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Flow patterns in the sedimentation of an elliptical particle

Published online by Cambridge University Press:  14 April 2009

ZHENHUA XIA ,
KEVIN W. CONNINGTON ,
SAIKIRAN RAPAKA ,
PENGTAO YUE ,
JAMES J. FENG  and
SHIYI CHEN
ZHENHUA XIA
Affiliation:
State Key Laboratory for Turbulence & Complex Systems, CAPT and CCST, College of Engineering, Peking University, Beijing, China Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA
KEVIN W. CONNINGTON
Affiliation:
Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA
SAIKIRAN RAPAKA
Affiliation:
Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA
PENGTAO YUE
Affiliation:
Department of Chemical and Biological Engineering and Department of Mathematics, University of British Columbia, Vancouver, BCCanadaV6T 1Z3
JAMES J. FENG
Affiliation:
Department of Chemical and Biological Engineering and Department of Mathematics, University of British Columbia, Vancouver, BCCanadaV6T 1Z3
SHIYI CHEN*
Affiliation:
State Key Laboratory for Turbulence & Complex Systems, CAPT and CCST, College of Engineering, Peking University, Beijing, China Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA
*
†Email address for correspondence: saikiran@jhu.edu, syc@jhu.edu
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Abstract

We study the dynamics of a single two-dimensional elliptical particle sedimenting in a Newtonian fluid using numerical simulations. The main emphasis in this work is to study the effect of boundaries on the flow patterns observed during sedimentation. The simulations were performed using a multi-block lattice Boltzmann method as well as a finite-element technique and the results are shown to be consistent. We have conducted a detailed study on the effects of density ratio, aspect ratio and the channel blockage ratio on the flow patterns during sedimentation. As the channel blockage ratio is varied, our results show that there are five distinct modes of sedimentation: oscillating, tumbling along the wall, vertical sedimentation, horizontal sedimentation and an inclined mode where the particle sediments with a non-trivial orientation to the vertical. The inclined mode is shown to form a smooth bridge between the vertical and horizontal modes of sedimentation. For narrow channels, the mode of sedimentation is found to be sensitively dependent on the initial orientation of the particle. We present a phase diagram showing the transitions between the various modes of sedimentation with changing blockage ratio of the channel.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 625 , 25 April 2009 , pp. 249 - 272
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Aidun, C. K. & Ding, E.-J. 2003 Dynamics of particle sedimentation in a vertical channel: period-doubling bifurcation and chaotic state. Phys. Fluids 15, 1612.CrossRefGoogle Scholar
Aidun, C. & Lu, Y. 1995 Lattice boltzmann simulation of solid particles suspended in fluid. J. Stat. Phys. 81 (1–2), 49–61.CrossRefGoogle Scholar
Aidun, C., Lu, Y. & Ding, E. 1998 Direct analysis of particulate suspensions with inertia using the discrete boltzmann equation. J. Fluid Mech. 373, 287–311.CrossRefGoogle Scholar
Allen, M. & Tildesley, D. 1987 Computer Simulation of Liquids. Clarendon.Google Scholar
Bhatnagar, P., Gross, E. & Krook, M. 1954 A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94 (3), 511–525.CrossRefGoogle Scholar
Brady, J. & Bossis, G. 1985 The rheology of concentrated suspensions of spheres in simple shear flow by numerical simulation. J. Fluid Mech. 155, 105–129.CrossRefGoogle Scholar
Chen, H., Chen, S. & Matthaeus, W. 1992 Recovery of the navier-stokes equations using a lattice-gas boltzmann method. Phys. Rev. A 45, R5339–R5342.CrossRefGoogle ScholarPubMed
Chen, S. & Doolen, G. 1998 Lattice boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 30, 329–364.CrossRefGoogle Scholar
