A wall-function approach to incorporating Knudsen-layer effects in gas micro flow simulations

Duncan A. Lockerby, Jason Reese, Michael A. Gallis

Research output: Chapter in Book/Report/Conference proceedingChapter

2 Citations (Scopus)

Abstract

For gas flows in microfluidic configurations, the Knudsen layer close to the wall can comprise a substantial part of the entire flow field and has a major effect on quantities such as the mass flow rate through micro devices. The Knudsen layer itself is characterized by a highly nonlinear relationship between the viscous stress and the strain rate of the gas, so even if the Navier-Stokes equations can be used to describe the core gas flow they are certainly inappropriate for the Knudsen layer itself. In this paper we propose a "wall-function" model for the stress/strain rate relations in the Knudsen layer. The constitutive structure of the Knudsen layer has been derived from results from kinetic theory for isothermal shear flow over a planar surface. We investigate the ability of this simplified model to predict Knudsen-layer effects in a variety of configurations. We further propose a semi-empirical Knudsen-number correction to this wall function, based on high-accuracy DSMC results, to extend the predictive capabilities of the model to greater degrees of rarefaction.
LanguageEnglish
Title of host publicationRarefied Gas Dynamics
Pages731-736
Volume762
DOIs
Publication statusPublished - 10 Jul 2004
Event24th International Symposium on Rarefied Gas Dynamics, Bari, Italy -
Duration: 1 Jan 1900 → …

Publication series

NameAIP Conference Proceedings
PublisherAmerican Institute of Physics
No.1
Volume762

Conference

Conference24th International Symposium on Rarefied Gas Dynamics, Bari, Italy
Period1/01/00 → …

Fingerprint

gases
simulation
strain rate
gas flow
rarefaction
Knudsen flow
mass flow rate
configurations
kinetic theory
shear flow
Navier-Stokes equation
flow distribution

Keywords

  • knudsen layer
  • wall-function
  • gas microflows

Cite this

Lockerby, D. A., Reese, J., & Gallis, M. A. (2004). A wall-function approach to incorporating Knudsen-layer effects in gas micro flow simulations. In Rarefied Gas Dynamics (Vol. 762, pp. 731-736). (AIP Conference Proceedings; Vol. 762, No. 1). https://doi.org/10.1063/1.1941622
Lockerby, Duncan A. ; Reese, Jason ; Gallis, Michael A. / A wall-function approach to incorporating Knudsen-layer effects in gas micro flow simulations. Rarefied Gas Dynamics. Vol. 762 2004. pp. 731-736 (AIP Conference Proceedings; 1).
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Lockerby, DA, Reese, J & Gallis, MA 2004, A wall-function approach to incorporating Knudsen-layer effects in gas micro flow simulations. in Rarefied Gas Dynamics. vol. 762, AIP Conference Proceedings, no. 1, vol. 762, pp. 731-736, 24th International Symposium on Rarefied Gas Dynamics, Bari, Italy, 1/01/00. https://doi.org/10.1063/1.1941622

A wall-function approach to incorporating Knudsen-layer effects in gas micro flow simulations. / Lockerby, Duncan A. ; Reese, Jason; Gallis, Michael A.

Rarefied Gas Dynamics. Vol. 762 2004. p. 731-736 (AIP Conference Proceedings; Vol. 762, No. 1).

Research output: Chapter in Book/Report/Conference proceedingChapter

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Lockerby DA, Reese J, Gallis MA. A wall-function approach to incorporating Knudsen-layer effects in gas micro flow simulations. In Rarefied Gas Dynamics. Vol. 762. 2004. p. 731-736. (AIP Conference Proceedings; 1). https://doi.org/10.1063/1.1941622