近年來PEMFC技術廣受注目，世界各國均將大力投入發展 FCEV並預期於2030至2040年間興建數千至上萬加氫站，且銷售數十萬至上百萬台FCEV，並投入數百億至千億台幣資金進入相關產業，而在PEMFC中，PEM 需適度含水方可順利輸送質子。但若陰極液態水含量過高未能適當排出，使得氣體擴散層發生阻塞，則電極表面上部分位置將未能有充足之反應氣體供應，導致發電效率下降。
而為了解析擴散層中之現象我們根據現有文獻展出一套數值模型。原有模型可於多孔介質中計算氣液兩相流，但其陰極須為純氧而非商業上常用之空氣，我們引入燃燒學中的多物種反應系統使得模型能計算氣相中不同組份間的流動現象，以及使得氧氣和其他氣體能於反應邊界有不同行為，達成陰極使用空氣計算之目的，且藉由分離擾動項等演算法使的我們的模型可於高寬比約為0.0025的多孔介質中運算。
我們發現擴散層內氧氣分壓皆低於流道內氧氣分壓，相反地擴散層內氮氣分壓皆高於流道內氮氣分壓；且漸縮阻擋物較三角形阻擋物在相同條件下有較好之表現；而障礙物高度為入口高度0.8倍的三角形流道相對於無障礙物流道液態水質量流率高了57%，而相同條件下漸縮流道則高了80%。
但我們也發現水飽和度邊界條件主導了整體擴散層的水飽和度分佈，因此我們應該更嚴謹的審視這條邊界條件，且對我們觀察到的結果與實際燃料電池物性之關聯保持懷疑的態度，再使水飽和度邊界條件其與交界面之局部物性相關而非與反應面之平均物性相關。

Nowadays, proton exchange membrane fuel cells (PEMFCs) are more and more important. Many countries are working hard to promote hydrogen and PEMFC related products. Including build thousands of hydrogen refueling stations, sold hundreds of thousands of fuel cell electric vehicles (FCEVs), invest tens of billions of funds.
For PEMFC’s efficiency enhancement, water management is an unavoidable problem. PEM need moderate water to transport proton. However, the cathode is where water is produced, and will be blocked when water is excessively producing.
For dealing with this problem, we refer to existing literature to develop a numerical model. The existing literature cover a model with two phase flow in porous media. However, the fluid in cathode is pure oxygen not air which is commonly used in commerce. And the model does not explain how to apply itself into a low aspect ratio domain.
For using air in cathode, we introduce multicomponent reacting system which is commonly used in combustion into our model. For dealing with low aspect ratio issue, we also introduce separate perturbation algorithm into our model.
We discover the pressure of nitrogen in GDL will greater then channel, but oxygen in GDL lower than channel. And shrink baffle is better than triangular baffle. While the height of baffle is 0.8 times of inlet height, shrink baffle makes the efficiency greater then no baffle 80% and triangular baffle make the efficiency greater 57%.
We also discover standard water saturation dominate all water saturation in GDL. So we need to critical the assumption of standard water saturation more severely. This assumption connects average current density and standard water saturation directly. But one of them is physical property at connect boundary the other is physical property at reaction boundary. We think this assumption need to be local physical model. So we are suspicious of the connection between model and real PEMFC.

[1] N. Dyantyi, A. Parsons, C. Sita, S. Pasupathi, “PEMFC for aeronautic applications: A review on the durability aspects” Open Engineering, Vol. 7, pp. 287‒302, 2017.
[2] N. L. Rey, J. Mosquera, E. Bataller, F. Orti, C. Dudfield, A. Orsillo, “Environmentally friendly power sources for aerospace applications” Journal of Power Sources, Vol. 181, pp. 353‒362, 2008.
[3] N. L. Rey, J. Mosquera, E. Bataller, F. Orti, C. Dudfield, A. Orsillo, “Fuel Cell Systems for Aircraft Application” The Electrochemical Society, Vol. 25, pp. 193‒202, 2009.
[4] A. Pessota, C. Turpin, A. Jaafar, E. Soyez, O. Rallières, G. Gager , J. d’Arbignyc “Contribution to the modelling of a low temperature PEM fuel cell in aeronautical conditions by design of experiments” Mathematics and Computers in Simulation, Vol 158, pp. 179-198, 2019.
[5] N. Dyantyi, A.Parsons, P. Bujlo, S. Pasupathi “Behavioural study of PEMFC during start up/shutdown cycling for aeronautic applications” Materials for Renewable and Sustainable Energ, Vol. 8, No.4, 2019.
