A lattice Boltzmann method for axisymmetric multicomponent flows with high viscosity ratio

Haihu Liu, Lei Wu, Yan Ba, Guang Xi, Yonghao Zhang

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

A color-gradient lattice Boltzmann method (LBM) is proposed to simulate ax- isymmetric multicomponent flows. This method uses a collision operator that is a combination of three separate parts, namely single-component collision op- erator, perturbation operator, and recoloring operator. A source term is added into the single-component collision operator such that in each single-component region the axisymmetric continuity and momentum equations can be exactly re- covered. The interfacial tension effect is realized by the perturbation operator, in which an interfacial force of axisymmetric form is derived using the concept of continuum surface force. A recoloring operator proposed by Latva-Kokko and Rothman is extended to the axisymmetric case for phase segregation and maintenance of the interface. To enhance the method’s numerical stability for handling binary fluids with high viscosity ratio, a multiple-relaxation-time mod- el is used for the collision operator. Several numerical examples, including static droplet test, oscillation of a viscous droplet, and breakup of a liquid thread, are presented to test the capability and accuracy of the proposed color-gradient LB- M. It is found that the present method is able to accurately capture the phase interface and produce low spurious velocities. Also, the LBM results are all in good agreement with the analytical solutions and/or available experimental data for a very broad range of viscosity ratios.
LanguageEnglish
JournalJournal of Computational Physics
Early online date6 Oct 2016
DOIs
Publication statusE-pub ahead of print - 6 Oct 2016

Fingerprint

axisymmetric flow
Viscosity
viscosity
Color
Drop breakup
Phase interfaces
operators
Convergence of numerical methods
Relaxation time
Surface tension
Momentum
collisions
Fluids
Liquids
static tests
color
binary fluids
perturbation
gradients
numerical stability

Keywords

  • lattice Boltzmann method
  • axisymmetric flow
  • color-gradient model
  • high viscosity ratio
  • Rayleigh instability
  • collision operator
  • single-component collision operator
  • perturbation operator
  • recolouring operator
  • interfacial tension
  • binary fluids
  • high-viscosity ratio
  • multiple-relaxation model

Cite this

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title = "A lattice Boltzmann method for axisymmetric multicomponent flows with high viscosity ratio",
abstract = "A color-gradient lattice Boltzmann method (LBM) is proposed to simulate ax- isymmetric multicomponent flows. This method uses a collision operator that is a combination of three separate parts, namely single-component collision op- erator, perturbation operator, and recoloring operator. A source term is added into the single-component collision operator such that in each single-component region the axisymmetric continuity and momentum equations can be exactly re- covered. The interfacial tension effect is realized by the perturbation operator, in which an interfacial force of axisymmetric form is derived using the concept of continuum surface force. A recoloring operator proposed by Latva-Kokko and Rothman is extended to the axisymmetric case for phase segregation and maintenance of the interface. To enhance the method’s numerical stability for handling binary fluids with high viscosity ratio, a multiple-relaxation-time mod- el is used for the collision operator. Several numerical examples, including static droplet test, oscillation of a viscous droplet, and breakup of a liquid thread, are presented to test the capability and accuracy of the proposed color-gradient LB- M. It is found that the present method is able to accurately capture the phase interface and produce low spurious velocities. Also, the LBM results are all in good agreement with the analytical solutions and/or available experimental data for a very broad range of viscosity ratios.",
keywords = "lattice Boltzmann method, axisymmetric flow, color-gradient model, high viscosity ratio, Rayleigh instability, collision operator, single-component collision operator, perturbation operator, recolouring operator, interfacial tension, binary fluids, high-viscosity ratio, multiple-relaxation model",
author = "Haihu Liu and Lei Wu and Yan Ba and Guang Xi and Yonghao Zhang",
year = "2016",
month = "10",
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doi = "10.1016/j.jcp.2016.10.007",
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A lattice Boltzmann method for axisymmetric multicomponent flows with high viscosity ratio. / Liu, Haihu; Wu, Lei; Ba, Yan; Xi, Guang; Zhang, Yonghao.

In: Journal of Computational Physics, 06.10.2016.

Research output: Contribution to journalArticle

TY - JOUR

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AU - Wu, Lei

AU - Ba, Yan

AU - Xi, Guang

AU - Zhang, Yonghao

PY - 2016/10/6

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N2 - A color-gradient lattice Boltzmann method (LBM) is proposed to simulate ax- isymmetric multicomponent flows. This method uses a collision operator that is a combination of three separate parts, namely single-component collision op- erator, perturbation operator, and recoloring operator. A source term is added into the single-component collision operator such that in each single-component region the axisymmetric continuity and momentum equations can be exactly re- covered. The interfacial tension effect is realized by the perturbation operator, in which an interfacial force of axisymmetric form is derived using the concept of continuum surface force. A recoloring operator proposed by Latva-Kokko and Rothman is extended to the axisymmetric case for phase segregation and maintenance of the interface. To enhance the method’s numerical stability for handling binary fluids with high viscosity ratio, a multiple-relaxation-time mod- el is used for the collision operator. Several numerical examples, including static droplet test, oscillation of a viscous droplet, and breakup of a liquid thread, are presented to test the capability and accuracy of the proposed color-gradient LB- M. It is found that the present method is able to accurately capture the phase interface and produce low spurious velocities. Also, the LBM results are all in good agreement with the analytical solutions and/or available experimental data for a very broad range of viscosity ratios.

AB - A color-gradient lattice Boltzmann method (LBM) is proposed to simulate ax- isymmetric multicomponent flows. This method uses a collision operator that is a combination of three separate parts, namely single-component collision op- erator, perturbation operator, and recoloring operator. A source term is added into the single-component collision operator such that in each single-component region the axisymmetric continuity and momentum equations can be exactly re- covered. The interfacial tension effect is realized by the perturbation operator, in which an interfacial force of axisymmetric form is derived using the concept of continuum surface force. A recoloring operator proposed by Latva-Kokko and Rothman is extended to the axisymmetric case for phase segregation and maintenance of the interface. To enhance the method’s numerical stability for handling binary fluids with high viscosity ratio, a multiple-relaxation-time mod- el is used for the collision operator. Several numerical examples, including static droplet test, oscillation of a viscous droplet, and breakup of a liquid thread, are presented to test the capability and accuracy of the proposed color-gradient LB- M. It is found that the present method is able to accurately capture the phase interface and produce low spurious velocities. Also, the LBM results are all in good agreement with the analytical solutions and/or available experimental data for a very broad range of viscosity ratios.

KW - lattice Boltzmann method

KW - axisymmetric flow

KW - color-gradient model

KW - high viscosity ratio

KW - Rayleigh instability

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KW - single-component collision operator

KW - perturbation operator

KW - recolouring operator

KW - interfacial tension

KW - binary fluids

KW - high-viscosity ratio

KW - multiple-relaxation model

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