Derivation and numerical validation of a homogenized isothermal Li-ion battery model

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• 作者：Vasilena Taralova ; Oleg Iliev ; Yalchin Efendiev
• 关键词：Coupled macro ; microscale model ; Effective transport coefficients ; Homogenization theory ; Li ; ion batteries ; Numerical results
• 刊名：Journal of Engineering Mathematics
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：101
• 期：1
• 页码：1-27
• 全文大小：3,336 KB
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mechanics
  Applications of Mathematics
  Analysis
  Mathematical Modeling and IndustrialMathematics
  Numeric Computing
  
• 出版者：Springer Netherlands
• ISSN：1573-2703
• 卷排序：101

文摘

Lithium-ion batteries are multiscale systems with processes occurring at different scales. We start from a mathematical model derived on the microscale level of a single battery cell [Latz et al., NMA’10, 2011, pp. 329–337] where we can resolve the porous structure of the electrodes. Direct numerical simulations on this scale lead to a huge number of degrees of freedom and, consequently, very high computational costs. From an application perspective, it is often sufficient to predict the macroscopic properties of the electrodes. Therefore, we derive homogenized macroscopic equations with effective transport coefficients for the concentration of lithium ions in the electrolyte, potential in the electrolyte, and potential in the solid particles. These upscaled equations are coupled via the Butler–Volmer interface conditions to a microscale equation for the concentration of lithium ions in the electrode particles. We follow the idea developed by Ciucci and Lai [Transport Porous Med 88(2):249–270, 2011] and extend their analysis by computing the asymptotic order of the interface exchange current densities, which is an important factor in the homogenization study of the problem. We also perform a numerical homogenization and run extensive numerical simulations in order to validate the derived upscaled model. The numerical experiments show very good agreement between the homogenized model and the microscale one. Hence we are able to predict the macroscopic properties of the porous electrodes and capture the small-scale effects on the large scales without fully resolving all the microscale features.