle, we employ the same contact detection strategy based on a Gilbert–Johnson–Keerthi algorithm and a linked-cell spatial sorting that accelerates the resolution of the contact, that we introduced in [39]. Our glued convex model is implemented as a new module of our code Grains3D and is therefore automatically fully parallel. We illustrate the new modelling capabilities of Grains3D in two test cases: (1) the filling of a container and (2) the flow dynamics in a rotating drum.

Keywords

Granular flow Discrete element method Non-convex shape GJK algorithm Glued convex 

Notes

Acknowledgements

We would like to thank Prof. Neil Balmforth, University of British Columbia, Canada, for giving us access to his rotating drum experimental set-up and for providing assistance to conduct the experiments. We also would like to acknowledge the help and continuous support of Dr. Abdelkader Hammouti, IFP Energies nouvelles, France, in sharpening up this paper.

Compliance with ethical standards

Conflicts of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Supplementary material

40571_2018_198_MOESM1_ESM.mp4 (2.5 mb)
Supplementary material 1 (mp4 2524 KB)

References

  1. 1.
    Abbaspour-Fard M (2004) Theoretical validation of a multi-sphere, discrete element model suitable for biomaterials handling simulation. Biosyst Eng 88(2):153–161CrossRefGoogle Scholar
  2. 2.
    Alonso-Marroquín F, Wang Y (2009) An efficient algorithm for granular dynamics simulations with complex-shaped objects. Granul Matter 11(5):317–329CrossRefzbMATHGoogle Scholar
  3. 3.
    Bekker H, Roerdink J B (2001) An efficient algorithm to calculate the minkowski sum of convex 3d polyhedra. In: Computational science–ICCS 2001. Springer, pp 619–628Google Scholar
  4. 4.
    Camborde F, Mariotti C, Donzé F (2000) Numerical study of rock and concrete behaviour by discrete element modelling. Comput Geotech 27(4):225–247CrossRefGoogle Scholar
  5. 5.
    Coumans E (2015) Bullet 2.83 Physics Library manualGoogle Scholar
  6. 6.
    Cundall PA (1988) Formulation of a three-dimensional distinct element model–Part I. A scheme to detect and represent contacts in a system composed of many polyhedral blocks. Int J Rock Mech Min Sci Geomech Abstracts 25(3):107–116CrossRefGoogle Scholar
  7. 7.
    Cundall P, Strack O (1979) A discrete numerical model for granular assemblies. Geotechnique 29(1):47–65CrossRefGoogle Scholar
  8. 8.
    Doe R (2009) Computational Geometry Algorithms Library (CGAL)Google Scholar
  9. 9.
    Džiugys A, Peters B (2001) An approach to simulate the motion of spherical and non-spherical fuel particles in combustion chambers. Granul Matter 3(4):231–266CrossRefGoogle Scholar
  10. 10.
    Feng Y, Owen D (2004) A 2D polygon/polygon contact model: algorithmic aspects. Eng Comput 21(2/3/4):265–277CrossRefzbMATHGoogle Scholar
  11. 11.
    Fraige FY, Langston PA, Chen GZ (2008) Distinct element modelling of cubic particle packing and flow. Powder Technol 186(3):224–240CrossRefGoogle Scholar
  12. 12.
    Gilbert EG, Foo C (1990) Computing the distance between general convex objects in three-dimensional space. IEEE Trans Robot Autom 6(1):53–61CrossRefGoogle Scholar
  13. 13.
    Gilbert EG, Johnson DW, Keerthi SS (1988) A fast procedure for computing the distance between complex objects in three-dimensional space. IEEE Trans Robot Autom 4(2):193–203CrossRefGoogle Scholar
  14. 14.
