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Entropy 2018, 20(9), 680; https://doi.org/10.3390/e20090680

Evaporation Boundary Conditions for the Linear R13 Equations Based on the Onsager Theory

1
Department of Mechanical Engineering, University of Victoria, Victoria, BC V8W 3P6, Canada
2
Mathematics Institute, University of Warwick, Warwick CV4 7AL, UK
3
Center for Computational Engineering Science (CCES), RWTH Aachen University, 52056 Aachen, Germany
*
Author to whom correspondence should be addressed.
Received: 17 July 2018 / Revised: 28 August 2018 / Accepted: 3 September 2018 / Published: 6 September 2018
(This article belongs to the Special Issue Thermodynamics of Non-Equilibrium Gas Flows)
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Abstract

Due to the failure of the continuum hypothesis for higher Knudsen numbers, rarefied gases and microflows of gases are particularly difficult to model. Macroscopic transport equations compete with particle methods, such as the Direct Simulation Monte Carlo method (DSMC), to find accurate solutions in the rarefied gas regime. Due to growing interest in micro flow applications, such as micro fuel cells, it is important to model and understand evaporation in this flow regime. Here, evaporation boundary conditions for the R13 equations, which are macroscopic transport equations with applicability in the rarefied gas regime, are derived. The new equations utilize Onsager relations, linear relations between thermodynamic fluxes and forces, with constant coefficients, that need to be determined. For this, the boundary conditions are fitted to DSMC data and compared to other R13 boundary conditions from kinetic theory and Navier–Stokes–Fourier (NSF) solutions for two one-dimensional steady-state problems. Overall, the suggested fittings of the new phenomenological boundary conditions show better agreement with DSMC than the alternative kinetic theory evaporation boundary conditions for R13. Furthermore, the new evaporation boundary conditions for R13 are implemented in a code for the numerical solution of complex, two-dimensional geometries and compared to NSF solutions. Different flow patterns between R13 and NSF for higher Knudsen numbers are observed. View Full-Text
Keywords: rarefied gas dynamics; modelling evaporation; R13-equations rarefied gas dynamics; modelling evaporation; R13-equations
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Beckmann, A.F.; Rana, A.S.; Torrilhon, M.; Struchtrup, H. Evaporation Boundary Conditions for the Linear R13 Equations Based on the Onsager Theory. Entropy 2018, 20, 680.

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