Chen, S., Martinez, D. & Mei, R. 1996 On boundary conditions in lattice boltzmann methods. Phys. Fluids 8, 2527–2536.CrossRefGoogle Scholar
Ding, E. & Aidun, C. 2000 The dynamics and scaling law for particles suspended in shear flow with inertia. J. Fluid Mech. 423, 317–344.CrossRefGoogle Scholar
Fang, H. & Chen, S. Y. 2004 Lattice boltzmann method for three-dimensional moving particles in a newtonian fluid. Chin. Phys. 13 (1), 47–53.Google Scholar
Fang, H., Wang, Z., Lin, Z. & Liu, M. 2002 Lattice boltzmann method for simulating the viscous flow in large distensible blood vessels. Phys. Rev. E 65, 051925.CrossRefGoogle ScholarPubMed
Feng, J., Hu, H. & Joseph, D. 1994 a Direct simulation of initial value problems for the motion of solid bodies in a newtonian fluid Part 1. Sedimentation. J. Fluid Mech. 261, 95–134.CrossRefGoogle Scholar
Feng, J., Hu, H. & Joseph, D. 1994 b Direct simulation of initial value problems for the motion of solid bodies in a newtonian fluid Part 2. Couette and Poiseuille flows. J. Fluid Mech. 277, 271–301.CrossRefGoogle Scholar
Feng, J., Huang, P. & Joseph, D. 1995 Dynamic simulation of the motion of capsules in pipelines. J. Fluid Mech. 286, 201–227.CrossRefGoogle Scholar
Feng, J. & Joseph, D. 1995 The unsteady motion of solid bodies in creeping flows. J. Fluid Mech. 303, 83–102.CrossRefGoogle Scholar
Feng, Z. & Michaelides, E. 2004 The immersed boundary-lattice boltzmann method for solving fluid-particles interaction problems. J. Comput. Phys. 195, 602–628.CrossRefGoogle Scholar
Filippova, O. & Hanel, D. 1997 Lattice-Boltzmann simulation of gas-particle flow in filters. Comput. Fluids 26 (7), 697–712.CrossRefGoogle Scholar
Filippova, O. & Hanel, D. 1998 Grid refinement for lattice bgk models. J. Comput. Phys. 147, 219–228.CrossRefGoogle Scholar
Frisch, U., d'Humieres, D., Hasslacher, B., Lallemand, P., Pomeau, Y. & Rivet, J. 1987 Lattice gas hydrodynamics in two and three dimensions. Complex Syst. 1, 649–707.Google Scholar
Glowinski, R., Pan, T., Hesla, T., Joseph, D. & Periaux, J. 2001 A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: application to particulate flow. J. Comput. Phys. 169, 363–426.CrossRefGoogle Scholar
He, X. & Doolen, G. D. 1997 Lattice Boltzmann method on curvilinear coordinates system: flow around a circular cylinder. J. Comput. Phys. 134, 306.CrossRefGoogle Scholar
He, X. & Luo, L. 1997 Lattice Boltzmann model for the incompressible Navier–Stokes equation. J. Stat. Phys. 88 (3–4), 927–944.CrossRefGoogle Scholar
He, X., Luo, L. & Dembo, M. 1996 Some progress in lattice Boltzmann method. Part I. Nonuniform mesh grids. J. Comput. Phys. 129, 357–363.CrossRefGoogle Scholar
Höfler, K. & Schwarzer, S. 2000 Navier–Stokes simulation with constraint forces: finite-difference method for particle-laden flows and complex geometries. Phys. Rev. E 61, 7146–7160.CrossRefGoogle ScholarPubMed
Hu, H. 1995 Motion of a circular cylinder in a viscous liquid between parallel plates. Theor. Comput. Fluid Dyn. 7, 441–455.CrossRefGoogle Scholar
Hu, H. 1996 Direct simulation of flows of solid-liquid mixtures. Intl J. Multiphase Flow 22 (2), 335–352.CrossRefGoogle Scholar
Hu, H., Joseph, D. & Crochet, M. 1992 Direct simulation of fluid particle motions. Theor. Comput. Fluid Dyn. 3, 285–306.CrossRefGoogle Scholar
Hu, H. H., Patankar, N. A. & Zhu, M. Y. 2001 Direct numerical simulations of fluid–solid systems using the arbitrary Lagrangian–Eulerian technique. J. Comp. Phys. 169, 427–462.CrossRefGoogle Scholar
Huang, P., Feng, J. & Joseph, D. 1994 The turning couples on an elliptic particle settling in a vertical channel. J. Fluid Mech. 271, 1–16.CrossRefGoogle Scholar
Huang, P., Hu, H. & Joseph, D. 1998 Direct simulation of the sedimentation of elliptic particles in oldroyd-b fluids. J. Fluid Mech. 362, 297–325.CrossRefGoogle Scholar
