Poly-superquadric model for DEM simulations of asymmetrically shaped particles

Abstract

The superquadric function is employed to represent spherical and non-spherical particles. Although particles with different aspect ratios and surface blockiness can be described using the superquadric equation, the shapes of these particles are geometrically symmetric and further engineering applications are limited. In this work, a poly-superquadric element based on the superquadric function is developed. This model is composed of eight one-eighth superquadric elements and is used to represent superquadric elements, poly-ellipsoids, and asymmetrically shaped particles. To examine the validity of the poly-superquadric DEM model, the numerical results of a hemisphere impacting a plane are obtained and compared with the theoretical results. Then, the mass flow rates of particles of different shapes are investigated. The results show that the spheres have the fastest flow rate, and the flow rate of the pebble-shaped particles constructed by the poly-superquadric elements is faster than that of the cube-like particles. Moreover, the flow rate of superquadric and poly-superquadric elements decreases as the blockiness parameter increases. Geometrically asymmetric and elongated particles are rearranged to form interlocking and local clusters, which limit the relative motion between particles and reduce the flowability of non-spherical granular materials.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

References

  1. 1.

    Cundall PA, Strack ODL (1979) A discrete numerical mode for granular assemblies. Géotechnique 29(1):47–65. https://doi.org/10.1680/geot.1979.29.1.47

    Article  Google Scholar 

  2. 2.

    Sinnott MD, Cleary PW (2015) The effect of particle shape on mixing in a high shear mixer. Comput Particle Mech 3(4):477–504. https://doi.org/10.1007/s40571-015-0065-4

    Article  Google Scholar 

  3. 3.

    Xu W, Zhang Y, Jiang J, Liu Z, Jiao Y (2021) Thermal conductivity and elastic modulus of 3D porous/fractured media considering percolation. Int J Eng Sci 161:103456. https://doi.org/10.1016/j.ijengsci.2021.103456

    Article  MATH  Google Scholar 

  4. 4.

    Ji S (2013) Probability analysis of contact forces in quasi-solid-liquid phase transition of granular shear flow. Sci China Phys Mech Astron 56(2):395–403. https://doi.org/10.1007/s11433-012-4979-z

    Article  Google Scholar 

  5. 5.

    Xue J, Schiano S, Zhong W, Chen L, Wu C-Y (2019) Determination of the flow/no-flow transition from a flat bottom hopper. Powder Technol 358:55–61. https://doi.org/10.1016/j.powtec.2018.08.063

    Article  Google Scholar 

  6. 6.

    Li Y, Gui N, Yang X, Tu J, Jiang S (2016) Effect of friction on pebble flow pattern in pebble bed reactor. Ann Nucl Energy 94:32–43. https://doi.org/10.1016/j.anucene.2016.02.022

    Article  Google Scholar 

  7. 7.

    Boton M, Azéma E, Estrada N, Radjaï F, Lizcano A (2013) Quasistatic rheology and microstructural description of sheared granular materials composed of platy particles. Phys Rev E 87:032206. https://doi.org/10.1103/PhysRevE.87.032206

    Article  Google Scholar 

  8. 8.

    Höhner D, Wirtz S, Scherer V (2012) A numerical study on the influence of particle shape on hopper discharge within the polyhedral and multi-sphere discrete element method. Powder Technol 226(8):16–28

    Article  Google Scholar 

  9. 9.

    Lu G, Third JR, Müller CR (2015) Discrete element models for non-spherical particle systems: from theoretical developments to applications. Chem Eng Sci 127:425–465. https://doi.org/10.1016/j.ces.2014.11.050

    Article  Google Scholar 

  10. 10.

    Zhong W, Yu A, Liu X, Tong Z, Zhang H (2016) DEM/CFD-DEM Modelling Of Non-Spherical Particulate Systems: Theoretical Developments And Applications. Powder Technol 302:108–152. https://doi.org/10.1016/j.powtec.2016.07.010

    Article  Google Scholar 

  11. 11.

