Lattice Boltzmann simulation of rarefied gas flows

G.H. Tang, Yonghao Zhang, X.J. Gu, Jason Reese, Robert W. Barber, David Emerson

Research output: Contribution to conferencePaper

Abstract

For gas flows in microchannels, slip motion at the solid surface can occur even if the Mach number is negligibly small. Since the Knudsen number of the gas flow in a long microchannel can vary widely and the Navier-Stokes equations are not valid for Knudsen numbers beyond 0.1, an alternative method that can be applicable to continuum, slip and transition flow regimes is highly desirable. The lattice Boltzmann equation (LBE) approach has recently been expected to have such potential. However, some hurdles need to be overcome before it can be applied to simulate rarefied gas flows. The first major hurdle is to accurately model the gas molecule and wall surface interactions. In addition, the Knudsen number needs to be clearly defined in terms of LBE properties to ensure that the LBE simulation results can be checked against experimental measurements and other simulation results. In this paper, the Maxwellian scattering kernel is adopted to address the gas molecule and surface interactions with an accommodation coefficient (in addition to the Knudsen number) controlling the amount of slip motion. The Knudsen number is derived consistently with the macroscopic property based definition. The simulation results of the present LBE model are in quantitative agreement with the established theory in the slip flow regime. In the transition flow regime, the model captures the Knudsen minimum phenomenon qualitatively. Therefore, the LBE can be a competitive method for simulation of rarefied gas flows in microdevices.

Conference

Conference51st IUVSTA Workshop on Modern Problems and Capability of Vacuum Gas Dynamics
CityVärmdö, Sweden
Period1/07/07 → …

Fingerprint

Knudsen flow
rarefied gases
gas flow
transition flow
slip flow
microchannels
simulation
surface reactions
slip
continuum flow
accommodation coefficient
gases
Mach number
solid surfaces
Navier-Stokes equation
molecules
scattering
interactions

Keywords

  • Lattice Boltzmann
  • gas flows
  • microchannel
  • Navier-Stokes equation
  • Knudsen number
  • microdevices

Cite this

Tang, G. H., Zhang, Y., Gu, X. J., Reese, J., Barber, R. W., & Emerson, D. (2007). Lattice Boltzmann simulation of rarefied gas flows. Paper presented at 51st IUVSTA Workshop on Modern Problems and Capability of Vacuum Gas Dynamics, Värmdö, Sweden, .
Tang, G.H. ; Zhang, Yonghao ; Gu, X.J. ; Reese, Jason ; Barber, Robert W. ; Emerson, David. / Lattice Boltzmann simulation of rarefied gas flows. Paper presented at 51st IUVSTA Workshop on Modern Problems and Capability of Vacuum Gas Dynamics, Värmdö, Sweden, .
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abstract = "For gas flows in microchannels, slip motion at the solid surface can occur even if the Mach number is negligibly small. Since the Knudsen number of the gas flow in a long microchannel can vary widely and the Navier-Stokes equations are not valid for Knudsen numbers beyond 0.1, an alternative method that can be applicable to continuum, slip and transition flow regimes is highly desirable. The lattice Boltzmann equation (LBE) approach has recently been expected to have such potential. However, some hurdles need to be overcome before it can be applied to simulate rarefied gas flows. The first major hurdle is to accurately model the gas molecule and wall surface interactions. In addition, the Knudsen number needs to be clearly defined in terms of LBE properties to ensure that the LBE simulation results can be checked against experimental measurements and other simulation results. In this paper, the Maxwellian scattering kernel is adopted to address the gas molecule and surface interactions with an accommodation coefficient (in addition to the Knudsen number) controlling the amount of slip motion. The Knudsen number is derived consistently with the macroscopic property based definition. The simulation results of the present LBE model are in quantitative agreement with the established theory in the slip flow regime. In the transition flow regime, the model captures the Knudsen minimum phenomenon qualitatively. Therefore, the LBE can be a competitive method for simulation of rarefied gas flows in microdevices.",
keywords = "Lattice Boltzmann, gas flows, microchannel, Navier-Stokes equation, Knudsen number, microdevices",
author = "G.H. Tang and Yonghao Zhang and X.J. Gu and Jason Reese and Barber, {Robert W.} and David Emerson",
note = "This is a variant record.; 51st IUVSTA Workshop on Modern Problems and Capability of Vacuum Gas Dynamics ; Conference date: 01-07-2007",
year = "2007",
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Tang, GH, Zhang, Y, Gu, XJ, Reese, J, Barber, RW & Emerson, D 2007, 'Lattice Boltzmann simulation of rarefied gas flows' Paper presented at 51st IUVSTA Workshop on Modern Problems and Capability of Vacuum Gas Dynamics, Värmdö, Sweden, 1/07/07, .

