固体氧化物燃料电池性能的微结构理论与多尺度多物理场模拟
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摘要
固体氧化物燃料电池(SOFC)具有高效清洁和燃料灵活等显著优点,是当前国际新能源技术发展的一大热点。由于实物制作具有昂贵、耗时而不能全面细致地探索各种材料参数,结构设计和工作条件影响的缺陷,根据已知原理建立理论与模拟工具,进而系统全面地探讨各种材料选择,电池设计方案和运行方式对电池性能的影响便成为加速SOFC技术发展的重要手段,
本论文主要针对SOFC建立多尺度多物理场耦合的数值模型用于进行相关的理论研究和工程优化设计。这里指的多尺度主要指包括微观复合电极尺度模型的研究和发展、电池层面尺度模型的研究和发展以及两个尺度模型的耦合工作。多物理场主要包括电化学过程、电子和离子混合传导过程、反应气体传输过程以及固—气体混合热传输过程的综合分析。
第一章首先简单介绍了燃料电池的发展简史,以及不同的电池分类。其次针对SOFC介绍了电池的基本工作原理,并细致推导了SOFC的理论电动势、开路电动势和局域能斯特电动势的表达式。而后简单分析了SOFC的结构和部件的材料特点。最后针对SOFC各个层面的数值模拟工作近况进行了大概的文献概述。
第二章首先对现有的微观电极层面模型进行了概述。其次针对现有的基于球形颗粒随机堆叠的逾渗微观模型进行了详细的介绍,并指出了现有模型的优点和不足。基于大量的文献分析作者提出了更为准确合理的用于预测SOFC复合电极有效性质与微观结构参数之间关系的逾渗微观模型。并详细分析了三种不同材料配比对应的逾渗三相区域的分布情况。该模型不仅适用于二元混合物结构,同时也适用于具有多种颗粒尺寸的多元混合物结构。模型依赖的微观参数包括：各类颗粒的半径、体积分数,颗粒间重叠接触角以及孔隙率。可预测的复合电极有效性质包括：有效离子／电子体电导率和边界电导率,单位体积的逾渗三相线长度、单位致密电解质表面的逾渗三相线长度、两相接触面积以及气孔通道的水力半径等。同时,为了增加模型的实用性,所有结果都以无量纲化的形式展示。
第三章在第二章微观模型的基础上发展了针对具有真实颗粒尺寸分布的复合电极逾渗微观模型。基于该模型,正态分布函数被分别用于描述电极材料颗粒和电解质材料颗粒在复合电极中的颗粒尺寸分布情况。模型依赖的微观结构参数包括：电极材料颗粒和电解质材料颗粒的平均半径、反映颗粒尺寸分布宽度的正态分布标准偏差、材料组分配比以及复合电极结构的孔隙率。通过该模型计算的结果与通过球形颗粒随机排列电极重构方法所得的结果非常吻合,从而有力的说明了该模型的有效性。通过计算得出,具有真实颗粒尺寸分布的复合电极与具有均匀颗粒尺寸分布的复合电极相比,单位体积逾渗三相线长度的最大值减小约32%。最后为了扩展模型的实用性,我们结合SOFC阳极和阴极的特点对模拟结果进行了分析。结果显示,复合电极使用较小的电极材料颗粒和电解质材料颗粒平均半径以及相对较窄的颗粒尺寸分布有利于提高SOFC复合阴极(LSM和YSZ)的性能。而对于典型的SOFC复合阳极(Ni和YSZ)而言,采用较大的电解质材料颗粒平均半径和相对较宽的颗粒尺寸分布则可得到较高的电池性能。
第四章针对SOFC提出了一个等效电路模型用于细致的描述SOFC内部的局域电化学反应情况以及电子和离子电流的传导过程。基于局域反应位置的电化学势平衡,我们详细描述了局域浓差损耗和局域活化过电势等各部分损耗的定义。进而基于理论基础给出了各个物理、化学过程的数学描述,并针对电池单元多物理场模型的建立推导出了各种等效的模拟处理方法。最后,通过与第二章提出的逾渗微观模型相结合系统分析了复合阴极功能层厚度、材料参数性质(如：基于单位三相线长度的交换输运电流密度(表征材料电化学活性)、本征电子和离子电导率)、电池工作环境(如工作温度和输出电流密度)以及复合电极微观参数(如平均颗粒尺寸、电极颗粒和电解质颗粒半径比例、组分配比和孔隙率)对复合阴极功能层工作性能的作用。模拟结果显示在各种不同的参数环境下,采用10-20μm之间的阴极间隙层厚度可以得到较优化的电池性能。
第五章在第四章的基础上,分析了复合阴极的材料组分配比、阴极间隙层厚度、电池工作环境以及复合电极有效性质等因素对阴极间隙层内部电化学活化区域分布的影响。由于SOFC的活化损耗主要发生在阴极间隙层内的电化学活化区域,因此准确的预计阴极间隙层内电化学活化区间的厚度至关重要。考虑到繁琐的数值建模过程和复杂的数值计算不利于其它实验工作者结合不同的材料参数和具体的工作条件对复合电极的电化学活化区域作出预测。我们通过理论分析,推导了用于预测不同工作参数对应的电化学活化区域潜在最大厚度的解析表达式。同时,为了验证该解析表达式的有效性。我们将通过解析表达式计算的结果与通过第四章数值模型的数值模拟结果进行比较,从而证明了该解析表达式的有效性。至此,其他实验工作人员可通过该解析表达式简单的预测出与不同输出电流密度、逾渗三相线长度、有效电子和离子电导率等材料参数和工作条件对应的电化学反应区间的潜在最大厚度。这将有利于为阴极间隙层的制作提供大致的参数指导。
第六章主要针对本文的工作内容进行了简单的总结。
