燃料電池的研究包含了各種物理問題，包括流體力學、質傳學、熱傳學、電化學、二相流與孔隙材料等。本研究討論一個二維陰極側的電池結構，發生在膜電極(MEA)上的電化學反應以及物種輸送機制，此膜電極為五層結構：包括了陽極氣體擴散層、陽極觸媒層、質子交換膜、陰極觸媒層和陰極氣體擴散層。燃料(O2)及生成物(H2O)的進出入均是利用濃度的擴散機制驅動。本文所使用到的統御方程式如下：採用Darcy's Law來描述孔隙材料內的速度、壓力分佈。用Stefan-Maxwell氣體擴散方程式來描述各種的反應物種在電池內的消長情況，加上Bruggemann模型修正孔隙材料內的有效氣體擴散係數。此外，電化學所產生的電流以Butler -Volmer方程式表示之，並透過電流守恆方程式得到電池內質子、電子電位及活化過電位的分佈情況。而總過電位為活化、歐姆及濃度過電位的總和，燃料電池的操作電壓可由電池的理論電壓扣掉總過電位得到。利用操作電壓與電流密度的關係可以得到電池操作性能曲線，透過比較電池性能曲線分別在模擬與實驗上的誤差，可以瞭解數值方法所造成的誤差可能發生之處，並加以改善研究用的數值模擬模型。

    本文在數值求解方面透過COMSOL Multiphysics商用軟體。在數值模擬中，可以從Butler-Volmer方程式中直接控制電池的活化過電位，本研究在模擬結果部分，分別透過不同的活化過電位來觀察各種物理量的變化。在陰極中，越接近大氣開孔端其過電位越低，越遠離大氣開孔端則過電位就越高，結果反應出燃料(O2)的分佈對於電化學反應的影響。當過電位越高也代表著反應越顯得劇烈，反應後生成物(H2O)增加，水的排放也帶動整體電池內部的燃料流動現象，明顯的增加燃料在下游開孔處離開時的速度。此外，本文也探討Butler-Volmer方程式中的參數 Sa、alpha 和 i0 對於電池性能曲線所造成的影響。

The study of fuel cell includes several physical and chemical phenomena, such as fluid dynamics, heat and mass transfer, electrochemical reaction, two phase flow, and porous media. This thesis discussed the phenomena of the electrochemical reaction and species transportation on the MEA for a two-dimensional cathode structure. The MEA is a five layer structure which includes anode gas diffusion layer, anode catalyst layer, a proton exchange membrane, cathode catalyst layer, and cathode gas diffusion layer. The flowing in and out of the fuel of oxygen and product of water are driven by the concentration diffusion mechanism. The related governing equations adopted in the research are illustrated as follows: the distributions of the velocity and pressure inside the porous media are based on the Darcy’s law, and the species transporting in the cathode is described by the Stefan-Maxwell gas diffusion equation and the effective gas diffusion coefficient of the porous material is amended by the Bruggemann model. In addition, the current generated by electrochemical reaction is calculated by the Butler-Volmer equation, and the distributions of the ionic, electronic potential and the activation overpotential are obtained by the current conservation equations. The overall overpotential is the summation of activation, ohmic, and concentration overpotential. The cell voltage can be acquired via the theoretical cell potential minus the overall cell potential. Moreover, the cell performance curve can be derived by the relationship of the operating voltage and current density. The cell performance curve can be utilized to understand the numerical error compared with the experimental results which could help to improve the simulation model. 

    In this research work, the numerical simulation was accomplished via the COMSOL Multiphysics commercial solver. The cell activation overpotential of the Butler-Volmer equation can be defined directly and the related phenomena variation under different activation overpotential were further observed. In the catalyst layer, the overpotential is decreased when near the opening holes and increased when far away the opening holes. The results also express the effect of oxygen distribution on the electrochemical reaction. If the higher overpotential is higher, the reaction is more active and the product water is also increased. The water discharge also derives the fuel flow inside the cell which enhances the velocity of the downstream where is closed to the opening holes. In addition, this thesis also discusses the effects of Sa, alpha, and i0 on the cell performance curve.

