本研究建立了完整的質子交換膜燃料電池之單電池與雙電池三維模型，並透過以有限元素法為基礎的套裝軟體ANSYS15.0進行結構分析，進一步觀察螺栓鎖緊力變化對於擴散層的接觸電阻以及多孔性的影響;然後將氣體擴散層之特性變化代入電化學分析軟體Fluent15.0，進一步探討螺栓鎖緊力變化對於質子交換膜燃料電池整體發電效率的影響。
在結構分析中，本研究透過SolidWorks 建立出完整的質子交換模燃料電池三維模型，其反應區域為25cm2，此模型是由交換膜、催化層、擴散層、流道板、油封、電流收集板及端板所組成，並透過12組螺栓及螺帽鎖緊固定。在負載設定方面將螺帽固定，並透過ANSYS15.0內建的 Bolt Pretension 的功能將鎖緊壓力施加在螺栓上，以計算螺栓內部的力量及傳遞到此模型各個部位的力量。分析結果顯示，擴散層受到鎖緊壓力作用後，表面之接觸電阻及內部多孔性都呈現遞減的趨勢。接觸電阻的降低有助於減少歐姆損失，進而提升燃料電池的效率，相反的，擴散層多孔性的下降將導致氣體穿透阻力增加，進而使燃料電池效率下降。電化學分析結果顯示，在單電池結構中16MPa鎖緊壓力所計算出的最大功率密度與5MPa鎖緊壓力所模擬出的最大功率密度相比，約提升75.7%。在雙電池結構中，由於流道板總厚度的增加使得氣體擴散層所受到的平均等效應力上升，因此使得接觸電阻大幅下降。從分析結果可發現，在雙電池模組中，因接觸電阻降低的貢獻，可導致其最大功率密度平均提升了37.8%。
關鍵字: 質子交換膜燃料電池、接觸電阻、多孔性、鎖緊壓力、功率密度

In this study, 3D FEM (finite element method) models of both single cell and dual-cell of PEMFC (proton exchange membrane fuel cell) had been established, separately. The commercial software ANSYS15.0 was adopted in order to observe the effect of bolt pre-loading variation on the contact resistance and porosity of GDL (gas diffusion layer) in PEMFC. Then, the obtained values of contact resistance and porosity of GDL were substituted into the electro-chemistry simulation software Fluent 15.0 and the effect of bolt pre-loading variation on the efficiency of PEMFC was discussed.
In stress-strain analysis, a 3D PEMFC model with the reactive area of 25cm2 had been established through 3D drawing software SolidWroks 2013. The model includes membrane, catalyst layer, gas diffusion layer, flow channel plate, current collector and body plate which all elements were fixed by 12 pairs of bolt and nut. In order to apply bolt pre-loading on each pair of bolt and nut, the nuts were assumed to be fixed and the ANSYS built-in function, bolt pretension, was adopted. According to the simulative results, both contact resistance and porosity of GDL are decreasing while the bolt pre-loading increasing. The decreasing of contact resistance can reduce the ohmic loss effectively, and increase the efficiency of PEMFC. However, the decreasing of porosity of GDL will cause the increasing of resistance of permeability and resulted in the decreasing of the efficiency of PEMFC. The results of electro-chemistry simulation show that by increasing bolt pre-loading from 5MPa to 16MPa will result in 75.7% improvement of maxima power density of PEMFC. In a dual-cell PEMFC, the average equivalent stress of the GDL is increased due to the increase in the total thickness of the flow channel plates, thus greatly reduce the contact resistance of GDL. The simulative results indicate that due to the contribution of the reduction of contact resistance of GDL, the maximum power density of the dual-cell module is increased by 37.8%.
Keywords: Proton Exchange Membrane Fuel Cell, Contact Resistance, Porosity, Bolt Pre-loading, Power Density

目 錄
論文審定書 i
誌 謝 ii
摘 要 iii
Abstract iv
目 錄 v
表目錄 vii
圖目錄 viii
第一章 緒論 1
1.1前言 1
1.2燃料電池簡介 2
1.3文獻回顧 5
1.4研究動機與目的 9
1.5全文架構 11
第二章 基礎理論簡介 23
2.1 FEM有限元素法簡介 23
2.1.1應力與平衡方程式 23
2.1.2應變與位移關係 24
2.1.3應力與應變之關係 25
2.1.4能量法 26
2.1.5形狀函數與剛性矩陣 26
2.2 FDM有限體積法簡介 30
2.2.1流體控制方程式 30
2.2.2 FDM計算方式 32
2.3套裝軟體ANSYS 15.0/Workbench簡介 33
2.4 Fluent 15.0簡介 35
第三章 研究方法 44
3.1 研究流程 44
3.2 基本假設 45
3.3模型收斂性分析 45
3.4 FEM結構分析模型 46
3.5 FVM電化學分析模型 47
3.6 GDL接觸電阻分析 49
3.7 GDL多孔性分析 50
第四章 結果與討論 60
4.1模擬驗證 60
4.2螺栓鎖緊壓力變化於溫度分佈之影響 61
4.3 GDL應力及應變分佈 62
4.4 GDL之接觸電阻與多孔性變化 62
4.5螺栓鎖緊力對於質子交換膜燃料電池單電池效率之提升 63
4.6螺栓鎖緊壓力變化於電流密度分佈之影響 63
4.7螺栓鎖緊壓力變化對於反應氣體分布之影響 64
4.8雙電池結構對於GDL特性之影響 65
4.9雙電池結構對於質子交換膜料電池整體發電效率之影響 65
第五章 結論與未來展望 92
5.1 結論 92
5.2 未來展望 94
參考文獻 95

參考文獻
[1]黃鎮江, "燃料電池," 全華圖書股份有限公司, 2007.