As a clean, highly efficient, fuel flexible power generating device, solid oxide fuel cell (SOFC) is an important part of the new energy technologies. As the experiments are of high cost, time consuming and difficult to comprehensively explore the effects of various material parameters, structural designs and the working conditions on the SOFC performance, theory and modeling are considered as important tools for accelerating the development of SOFC technologies.
This dissertation focuses on developing a multi-scale and multi-physics coupled model for the theoretical study and parametric optimizations of SOFCs. The multi-scale mainly includes the development of percolation micro models for composite electrodes, multi-physical coupled macro models for cell processes and the combination of the micro and macro model for the simulations of the cell unit. The multi-physics coupling here means that the model comprehensively considers the coupled behavior of the detail electrochemical reaction process, the conductions of electronic and ionic currents, the transport of reacting gas species and the mixed heat transfer through the solid and gas parts.
In chapter one, the development history of fuel cells and their classifications are briefly introduced. The basic working principle, components and stack structures of SOFCs are then described. The expressions for the Nernst potential at open circuit and the local Nernst potential are deduced in detail based on underlying thermodynamics theory. Finally, a brief literature overview about the SOFC theory and simulation on three different length scales is given.
In chapter two, a detailed review about the present micro scale electrode models are presented. The advantages and disadvantages of Bouvard and Suzuki's percolation micro model based on the randomly packing of spheres are discussed. Then, a novel percolation micro model, based upon significant earlier literatures, is developed to predict effective electrode properties from microstructure parameters. This model is applicable to both the binary and multi-component mixtures of particles. The model predicts effective ionic and electronic conductivities, three-phase boundary lengths, and hydraulic pore radii. The effective properties depend upon primary physical characteristics, including average particle-radii, volumetric packing densities, particle contact angles, and porosity. All results are presented in nondimensional form, which provides considerable generality in their practical application.