    Kafashan J, Wiącek J, Abd Rahman N, Gan J (2019) Two-dimensional particle shapes modelling for DEM simulations in engineering: a review. Granul Matter 21:80. https://doi.org/10.1007/s10035-019-0935-1

    Article  Google Scholar 

  12. 12.

    Liu L, Ji S (2020) A new contact detection method for arbitrary dilated polyhedra with potential function in discrete element method. Int J Numer Methods Eng. https://doi.org/10.1002/nme.6522

    MathSciNet  Article  Google Scholar 

  13. 13.

    Cleary PW (2019) Effect of rock shape representation in DEM on flow and energy utilisation in a pilot SAG mill. Comput Particle Mech 6(3):461–477. https://doi.org/10.1007/s40571-019-00226-3

    Article  Google Scholar 

  14. 14.

    Gong Z, Wu Y, Zhu Z, Wang Y, Liu Z, Xu W (2020) DEM and dual-probability-Brownian motion scheme for thermal conductivity of multiphase granular materials with densely packed non-spherical particles and soft interphase networks. Comput Methods Appl Mech Eng 372:113372. https://doi.org/10.1016/j.cma.2020.113372

    MathSciNet  Article  MATH  Google Scholar 

  15. 15.

    He SY, Gan JQ, Pinson D, Yu AB, Zhou ZY (2019) Flow regimes of cohesionless ellipsoidal particles in a rotating drum. Powder Technol 354:174–187. https://doi.org/10.1016/j.powtec.2019.05.083

    Article  Google Scholar 

  16. 16.

    Tangri H, Guo Y, Curtis JS (2019) Hopper discharge of elongated particles of varying aspect ratio: experiments and DEM simulations. Chem Eng Sci X 4:100040. https://doi.org/10.1016/j.cesx.2019.100040

    Article  Google Scholar 

  17. 17.

    Govender N, Wilke DN, Pizette P, Abriak N-E (2018) A study of shape non-uniformity and poly-dispersity in hopper discharge of spherical and polyhedral particle systems using the Blaze-DEM GPU code. Appl Math Comput 319:318–336. https://doi.org/10.1016/j.amc.2017.03.037

    Article  MATH  Google Scholar 

  18. 18.

    Höhner D, Wirtz S, Scherer V (2013) Experimental and numerical investigation on the influence of particle shape and shape approximation on hopper discharge using the discrete element method. Powder Technol 235:614–627. https://doi.org/10.1016/j.powtec.2012.11.004

    Article  Google Scholar 

  19. 19.

    Zhao Y, Chew JW (2020) Discrete element method study on hopper discharge behaviors of binary mixtures of nonspherical particles. AIChE J 66(8):e16254. https://doi.org/10.1002/aic.16254

    Article  Google Scholar 

  20. 20.

    Li C, Peng Y, Zhang P, Zhao C (2019) The contact detection for heart-shaped particles. Powder Technol 346:85–96. https://doi.org/10.1016/j.powtec.2019.01.079

    Article  Google Scholar 

  21. 21.

    Garboczi EJ, Bullard JW (2017) 3D analytical mathematical models of random star-shape particles via a combination of X-ray computed microtomography and spherical harmonic analysis. Adv Powder Technol 28(2):325–339. https://doi.org/10.1016/j.apt.2016.10.014

    Article  Google Scholar 

  22. 22.

    Kawamoto R, Andò E, Viggiani G, Andrade JE (2016) Level set discrete element method for three-dimensional computations with triaxial case study. J Mech Phys Solids 91:1–13. https://doi.org/10.1016/j.jmps.2016.02.021

    MathSciNet  Article  Google Scholar 

  23. 23.

    Boon CW, Houlsby GT, Utili S (2013) A new contact detection algorithm for three-dimensional non-spherical particles. Powder Technol 248:94–102. https://doi.org/10.1016/j.powtec.2012.12.040

    Article  Google Scholar 

  24. 24.

    Mollon G, Zhao J (2014) 3D generation of realistic granular samples based on random fields theory and Fourier shape descriptors. Comput Methods Appl Mech Eng 279:46–65. https://doi.org/10.1016/j.cma.2014.06.022

    Article  MATH  Google Scholar 

  25. 25.

