Hostname: page-component-77c89778f8-sh8wx Total loading time: 0 Render date: 2024-07-18T13:00:12.880Z Has data issue: false hasContentIssue false
  • English
  • Français

Single Component Multiphase Lattice Boltzmann Method for Taylor/Bretherton Bubble Train Flow Simulations

Published online by Cambridge University Press:  12 April 2016

Michał Dzikowski ,
Łukasz Łaniewski-Wołłk  and
Jacek Rokicki
Michał Dzikowski*
Affiliation:
Institute of Aeronautics and Applied Mechanics, Warsaw University of Technology, Nowowiejska 24, 00-665 Warsaw, Poland
Łukasz Łaniewski-Wołłk
Affiliation:
Institute of Aeronautics and Applied Mechanics, Warsaw University of Technology, Nowowiejska 24, 00-665 Warsaw, Poland
Jacek Rokicki
Affiliation:
Institute of Aeronautics and Applied Mechanics, Warsaw University of Technology, Nowowiejska 24, 00-665 Warsaw, Poland
*
*Corresponding author. Email addresses:mdzikowski@meil.pw.edu.pl (M. Dzikowski), llaniewski@meil.pw.edu.pl (Ł. Łaniewski-Wołłk), jack@meil.pw.edu.pl (J. Rokicki)
Get access

Abstract

In this study long bubble rising in a narrow channel was investigated using multiphase lattice Boltzmann method. The problem is known as a Bretherton or Taylor bubble flow [2] and is used here to verify the performance of the scheme proposed by [13]. The scheme is modified by incorporation of multiple relaxation time (MRT) collision scheme according to the original suggestion of the author. The purpose is to improve the stability of the method. The numerical simulation results show a good agreement with analytic solution provided by [2]. Moreover the convergence study demonstrates that the method achieves more than the first order of convergence. The paper investigates also the influence of simulation parameters on the interface resolution and shape.

Keywords

Bretherton problemmicrochannel simulationmultiphase flowlattice Boltzmann methodflow between plates
Type
Research Article
Information
Communications in Computational Physics , Volume 19 , Issue 4 , April 2016 , pp. 1042 - 1066
Copyright
Copyright © Global-Science Press 2016 