In chapter three, percolation micro-model is extended to predict the effective properties in composite electrode formed by polydisperse electronic and ionic conductors (i.e., normal standard distribution for each phase), such as the percolated triple-phase-boundary (TPB) lengths, hydraulic pore radius, intra- and inter-particles conductivities and so on. And the independent microstructure parameters include:the mean particle size of electrode-and electrolyte-materials, volume fraction of electrode-material, the relevant standard deviations of each phase and porosity. The validity of this model is verified by comparing the calculated results based on the percolation micro-model equations and the results based on random packing reconstruction reported by Kenney et al.. Finally, the specific natures of anode and cathode are considered into the percolation micro-model for discussing what kind of composite electrodes with actual particle size distributions, would maximize the performance of anode and cathode, respectively. The results shows that:the composite electrode with small mean particle size of electrode- and electrolyte-materials and relatively narrow particle size distribution would be helpful for enhancing the performance of composite cathode (LSM and YSZ); And a higher SOFC composite anode performance can be obtained by using a composite electrode with larger electrolyte-particle and relatively wide particle size distribution.
In chapter four, the processes of electrochemical reactions, electronic and ionic conductions within an SOFC are clearly described through a proposed equivalent circuit model. With this model, the local electronic and ionic electric potential profiles in the electrode- and electrolyte-phases can be described based on local gas compositions and electrochemical kinetic analysis. Correspondingly, the cell-level scale macro-model and the percolation micro-model, described in chapter two, are combined to systematically examine the effects of various parameters on the performance of a composite cathode inter-layer. The examined parameters include the thickness, effective electronic and ionic conductivities, exchange current density, operating temperature, output current density, electrode- and electrolyte-particle radii, composition and porosity of the cathode inter-layer. The comprehensive study shows conclusively that a cathode inter-layer thickness in a range of 10-20μm is optimal for all practical material choices and microstructure designs.
Chapter five can be considered as a extending of chapter four. As most of the SOFC activation overpotential is caused within cathode inter-layer, understanding the effects of each parameter on the distribution of cathode electrochemically active zone (CEAZ) is essential to enhance the SOFC performance. Although CEAZ can be exactly simulated through the numerical model, such as the cell lever model described in chapter 4, these kinds of model often rely on complicated numerical procedures