    Feng YT, Han K, Owen DRJ (2012) Energy-conserving contact interaction models for arbitrarily shaped discrete elements. Comput Methods Appl Mech Eng 205(1):169–177

    MathSciNet  Article  Google Scholar 

  26. 26.

    Feng YT (2021) An energy-conserving contact theory for discrete element modelling of arbitrarily shaped particles: Basic framework and general contact model. Comput Methods Appl Mech Eng. https://doi.org/10.1016/j.cma.2020.113454

    MathSciNet  Article  MATH  Google Scholar 

  27. 27.

    Meng L, Wang C, Yao X (2018) Non-convex shape effects on the dense random packing properties of assembled rods. Phys A 490:212–221. https://doi.org/10.1016/j.physa.2017.08.026

    MathSciNet  Article  Google Scholar 

  28. 28.

    Zhao B, An X, Zhao H, Shen L, Sun X, Zhou Z (2019) DEM simulation of the local ordering of tetrahedral granular matter. Soft Matter 15(10):2260–2268. https://doi.org/10.1039/c8sm02166j

    Article  Google Scholar 

  29. 29.

    Yu F, Zhang S, Zhou G, Zhang Y, Ge W (2018) Geometrically exact discrete-element-method (DEM) simulation on the flow and mixing of sphero-cylinders in horizontal drums. Powder Technol 336:415–425. https://doi.org/10.1016/j.powtec.2018.05.040

    Article  Google Scholar 

  30. 30.

    Rakotonirina AD, Delenne J-Y, Radjai F, Wachs A (2019) Grains3D, a flexible DEM approach for particles of arbitrary convex shape—part III: extension to non-convex particles modelled as glued convex particles. Comput Particle Mech 6(1):55–84. https://doi.org/10.1007/s40571-018-0198-3

    Article  Google Scholar 

  31. 31.

    Peters John F (2009) A poly-ellipsoid particle for non-spherical discrete element method. Eng Comput 26(6):645–657. https://doi.org/10.1108/02644400910975441

    Article  Google Scholar 

  32. 32.

    Zhang B, Regueiro R, Druckrey A, Alshibli K (2018) Construction of poly-ellipsoidal grain shapes from SMT imaging on sand, and the development of a new DEM contact detection algorithm. Eng Comput 35(2):733–771. https://doi.org/10.1108/ec-01-2017-0026

    Article  Google Scholar 

  33. 33.

    Liu Z, Zhao Y (2020) Multi-super-ellipsoid model for non-spherical particles in DEM simulation. Powder Technol 361:190–202. https://doi.org/10.1016/j.powtec.2019.09.042

    Article  Google Scholar 

  34. 34.

    Zhao S, Zhao J (2019) A poly-superellipsoid-based approach on particle morphology for DEM modeling of granular media. Int J Numer Anal Meth Geomech 43(13):2147–2169. https://doi.org/10.1002/nag.2951

    Article  Google Scholar 

  35. 35.

    Barrr AH (1981) Superquadrics and angle-preserving transformations. IEEE Comput Gr Appl 1(1):11–23. https://doi.org/10.1109/MCG.1981.1673799

    Article  Google Scholar 

  36. 36.

    Zhao Y, Xu L, Umbanhowar PB, Lueptow RM (2019) Discrete element simulation of cylindrical particles using super-ellipsoids. Particuology 46:55–66. https://doi.org/10.1016/j.partic.2018.04.007

    Article  Google Scholar 

  37. 37.

    Chen H, Zhao S, Zhou X (2020) DEM investigation of angle of repose for super-ellipsoidal particles. Particuology 50:53–66. https://doi.org/10.1016/j.partic.2019.05.005

    Article  Google Scholar 

  38. 38.

    Eberly D (2002) Dynamic collision detection using oriented bounding boxes. Geometric tools

  39. 39.

    Wellmann C, Lillie C, Wriggers P (2008) A contact detection algorithm for superellipsoids based on the common-normal concept. Eng Comput 25(5):432–442. https://doi.org/10.1108/02644400810881374

    Article  MATH  Google Scholar 

  40. 40.

