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

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Lockerby, Duncan A. and Reese, Jason and Gallis, Michael A.; (2004) A wall-function approach to incorporating Knudsen-layer effects in gas micro flow simulations. In: Rarefied Gas Dynamics. AIP Conference Proceedings, 762 . American Institute of Physics, pp. 731-736. ISBN 0-7354-0247-7 (https://doi.org/10.1063/1.1941622)

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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.

ORCID iDs

Lockerby, Duncan A., Reese, Jason ORCID logoORCID: https://orcid.org/0000-0001-5188-1627 and Gallis, Michael A.;
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