[6] T. M. Bachmann, F. Carnicelli, P. Preiss “Life cycle ssessment of domestic fuel cell micro combined heat and power generation: Exploring influential factors” International Journal of Hydrogen Energy, Vol. 44, pp. 3891-3905, 2019.
[7] T. Elmer, M. Worall, S. Wu, S. B. Riffat “Fuel cell technology for domestic built environment applications: State of-the-art review” Renewable and Sustainable Energy Reviews, Vol. 42, pp.913-931, 2015.
[8] M. Mehrpooya, F. K. Bahnamiri, S. M. A. Moosavian “Energy analysis and economic evaluation of a new developed integrated process configuration to produce power, hydrogen, and heat” Journal of Cleaner Production, Vol. 239, No. 118042, 2019.
[9] S. Sui, R. Rasheed1, Q. Li, Y. Su1, S. Riffat “Technoeconomic modelling and environmental assessment of a modern PEMFC CHP system: a case study of an eco-house at University of Nottingham” Environmental Science and Pollution Research, Vol. 26, pp.29883-29895, 2019.
[10] G. D. Marcoberardino, L. Chiarabaglio, G. Manzolini, S. Campanari “A Techno-economic comparison of micro-cogeneration systems based on polymer electrolyte membrane fuel cell for residential applications” Applied Energy, Vol. 239, pp.692-705, 2019.
[11] 徐冠華, 米樹華, 萬燕鳴等人(2019) 中國氫能源及燃料電池產業白皮書 中國氫能聯盟
[12] Yasuhiro Nonobe, “Development of the Fuel Cell Vehicle Mirai” IEEJ Trans, Vol. 12, 5-9, 2017.
[13] N. Konno, S. Mizuno, H. Nakaji, Y. Ishikawa “Development of Compact and High-Performance Fuel Cell Stack” SAE International Journal Alt. Power. Vol 4, pp.123-129, 2015.
[14] S. E. Hosseini, B. Butler “An overview of development and challenges in hydrogen powered vehicles” International Journal of Green Energy, DOI: 10.1080/15435075.2019.1685999.
[15] O. Groger, H. A. Gasteiger, J. P. Suchsland, “Review—Electromobility: Batteries or Fuel Cells?” Journal of The Electrochemical Society, Vol. 162, A2605-A2622, 2015.
[16] 黃鎮江(2017) 燃料電池(第四版) 全華圖書股份有限公司
[17] R. O’Hayre, S. W. Cha, W. Colella, F. B. Prinz著 王曉紅, 黃宏譯(2008) 燃料電池基礎 全華圖書股份有限公司
[18] 陸冠廷(2018) 質子交換模燃料電池電化學性能之數值計算與分析 國立成功大學機械工程學系碩士論文 (楊天祥教授指導)
[19] B. Han, J. Mo, Z. Kang, G. Yang, W. Barnhill, F. Y. Zhang, “Modeling of two-phase transport in proton exchange membrane electrolyzer cells for hydrogen energy” International Journal of Hydrogen Energy, Vol. 42, pp. 4478‒4489, 2017.
[20] C. Kunusch, P. F. Puleston, M. A. Mayosky, A. P. Husar “Control-Oriented Modeling and Experimental Validation of a PEMFC Generation System” IEEE Transactions on energy conversion, Vol. 26, pp. 851-861, 2011.
[21] Y. Yin, T. Wu, P. He, Q. Du, K. Jiao “Impact of PTFE content and distribution on liquid-gas flow in PEMFC carbon paper gas distribution layer: 3D lattice Boltzmann simulations” International Journal of Hydrogen Energy, Vol. 41, pp. 8550-8562 2016.
[22] J. Zhao, X. Li “A review of polymer electrolyte membrane fuel cell durability for vehicular applications: Degradation modes and experimental techniques” Energy Conversion and Management, vol. 199, No. 112022, 2019.
[23] P. Pei, H. Chen “Main factors affecting the lifetime of Proton Exchange Membrane fuel cells in vehicle applications: A review” Applied Energy, vol. 125, pp.60-75, 2014.
[24] H. Wang, A. Gaillard, D. Hissel “A review of DC/DC converter-based electrochemical impedance spectroscopy for fuel cell electric vehicles” Renewable Energy, vol. 141, pp. 124-138, 2019.
[25] Z. Niu. K. Jiao, Y. Wang. Q. Du, Y. Yin “Numerical simulation of two‐phase cross flow in the gas diffusion layer microstructure of proton exchange membrane fuel cells” International Journal of Energy Research. Vol 42, pp.802-816, 2018.
