Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-14T21:27:21.775Z Has data issue: false hasContentIssue false
  • English
  • Français

Rotational Slip Flow in Coaxial Cylinders by the Finite-Difference Lattice Boltzmann Methods

Published online by Cambridge University Press:  20 August 2015

Minoru Watari
Minoru Watari*
Affiliation:
LBM Fluid Dynamics Laboratory, 3-2-1 Mitahora-higashi, Gifu 502-0003, Japan
*
*Corresponding author.Email:[email protected]
Get access

Abstract

Recent studies on applications of the lattice Boltzmann method (LBM) and the finite-difference lattice Boltzmann method (FDLBM) to velocity slip simulations are mostly on one-dimensional (1D) problems such as a shear flow between parallel plates. Applications to a 2D problem may raise new issues. The author performed numerical simulations of rotational slip flow in coaxial cylinders as an example of 2D problem. Two types of 2D models were used. The first were multi-speed FDLBM models proposed by the author. The second was a standard LBM, the D2Q9 model. The simulations were performed applying a finite difference scheme to both the models. The study had two objectives. The first was to investigate the accuracies of LBM and FDLBM on applications to rotational slip flow. The second was to obtain an experience on application of the cylindrical coordinate system. The FDLBM model with 8 directions and the D2Q9 model showed an anisotropic flow pattern when the relaxation time constant or the Knudsen number was large. The FDLBM model with 24 directions showed accurate results even at large Knudsen numbers.

Keywords

47.11.-j47.45.-n51.10.+yFinite-difference lattice Boltzmann methodrarefied gas flowrotational slip flowcylindrical coordinate
Type
Research Article
Information
Communications in Computational Physics , Volume 9 , Issue 5 , May 2011 , pp. 1293 - 1314
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]Lim, C. Y., Shu, C., Niu, X. D., and Chew, Y. T., Application of lattice Boltzmann method to simulate microchannel flows, Phys. Fluids., 14 (2002), 2299–2308.Google Scholar
[2]Nie, X., Doolen, G. D., and Chen, S., Lattice-Boltzmann simulations of fluid flows in MEMS, J. Stat. Phys. 107 (2002), 279–289.Google Scholar
[3]Sbragaglia, M., and Succi, S., Analytical calculation of slip flow in lattice Boltzmann models with kinetic boundary conditions, Phys. Fluids., 17 (2005), 093602.CrossRefGoogle Scholar
[4]Ansumali, S., and Karlin, I. V., Kinetic boundary conditions in the lattice Boltzmann method, Phys. Rev. E., 66 (2002), 026311.CrossRefGoogle ScholarPubMed
[5]Tang, G. H., Tao, W. Q., and He, Y. L., Lattice Boltzmann method for gaseous microflows using kinetic theory boundary conditions, Phys. Fluids., 17 (2005), 058101.CrossRefGoogle Scholar
[6]Zhang, Y., Qin, R., and Emerson, D. R., Lattice Boltzmann simulation of rarefied gas flows in microchannels, Phys. Rev. E., 71 (2005), 047702.Google Scholar
[7]Niu, X. D., Hyodo, S. A., Munekata, T., and Suga, K., Kinetic lattice Boltzmann method for microscale gas flows: issues on boundary condition, relaxation time, and regularization, Phys. Rev. E., 76 (2007), 036711.CrossRefGoogle ScholarPubMed
[8]Sofonea, V., and Sekerka, R. F., Diffuse-reflection boundary conditions for a thermal lattice Boltzmann model in two dimensions: evidence of temperature jump and slip velocity in microchannels, Phys. Rev. E., 71 (2005), 066709.Google Scholar
[9]Sofonea, V., and Sekerka, R. F., Boundary conditions for the upwind finite difference lattice Boltzmann model: evidence of slip velocity in micro-channel flow, J. Comput. Phys., 207 (2005), 639–659.CrossRefGoogle Scholar
[10]Watari, M., Velocity slip and temperature jump simulations by the three-dimensional thermal finite-difference lattice Boltzmann method, Phys. Rev. E., 79 (2009), 066706.Google Scholar
[11]Watari, M., Relationship between accuracy and number of velocity particles of the finite-difference lattice Boltzmann method in velocity slip simulations, J. Fluids. Eng., 132 (2010), 101401.Google Scholar
[12]Watari, M., and Tsutahara, M., Two-dimensional thermal model of the finite-difference lattice Boltzmann method with high spatial isotropy, Phys. Rev. E., 67 (2003), 036306.Google Scholar
[13]Qian, Y. H., D. D’Humieres, and Lallemand, P., Lattice BGK models for Navier-Stokes equation, Europhys. Lett., 17 (1992), 479–484.CrossRefGoogle Scholar
[14]Millikan, R. A., Coefficients of slip in gases and the law of reflection of molecules from the surfaces of solids and liquids, Phys. Rev., 21 (1923), 217–238.Google Scholar
[15]Kogan, M. N., Rarefied Gas Dynamics, Plenum, New York, 1969.Google Scholar
[16]Sone, Y., Molecular Gas Dynamics: Theory, Techniques, and Applications, Birkhäuser, Boston, 2006.Google Scholar