固体氧化物燃料电池在裂纹影响下力-热-电化学耦合行为的数值仿真

Over the last few decades, Solid Oxide Fuel Cell (SOFC) has been a promising energy conversion device that has drawn a lot of attention due to its high conversion efficiency, fuel flexibility and low pollutant emission. However, as the high operating temperature leads to complex material problems in SOFC, the energy conversion efficiency and life expectancy remain as challenging issues regarding design and manufacturing of fuel cells. In this proposal, a numerical approach based on a combination of several advanced numerical methods is developed to model coupled thermo-mechanical-electrochemical processes in a cracked SOFC unit. In the proposed model, the fluid flow, governed by Navier-Stokes in the SOFC flow channels and Darcy-Brinkman in porous electrodes, is solved using the nonconforming Crouzeix-Raviart finite element method with an upstream scheme for the nonlinear convective term. A combination of Discontinuous Galerkin and Multi-Point Flux Approximation methods is used to solve the convection-diffusion heat and mass transport equations. The presence of crack is assumed to affect the charge transport in SOFC. It also induces discontinuities of displacements at the crack surface and singularities of stresses at the crack tip. Thus, the eXtended Finite Element Method is used to solve charge transport equations and the thermo-mechanical problem in SOFC. Using this approach, numerical simulations of the SOFC in-service are carried out to investigate the influence of crack on electrochemical performance and thermo-stresses throughout the SOFC structure. Moreover, Global Sensitivity Analysis is conducted for model parameters of interests based on a Bayesian sparse polynomial chaos expansion. Using resulted sensitivity indices, we can study the influence of each parameter on the model response quantitatively. Thereby the most influential parameters on cell performance and life expectancy can be identified, which is of great importance for the design and optimization of SOFC components.

固体氧化物燃料电池作为一种高效清洁的全固态新型化学发电装置，近年来受到了广泛的关注。燃料电池材料中初始缺陷和微裂纹的存在使得其在高温工作环境下易发生疲劳断裂、组件开裂脱离等问题，直接影响电池的工作效率和使用寿命。对固体氧化物燃料电池的工作过程进行数值仿真，探明裂纹对电池输出功率及力学性能的影响机理，对电池组件的优化设计具有重要意义。本项目拟结合有限体积法、间断伽辽金法、多点流量近似法及扩展有限单元法建立力-热-电化学多场耦合的数值仿真平台，模拟固体氧化物燃料电池在裂纹影响下的电化学反应与热力学耦合过程，从细观上研究裂纹对燃料电池能量转换效率及力学行为的影响机制。进一步利用稀疏多项式混沌展开对该数值模型进行全局敏感性分析，定量地研究各物理参数对电池综合性能的影响，并确定关键影响因素，为提高燃料电池输出功率和改善其力学性能提供理论基础和技术支持。

固体氧化物燃料电池是一种高效清洁的全固态新型化学发电装置，具有广阔的应用前景。但高温工作条件导致电池易开裂破坏，严重影响其工作效率和使用寿命。本项目针对固体氧化物燃料电池的断裂和分层破坏问题，围绕电池的力、热、流、电化学等多物理场耦合行为，开发了一系列理论模型与计算方法，揭示了影响电池力学和电化学性能的关键参数，为燃料电池组件的优化设计提供了理论基础和技术支撑。主要研究内容及结果如下：（1）发展了高精度的半解析求解方法，准确模拟了多孔材料中的三维对流-扩散传热传质行为，揭示了非均质性对多孔介质中流体流动及传热行为的影响，并为其他对流-扩散问题提供了稳定的参考解。（2）建立了固体氧化物燃料电池电化学模型，准确预测了燃料电池的输出电压和功率密度，并利用稀疏多项式混沌展开方法对燃料电池的工作性能开展了全局敏感性分析，揭示了影响电池电化学性能的关键参数，为燃料电池的优化设计提供了理论基础。（3）结合杂交元与扩展有限单元法，建立了含裂隙多孔材料的一维/二维模型，高效准确地模拟了含裂隙多孔材料的流固耦合行为。结果表明当材料初始缺陷增多时，采用该模型可显著提升计算效率。（4）发展了考虑电池力-热-电多场耦合的扩展有限单元法，构建了双材料层间裂纹的力-热-电多场耦合模型，揭示了焦耳热对双材料层间裂纹处应力分布和裂尖能量释放率的影响。结果表明焦耳热效应可显著升高结构内部温度并导致温度分布不均，继而产生较大温度应力并导致裂尖能量释放率增大。（5）发展了贝叶斯理论框架下的敏感性和可靠度分析方法，标定了多尺度数值模型中桥域多尺度方法各耦合参数的取值范围，为燃料电池多尺度模型中耦合参数的选取提供了统计学依据，该研究方法亦可推广至其他模型参数分析。