    Houlsby GT (2009) Potential particles: a method for modelling non-circular particles in DEM. Comput Geotech 36(6):953–959. https://doi.org/10.1016/j.compgeo.2009.03.001

    Article  Google Scholar 

  41. 41.

    Podlozhnyuk A, Pirker S, Kloss C (2016) Efficient implementation of superquadric particles in discrete element method within an open-source framework. Comput Particle Mech 4(1):101–118. https://doi.org/10.1007/s40571-016-0131-6

    Article  Google Scholar 

  42. 42.

    Soltanbeigi B, Podlozhnyuk A, Papanicolopulos S-A, Kloss C, Pirker S, Ooi JY (2018) DEM study of mechanical characteristics of multi-spherical and superquadric particles at micro and macro scales. Powder Technol 329:288–303. https://doi.org/10.1016/j.powtec.2018.01.082

    Article  Google Scholar 

  43. 43.

    Zhu HP, Zhou ZY, Yang RY, Yu AB (2007) Discrete particle simulation of particulate systems: theoretical developments. Chem Eng Sci 62(13):3378–3396. https://doi.org/10.1016/j.ces.2006.12.089

    Article  Google Scholar 

  44. 44.

    Zhou ZY, Zou RP, Pinson D, Yu A-B (2011) Dynamic simulation of the packing of ellipsoidal particles. Ind Eng Chem Res 50(16):9787–9798. https://doi.org/10.1021/ie200862n

    Article  Google Scholar 

  45. 45.

    Dong K, Wang C, Yu A (2015) A novel method based on orientation discretization for discrete element modeling of non-spherical particles. Chem Eng Sci 126:500–516. https://doi.org/10.1016/j.ces.2014.12.059

    Article  Google Scholar 

  46. 46.

    Fritzer HP (2001) Molecular symmetry with quaternions. Spectrochim Acta Part A 57(10):1919–1930. https://doi.org/10.1016/S1386-1425(01)00477-2

    Article  Google Scholar 

  47. 47.

    Kosenko II (1998) Integration of the equations of a rotational motion of a rigid body in quaternion algebra: The Euler case. J Appl Math Mech 62(2):193–200. https://doi.org/10.1016/S0021-8928(98)00025-2

    MathSciNet  Article  MATH  Google Scholar 

  48. 48.

    Tfm III, Eleftheriou M, Pattnaik P, Ndirango A, Newns D, Martyna GJ (2002) Symplectic quaternion scheme for biophysical molecular dynamics. J Chem Phys 116(20):8649–8659. https://doi.org/10.1063/1.1473654

    Article  Google Scholar 

  49. 49.

    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):5863–5871. https://doi.org/10.1016/j.ces.2010.08.007

    Article  Google Scholar 

  50. 50.

    Wang S, Fan Y, Ji S (2018) Interaction between super-quadric particles and triangular elements and its application to hopper discharge. Powder Technol 339:534–549. https://doi.org/10.1016/j.powtec.2018.08.026

    Article  Google Scholar 

  51. 51.

    Langston PA, Al-Awamleh MA, Fraige FY, Asmar BN (2004) Distinct element modelling of non-spherical frictionless particle flow. Chem Eng Sci 59(2):425–435. https://doi.org/10.1016/j.ces.2003.10.008

    Article  Google Scholar 

Download references

Acknowledgements

This study is financially supported by the National Key Research and Development Program of China (Grant Nos. 2018YFA0605902, 2016YFC1401505, and 2016YFC1402706) and the National Natural Science Foundation of China (Grant Nos. 11872136 and 11772085).

Author information

Affiliations

Authors

Corresponding author

Correspondence to Shunying Ji.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Wang, S., Ji, S. Poly-superquadric model for DEM simulations of asymmetrically shaped particles. Comp. Part. Mech. (2021). https://doi.org/10.1007/s40571-021-00410-4

Download citation

Keywords

  • Discrete element method
  • Poly-superquadric model
  • Particle shape
  • Flow rate