A phenomenological and extended continuum approach for modelling non-equilibrium flows |
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Authors: | S Mizzi R W Barber D R Emerson J M Reese S K Stefanov |
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Institution: | (1) Centre for Microfluidics and Microsystems Modelling, Computational Science and Engineering Department, CCLRC Daresbury Laboratory, Keckwick Lane, Daresbury, WA4 4AD, Warrington, UK;(2) Mechanical Engineering Department, University of Strathclyde, James Weir Building, G1 1XJ Glasgow, UK;(3) Institute of Mechanics, Bulgarian Academy of Sciences, Block 4, Acad. G. Bonchev Street, 1113 Sofia, Bulgaria |
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Abstract: | This paper presents a new technique that combines Grad’s 13-moment equations (G13) with a phenomenological approach to rarefied
gas flows. This combination and the proposed solution technique capture some important non-equilibrium phenomena that appear
in the early continuum-transition flow regime. In contrast to the fully coupled 13-moment equation set, a significant advantage
of the present solution technique is that it does not require extra boundary conditions explicitly; Grad’s equations for viscous
stress and heat flux are used as constitutive relations for the conservation equations instead of being solved as equations
of transport. The relative computational cost of this novel technique is low in comparison to other methods, such as fully
coupled solutions involving many moments or discrete methods. In this study, the proposed numerical procedure is tested on
a planar Couette flow case, and the results are compared to predictions obtained from the direct simulation Monte Carlo method.
This test case highlights the presence of normal viscous stresses and tangential heat fluxes that arise from non-equilibrium
phenomena, which cannot be captured by the Navier–Stokes–Fourier constitutive equations or phenomenological modifications.
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Keywords: | Flows in micro-electromechanical systems (MEMS) and nano-electromechanical systems (NEMS) Micro- and nano- scale flow phenomena Rarefied gas dynamics Non-continuum effects Non-equilibrium gas dynamics |
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