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On the modelling of isothermal gas flows at the microscale

Published online by Cambridge University Press:  14 May 2008

DUNCAN A. LOCKERBY  and
JASON M. REESE
DUNCAN A. LOCKERBY
Affiliation:
School of Engineering, University of Warwick, Coventry CV4 7AL, UK
JASON M. REESE
Affiliation:
Department of Mechanical Engineering, University of Strathclyde, Glasgow G1 1XJ, UK
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Abstract

This paper makes two new propositions regarding the modelling of rarefied (non-equilibrium) isothermal gas flows at the microscale. The first is a new test case for benchmarking high-order, or extended, hydrodynamic models for these flows. This standing time-varying shear-wave problem does not require boundary conditions to be specified at a solid surface, so is useful for assessing whether fluid models can capture rarefaction effects in the bulk flow. We assess a number of different proposed extended hydrodynamic models, and we find the R13 equations perform the best in this case.

Our second proposition is a simple technique for introducing non-equilibrium effects caused by the presence of solid surfaces into the computational fluid dynamics framework. By combining a new model for slip boundary conditions with a near-wall scaling of the Navier--Stokes constitutive relations, we obtain a model that is much more accurate at higher Knudsen numbers than the conventional second-order slip model. We show that this provides good results for combined Couette/Poiseuille flow, and that the model can predict the stress/strain-rate inversion that is evident from molecular simulations. The model's generality to non-planar geometries is demonstrated by examining low-speed flow around a micro-sphere. It shows a marked improvement over conventional predictions of the drag on the sphere, although there are some questions regarding its stability at the highest Knudsen numbers.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 604 , 10 June 2008 , pp. 235 - 261
Copyright
Copyright © Cambridge University Press 2008

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