    Hart R, Cundall P, Lemos J (1988) Formulation of a three-dimensional distinct element model–Part II. Mechanical calculations for motion and interaction of a system composed of many polyhedral blocks. In: International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, vol 25. Elsevier, pp 117–125Google Scholar
  15. 15.
    Hentz S, Daudeville L, Donzé FV (2004) Identification and validation of a discrete element model for concrete. J Eng Mech 130(6):709–719CrossRefGoogle Scholar
  16. 16.
    Höhner D, Wirtz S, Kruggel-Emden H, Scherer V (2011) Comparison of the multi-sphere and polyhedral approach to simulate non-spherical particles within the discrete element method: influence on temporal force evolution for multiple contacts. Powder Technol 208(3):643–656CrossRefGoogle Scholar
  17. 17.
    Jin F, Xin H, Zhang C, Sun Q (2011) Probability-based contact algorithm for non-spherical particles in DEM. Powder Technol 212(1):134–144CrossRefGoogle Scholar
  18. 18.
    Jing L (1998) Formulation of discontinuous deformation analysis (dda)-an implicit discrete element model for block systems. Eng Geol 49(3):371–381CrossRefGoogle Scholar
  19. 19.
    Kodam M, Bharadwaj R, Curtis J, Hancock B, Wassgren C (2010) Cylindrical object contact detection for use in discrete element method simulations. Part II-Experimental validation. Chem Eng Sci 65(22):5863–5871CrossRefGoogle Scholar
  20. 20.
    Kruggel-Emden H, Rickelt S, Wirtz S, Scherer V (2008) A study on the validity of the multi-sphere discrete element method. Powder Technol 188(2):153–165CrossRefGoogle Scholar
  21. 21.
    Langston P, Tüzün U, Heyes D (1994) Continuous potential discrete particle simulations of stress and velocity fields in hoppers: transition from fluid to granular flow. Chem Eng Sci 49(8):1259–1275CrossRefGoogle Scholar
  22. 22.
    Langston P, Tüzün U, Heyes D (1995) Discrete element simulation of granular flow in 2d and 3d hoppers: dependence of discharge rate and wall stress on particle interactions. Chem Eng Sci 50(6):967–987CrossRefGoogle Scholar
  23. 23.
    Lee Y, Fang C, Tsou Y-R, Lu L-S, Yang C-T (2009) A packing algorithm for three-dimensional convex particles. Granular Matter 11(5):307–315CrossRefzbMATHGoogle Scholar
  24. 24.
    Li J, Langston PA, Webb C, Dyakowski T (2004) Flow of sphero-disc particles in rectangular hoppers-a DEM and experimental comparison in 3D. Chem Eng Sci 59(24):5917–5929CrossRefGoogle Scholar
  25. 25.
    Lu G, Third J, Müller C (2015) Discrete element models for non-spherical particle systems: from theoretical developments to applications. Chem Eng Sci 127:425–465CrossRefGoogle Scholar
  26. 26.
    Luchnikov V, Medvedev N, Oger L, Troadec J-P (1999) Voronoi–Delaunay analysis of voids in systems of nonspherical particles. Phys Rev E 59:7205–7212CrossRefGoogle Scholar
  27. 27.
    Mellmann J (2001) The transverse motion of solids in rotating cylinders-forms of motion and transition behavior. Powder Technol 118(3):251–270CrossRefGoogle Scholar
  28. 28.
    Munjiza A, Peters JF, Hopkins MA, Kala R, Wahl RE (2009) A poly-ellipsoid particle for non-spherical discrete element method. Eng Comput 26(6):645–657CrossRefGoogle Scholar
  29. 29.
    Nolan G, Kavanagh P (1995) Random packing of nonspherical particles. Powder Technol 84(3):199–205CrossRefGoogle Scholar
  30. 30.
    Park J (2003) Modeling the dynamics of fabric in a rotating horizontal drum. Ph.D. thesis, Purdue UniversityGoogle Scholar
  31. 31.
    Petit D, Pradel F, Ferrer G, Meimon Y (2001) Shape effect of grain in a granular flow. In: Kishino Y (ed) Powders and grains. CRC Press, pp 425Google Scholar
