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The Motion of a Neutrally Buoyant Ellipsoid Inside Square Tube Flows

Part of: Incompressible viscous fluids Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  09 January 2017

Xin Yang ,
Haibo Huang  and
Xiyun Lu
Xin Yang*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China
Haibo Huang*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China
Xiyun Lu*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China
*
*Corresponding author. Email:[email protected] (X. Yang), [email protected] (H. B. Huang), [email protected] (X. Y. Lu)
*Corresponding author. Email:[email protected] (X. Yang), [email protected] (H. B. Huang), [email protected] (X. Y. Lu)
*Corresponding author. Email:[email protected] (X. Yang), [email protected] (H. B. Huang), [email protected] (X. Y. Lu)
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Abstract

The motion and rotation of an ellipsoidal particle inside square tubes and rectangular tubes with the confinement ratio R/a∈(1.0,4.0) are studied by the lattice Boltzmann method (LBM), where R and a are the radius of the tube and the semi-major axis length of the ellipsoid, respectively. The Reynolds numbers (Re) up to 50 are considered. For the prolate ellipsoid inside square and rectangular tubes, three typical stable motion modes which depend on R/a are identified, namely, the kayaking mode, the tumbling mode, and the log-rolling mode are identified for the prolate spheroid. The diagonal plane strongly attracts the particle in square tubes with 1.2≤R/a<3.0. To explore the mechanism, some constrained cases are simulated. It is found that the tumbling mode in the diagonal plane is stable because the fluid force acting on the particle tends to diminish the small displacement and will bring it back to the plane. Inside rectangular tubes the particle will migrate to a middle plane between short walls instead of the diagonal plane. Through the comparisons between the initial unstable equilibrium motion state and terminal stable mode, it is seems that the particle tend to adopt the mode with smaller kinetic energy.

Keywords

LBMPoiseuille flowsquare tubesellipsoidal particles

MSC classification

Secondary: 65M99: None of the above, but in this section 76D99: None of the above, but in this section
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 2 , April 2017 , pp. 233 - 249
Copyright
Copyright © Global-Science Press 2017 

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References

[1] Jeffery, G. B., The motion of ellipsoidal particles immersed in a viscous fluid, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, The Royal Society, 102(715) (1922), pp. 161–179.Google Scholar
[2] Aidun, C. K., Lu, Y. and Ding, E. J., Direct analysis of particulate suspensions with inertia using the discrete Boltzmann equation, J. Fluid Mech., 373 (1998), pp. 287–311.Google Scholar
[3] Qi, D. and Luo, L. S., Rotational and orientational behaviour of three-dimensional spheroidal particles in Couette flows, J. Fluid Mech., 477 (2003), pp. 201–213.Google Scholar
[4] Huang, H., Yang, X. and Krafczyk, M. et al., Rotation of spheroidal particles in Couette flows, J. Fluid Mech., 692 (2012), pp. 369–394.Google Scholar
[5] Yu, Z., Phan-Thien, N. and Tanner, R. I., Rotation of a spheroid in a Couette flow at moderate Reynolds numbers, Phys. Rev. E, 76(2) (2007), 026310.Google Scholar
[6] Huang, H., Y. F., and Lu, X., Shear viscosity of dilute suspensions of ellipsoidal particles with a lattice Boltzmann method, Phys. Rev. E, 86(4) (2012), 046305.Google Scholar
[7] Chen, Y., Kang, Q. and Cai, Q. et al., Lattice Boltzmann simulation of particle motion in binary immiscible fluids, Commun. Comput. Phys., 18(03) (2015), pp. 757–786.CrossRefGoogle Scholar
[8] Segre, G., Radial particle displacements in Poiseuille flow of suspensions, Nature, 189 (1961), pp. 209–210.CrossRefGoogle Scholar
[9] Karnis, A., Goldsmith, H. L. and Mason, S. G., The flow of suspensions through tubes: V. Inertial effects, The Canadian Journal of Chemical Engineering, 44(4) (1966), pp. 181–193.Google Scholar
[10] Feng, J., Hu, H. H. and Joseph, D. D., Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid Part 1. Sedimentation, J. Fluid Mech., 261 (1994), pp. 95–134.Google Scholar
[11] Yang, B. H., Wang, J. and Joseph, D. D. et al., Migration of a sphere in tube flow, J. Fluid Mech., 540 (2005), pp. 109–131.Google Scholar
[12] Sugihara-Seki, M., The motion of an ellipsoid in tube flow at low Reynolds numbers, J. Fluid Mech., 324 (1996), pp. 287–308.CrossRefGoogle Scholar
[13] Yu, Z., Phan-Thien, N. and Tanner, R. I., Dynamic simulation of sphere motion in a vertical tube, J. Fluid Mech., 518 (2004), pp. 61–93.Google Scholar
[14] Pan, T. W., Chang, C. C. and Glowinski, R., On the motion of a neutrally buoyant ellipsoid in a three-dimensional Poiseuille flow, Comput. Methods Appl. Mech. Eng., 197(25) (2008), pp. 2198–2209.Google Scholar
[15] Lallemand, P. and Luo, L. S., Lattice Boltzmann method for moving boundaries, J. Comput. Phys., 184(2) (2003), pp. 406–421.Google Scholar
[16] D’Humieres, D., Multiple-relaxation-time lattice Boltzmann models in three dimensions, Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 360(1792) (2002), pp. 437–451.Google Scholar
[17] Huang, H., Yang, X. and Lu, X., Sedimentation of an ellipsoidal particle in narrow tubes, Phys. Fluids, 26(5) (2014), pp. 053302.CrossRefGoogle Scholar
[18] Chen, Y., Cai, Q. and Xia, Z. et al., Momentum-exchange method in lattice Boltzmann simulations of particle-fluid interactions, Phys. Rev. E, 88(1) (2013), 013303.Google Scholar
[19] Swaminathan, T. N., Mukundakrishnan, K. and Hu, H. H., Sedimentation of an ellipsoid inside an infinitely long tube at low and intermediate Reynolds numbers, J. Fluid Mech., 551 (2006), pp. 357–385.CrossRefGoogle Scholar
[20] Yang, X., Huang, H. and Lu, X., Sedimentation of an oblate ellipsoid in narrow tubes, Phys. Rev. E, 92(6) (2015), 063009.Google Scholar
[21] Qi, D., Lattice-Boltzmann simulations of particles in non-zero-Reynolds-number flows, J. Fluid Mech., 385 (1999), pp. 41–62.Google Scholar