Simulation of Two Circular Particles Falling in Vertical Channel: Combination of Immersed Boundary Lattice Boltzmann Method and Discrete Element Method

Document Type : Research Article

Authors

Mechanical Engineering Department, Shahrood University of Technology, Shahrood, Iran

Abstract

In this study, Immersed Boundary-Lattice Boltzmann Method (IB-LBM) as a fluid solver is combined with Discrete Element Method (DEM) as a collision model. The consequences of this arrangement go to a numerical great model (IB-LB-DEM) which is capable to simulate particulate flows with second-order accuracy. To apply non-slip boundary condition, Eulerian velocities are interpolated in Lagrangian nodes using diffuse delta function. In DEM, two particles can penetrate to each other which this approach generates more realistic model rather other collision rules. Generally, in this model, the most important parameter is overlap distance between two particles which is directly related to amount of particles rigidity. The mentioned hybrid method is validated by simulation of dry-contact of two particles and sedimentation of single particle in vertical channel, individually. Finally, sedimentation of two circular particles in vertical channel is studied and effects of physical parameters such as rigidity, restitution coefficient and friction coefficient in particles behavior has been investigated. Finally, it is shown that increasing friction coefficient leads to increasing in kissing time that causes a change in particles path. For this particular model, It is also dedicated that restitution coefficient does not have significant effect in particles behavior.

