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

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...

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Autores principales: Beckmann, Alexander Felix, Rana, Anirudh Singh, Torrilhon, Manuel, Struchtrup, Henning
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2018
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7513205/
https://www.ncbi.nlm.nih.gov/pubmed/33265769
http://dx.doi.org/10.3390/e20090680
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author Beckmann, Alexander Felix
Rana, Anirudh Singh
Torrilhon, Manuel
Struchtrup, Henning
author_facet Beckmann, Alexander Felix
Rana, Anirudh Singh
Torrilhon, Manuel
Struchtrup, Henning
author_sort Beckmann, Alexander Felix
collection PubMed
description 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.
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spelling pubmed-75132052020-11-09 Evaporation Boundary Conditions for the Linear R13 Equations Based on the Onsager Theory Beckmann, Alexander Felix Rana, Anirudh Singh Torrilhon, Manuel Struchtrup, Henning Entropy (Basel) Article 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. MDPI 2018-09-06 /pmc/articles/PMC7513205/ /pubmed/33265769 http://dx.doi.org/10.3390/e20090680 Text en © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Beckmann, Alexander Felix
Rana, Anirudh Singh
Torrilhon, Manuel
Struchtrup, Henning
Evaporation Boundary Conditions for the Linear R13 Equations Based on the Onsager Theory
title Evaporation Boundary Conditions for the Linear R13 Equations Based on the Onsager Theory
title_full Evaporation Boundary Conditions for the Linear R13 Equations Based on the Onsager Theory
title_fullStr Evaporation Boundary Conditions for the Linear R13 Equations Based on the Onsager Theory
title_full_unstemmed Evaporation Boundary Conditions for the Linear R13 Equations Based on the Onsager Theory
title_short Evaporation Boundary Conditions for the Linear R13 Equations Based on the Onsager Theory
title_sort evaporation boundary conditions for the linear r13 equations based on the onsager theory
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7513205/
https://www.ncbi.nlm.nih.gov/pubmed/33265769
http://dx.doi.org/10.3390/e20090680
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