Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-26T06:15:20.807Z Has data issue: false hasContentIssue false
  • English
  • Français

Behaviors of Spherical and Nonspherical Particles in a Square Pipe Flow

Published online by Cambridge University Press:  20 August 2015

Takaji Inamuro ,
Hirofumi Hayashi  and
Masahiro Koshiyama
Takaji Inamuro*
Affiliation:
Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japan Advanced Research Institute of Fluid Science and Engineering, Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japan
Hirofumi Hayashi
Affiliation:
Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japan
Masahiro Koshiyama
Affiliation:
Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japan
*
*Corresponding author.Email:[email protected]
Get access

Abstract

The lattice Boltzmann method (LBM) for multicomponent immiscible fluids is applied to the simulations of solid-fluid mixture flows including spherical or non-spherical particles in a square pipe at Reynolds numbers of about 100. A spherical solid particle is modeled by a droplet with strong interfacial tension and large viscosity, and consequently there is no need to track the moving solid-liquid boundary explicitly. Nonspherical (discoid, flat discoid, and biconcave discoid) solid particles are made by applying artificial forces to the spherical droplet. It is found that the spherical particle moves straightly along a stable position between the wall and the center of the pipe (the Segré-Silberberg effect). On the other hand, the biconcave discoid particle moves along a periodic helical path around the center of the pipe with changing its orientation, and the radius of the helical path and the polar angle of the orientation increase as the hollow of the concave becomes large.

Keywords

76D9976M2876T9976Z05Lattice Boltzmann methodsquare pipe flowspherical particlebiconcave discoid particle
Type
Research Article
Information
Communications in Computational Physics , Volume 9 , Issue 5 , May 2011 , pp. 1179 - 1192
Copyright
Copyright © Global Science Press Limited 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Segré, G., and Silberberg, A., Radial particle displacements in Poiseuille flow of suspensions, Nature., 189 (1961), 209–210.Google Scholar
[2]Karnis, A., Goldsmith, H. L., and Mason, S. G., The flow of suspensions through tubes, Can. J. Chem. Eng., 44 (1966), 181–193.Google Scholar
[3]Tachibana, M., On the behavior of a sphere in the laminar tube flows, Rheol. Acta., 12 (1973), 58–69.Google Scholar
[4]Saffman, P. G., The lift on a small sphere in a slow shear flow, J. Fluid. Mech., 22 (1965), 385–400.Google Scholar
[5]Ho, B. P., and Leal, L. G., Inertial migration of rigid spheres in two-dimensional unidirectional flows, J. Fluid. Mech., 35 (1974), 365–400.Google Scholar
[6]Vasseur, P., and Cox, R. G., The lateral migration of a spherical particle in two-dimensional shear flows, J. Fluid. Mech., 78 (1976), 385–413.Google Scholar
[7]Schonberg, J. A., and Hinch, E. J., Inertial migration of a sphere in Poiseuille flow, J. Fluid. Mech., 203 (1989), 517–524.Google Scholar
[8]McLaughlin, J. B., The lift on a small sphere in wall-bounded linear shear flows, J. Fluid. Mech., 246 (1993), 249–265.Google Scholar
[9]Asmolov, E. S., The iniertial lift on a spherical particle in a plane Poiseuiile flow at large channel Reynolds number, J. Fluid. Mech., 381 (1999), 63–87.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 2: Couette and Poseuille flows, J. Fluid. Mech., 277 (1994), 271–301.Google Scholar
[11]Nirschl, H., Dwyer, H. A., and Denk, V., Three-dimensional calculations of the simple shear flow around a single particle between two moving walls, J. Fluid. Mech., 283 (1995), 273–285.CrossRefGoogle Scholar
[12]Inamuro, T., Maeba, K., and Ogino, F., Flow between parallel walls containing the lines of neutrally buoyant circular cylinders, Int. J. Multiphase. Flow., 26 (2000), 1981–2004.Google Scholar
[13]Pan, T. W., and Glowinski, R., Direct simulation of the motion of neutrally buoyant balls in a three-dimensional Poiseuille flow, C. R. Mecanique., 333 (2005), 884–895.Google Scholar
[14]Inamuro, T., and Ii, T., Lattice Boltzmann simulation of the dispersion of aggregated particles under shear flows, Math. Comput. Sim., 72 (2006), 141–146.CrossRefGoogle Scholar
[15]Inamuro, T., Lattice Boltzmann methods for viscous fluid flows and for two-phase fluid flows, Fluid. Dyn. Res., 38 (2006), 641–659.Google Scholar
[16]Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T., Jacobi Transformations of A Symmetric Matrix, in Numerical Recipes (FORTRAN Version), Cambridge University Press, 1989.Google Scholar
[17]Aidun, C. K., and Lu, Y., Lattice Boltzmann simulation of solid particles suspended in fluid, J. Stat. Phys., 81 (1995), 49–61.CrossRefGoogle Scholar
[18]ten Cate, A., Nieuwstad, C. H., Derksen, J. J., and Van den Akker, H. E. A., Particle imaging ve-locimetry experiments and lattice-Boltzmann simulations on a single sphere settling under gravity, Phys. Fluids., 14 (2002), 4012–4025.Google Scholar
[19]Feng, Z.-G., and Michaelides, E. E., Proteus: a direct forcing method in the simulations of particulate flows, J. Comput. Phys., 202 (2005), 20–51.Google Scholar
[20]Inamuro, T., Yoshino, M., and Ogino, F., A non-slip boundary condition for lattice Boltzmann simulations, Phys. Fluids., 7 (1995), 2928–2930 (Erratum: 8 (1996) 1124).Google Scholar
[21]Inamuro, T., Yoshino, M., and Ogino, F., Lattice Boltzmann simulation of flows in a three-dimensional porous structure, Int. J. Numer. Meth. Fluids., 29 (1999), 737–748.Google Scholar