[26] G.R. Molaeimanesh, M.H. Akbari, “Impact of PTFE distribution on the removal of liquid water from a PEMFC electrode by lattice Boltzmann method” International Journal of Hydrogen Energy, Vol. 39, pp. 8401‒8409 2014.
[27] M. Dehsara, M. J. Kermani “Proton exchange membrane fuel cells performance enhancement using bipolar channel indentation” Journal of Mechanical Science and Technology, Vol. 28, pp.365-376, 2014.
[28] S. W. Perng, H. W. Wu, “A three-dimensional numerical investigation of trapezoid baffles effect on non-isothermal reactant transport and cell net power in a PEMFC” Applied Energy, Vol. 36, pp. 3614‒3622, 2011.
[29] H. Heidary, M. J. Kermani, B. Dabir, “Influences of bipolar plate channel blockages on PEM fuel cell performances” Energy Conversion and Management, Vol. 124, pp. 51-60, 2016.
[30] S. W. Perng, H. W. Wu, “Mid-baffle interdigitated flow fields for proton exchange membrane fuel cells” International Journal of Heat and Mass Transfer, Vol. 36, pp. 3614‒3622, 2011.
[31] S. W. Perng, H. W. Wu, “Non-isothermal transport phenomenon and cell performance of a cathodic PEM fuel cell with a baffle plate in a tapered channel” Applied Energy, Vol. 88, pp. 52‒67, 2011.
[32] J. Kin, G. Luo, C. Y. Wang, “Modeling two-phase flow in three-dimensional complex flow-fields of proton exchange membrane fuel cells” Journal of Power Sources, Vol. 365, pp. 419‒429, 2017.
[33] Z. Niu, J. Wu, Z. Bao, Y. Wang, Y. Yin and K. Jiao, “Two-phase flow and oxygen transport in the perforated gas diffusion layer of proton exchange membrane fuel cell” International Journal of Heat and Mass Transfer, Vol. 139, pp. 58‒68, 2019.
[34] W. Z. Fang, Y. Q. Tang, L. Chen, Q. J. Kang, W. Q. Tao, “Influences of the perforation on effective transport properties of gas diffusion layers” International Journal of Heat and Mass Transfer, Vol. 126, pp. 243‒255, 2018.
[35] C.Z. Qin, S.M. Hassanizadeh, “Multiphase flow through multilayers of thin porous media: General balance equations and constitutive relationships for a solid–gas–liquid three-phase system” International Journal of Hydrogen Energy, Vol. 70, pp. 693‒708, 2014.
[36] C.Z. Qin, S.M. Hassanizadeh, “A new approach to modelling water flooding
in a polymer electrolyte fuel cell” International Journal of Hydrogen Energy, Vol. 40, pp. 3348‒3358, 2015.
[37] U. Pasaogullari, C. Y. Wang∗, “Two-phase transport and the role of micro-porous layer in polymer electrolyte fuel cells” Electrochimica Acta, Vol. 49, pp. 4359‒4369, 2004.
[38] M. Shahraeeni, M. Hoorfar, “Pore-network modeling of liquid water flow in gas diffusion layers of proton exchange membrane fuel cells” International Journal of Hydrogen Energy, Vol. 39, pp. 10697-10709 2014.
[39] S. P. Kuttanikkad, M. Pratb, J. Pauchet “Pore-network simulations of two-phase flow in a thin porous layer of mixed wettability: Application to water transport in gas diffusion layers of proton exchange membrane fuel cells” Journal of Power Sources, Vol. 196, pp. 1145-1155 2011.
[40] T. E. Springer, T.A. Zawodzinski, S. Gottesfeld “Polymer electrolyte fuel cell model” Journal of Eletrochemical Society, vol. 138, pp. 2334-2342, 1991.
[41] T. V. Nguyen, R. E. White “A Water and Heat Management Model for Proton-Exchange-Membrane Fuel Cells”Journal of Eletrochemical Society, vol. 140, pp. 2178-2186, 1993.
[42] Y. Wana, K. S. Chen, “Through-Plane Water Distribution in a Polymer Electrolyte Fuel Cell: Comparison of Numerical Prediction with Neutron Radiography Data” Journal of The Electrochemical Society, Vol. 157, B1878-B1886, 2010.
[43] Y. Wang, K. S. Chen, “Effect of Spatially-Varying GDL Properties and Land Compression on Water Distribution in PEM Fuel Cells” Journal of The Electrochemical Society, Vol. 158, B1292-B1299, 2011.