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]Bhatnagar, P. L., Gross, E. P., and Krook, M.. A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Physical Review, 94(3):511–525, 1954.CrossRefGoogle Scholar
[2]Bretherton, F. P.. The motion of long bubbles in tubes. Journal of Fluid Mechanics, 10(02):166–188, 1961.CrossRefGoogle Scholar
[3]Brackbill, J. U., Jamet, D., and Torres, D.. On the theory and computation of surface tension: The elimination of parasitic currents through energy conservation in the second-gradient method. Journal of Computational Physics, 182(1):262–276, 2002.Google Scholar
[4]Wheeler, A. A., Anderson, D. M., and McFadden, G. B.. Diffuse-interface methods in fluid mechanics. Annual Review of Fluid Mechanics, 30(1):139–165, 1998.Google Scholar
[5]d'Humières, D., Ginzburg, I., Krafczyk, M., Lallemand, P., and Luo, L.-S.. Multiple-relaxation-time lattice Boltzmann models in three dimensions. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 360(1792):437–451, 2002.CrossRefGoogle ScholarPubMed
[6]Yiotis, A. G., Kikkinides, E. S., Kainourgiakis, M. E., and Stubos, A. K.. Thermodynamic consistency of liquid-gas lattice Boltzmann methods: Interfacial property issues. Physical Review E, 78(3):036702, 2008.Google Scholar
[7]Gunstensen, A. K.. Lattice-boltzmann studies of multiphase flow through porous media. PhD Thesis, Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology. 1992.Google Scholar
[8]Krafczyk, M., Huang, H., and Lu, X.. Forcing term in single-phase and shan-chen-type multiphase lattice Boltzmann models. Physical Review E, 84(4):046710, 2011.Google Scholar
[9]Halpern, D. and Gaver, D. P. III. Boundary element analysis of the time-dependent motion of a semi-infinite bubble in a channel. J. Comput. Phys., 115(2):366–375, 1994.CrossRefGoogle Scholar
[10]Jacqmin, D.. Calculation of two-phase Navier-Stokes flows using phase-field modeling. Journal of Computational Physics, 155(1):96–127, 1999.CrossRefGoogle Scholar
[11]Jamet, D., Lebaigue, O., Coutris, N., and Delhaye, J. M.. The second gradient theory: A tool for the direct numerical simulation of liquid–vapor flows with phase-change. Nuclear Engineering and Design, 204(1-3):155–166, 2001.Google Scholar
[12]Kupershtokh, A. L.. Criterion of numerical instability of liquid state in LBE simulations. Computers and Mathematics with Applications, 59(7):2236–2245, 2010.Google Scholar
[13]Kupershtokh, A. L., Medvedev, D. A., and Karpov, D. I.. On equations of state in a lattice Boltzmann method. Computers and Mathematics with Applications, 58(5):965–974, 2009.Google Scholar
[14]Kuzmin, A., Januszewski, M., Eskin, D., Mostowfi, F., and Derksen, J. J.. Simulations of gravity-driven flow of binary liquids in microchannels. Chemical Engineering Journal, 171(2):646–654, 2011.CrossRefGoogle Scholar
[15]Lafaurie, B., Nardone, C., Scardovelli, R., Zaleski, S., and Zanetti, G.. Modelling merging and fragmentation in multiphase flows with SURFER. Journal of Computational Physics, 113(1):134–147, 1994.Google Scholar
[16]Łaniewski-Wołłk, Ł. and Rokicki, J.. Adjoint lattice Boltzmann for topology optimization on multi-GPU architecture. Computers & Mathematics with Applications, 71(3), 2015.Google Scholar
[17]Lee, T.. Eliminating parasitic currents in the lattice Boltzmann equation method for nonideal gases. Physical Review E, 74(4), 2006.Google Scholar
[18]Li, Q., Luo, K. H., and Li, X. J.. Forcing scheme in pseudopotential lattice Boltzmann model for multiphase flows. Physical Review E, 86(1):016709, 2012.Google Scholar
[19]Lou, Q., Guo, Z. L., and Shi, B. C.. Effects of force discretization on mass conservation in lattice Boltzmann equation for two-phase flows. Europhysics Letters, 99(6):64005, 2012.Google Scholar
[20]Lycett-Brown, D. J. and Luo, K. H. Multiphase cascaded lattice Boltzmann method. Computers and Mathematics with Applications, 67(2):350–362, 2014.Google Scholar
[21]McCracken, M. E. and Abraham, J.. Multiple-relaxation-time lattice-Boltzmann model for multiphase flow. Physical Review E, 71(3):036701, 2005.Google Scholar
[22]Mei, R., Shyy, W., Yu, D., and Luo, L. S.. Lattice Boltzmann method for 3-D flows with curved boundary. Journal of Computational Physics, 161(2):680–699, 2000.CrossRefGoogle Scholar
[23]Pooley, C. M. and Furtado, K.. Eliminating spurious velocities in the free-energy lattice Boltzmann method. Physical Review E, 77(4):046702, 2008.Google Scholar
[24]Premnath, K. N. and Abraham, J.. Three-dimensional multi-relaxation time (MRT) lattice-boltzmann models for multiphase flow. Journal of Computational Physics, 224(2):539–559, 2007.Google Scholar
[25]He, X. and Zou., Q.Derivation of the macroscopic continuum equations for multiphase flow. Physical Review E, 59(1):1253–1255, 1999.Google Scholar
[26]Sankaranarayanan, K., Shan, X., Kevrekidis, I. G., and Sundaresan, S.. Analysis of drag and virtual mass forces in bubbly suspensions using an implicit formulation of the lattice Boltzmann method. Journal of Fluid Mechanics, 452, 2002.Google Scholar
[27]Succi, S.. The Lattice Boltzmann Equation for Fluid Dynamics and Beyond. Oxford University Press, USA, 2001.Google Scholar
[28]Chen, H. and Shan, X.. Simulation of non-ideal gases and liquid-gas phase transitions by lattice Boltzmann equation. arXiv e-print comp-gas/9401001, 1994.Google Scholar
[29]Xiong, Y. and Guo, Z.. Effects of density and force discretizations on spurious velocities in lattice Boltzmann equation for two-phase flows. Journal of Physics A: Mathematical and Theoretical, 47(19):195502, 2014.Google Scholar
[30]Yang, Z. L., Palm, B., and Sehgal, B. R.. Numerical simulation of bubbly two-phase flow in a narrow channel. International Journal of Heat and Mass Transfer, 45(3):631–639, 2002.Google Scholar