Lockerby, Duncan and Reese, Jason. (2008) On the modelling of isothermal gas flows at the microscale. Journal of Fluid Mechanics, Vol.604 . pp. 235-261. ISSN 0022-1120

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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.

Item Type:	Journal Article
Subjects:	T Technology > T Technology (General) Q Science > QA Mathematics Q Science > QC Physics
Divisions:	Faculty of Science > Engineering
Library of Congress Subject Headings (LCSH):	Rarefied gas dynamics, Geometry, Plane, Navier-Stokes equations -- Numerical solutions, Transport theory, Gas dynamics, Fluid dynamics
Journal or Publication Title:	Journal of Fluid Mechanics
Publisher:	Cambridge University Press
ISSN:	0022-1120
Date:	June 2008
Volume:	Vol.604
Number of Pages:	27
Page Range:	pp. 235-261
Identification Number:	10.1017/S0022112008001158
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access
Funder:	Engineering and Physical Sciences Research Council (EPSRC)
Grant number:	EP/D007488/1 (EPSRC)
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URI:	http://wrap.warwick.ac.uk/id/eprint/863

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