[44] B. Carnes, D. Spernjak, G. Luo, L. Hao, K. S. Chen, C.Y. Wang, R. Mukundan, R. L. Borup “Validation of a two-phase multidimensional polymer electrolyte membrane fuel cell computational model using current distribution measurements” Journal of Power Sources, Vol. 236, pp. 126-137 2013.
[45] L. Hao, K. Moriyama, W. Gu, C. Y. Wang, “Modeling and Experimental Validation of Pt Loading and Electrode Composition Effects in PEM Fuel Cells” Journal of The Electrochemical Society, Vol. 162, F854-F867, 2015.
[46] L. Hao, K. Moriyama, W. Gu, C. Y. Wang, “Three Dimensional Computations and Experimental Comparisons for a Large-Scale Proton Exchange Membrane Fuel Cell” Journal of The Electrochemical Society, Vol. 163, F744-F751, 2016.
[47] T. Kotaka, Y. Tabuchi, U. Pasaogullari, C. Y. Wang, “Impact of Interfacial Water Transport in PEMFCs on Cell Performance” Electrochimica Acta, Vol. 146, pp. 618‒629, 2014.
[48] Y. Wang “Modeling of two-phase transport in the diffusion media of polymer electrolyte fuel cells” Journal of Power Sources, Vol. 185, pp. 261-271 2008.
[49] J.J. Baschuk, X. Li “A general formulation for a mathematical PEM fuel cell model” Journal of Power Sources, Vol. 142, pp. 134-153 2004.
[50] Y. Wang, S. Basu, C. Y. Wang “Modeling two-phase flow in PEM fuel cell channels” Journal of Power Sources, Vol. 179, pp. 603-617 2008.
[51] Z. H. Wang, C.Y. Wang and K. S. Chen, “Two-phase flow and transport in the air cathode of proton exchange membrane fuel cells” Journal of Power Sources, Vol. 94, pp. 40‒50, 2001.
[52] J. Kim (2019) “Modeling micro and macro scale two phase flow in 3D flow channels of Proton Exchange Membrane Fuel Cells” The Pennsylvania State University The Graduate School College of Engineering.
[53] Y. Yin, T. Wu, P. He, Q. Du, K. Jiao “Numerical simulation of two-phase cross flow in microstructure of gas diffusion layer with variable contact angle” International Journal of Hydrogen Energy, Vol. 39, pp. 15772-15785 2014.
[54] J. W. Park, K. Jiao, X. Li, “Numerical investigations on liquid water removal from the porous gas diffusion layer by reactant flow” Applied Energy, Vol. 87, pp. 2180‒2186, 2010.
[55] Z. Niu, Z. Bao, J. Wu, Y. Wang and K. Jiao “Two-Phase Flow Dynamics in the Gas Diffusion Layer of Proton Exchange Membrane Fuel Cells: Volume of Fluid Modeling and Comparison with Experiment” Journal of The Electrochemical Society, Vol. 165, pp. 613‒620, 2018.
[56] L. Chen, H. B. Luan, Y. L. He, W. Q. Tao “Pore-scale flow and mass transport in gas diffusion layer of proton exchange membrane fuel cell with interdigitated flow fields” International Journal of Thermal Sciences, Vol. 51, pp.132-144, 2012.
[57] M. E. Hannach, J. Pauchet, M. Prat , “Pore network modeling: Application to multiphase transport inside the cathode catalyst layer of proton exchange membrane fuel cell” Electrochimica Acta, Vol. 56, pp. 10796-10858, 2011.
[58] J. Du, M. Ouyang, J. Chen “Prospects for Chinese electric vehicle technologies in 2016-2020:Ambition and rationality” Energy, Vol. 120, pp. 584-596 2017.
[59] K.A. Culligan, D. Wildenschild, B.S.B. Christensen, W.G. Gray, M.L. Rivers “Interfacial area measurements for unsaturated flow through a porous medium” Water Resources Research, Vol. 40, W12413 2004.
[60] K.A. Culligan, D. Wildenschild, B.S.B. Christensen, W.G. Gray, M.L. Rivers “Pore-scale characteristics of multiphase flow in porous media: A comparison of air–water and oil–water experiments” Advances in Water Resources, Vol. 29, pp. 227-238 2006.
[61] L. Hao, K. Moriyama, W. Gu, C. Y. Wang, “Investigation of liquid water in gas diffusion layers of polymer electrolyte fuel cells using X-ray tomographic microscopy” Electrochimica Acta, Vol. 56, 2254-2262, 2011.
