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Direct Numerical Simulation of Multiple Particles Sedimentation at an Intermediate Reynolds Number

Published online by Cambridge University Press:  03 June 2015

Deming Nie ,
Jianzhong Lin  and
Mengjiao Zheng
Deming Nie*
Affiliation:
Institute of Fluid Mechanics, China Jiliang University, Hangzhou, 310018, China
Jianzhong Lin*
Affiliation:
Institute of Fluid Mechanics, China Jiliang University, Hangzhou, 310018, China State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, China
Mengjiao Zheng*
Affiliation:
Institute of Fluid Mechanics, China Jiliang University, Hangzhou, 310018, China
*
Email:nieinhz@cjlu.edu.cn
Corresponding author.Email:mecjzlin@public.zju.edu.cn
Email:dreambanana@163.com
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Abstract

In this work the previously developed Lattice Boltzmann-Direct Forcing/ Fictitious Domain (LB-DF/FD) method is adopted to simulate the sedimentation of eight circular particles under gravity at an intermediate Reynolds number of about 248. The particle clustering and the resulting Drafting-Kissing-Tumbling (DKT) motion which takes place for the first time are explored. The effects of initial particle-particle gap on the DKT motion are found significant. In addition, the trajectories of particles are presented under different initial particle-particle gaps, which display totally three kinds of falling patterns provided that no DKT motion takes place, i.e. the concave-down shape, the shape of letter “M” and “in-line” shape. Furthermore, the lateral and vertical hydrodynamic forces on the particles are investigated. It has been found that the value of Strouhal number for all particles is the same which is about 0.157 when initial particle-particle gap is relatively large. The wall effects on falling patterns and particle expansions are examined in the final.

Keywords

76T2076-0276M2847.11.-j47.57.ef47.57.E-47.55.-tLattice Boltzmann methodsedimentationfictitious domainfalling pattern
Type
Research Article
Information
Communications in Computational Physics , Volume 16 , Issue 3 , September 2014 , pp. 675 - 698
Copyright
Copyright © Global Science Press Limited 2014