  32. 32.
    Pournin L, Liebling T (2005) A generalization of distinct element method to tridimensional particles with complex shapes. In: García-Rojo R, Herrmann HJ, McNamara S (eds) Powders and grains, vol 5805, pp 1375–1378Google Scholar
  33. 33.
    Rakotonirina AD, Wachs A (2018) Grains3D, a flexible DEM approach for particles of arbitrary convex shape–Part II: parallel implementation and scalable performance. Powder Technol 324:18–35CrossRefGoogle Scholar
  34. 34.
    Rémond S, Gallias J, Mizrahi A (2008) Simulation of the packing of granular mixtures of non-convex particles and voids characterization. Granul Matter 10(3):157–170CrossRefzbMATHGoogle Scholar
  35. 35.
    Song Y, Turton R, Kayihan F (2006) Contact detection algorithms for DEM simulations of tablet-shaped particles. Powder Technol 161(1):32–40CrossRefGoogle Scholar
  36. 36.
    Tangri H, Guo Y, Curtis J (2017) Packing of cylindrical particles: DEM simulations and experimental measurements. Powder Technol 317:72–82CrossRefGoogle Scholar
  37. 37.
    van den Bergen G (1999) A fast and robust GJK implementation for collision detection of convex objects. J Graph Tools 4(2):7–25CrossRefGoogle Scholar
  38. 38.
    Wachs A (2009) A DEM-DLM/FD method for direct numerical simulation of particulate flows: sedimentation of polygonal isometric particles in a Newtonian fluid with collisions. Comput Fluids 38(8):1608–1628CrossRefzbMATHGoogle Scholar
  39. 39.
    Wachs A, Girolami L, Vinay G, Ferrer G (2012) Grains3D, a flexible DEM approach for particles of arbitrary convex shape—Part I: numerical model and validations. Powder Technol 224:374–389CrossRefGoogle Scholar
  40. 40.
    Williams JR, O’Connor R (1995) A linear complexity intersection algorithm for discrete element simulation of arbitrary geometries. Eng Comput 12(2):185–201CrossRefGoogle Scholar
  41. 41.
    Williams JR, Pentland AP (1992) Superquadrics and modal dynamics for discrete elements in interactive design. Eng Comput 9(2):115–127CrossRefGoogle Scholar
  42. 42.
    Wu Y, An X, Yu A (2017) DEM simulation of cubical particle packing under mechanical vibration. Powder Technol 314:89–101CrossRefGoogle Scholar
  43. 43.
    Yang R, Zou R, Yu A (2003) Microdynamic analysis of particle flow in a horizontal rotating drum. Powder Technol 130(1–3):138–146CrossRefGoogle Scholar
  44. 44.
    Yang R, Yu A, McElroy L, Bao J (2008) Numerical simulation of particle dynamics in different flow regimes in a rotating drum. Powder Technol 188(2):170–177CrossRefGoogle Scholar
  45. 45.
    Zhao B, An X, Wang Y, Qian Q, Yang X, Sun X (2017) DEM dynamic simulation of tetrahedral particle packing under 3D mechanical vibration. Powder Technol 317:171–180CrossRefGoogle Scholar

Copyright information

© OWZ 2018

Authors and Affiliations

  1. 1.Fluid Mechanics DepartmentIFP Energies nouvellesSolaizeFrance
  2. 2.Department of MathematicsUniversity of British ColumbiaVancouverCanada
  3. 3.Department of Chemical and Biological EngineeringUniversity of British ColumbiaVancouverCanada
  4. 4.IATE, UMR 1208 INRA – CIRAD – Montpellier SupagroUniversité Montpellier 2Montpellier CedexFrance
  5. 5.CNRS, LMGC UMR 5508University Montpellier 2Montpellier CedexFrance
  6. 6.MultiScale Material Science for Energy and Environment, UMI 3466 CNRS-MIT, DCEEMassachusetts Institute of TechnologyCambridgeUSA

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