The usefulness of higher-order constitutive relations for describing the Knudsen layer

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

Research output: Contribution to journalArticle

80 Citations (Scopus)

Abstract

The Knudsen layer is an important rarefaction phenomenon in gas flows in and around microdevices. Its accurate and efficient modeling is of critical importance in the design of such systems and in predicting their performance. In this paper we investigate the potential that higher-order continuum equations may have to model the Knudsen layer, and compare their predictions to high-accuracy DSMC (direct simulation Monte Carlo) data, as well as a standard result from kinetic theory. We find that, for a benchmark case, the most common higher-order continuum equation sets (Grad's 13 moment, Burnett, and super-Burnett equations) cannot capture the Knudsen layer. Variants of these equation families have, however, been proposed and some of them can qualitatively describe the Knudsen layer structure. To make quantitative comparisons, we obtain additional boundary conditions (needed for unique solutions to the higher-order equations) from kinetic theory. However, we find the quantitative agreement with kinetic theory and DSMC data is only slight.
LanguageEnglish
Pages100609
JournalPhysics of Fluids
Volume17
Issue number10
DOIs
Publication statusPublished - 2005

Fingerprint

Kinetic theory
kinetic theory
Burnett equations
continuums
rarefaction
Flow of gases
Boundary conditions
gas flow
simulation
boundary conditions
moments
predictions
Monte Carlo simulation

Keywords

  • knudsen flow
  • slip flow
  • flow simulation
  • fluid dynamics
  • mechanical engineering
  • kinetic theory

Cite this

Lockerby, Duncan A. ; Reese, Jason M. ; Gallis, Michael A. / The usefulness of higher-order constitutive relations for describing the Knudsen layer. In: Physics of Fluids. 2005 ; Vol. 17, No. 10. pp. 100609.
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The usefulness of higher-order constitutive relations for describing the Knudsen layer. / Lockerby, Duncan A. ; Reese, Jason M.; Gallis, Michael A.

In: Physics of Fluids, Vol. 17, No. 10, 2005, p. 100609.

Research output: Contribution to journalArticle

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AB - The Knudsen layer is an important rarefaction phenomenon in gas flows in and around microdevices. Its accurate and efficient modeling is of critical importance in the design of such systems and in predicting their performance. In this paper we investigate the potential that higher-order continuum equations may have to model the Knudsen layer, and compare their predictions to high-accuracy DSMC (direct simulation Monte Carlo) data, as well as a standard result from kinetic theory. We find that, for a benchmark case, the most common higher-order continuum equation sets (Grad's 13 moment, Burnett, and super-Burnett equations) cannot capture the Knudsen layer. Variants of these equation families have, however, been proposed and some of them can qualitatively describe the Knudsen layer structure. To make quantitative comparisons, we obtain additional boundary conditions (needed for unique solutions to the higher-order equations) from kinetic theory. However, we find the quantitative agreement with kinetic theory and DSMC data is only slight.

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