[2]"ANSYS 15.0 Help," 2013.
[3]W. K. Lee, C. H. Ho, J. W. V. Zee, and M. Murthy, "The Effects of Compression and Gas Diffusion Layers on the Performance of a PEM Fuel Cell," Journal of Power Sources, vol. 84, pp. 45-51, 1999.
[4]J. Nordlund, "A model for the porous direct methanol fuel cells anode," Journal of Electrochem Society, vol. 149, pp. 1107-1113, 2002.
[5]P. T. Nguyen, T. Berning, and N. Djilali, "Computational model of a PEM fuel cell with serpentine gas flow channels," Journal of Power Sources, vol. 130, pp. 149-157, 2003.
[6]J. Ge, A. Higier, and H. Liu, "Effect of gas diffusion layer compression on PEM fuel cell performance," Journal of Power Sources, vol. 159, pp. 922-927, 2005.
[7]P. Zhou, C. W. Wu, and G. J. Ma, "Contact resistance prediction and structure optimization of bipolar plates," Journal of Power Sources, vol. 163, pp. 1115-1122, 2006.
[8]P. Zhou, C. W. Wu, and G. J. Ma, "Influence of clamping force on the performance of PEMFCs," Journal of Power Sources, vol. 163, p. 874881, 2006.
[9]C. H. Chien, Y. L. Huang, W. F. Chen, C. W. Lin, and S. C. Li, "3-Dimensional Numerical Stress Analysis around a Micro-Channel Wall Crack Tip in a Micro-PEMFC," The 31 th National Conference on Theoretical and Applied Mechanics, Kaohsiung, Taiwan, December 21-22, 2007.
[10]C. H. Chien, Y. S. Shih, S. S. Hsieh, H. H. Tsai, Y. L. Huang, and C. W. Lin, "The Effects of Variations of Flow Field and Geometry of Micro-Channel on the Cracked Ag-SU8 Interface in a
Micro-PEMFC," Journal of the Chinese Society of Mechanical Engineers, vol. 28, pp. 357-365, 2007.
[11]J. H. Lin, W. H. Chen, C. J. Su, and T. H. Ko, "Effect of gas diffusion layer compression on the performance in a proton exchange membrane fuel cell," Fuel, vol. 87, pp. 2420-2424, 2007.
[12]P. Zhou and C. W. Wu, "Numerical study on the compression effect of gas diffusion layer on PEMFC performance," Journal of Power Sources, vol. 170, pp. 93-100, 2007.
[13]A. P. Manso, F. F. Marzo, M. G. Mujika, J. Barranco, and A. Lorenzo, "Numerical analysis of the influence of the channel cross-section aspect ratio on the performance of a PEM fuel cell with serpentine flow field design," International Journal of Hydrogen Energy, vol. 36, pp. 6795-6808, 2011.
[14]S. Al-Baghdadi, "A CFD study of hygro–thermal stresses distribution in PEM fuel cell during regular cell operation," Renewable Energy, vol. 34, pp. 674-682, 2007.
[15]A. Bazylak, D. Sinton, Z. S. Lui, and N. Djilali, "Effect of compression on liquid water transportation and microstructure of PEMFC gas diffusion layers," Journal of Power Sources, vol. 163, pp. 784-792, 2007.
[16]W. R. Chang, J. J. Hwang, F. B. Weng, and S. H. Chan, "Effect of clamping pressure on the performance of a PEM fuel cell," Journal of Power Sources, vol. 166, pp. 149-154, 2007.
[17]D. H. Ahmed, H. J. Sung, and J. Bae, "Effect of GDL permeability on water and thermal management in PEMFCs-II. Clamping force," International Journal of Hydrogen Energy, vol. 33, pp. 3786-3800, 2008.
[18]J. H. Jang, W. M. Yan, H. Y. Li, and W. C. Tsai, "Three-dimensional numerical study on cell performance and transport phenomena of PEM fuel cell with conventional flow fields," Journal of Hydrogen Energy, vol. 33, pp. 156-164, 2008.
[19]H. Mehboob, P. M. Kyun, K. An-Soo, B. A. Zai, and R. Ali, "Analysis of the Clamping Pressure Effect in PEM Fuel Cell Structure by FEM and Experiment," Third European fuel cell technology & application Piero Lunghi Conference, vol. Rome, Italy, p. 95, 2009.