目錄

1 緒論 .......................1
1.1 前言 ....................1
1.2 燃料電池發展背景 ...............1
1.3 燃料電池特點 ..................3
1.4 燃料電池種類 ...............	5
1.5 質子交換膜燃料電池 ...........7
1.6 工作原理 .............8
1.7 文獻回顧 .............9
1.8 研究動機 .............11
	
2 理論基礎 .............	12
2.1 基本假設 .............12
2.2 幾何外形說明 .............13
2.2.1 氣體擴散層 ...........15
2.2.2 觸媒層 .............15
2.2.3 質子交換膜（Proton Exchange Membrane）...16
2.2.4 集電板（Current Collectors）.......16
2.3 電極反應動力學 ...........17
2.3.1 極化現象 .............17
2.3.2 活化過電位 ...........18
2.3.2.1 交換電流密度（Exchange Current Density，i0）.20
2.3.2.2 傳送係數（Transfer Coefficient，alpha）...22
2.3.3 歐姆過電位 ...........24
2.3.4 濃度過電位 ...........25
2.3.5 極化曲線與電池性能曲線 .......28
2.4 統御方程式 .............31
2.4.1 連續方程式 ...........32
2.4.2 Stefan-Maxwell 氣體擴散方程式 .....33
2.4.3 Butler-Volmer 方程式 .........35
2.4.4 電流守恆 .............37
2.5 邊界條件 .............38
	
3 數值方法 .............	40
3.1 數值模擬軟體介紹 ...........40
3.1.1 挑選多重物理量方程式 .........41
3.1.2 操作介面介紹 ...........42
3.1.3 建立幾合外型 ...........43
3.1.4 網格生成 .............45
3.1.5 統御方程式設定 ...........	47
3.1.6 統御方程式的參數設定 .........49
3.1.7 求解器設定 ...........50
3.1.8 後處理操作 ...........53
3.1.9 後處理結果輸出 ...........	58
3.2 求解器數值方法 ...........	60
3.3 後處理器介紹：Tecplot  .........61
3.4 網格後處理顯示 ...........62
3.5 網格獨立測試 .............63
3.6 模擬流程步驟 .............65
	
4 結果與討論 ...........67
4.1 電池性能之模擬與實驗比較 .........67
4.2 Butler-Volmer方程式的參數影響討論 .....68
4.2.1 Sa & i0 對電池性能的影響 .......70
4.2.2 alpha 對電池性能的影響 .........70
4.3 過電位對燃料質量分率的分佈影響討論 ...72
4.4 過電位對電池內速度場的分佈影響討論 .....75
4.5 電池內電位分佈（phil & phis）與活化過電位分佈 ...77
4.6 過電位對電池內電場強度的分佈影響討論 ...82
	
5總結 .............87
5.1 研究成果 .............87
5.2 未來研究展望與要點 .........87
	
附錄 ...............90
A 符號參數資料表 ...........90
B 自變數/未知數對應COMSOL程式輸入 .....94
C 參數對應COMSOL Constant 程式輸入 .....95
D 參數對應COMSOL Global Expressions 程式輸入 ..98
	