[62] D. Wildenschilda, J. W. Hopmans, C. M. P. Vaz, M. L. Rivers, D. Rikard, B. S. B. Christensen “Using X-ray computed tomography in hydrology: systems, resolutions, and limitations” Journal of Hydrology, Vol. 267, pp.285–297, 2002.
[63] M. E. Coles, R. D. Hazlett, P. Spanne, W. E. Soll, E. L. Muegge, K. W. Jones “Pore level imaging of fluid transport using synchrotron X-ray microtomography” Journal of Petroleum Science and Engineering, Vol. 19, pp. 55-63, 1998.
[64] F. M. Auzerais, J. Dunsmuir, B. B. Ferreol , N. Martys , J. Olson, T. S. Ramakrishnan, D. H. Rothman, L. M. Schwartz “Transport in sandstone: A study based on three dimensional micotomography” Geophysical Research Letters, Vol. 23, pp. 705-708, 1996.
[65] T. Saba, T. H. Illangasekare, J. Ewing “Investigation of surfactant-enhanced dissolution of
entrapped nonaqueous phase liquid chemicals in a two-dimensional groundwater flow field” Journal of Contaminant Hydrology, Vol. 51, pp. 63-82, 2001.
[66] M. L. Johns, L. F. Gladden “Magnetic Resonance Imaging Study of the Dissolution Kinetics of Octanol in Porous Media” Journal of Colloid and Interface Science, Vol. 210, pp. 96–104, 1999.
[67] M. L. Johns, L. F. Gladden “Probing Ganglia Dissolution and Mobilization in a Water-Saturated
Porous Medium using MRI” Journal of Colloid and Interface Science, Vol. 225, pp.119–127, 2000.
[68] M. L. Johns, L. F. Gladden “Surface-to-Volume Ratio of Ganglia Trapped in Small-Pore Systems Determined by Pulsed-Field Gradient Nuclear Magnetic Resonance” Journal of Colloid and Interface Science, Vol. 238, pp.96–104, 2001.
[69] K. Noborio “Measurement of soil water content and electrical conductivity by time domain reflectometry: a review” Computers and Electronics in Agriculture, Vol. 31, pp.213-237, 2001.
[70] S. W. Perng, H. W. Wu, “Mid-baffle interdigitated flow fields for proton exchange membrane fuel cells” International Journal of Heat and Mass Transfer, Vol. 36, pp. 3614‒3622, 2011.
[71] W. D. Hui, Y. L. Zhi, P. Z. Yu1, L. C. Da, L.G., L. Q. Hui “A novel intersectant flow field of metal bipolar plate for proton exchange membrane fuel cell” International Journal of Energy Research. Vol. 41, pp.2184-2193, 2017.
[72] H. Heidary, M. J. Kermani, S. G. Advani, A. K. Prasad “Experimental investigation of in-line and staggered blockages in parallel flowfield channels of PEM fuel cells” International Journal of Hydrogen Energy, Vol. 41, pp. 6885-6893 2016.
[73] L Lia, W. Fan, J. Xuan, M. K. H. Leung, K. Zheng, Y. She “Optimal design of current collectors for microfluidic fuel cell with flowthrough porous electrodes: Model and experiment” Applied Energy, Vol. 206, pp.413-424, 2017.
[74] 徐子軒(2016) 質子交換膜燃料電池流道之壓降分析與幾何優化設計 國立成功大學機械工程學系碩士論文 (楊天祥教授指導)
[75] Y. Wang, C. Y. Wang, K. S. Chen “Elucidating differences between carbon paper and carbon cloth in polymer electrolyte fuel cells” Electrochimica Acta, Vol. 52, pp. 3965-3975, 2007.
[76] M. C. Leverette “Capillary Behavior in Porous Solids” Tulsa Meeting , 1940.
[77] E. C. Kumbur, K. V. Sharp, M. M. Mench “On the effectiveness of Leverette approach for describing the water transport in fuel cell diffusion media” Journal of Power Sources, Vol 168, pp.356-368, 2007
[78] G. S. Beavers, D. D. Joseph “Boundary conditions at a naturally permeable wall” Journal of Fluid Mechanics, Vol 30. pp. 197-207 ,1967
[79] G. Sheng, Y. Su, F. Javadpour, W. Wang, S. Zhan, J. Liu, Z. Zhong “New Slip Coefficient Model Considering Adsorbed Gas Diffusion in Shale Gas Reservoirs” Energy&Fuels, 2020