[20]V. Rouss, P. Lesage, S. Be´got, D. Candusso, W. Charon, F. Harel, et al., "Mechanical behaviour of a fuel cell stack under vibrating conditions linked to aircraft applications part I: Experimental," Journal of hydrogen energy, vol. 33, pp. 6755-6765, 2008.
[21]V. Rouss, D. Candusso, and W. Charon, "Mechanical behaviour of a fuel cell stack under vibrating conditions linked to aircraft applications part II: Three-dimensional modelling," Journal of hydrogen energy, vol. 33, pp. 6281-6288, 2008.
[22]S. K. Park and S. Y. Choe, "Dynamic modeling and analysis of a 20-cell PEM fuel cell stack considering temperature and two-phase effects," Journal of Power Sources, vol. 179, pp. 660-672, 2008.
[23]S. P. Philipps and C. Ziegler, "Computationally efficient modeling of the dynamic behavior of a portable PEM fuel stack," Journal of Power Sources, vol. 180, pp. 309-321, 2008.
[24]S. G. Kandlikar, T. Y. L. Z. Lu, D. Cooke, and M. Diano, "Uneven gas diffusion layer intrusion in gas channel arrays of proton exchange membrane fuel cell and its effects on flow distribution," Journal of Power Sources, vol. 194, pp. 328-337, 2009.
[25]M. Matia, A. Marquis, and N. P. Brandon, "Application of thermal imaging to validate a heat transfer model for polymer electrolyte fuel cells," International Journal of Hydrogen Energy, vol. 35, pp. 12308-12316, 2010.
[26]A. P. Manso, F. F. Marzo, M. G. Mujika, J. Barranco, and A. Lorenzo, "Numerical analysis of the influence of the channel cross-section aspect ratio on the performance of a PEM fuel cell with serpentine flow field design," International Journal of Hydrogen Energy, vol. 6795-6808, p. 36, 2011.
[27]S. Shimpalee, V. Lilavivat, J. W. V. Zee, H. McCrabb, and A. Lozano-Morales, "Understanding the effect of channel tolerances on performance of PEMFCs," International Journal of Hydrogen Energy, vol. 36, pp. 12512-12523, 2011.
[28]Y. P. Hou, W. Zhou, and C. Y. Shen, "Experimental investigation of gas-tightness and electrical insulation of fuel cell stack under strengthened road vibrating conditions," Journal of hydrogen energy, vol. 36, pp. 13763-13768, 2011.
[29]A. H.E.U., B. R., Z. J.W., and B. A., "Free vibration analysis of a polymer electrolyte membrane fuel cell," Journal of Power Sources, vol. 196, pp. 5520-5525, 2011.
[30]M. Kvesic, U. Reimer, D. Froning, L. Luke, W. Lehnert, and D. Stolten, "3D modeling of a 200 cm2 HT-PEFC short stack," International Journal of Hydrogen Energy, vol. 37, pp. 2430-2439, 2012.
[31]A. Bates, S. Mukherjee, S. C. L. S. Hwang, O. Kwan, G. H. Choi, and S. Park, "Simulation and experimental analysis of the clamping pressure distribution in a PEM fuel cell stac," Journal of Hydrogen Energy, vol. 38, pp. 6481-6493, 2013.
[32]S. Ravishankar and K. A. Prakash, "Numerical studies on thermal performance of novel cooling plate designs in polymer electrolyte membrane fuel cell stacks," Applied Thermal Engineering, vol. 66, pp. 239-251, 2014.
[33]B. Liu, M. Y. Wei, W. Zhang, and C. W. Wu, "Effect of impact acceleration on clamping force design of fuel cell stack," Journal of Power Sources, vol. 303, 2016.
[34]E. Alizadeh, M. M. Barzegari, M. Momenifar, M. Ghadimi, and S. H. M. Saadat, "Investigation of contact pressure distribution over the active area of PEM fuel cell stack," International Journal of Hydrogen Energy, vol. 41, pp. 3062-3071, 2016.
[35]B. Liu, L. F. Liu, M. Y. Wei, and C. W. Wu, "Vibration mode analysis of the proton exchange membrane fuel cell stack," Journal of Power Sources, vol. 331, pp. 299-307, 2016.
[36]C.-H. Chien, Y.-L. Hu, T.-H. Su, H.-T. Liu, C.-T. Wang, P.-F. Yang, et al., "Effects of bolt pre-loading variations on performance of GDL in a bolted PEMFC by 3-D FEM analysis," Energy, vol. 113, pp. 1174-1187, 2016.
[37]B. Osanloo, A. Mohammadi-Ahmar, and A. Solati, "A numerical analysis on the effect of different architectures of membrane, CL and GDL layers on the power and reactant transportation in the square tubular PEMFC," International Journal of Hydrogen Energy, vol. 41, pp. 10844-10853, 2016.
[38]T. R. Chandrupatla and A. D. Belegundu, "Introduction to Finite Elements in Engineering," Pearson, USA, 2012.
[39]鄭力銘, "ANSYS Fluent 15.0 流體計算-從入門到精通," 電子工業出版社, 2015.
[40]A. Inc., "Modeling a Single-Channel, Counter-Flow Polymer Electrolyte Membrane (PEM) Fuel Cell," 2007.