參考文獻 .............100


	
圖目錄
圖1.1 質子交換膜燃料電池之反應機制 ....... 9
圖2.1 質子交換膜燃料電池之陰極側的幾何外形圖形 ... 14
圖2.2 活化過電位與電流密度的關係圖 ....... 19
圖2.3 電流密度與過電位的關係圖 ....... 21
圖2.4 傳送係數alpha與活化能能階的關係 .....23
圖2.5 歐姆過電位與電流密度的關係圖 .......25
圖2.6 濃度過電位與電流密度的關係圖.......26
圖2.7 濃度過電位與電流密度的關係—理論與經驗公式比較....27
圖2.8 典型的燃料電池極化曲線關係 .......30
圖2.9 三種過電位與總過電位的關係圖曲線.....30
圖2.10 一般燃料電池性能曲線－電流密度曲線＆功率曲線 ...31
圖2.11 計算域上的邊界設置圖 .........39
圖3.1 介紹COMSOL軟體：挑選統御方程式 .....41
圖3.2 介紹COMSOL軟體：未知數與統御方程式的關連 ....42
圖3.3 介紹COMSOL軟體：操作介面 .......43
圖3.4 介紹COMSOL軟體：幾何繪製工具 .....44
圖3.5 介紹COMSOL軟體：修改幾何數值設定 ...44
圖3.6 介紹COMSOL軟體：網格生成設定 .....46
圖3.7 介紹COMSOL軟體：網格分佈比例 .....46
圖3.8 介紹COMSOL軟體：統御方程式設定 .....48
圖3.9 介紹COMSOL軟體：邊界條件設定 .....49
圖3.10 介紹COMSOL軟體：參數設定 .......50
圖3.11 介紹COMSOL軟體：參數副程式設定 .....50
圖3.12 介紹COMSOL軟體：求解器設定I .....51
圖3.13 介紹COMSOL軟體：求解器設定II .....52
圖3.14 介紹COMSOL軟體後處理：一般設定 .....53
圖3.15 介紹COMSOL軟體後處理：目標選擇設定 ...54
圖3.16 介紹COMSOL軟體後處理：平面圖分佈 ...54
圖3.17 介紹COMSOL軟體後處理：向量圖設定 ...55
圖3.18 介紹COMSOL軟體後處理：平面圖＆向量圖多重顯示設定 ...56
圖3.19 介紹COMSOL軟體後處理：電流積分設定 ...57
圖3.20 介紹COMSOL軟體：後處理輸出選項 .....58
圖3.21 介紹COMSOL軟體：後處理輸出一般設定 ...59
圖3.22 介紹COMSOL軟體：後處理輸出參數選擇設定 ....59
圖3.23 原始尺寸比例的幾何外型 .......62
圖3.24 原始尺寸比例的網格 .........62
圖3.25 放大尺寸比例的幾何外型 .......62
圖3.26 放大尺寸比例的網格 .........62
圖3.27 網格獨立測試：活化過電位比較 .....64
圖3.28 數值模擬流程圖 ...........65
圖4.1  模擬的電池性能比較 .........68
圖4.2 不同sa對電池性能的影響 .......71
圖4.3 不同alpha對電池性能的影響 .......71
圖4.4 氧氣質量分率（過電位0.1）.....73
圖4.5 氧氣質量分率（過電位0.3）.....73
圖4.6 氧氣質量分率（過電位0.5）.....73
圖4.7 氧氣質量分率（過電位0.7）.....73
圖4.8 水氣質量分率（過電位0.1）.....74
圖4.9 水氣質量分率（過電位0.3）.....74
圖4.10 水氣質量分率（過電位0.5）.....74
圖4.11 水氣質量分率（過電位0.7）.....74
圖4.12 速度分佈（過電位0.1）....... .76
圖4.13 速度分佈（過電位0.3）....... .76
圖4.14 速度分佈（過電位0.5）....... .76
圖4.15 速度分佈（過電位0.7）....... .76
圖4.16 觸媒層過電位分佈（過電位0.1）.....79
圖4.17 觸媒層過電位分佈（過電位0.3）.....79
圖4.18 觸媒層過電位分佈（過電位0.5）.....79
圖4.19 觸媒層過電位分佈（過電位0.7）.....79
圖4.20 質子電流電位分佈（過電位0.1）.....80
圖4.21 質子電流電位分佈（過電位0.3）.....80
圖4.22 質子電流電位分佈（過電位0.5）.....80
圖4.23 質子電流電位分佈（過電位0.7）.....80
圖4.24 電子電流電位分佈（過電位0.1）.....81
圖4.25 電子電流電位分佈（過電位0.3）.....81
圖4.26 電子電流電位分佈（過電位0.5）.....81
圖4.27 電子電流電位分佈（過電位0.7）.....81
圖4.28 質子電場分佈（過電位0.1）.....84
圖4.29 質子電場分佈（過電位0.3）.....84
圖4.30 質子電場分佈（過電位0.5）.....84
圖4.31 質子電場分佈（過電位0.7）.....84
圖4.32 電子電場分佈（過電位0.1）.....85
圖4.33 電子電場分佈（過電位0.3）.....85
圖4.34 電子電場分佈（過電位0.5）.....85
圖4.35 電子電場分佈（過電位0.7）.....85
圖4.36 質子電場分佈（過電位0.5）.....86
圖4.37 電子電場分佈（過電位0.5）.....86
圖4.38 放大觸媒層中質子電場分佈（過電位0.5）...86
圖4.39 放大觸媒層中電子電場分佈（過電位0.5）...86



表目錄
表1.1 燃料電池基本特性比較表 .........	6
表2.1 氣體擴散係數表 ............	34
表2.2 外界初始氣體質量分率表 .........	39
表3.1 網格獨立性的測試結果比較 .......	64
表4.1 過電位與速度最大值的比較 .......	75

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