Inamuro, T., Maeba, K. & Ogino, F. 2000 Flow between parallel walls containing the lines of neutrally buoyant circu;ar cylinders. Intl J. Multiphase Flow 26, 1981–2004.CrossRefGoogle Scholar
Ladd, A. 1994 a Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation. J. Fluid Mech. 271, 285–309.CrossRefGoogle Scholar
Ladd, A. 1994 b Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 2. Numerical results. J. Fluid Mech. 271, 311–339.CrossRefGoogle Scholar
Ladd, A. & Verberg, R. 2001 Lattice-Boltzmann simulations of particle-fluid suspensions. J. Stat. Phys. 104 (5–6), 1191–1251.CrossRefGoogle Scholar
Lai, M.-C. & Peskin, C. S. 2000 An immersed boundary method with formal second-order accuracy and reduced numerical viscosity. J. Comput. Phys. 160, 705–719.CrossRefGoogle Scholar
Li, H., Fang, H., Lin, Z., Xu, S. & Chen, S. 2004 a Lattice Boltzmann simulation on particle suspensions in a two-dimensional symmetric stenotic artery. Phys. Rev. E 69 (3), 031919.CrossRefGoogle Scholar
Li, H., Lu, X., Fang, H. & Qian, Y. 2004 b Force evaluations in lattice Boltzmann simulations with moving boundaries in two dimensions. Phys. Rev. E 70, 026701.CrossRefGoogle ScholarPubMed
Liu, Y. J., Nelson, J., Feng, J. & Joseph, D. D. 1993 Anomalous rolling of spheres down an inclined plane. J. Non-Newtonian Fluid Mech. 50, 305.CrossRefGoogle Scholar
McNamara, G. & Zanetti, G. 1988 Use of the boltzmann equation to simulate lattice-gas automata. Phys. Rev. Lett. 61 (20), 2332–2335.CrossRefGoogle ScholarPubMed
Mei, R., Luo, L. & Shyy, W. 1999 An accurate curved boundary treatment in the lattice Boltzmann method. J. Comput. Phys. 155, 307–330.CrossRefGoogle Scholar
Mei, R., Yu, D., Shyy, W. & Luo, L. 2002 Force evaluation in the lattice Boltzmann method involving curved geometry. Phys. Rev. E 65, 041203.CrossRefGoogle ScholarPubMed
Mittal, R. & Iaccarino, G. 2005 Immersed boundary methods. Annu. Rev. Fluid Mech. 37, 239–261.CrossRefGoogle Scholar
Nguyen, N. Q. & Ladd, A. J. C. 2002 Lubrication corrections for lattice-Boltzmann simulations of particle suspensions. Phys. Rev. E 66, 046708.CrossRefGoogle ScholarPubMed
Prosperetti, A. & Oguz, H. 2001 Physalis: a new o(n) method for the numerical simulation of disperse systems: potential flow of spheres. J. Comput. Phys. 167, 196–216.CrossRefGoogle Scholar
Qi, D. 1999 Lattice-Boltzmann simulations of particles in non-zero-Reynolds-number flows. J. Fluid Mech. 385, 41–62.CrossRefGoogle Scholar
Qi, D., Luo, L., Aravamuthan, R. & Strieder, W. 2002 Lateral migration and orientation of elliptical particles in poiseuille flows. J. Stat. Phys. 107 (1–2), 101–120.CrossRefGoogle Scholar
Qian, Y., d'Humieres, D. & Lallemand, P. 1992 Lattice bgk models for Navier–Stokes equation. Europhys. Lett. 17 (6), 479–484.CrossRefGoogle Scholar
Russel, W. B., Hinch, E. J., Leal, L. G. & Tieffenbruck, G. 1977 Rods falling near a vertical wall. J. Fluid Mech. 83, 273–287.CrossRefGoogle Scholar
Seddon, J. R. T. & Mullin, T. 2007 The motion of a prolate ellipsoid in a rotating Stokes flow. J. Fluid Mech. 583, 123–132.CrossRefGoogle Scholar
Sugihara-Seki, M. 1993 The motion of an elliptical cylinder in channel flow at low Reynolds numbers. J. Fluid Mech. 257, 575–596.CrossRefGoogle Scholar
Swaminathan, T. N., Mukundakrishnan, K. & Hu, H. H. 2006 Sedimentation of an ellipsoid inside an infinitely long tube at low and intermediate Reynolds numbers. J. Fluid Mech. 551, 357–385.CrossRefGoogle Scholar
Uhlmann, M. 2005 An immersed boundary method with direct forcing for the simulation of particulate flows. J. Comput. Phys. 209, 448–476.CrossRefGoogle Scholar
Yu, D., Mei, R., Luo, L.-S. & Shyy, W. 2003 Viscous flow computations with the method of lattice Boltzmann equation. Prog. Aero. Sci. 39, 329–367.CrossRefGoogle Scholar
Yu, D., Mei, R. & Shyy, W. 2002 A multi-block lattice Boltzmann method for viscous fluid flows. Intl J. Numer. Meth. Fluids 39, 99–120.CrossRefGoogle Scholar