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Evaporation boundary conditions for the linear R13 equations based on the onsager theory
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Beckmann, Alexander, Rana, Anirudh Singh, Torrilhon, Manuel and Struchtrup, Henning (2018) Evaporation boundary conditions for the linear R13 equations based on the onsager theory. Entropy, 20 (9). 680. doi:10.3390/e20090680 ISSN 1099-4300.
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Official URL: https://doi.org/10.3390/e20090680
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.
Item Type: | Journal Article | |||||||||||||||
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Subjects: | Q Science > QA Mathematics | |||||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||||||||
Library of Congress Subject Headings (LCSH): | Gas dynamics -- Mathematical models, Continuum hypothesis, Free molecular flow, Monte Carlo method | |||||||||||||||
Journal or Publication Title: | Entropy | |||||||||||||||
Publisher: | M D P I AG | |||||||||||||||
ISSN: | 1099-4300 | |||||||||||||||
Official Date: | 6 September 2018 | |||||||||||||||
Dates: |
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Volume: | 20 | |||||||||||||||
Number: | 9 | |||||||||||||||
Article Number: | 680 | |||||||||||||||
DOI: | 10.3390/e20090680 | |||||||||||||||
Status: | Peer Reviewed | |||||||||||||||
Publication Status: | Published | |||||||||||||||
Access rights to Published version: | Open Access (Creative Commons) | |||||||||||||||
Description: | This article belongs to the Special Issue Thermodynamics of Non-Equilibrium Gas Flows |
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Date of first compliant deposit: | 10 September 2018 | |||||||||||||||
Date of first compliant Open Access: | 10 September 2018 | |||||||||||||||
RIOXX Funder/Project Grant: |
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