and are difficult for the experimentalists to use with different material parameters and working conditions. In this chapter, analytical equations are deduced for predicting the upper limited thickness of CEAZ as a function of operational conditions and electrode properties such as, the output current density, effective ionic conductivity, percolated triple phase boundary length and the exchange transfer current per unit TPB length. And the analytical expressions are validated by numerical models without the effective circuit approximation.
In chapter six, a summary for this thesis are presented.
本论文主要针对SOFC建立多尺度多物理场耦合的数值模型用于进行相关的理论研究和工程优化设计。这里指的多尺度主要指包括微观复合电极尺度模型的研究和发展、电池层面尺度模型的研究和发展以及两个尺度模型的耦合工作。多物理场主要包括电化学过程、电子和离子混合传导过程、反应气体传输过程以及固—气体混合热传输过程的综合分析。
第一章首先简单介绍了燃料电池的发展简史,以及不同的电池分类。其次针对SOFC介绍了电池的基本工作原理,并细致推导了SOFC的理论电动势、开路电动势和局域能斯特电动势的表达式。而后简单分析了SOFC的结构和部件的材料特点。最后针对SOFC各个层面的数值模拟工作近况进行了大概的文献概述。
第二章首先对现有的微观电极层面模型进行了概述。其次针对现有的基于球形颗粒随机堆叠的逾渗微观模型进行了详细的介绍,并指出了现有模型的优点和不足。基于大量的文献分析作者提出了更为准确合理的用于预测SOFC复合电极有效性质与微观结构参数之间关系的逾渗微观模型。并详细分析了三种不同材料配比对应的逾渗三相区域的分布情况。该模型不仅适用于二元混合物结构,同时也适用于具有多种颗粒尺寸的多元混合物结构。模型依赖的微观参数包括：各类颗粒的半径、体积分数,颗粒间重叠接触角以及孔隙率。可预测的复合电极有效性质包括：有效离子／电子体电导率和边界电导率,单位体积的逾渗三相线长度、单位致密电解质表面的逾渗三相线长度、两相接触面积以及气孔通道的水力半径等。同时,为了增加模型的实用性,所有结果都以无量纲化的形式展示。
第三章在第二章微观模型的基础上发展了针对具有真实颗粒尺寸分布的复合电极逾渗微观模型。基于该模型,正态分布函数被分别用于描述电极材料颗粒和电解质材料颗粒在复合电极中的颗粒尺寸分布情况。模型依赖的微观结构参数包括：电极材料颗粒和电解质材料颗粒的平均半径、反映颗粒尺寸分布宽度的正态分布标准偏差、材料组分配比以及复合电极结构的孔隙率。通过该模型计算的结果与通过球形颗粒随机排列电极重构方法所得的结果非常吻合,从而有力的说明了该模型的有效性。通过计算得出,具有真实颗粒尺寸分布的复合电极与具有均匀颗粒尺寸分布的复合电极相比,单位体积逾渗三相线长度的最大值减小约32%。最后为了扩展模型的实用性,我们结合SOFC阳极和阴极的特点对模拟结果进行了分析。结果显示,复合电极使用较小的电极材料颗粒和电解质材料颗粒平均半径以及相对较窄的颗粒尺寸分布有利于提高SOFC复合阴极(LSM和YSZ)的性能。而对于典型的SOFC复合阳极(Ni和YSZ)而言,采用较大的电解质材料颗粒平均半径和相对较宽的颗粒尺寸分布则可得到较高的电池性能。
第四章针对SOFC提出了一个等效电路模型用于细致的描述SOFC内部的局域电化学反应情况以及电子和离子电流的传导过程。基于局域反应位置的电化学势平衡,我们详细描述了局域浓差损耗和局域活化过电势等各部分损耗的定义。进而基于理论基础给出了各个物理、化学过程的数学描述,并针对电池单元多物理场模型的建立推导出了各种等效的模拟处理方法。最后,通过与第二章提出的逾渗微观模型相结合系统分析了复合阴极功能层厚度、材料参数性质(如：基于单位三相线长度的交换输运电流密度(表征材料电化学活性)、本征电子和离子电导率)、电池工作环境(如工作温度和输出电流密度)以及复合电极微观参数(如平均颗粒尺寸、电极颗粒和电解质颗粒半径比例、组分配比和孔隙率)对复合阴极功能层工作性能的作用。模拟结果显示在各种不同的参数环境下,采用10-20μm之间的阴极间隙层厚度可以得到较优化的电池性能。
第五章在第四章的基础上,分析了复合阴极的材料组分配比、阴极间隙层厚度、电池工作环境以及复合电极有效性质等因素对阴极间隙层内部电化学活化区域分布的影响。由于SOFC的活化损耗主要发生在阴极间隙层内的电化学活化区域,因此准确的预计阴极间隙层内电化学活化区间的厚度至关重要。考虑到繁琐的数值建模过程和复杂的数值计算不利于其它实验工作者结合不同的材料参数和具体的工作条件对复合电极的电化学活化区域作出预测。我们通过理论分析,推导了用于预测不同工作参数对应的电化学活化区域潜在最大厚度的解析表达式。同时,为了验证该解析表达式的有效性。我们将通过解析表达式计算的结果与通过第四章数值模型的数值模拟结果进行比较,从而证明了该解析表达式的有效性。至此,其他实验工作人员可通过该解析表达式简单的预测出与不同输出电流密度、逾渗三相线长度、有效电子和离子电导率等材料参数和工作条件对应的电化学反应区间的潜在最大厚度。这将有利于为阴极间隙层的制作提供大致的参数指导。
第六章主要针对本文的工作内容进行了简单的总结。
As a clean, highly efficient, fuel flexible power generating device, solid oxide fuel cell (SOFC) is an important part of the new energy technologies. As the experiments are of high cost, time consuming and difficult to comprehensively explore the effects of various material parameters, structural designs and the working conditions on the SOFC performance, theory and modeling are considered as important tools for accelerating the development of SOFC technologies.