Keywords

Main Subjects


[1] S. Chen, G.D. Doolen, LATTICE BOLTZMANN METHOD FOR FLUID FLOWS, Annual Review of Fluid Mechanics, 30(1) (1998) 329-364.
[2] D. Yu, R. Mei, L.-S. Luo, W. Shyy, Viscous flow computations with the method of lattice Boltzmann equation, Progress in Aerospace Sciences, 39(5) (2003) 329-367.
[3] Z.-G. Feng, E.E. Michaelides, The immersed boundarylattice Boltzmann method for solving fluid–particles interaction problems, Journal of Computational Physics, 195(2) (2004) 602-628.
[4] M.-C. Lai, C.S. Peskin, An Immersed Boundary Method with Formal Second-Order Accuracy and Reduced Numerical Viscosity, Journal of Computational Physics, 160(2) (2000) 705-719.
[5] Z.-G. Feng, E.E. Michaelides, Proteus: a direct forcing method in the simulations of particulate flows, Journal of Computational Physics, 202(1) (2005) 20-51.
[6] X.D. Niu, C. Shu, Y.T. Chew, Y. Peng, A momentum exchange-based immersed boundary-lattice Boltzmann method for simulating incompressible viscous flows, Physics Letters A, 354(3) (2006) 173-182.
[7] A. Dupuis, P. Chatelain, P. Koumoutsakos, An immersed boundary–lattice-Boltzmann method for the simulation of the flow past an impulsively started cylinder, Journal of Computational Physics, 227(9) (2008) 4486-4498.
[8] S.K. Kang, Y.A. Hassan, A comparative study of directforcing immersed boundary-lattice Boltzmann methods for stationary complex boundaries, International Journal for Numerical Methods in Fluids, 66(9) (2011) 1132- 1158.
[9] J. Wu, C. Shu, Implicit velocity correction-based immersed boundary-lattice Boltzmann method and its applications, Journal of Computational Physics, 228(6) (2009) 1963-1979.
[10] Z. Guo, C. Zheng, B. Shi, Discrete lattice effects on the forcing term in the lattice Boltzmann method, Physical Review E, 65(4) (2002) 046308.
[11] S.-W. Su, M.-C. Lai, C.-A. Lin, An immersed boundary technique for simulating complex flows with rigid boundary, Computers & Fluids, 36(2) (2007) 313-324.
[12] D.V. Le, B.C. Khoo, K.M. Lim, An implicit-forcing immersed boundary method for simulating viscous flows in irregular domains, Computer Methods in Applied Mechanics and Engineering, 197(25) (2008) 2119-2130.
[13] A.M. Ardekani, S. Dabiri, R.H. Rangel, Collision of multi-particle and general shape objects in a viscous fluid, Journal of Computational Physics, 227(24) (2008) 10094-10107.
[14] R.H. Davis, Effects of surface roughness on a sphere sedimenting through a dilute suspension of neutrally buoyant spheres, Physics of Fluids A: Fluid Dynamics, 4(12) (1992) 2607-2619.
[15] M.L. Ekiel-Jeżewska, F. Feuillebois, N. Lecoq, K. Masmoudi, R. Anthore, F. Bostel, E. Wajnryb, Hydrodynamic interactions between two spheres at contact, Physical Review E, 59(3) (1999) 3182-3191.
[16] M.L. Ekiel-Jeżewska, N. Lecoq, R. Anthore, F. Bostel, F. Feuillebois, Rotation due to hydrodynamic interactions between two spheres in contact, Physical Review E, 66(5) (2002) 051504.
[17] J. Zhang, L.-S. Fan, C. Zhu, R. Pfeffer, D. Qi, Dynamic behavior of collision of elastic spheres in viscous fluids, Powder Technology, 106(1) (1999) 98-109.
[18] L. Jian-Zhong, W. Ye-Long, J.A. Olsen, Sedimentation of Rigid Cylindrical Particles with Mechanical Contacts, Chinese Physics Letters, 22(3) (2005) 628-631.
[19] R. Glowinski, T.W. Pan, T.I. Hesla, D.D. Joseph, A distributed Lagrange multiplier/fictitious domain method for particulate flows, International Journal of Multiphase Flow, 25(5) (1999) 755-794.
[20] A.M. Ardekani, R.H. Rangel, Numerical investigation of particle–particle and particle–wall collisions in a viscous fluid, Journal of Fluid Mechanics, 596 (2008) 437-466.
[21] R. Glowinski, Finite element methods for incompressible viscous flow, in: Handbook of Numerical Analysis, Elsevier, 2003, pp. 3-1176.
[22] P.A. Cundall, O.D.L. Strack, A discrete numerical model for granular assemblies, in: The Essence of Geotechnical Engineering: 60 years of Géotechnique, pp. 305-329.
[23] A. Wachs, A DEM-DLM/FD method for direct numerical simulation of particulate flows: Sedimentation of polygonal isometric particles in a Newtonian fluid with collisions, Computers & Fluids, 38(8) (2009) 1608- 1628.
[24] A. Wachs, L. Girolami, G. Vinay, G. Ferrer, Grains3D, a flexible DEM approach for particles of arbitrary convex shape — Part I: Numerical model and validations, Powder Technology, 224 (2012) 374-389.
[25] B. Afra, M. Nazari, M.H. Keyhani, Proposing Immersed Boundary-Lattice Boltzmann-Lattice Spring Algorithm for Simulation of 2-D Deformable Plate in Steady Flow, Amirkabir Journal of Mechanical Engineering, 50(4) (2018) 683-696 (In Persian).
[26] Background in Multiphase Flows with Reactions, in: Fundamentals of Turbulent and Multiphase Combustion, pp. 509-575.
[27] A. Džiugys, B. Peters, An approach to simulate the motion of spherical and non-spherical fuel particles in combustion chambers, Granular Matter, 3(4) (2001) 231- 266.
[28] M. Kodam, R. Bharadwaj, J. Curtis, B. Hancock, C. Wassgren, Cylindrical object contact detection for use in discrete element method simulations. Part I – Contact detection algorithms, Chemical Engineering Science, 65(22) (2010) 5852-5862.
[29] F.Y. Fraige, P.A. Langston, G.Z. Chen, Distinct element modelling of cubic particle packing and flow, Powder Technology, 186(3) (2008) 224-240.
[30] P.A. Cundall, 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, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 25(3) (1988) 107-116.P. A. Thompson and G. S. Grest, "Granular flow: friction and the dilatancy transition," Physical Review Letters, vol. 67, p. 1751, 1991.
[31] P.A. Thompson, G.S. Grest, Granular flow: Friction and the dilatancy transition, Physical Review Letters, 67(13) (1991) 1751-1754.
[32] G.H. Ristow, Dynamics of granular materials in a rotating drum, Europhysics Letters (EPL), 34(4) (1996) 263-268.
[33] P.W. Cleary, DEM prediction of industrial and geophysical particle flows, Particuology, 8(2) (2010) 106-118.
[34] W. Cleary Paul, Large scale industrial DEM modelling, Engineering Computations, 21(2/3/4) (2004) 169-204.
[35] C.-Y. Wu, A.C.F. Cocks, Numerical and experimental investigations of the flow of powder into a confined space, Mechanics of Materials, 38(4) (2006) 304-324.
[36] A. Amiri Delouei, M. Nazari, M.H. Kayhani, S.K. Kang, S. Succi, Non-Newtonian particulate flow simulation: A direct-forcing immersed boundary–lattice Boltzmann approach, Physica A: Statistical Mechanics and its Applications, 447 (2016) 1-20.
[37] D. Wan, S. Turek, Direct numerical simulation of particulate flow via multigrid FEM techniques and the fictitious boundary method, International Journal for Numerical Methods in Fluids, 51(5) (2006) 531-566.
[38] J. Wu, C. Shu, Particulate flow simulation via a boundary condition-enforced immersed boundary-lattice Boltzmann scheme, Communications in Computational Physics, 7(4) (2010) 793.