M. Schulz, K. Nagatou, A. von der Weth, F. Arbeiter, V. Pasler
{"title":"Analytical Solution of a Gas Release Problem considering Permeation with Time-Dependent Boundary Conditions","authors":"M. Schulz, K. Nagatou, A. von der Weth, F. Arbeiter, V. Pasler","doi":"10.1080/23324309.2020.1828469","DOIUrl":null,"url":null,"abstract":"Abstract In preparation for determining material properties such as Sieverts’ constant (solubility) and diffusivity (transport rate) we give a detailed discussion on a model describing some gas release experiment. Aiming to simulate the time-dependent hydrogen fluxes and concentration profiles efficiently, we provide an analytical solution for the diffusion equations on a cylindrical specimen and a cylindrical container for three boundary conditions (B.C.). These (B.C.) occur in three phases – loading phase, evacuation phase and gas release phase. In the loading phase the specimen is charged with hydrogen assuring a constant partial pressure of hydrogen. The gas will be quickly removed in the second phase, in the third phase, the hydrogen is released from the specimen to the gaseous phase. The diffusion equation in each phase is a simple homogeneous equation. Due to the complex time-dependent (B.C.), we transform the homogeneous equations to the non-homogeneous ones with a zero Dirichlet (B.C.). Compared with the time consuming numerical methods our analytical approach has an advantage that the flux of desorbed hydrogen can be explicitly given and therefore can be evaluated efficiently. Our analytical solution also assures that the (B.C.) are exactly satisfied. The interaction between specimen and container is taken into account.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"49 1","pages":"389 - 412"},"PeriodicalIF":0.7000,"publicationDate":"2020-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23324309.2020.1828469","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational and Theoretical Transport","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1080/23324309.2020.1828469","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 4
Abstract
Abstract In preparation for determining material properties such as Sieverts’ constant (solubility) and diffusivity (transport rate) we give a detailed discussion on a model describing some gas release experiment. Aiming to simulate the time-dependent hydrogen fluxes and concentration profiles efficiently, we provide an analytical solution for the diffusion equations on a cylindrical specimen and a cylindrical container for three boundary conditions (B.C.). These (B.C.) occur in three phases – loading phase, evacuation phase and gas release phase. In the loading phase the specimen is charged with hydrogen assuring a constant partial pressure of hydrogen. The gas will be quickly removed in the second phase, in the third phase, the hydrogen is released from the specimen to the gaseous phase. The diffusion equation in each phase is a simple homogeneous equation. Due to the complex time-dependent (B.C.), we transform the homogeneous equations to the non-homogeneous ones with a zero Dirichlet (B.C.). Compared with the time consuming numerical methods our analytical approach has an advantage that the flux of desorbed hydrogen can be explicitly given and therefore can be evaluated efficiently. Our analytical solution also assures that the (B.C.) are exactly satisfied. The interaction between specimen and container is taken into account.
期刊介绍:
Emphasizing computational methods and theoretical studies, this unique journal invites articles on neutral-particle transport, kinetic theory, radiative transfer, charged-particle transport, and macroscopic transport phenomena. In addition, the journal encourages articles on uncertainty quantification related to these fields. Offering a range of information and research methodologies unavailable elsewhere, Journal of Computational and Theoretical Transport brings together closely related mathematical concepts and techniques to encourage a productive, interdisciplinary exchange of ideas.