Lattice Boltzmann simulation of rarefied gas flows. / Tang, G.H.; Zhang, Yonghao; Gu, X.J.; Reese, Jason; Barber, Robert W.; Emerson, David.

2007. Paper presented at 51st IUVSTA Workshop on Modern Problems and Capability of Vacuum Gas Dynamics, Värmdö, Sweden, .

Research output: Contribution to conferencePaper

TY - CONF

T1 - Lattice Boltzmann simulation of rarefied gas flows

AU - Tang, G.H.

AU - Zhang, Yonghao

AU - Gu, X.J.

AU - Reese, Jason

AU - Barber, Robert W.

AU - Emerson, David

N1 - This is a variant record.

PY - 2007

Y1 - 2007

N2 - For gas flows in microchannels, slip motion at the solid surface can occur even if the Mach number is negligibly small. Since the Knudsen number of the gas flow in a long microchannel can vary widely and the Navier-Stokes equations are not valid for Knudsen numbers beyond 0.1, an alternative method that can be applicable to continuum, slip and transition flow regimes is highly desirable. The lattice Boltzmann equation (LBE) approach has recently been expected to have such potential. However, some hurdles need to be overcome before it can be applied to simulate rarefied gas flows. The first major hurdle is to accurately model the gas molecule and wall surface interactions. In addition, the Knudsen number needs to be clearly defined in terms of LBE properties to ensure that the LBE simulation results can be checked against experimental measurements and other simulation results. In this paper, the Maxwellian scattering kernel is adopted to address the gas molecule and surface interactions with an accommodation coefficient (in addition to the Knudsen number) controlling the amount of slip motion. The Knudsen number is derived consistently with the macroscopic property based definition. The simulation results of the present LBE model are in quantitative agreement with the established theory in the slip flow regime. In the transition flow regime, the model captures the Knudsen minimum phenomenon qualitatively. Therefore, the LBE can be a competitive method for simulation of rarefied gas flows in microdevices.

AB - For gas flows in microchannels, slip motion at the solid surface can occur even if the Mach number is negligibly small. Since the Knudsen number of the gas flow in a long microchannel can vary widely and the Navier-Stokes equations are not valid for Knudsen numbers beyond 0.1, an alternative method that can be applicable to continuum, slip and transition flow regimes is highly desirable. The lattice Boltzmann equation (LBE) approach has recently been expected to have such potential. However, some hurdles need to be overcome before it can be applied to simulate rarefied gas flows. The first major hurdle is to accurately model the gas molecule and wall surface interactions. In addition, the Knudsen number needs to be clearly defined in terms of LBE properties to ensure that the LBE simulation results can be checked against experimental measurements and other simulation results. In this paper, the Maxwellian scattering kernel is adopted to address the gas molecule and surface interactions with an accommodation coefficient (in addition to the Knudsen number) controlling the amount of slip motion. The Knudsen number is derived consistently with the macroscopic property based definition. The simulation results of the present LBE model are in quantitative agreement with the established theory in the slip flow regime. In the transition flow regime, the model captures the Knudsen minimum phenomenon qualitatively. Therefore, the LBE can be a competitive method for simulation of rarefied gas flows in microdevices.

KW - Lattice Boltzmann

KW - gas flows

KW - microchannel

KW - Navier-Stokes equation

KW - Knudsen number

KW - microdevices

UR - http://www.vgd07.dl.ac.uk/

UR - http://strathprints.strath.ac.uk/5076/

UR - http://dx.doi.org/10.1103/PhysRevE.71.047702

M3 - Paper

ER -

Tang GH, Zhang Y, Gu XJ, Reese J, Barber RW, Emerson D. Lattice Boltzmann simulation of rarefied gas flows. 2007. Paper presented at 51st IUVSTA Workshop on Modern Problems and Capability of Vacuum Gas Dynamics, Värmdö, Sweden, .