This dissertation focuses on developing a multi-scale and multi-physics coupled model for the theoretical study and parametric optimizations of SOFCs. The multi-scale mainly includes the development of percolation micro models for composite electrodes, multi-physical coupled macro models for cell processes and the combination of the micro and macro model for the simulations of the cell unit. The multi-physics coupling here means that the model comprehensively considers the coupled behavior of the detail electrochemical reaction process, the conductions of electronic and ionic currents, the transport of reacting gas species and the mixed heat transfer through the solid and gas parts.
In chapter one, the development history of fuel cells and their classifications are briefly introduced. The basic working principle, components and stack structures of SOFCs are then described. The expressions for the Nernst potential at open circuit and the local Nernst potential are deduced in detail based on underlying thermodynamics theory. Finally, a brief literature overview about the SOFC theory and simulation on three different length scales is given.
In chapter two, a detailed review about the present micro scale electrode models are presented. The advantages and disadvantages of Bouvard and Suzuki's percolation micro model based on the randomly packing of spheres are discussed. Then, a novel percolation micro model, based upon significant earlier literatures, is developed to predict effective electrode properties from microstructure parameters. This model is applicable to both the binary and multi-component mixtures of particles. The model predicts effective ionic and electronic conductivities, three-phase boundary lengths, and hydraulic pore radii. The effective properties depend upon primary physical characteristics, including average particle-radii, volumetric packing densities, particle contact angles, and porosity. All results are presented in nondimensional form, which provides considerable generality in their practical application.
In chapter three, percolation micro-model is extended to predict the effective properties in composite electrode formed by polydisperse electronic and ionic conductors (i.e., normal standard distribution for each phase), such as the percolated triple-phase-boundary (TPB) lengths, hydraulic pore radius, intra- and inter-particles conductivities and so on. And the independent microstructure parameters include:the mean particle size of electrode-and electrolyte-materials, volume fraction of electrode-material, the relevant standard deviations of each phase and porosity. The validity of this model is verified by comparing the calculated results based on the percolation micro-model equations and the results based on random packing reconstruction reported by Kenney et al.. Finally, the specific natures of anode and cathode are considered into the percolation micro-model for discussing what kind of composite electrodes with actual particle size distributions, would maximize the performance of anode and cathode, respectively. The results shows that:the composite electrode with small mean particle size of electrode- and electrolyte-materials and relatively narrow particle size distribution would be helpful for enhancing the performance of composite cathode (LSM and YSZ); And a higher SOFC composite anode performance can be obtained by using a composite electrode with larger electrolyte-particle and relatively wide particle size distribution.
In chapter four, the processes of electrochemical reactions, electronic and ionic conductions within an SOFC are clearly described through a proposed equivalent circuit model. With this model, the local electronic and ionic electric potential profiles in the electrode- and electrolyte-phases can be described based on local gas compositions and electrochemical kinetic analysis. Correspondingly, the cell-level scale macro-model and the percolation micro-model, described in chapter two, are combined to systematically examine the effects of various parameters on the performance of a composite cathode inter-layer. The examined parameters include the thickness, effective electronic and ionic conductivities, exchange current density, operating temperature, output current density, electrode- and electrolyte-particle radii, composition and porosity of the cathode inter-layer. The comprehensive study shows conclusively that a cathode inter-layer thickness in a range of 10-20μm is optimal for all practical material choices and microstructure designs.
Chapter five can be considered as a extending of chapter four. As most of the SOFC activation overpotential is caused within cathode inter-layer, understanding the effects of each parameter on the distribution of cathode electrochemically active zone (CEAZ) is essential to enhance the SOFC performance. Although CEAZ can be exactly simulated through the numerical model, such as the cell lever model described in chapter 4, these kinds of model often rely on complicated numerical procedures and are difficult for the experimentalists to use with different material parameters and working conditions. In this chapter, analytical equations are deduced for predicting the upper limited thickness of CEAZ as a function of operational conditions and electrode properties such as, the output current density, effective ionic conductivity, percolated triple phase boundary length and the exchange transfer current per unit TPB length. And the analytical expressions are validated by numerical models without the effective circuit approximation.
In chapter six, a summary for this thesis are presented.
引文
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