Cargando…
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...
Autores principales: | , , , |
---|---|
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 |
_version_ | 1783586334286282752 |
---|---|
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. |
format | Online Article Text |
id | pubmed-7513205 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2018 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
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 |
work_keys_str_mv | AT beckmannalexanderfelix evaporationboundaryconditionsforthelinearr13equationsbasedontheonsagertheory AT ranaanirudhsingh evaporationboundaryconditionsforthelinearr13equationsbasedontheonsagertheory AT torrilhonmanuel evaporationboundaryconditionsforthelinearr13equationsbasedontheonsagertheory AT struchtruphenning evaporationboundaryconditionsforthelinearr13equationsbasedontheonsagertheory |