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References

[1]Aidun, C. K., Lu, Y., Ding, E., 1998. Direct analysis of particulate suspensions with inertia using the discrete Boltzmann equation. J. Fluid Mech. 373, 287–311.Google Scholar
[2]Alexander, M. L., Olga, M. L., Avinoam, N., 2003. The weakly inertial settling of particles in a viscous fluid. Proc. R. Soc. Lond. A 459,3079–3098.Google Scholar
[3]Brady, J. F., Bossis, G., 1988. Stokesian dynamics. Annu. Rev. Fluid Mech. 20,111–157.Google Scholar
[4]Braza, M., Chassaing, P., Minh, H. H., 1986. Numerical study and physical analysis of the pressure and velocity fields in the near wake of a circular cylinder. J. Fluid Mech. 163,79–130.CrossRefGoogle Scholar
[5]Crowley, J. M., 1971. Viscosity induced instability of a one-dimensional lattice of falling spheres. J. Fluid Mech. 45,151–159.CrossRefGoogle Scholar
[6]Ding, H., Shu, C., Yeo, K. S., Xu, D., 2007. Numerical simulation of flows around two circular cylinders by mesh-free least square-based finite difference methods. Int. J. Numer. Methods Fluids 53, 305–332.Google Scholar
[7]Feng, J., Joseph, D. D., 1995. The unsteady motion of solid bodies in creeping flows. J. Fluid Mech. 303,83–102.Google Scholar
[8]Feng, Z. G., Michaelides, E. E., 2004. The immersed boundary-lattice Boltzmann method for solving fluid-particles interaction problems, J. Comput. Phys. 195, 602–628.CrossRefGoogle Scholar
[9]Guo, Z. L., Zheng, C. G., Shi, B. C., 2002. Discrete lattice effects on the forcing term in the lattice Boltzmann method. Phys. Rev. E 65, 046308.Google Scholar
[10]Hocking, L. M., 1964. The behaviour of clusters of spheres falling in a viscous fluid. J. Fluid Mech. 20, 365–400.CrossRefGoogle Scholar
[11]Jenny, M., Dušek, J., Bouchet, G., 2004. Instabilities and transition of a sphere falling or ascending freely in a Newtonian fluid. J. Fluid Mech. 508, 201–239.CrossRefGoogle Scholar
[12]Koch, D. L., Subramanian, G., 2011. Collective hydrodynamics of swimming microorganisms: Living fluids. Annu. Rev. Fluid Mech. 43, 637–659.CrossRefGoogle Scholar
[13]Ladd, A. J. C., 1994. Numerical simulations of particulate suspensions via a discretized Boltzmann equation Part I. Theoretical foundation. J. Fluid Mech. 271, 285–310.Google Scholar
[14]Leichtberg, S., Weinbaum, S., Pfeffer, R., Gluckman, M. J., 1976. A study of unsteady forces at low Reynolds number: A strong interaction theory for the coaxial settling of three or more spheres. Phil. Trans. R. Soc. Lond. A 282, 585–610.Google Scholar
[15]Luo, L.-S., Liao, W., Chen, X.W., Peng, Y., Zhang, W., 2011. Numerics of the lattice Boltzmann method: Effects of collision models on the lattice Boltzmann simulations. Phys. Rev. E 83, 056710.Google Scholar
[16]Mark, N. L., Hermann, F. F., 2005. A high-order immersed interface method for simulating unsteady incompressible flows on irregular domains. J. Comput. Phys. 204,157–192.Google Scholar
[17]Metzger, B., Nicolas, M., Guazzelli, É., 2007. Falling clouds of particles in viscous fluids. J. Fluid Mech. 580, 283–301.Google Scholar
[18]Mo, G., Sangani, A. S., 1994. A method for computing Stokes flow interactions among spherical objects and its application to suspensions of drops and porous materials. Phys. Fluids 6, 1637–1652.Google Scholar
[19]Nguyen, N-Q, Ladd, A.J.C., 2005. Sedimentation of hard-sphere suspensions at low Reynolds number. J. Fluid Mech. 525, 73–104.Google Scholar
[20]Nie, D. M., Lin, J. Z., 2010. A LB-DF/FD method for particle suspensions. Commun. Comput. Phys. 7,544–563.Google Scholar
[21]Nie, D. M., Lin, J. Z., 2011a. A lattice Boltzmann-direct forcing/fictitious domain model for brownian particles in fluctuating fluids. Commun. Comput. Phys. 9, 959–973CrossRefGoogle Scholar
[22]Nie, D., Lin, J., 2011b. Dynamics of two elliptical particles sedimentation in a vertical channel: Chaotic state. Int. J. Comput. Fluid Dyn. 25,401–406.Google Scholar
[23]Nie, D., Lin, J., Qiu, L., 2013. Direct numerical simulations of the decaying turbulence in rotating flows via the MRT-lattice Boltzmann method. Int. J. Comput. Fluid Dyn. DOI:10.1080/10618562.2013.779679.Google Scholar
[24]Nie, D. M., Wang, Y., Zhang, K., 2011. Long-time decay of the translational/rotational velocity autocorrelation function for colloidal particles in two dimensions. Comput. Math. Appl. 61, 2152–2157.Google Scholar
[25]Nie, D., Lin, J., Zhang, K., 2012. Flow patterns in the sedimentation of a capsule-shaped particle. Chin. Phys. Lett. 29, 084703.Google Scholar
[26]Qian, Y. H., D’Humieres, D., Lallemand, P., 1992. Lattice BGK models for Navier-Stokes equation. Europhys. Lett. 17,479–484.Google Scholar
[27]Tian, F. B., Luo, H., Zhu, L., Liao, J. C., Lu, X. Y., 2011. An efficient immersed boundary-lattice Boltzmann method for the hydrodynamic interaction of elastic filaments. J. Comput. Phys. 230, 7266–7283.CrossRefGoogle ScholarPubMed
[28]Uhlmann, M., 2005. An immersed boundary method with direct forcing for the simulation of particulate flows. J. Comput. Phys. 209, 448–476.Google Scholar
[29]Wan, D., Turek, S., 2007. An efficient multigrid-FEM method for the simulation of solidliquid two phase flows. J. Comput. Appl. Math. 203,561–580.CrossRefGoogle Scholar
[30]Xu, S., 2008. The immersed interface method for simulating prescribed motion of rigid objects in an incompressible viscous flow. J. Comput. Phys. 227,5045–5071.Google Scholar
[31]Xu, S., Wang, Z. J., 2006. An immersed interface method for simulating the interaction of a fluid with moving boundaries. J. Comput. Phys. 216,454–493.Google Scholar
[32]Yacoubi, A. E., Xu, S., Wang, Z. J., 2012. Computational study of the interaction of freely moving particles at intermediate Reynolds numbers. J. Fluid Mech. 705,134–148.Google Scholar
[33]Yu, Z. S., Shao, X. M., 2007. A direct-forcing fictitious domain method for particulate flows. J. Comput. Phys. 227, 292–314.CrossRefGoogle Scholar