气体扩散层孔隙率对质子交换膜燃料电池性能影响的数值模拟研究

质子交换膜燃料电池（Proton Exchange Membrane Fuel Cell，PEMFC）是一种能够利用氢气发电的装置。气体扩散层是PEMFC的重要组成部件，为内部气体提供输运通道，孔隙率是影响其传质的核心参数。本研究以提高PEMFC电流密度以及优化传质为目的，为PEMFC生产实践提供参考。基于数值模拟方法，本文主要探究了气体扩散层孔隙率对不同进气相对湿度PEMFC性能影响的规律。

首先，本文建立了单流道的PEMFC三维模型，介绍了描述PEMFC内部电化学反应的基本数学方程，并且给出了具体的仿真流程，包括建立几何模型、导入数学模型、设置边界条件、进行网格独立性验证以及模型准确性验证等步骤。

其次，本文考察了进气相对湿度在10%-100%区间内变化时PEMFC的性能变化，具体包括电流密度变化情况、膜中水含量变化情况、阳极催化层氢气分布云图等。研究结果表明，在PEMFC的工作温度为353K、工作电压为0.7V的条件下，随着进气相对湿度的上升，PEMFC的电流密度呈现先上升后下降的趋势。PEMFC处于低湿度工况（进气相对湿度为10%）时，其水含量过低，无法充分润湿质子交换膜，造成其内阻较大限制了电流密度的上升；PEMFC处于高湿度工况（进气相对湿度为100%）时，其水含量过高造成水淹，限制了内部气体传输。在进气相对湿度为70%时，PEMFC的电流密度达到最大值。

最后，本文探究了气体扩散层孔隙率对PEMFC的性能影响。定义均匀气体扩散层的孔隙率沿气体流动方向均匀不变，非均匀气体扩散层的孔隙率沿气体流动方向梯度变化。根据文献选取气体扩散层孔隙率的范围为0.3-0.6。对于均匀气体扩散层，在PEMFC的工作温度为353K、工作电压为0.7V的条件下，孔隙率为0.3更有利于提升低湿度PEMFC的电流密度，孔隙率为0.6更有利于提升高湿度PEMFC的电流密度。但当工作电压小于0.7V时，孔隙率为0.6更有利于提升PEMFC的电流密度，并且对于高湿度工况的提升效果更加显著。对于非均匀气体扩散层，孔隙率梯度变化对电流密度的影响较不明显，其变化幅度小于0.5%，对PEMFC传质的影响更为显著。因此，在对电流密度无明显影响的情况下，选择孔隙率梯度递增的气体扩散层更有利于提升氢气、氧气以及水分布均匀性，降低催化层局部缺气、膜局部溶胀等现象发生的可能性，从而提升PEMFC的使用寿命。对于微孔层（MPL）和基底层（MPS）组合的气体扩散层结构，沿垂直厚度方向的孔隙率梯度设计有利于提升电流密度。该气体扩散层结构对于高湿度状态的PEMFC电流密度改善效果更显著，若考虑接触电阻进行仿真，改善效果将进一步提升。

[1] 李俊峰, 李广. 中国能源、环境与气候变化问题回顾与展望 [J]. 环境与可持续发展, 2020, 45(05): 8-17.
[2] BARBIR F. PEM fuel cells: theory and practice [M]. Academic press, 2012.
[3] RAZA R, AKRAM N, JAVED M S, et al. Fuel cell technology for sustainable development in Pakistan–An over-view [J]. Renewable and Sustainable Energy Reviews, 2016, 53: 450-461.
[4] CHI B, HOU S, LIU G, et al. Tuning hydrophobic-hydrophilic balance of cathode catalyst layer to improve cell performance of proton exchange membrane fuel cell (PEMFC) by mixing polytetrafluoroethylene (PTFE) [J]. Electrochimica Acta, 2018, 277: 110-115.
[5] THERDTHIANWONG A, MANOMAYIDTHIKARN P, THERDTHIANWONG S. Investigation of membrane electrode assembly (MEA) hot-pressing parameters for proton exchange membrane fuel cell [J]. Energy, 2007, 32(12): 2401-2411.
[6] 张华民, 明平文, 邢丹敏. 质子交换膜燃料电池的发展现状 [J]. 当代化工, 2001, (01): 7-11.
[7] 孟黎清. 燃料电池的历史和现状 [J]. 电力学报, 2002, (02): 99-104.
[8] AGUIAR P, BRETT D, BRANDON N. Feasibility study and techno-economic analysis of an SOFC/battery hybrid system for vehicle applications [J]. Journal of power sources, 2007, 171(1): 186-197.
[9] PATHAK S, DAS J N, RANGARAJAN J, et al. Development of prototype phosphoric acid fuel cell pick-up electric vehicle; proceedings of the 2006 IEEE Conference on Electric and Hybrid Vehicles, F, 2006 [C]. IEEE.
[10] WIENER F, BRAM M, BUCHKREMER H P, et al. Chemical interaction between Crofer 22 APU and mica-based gaskets under simulated SOFC conditions [J]. Journal of Materials Science, 2007, 42(8): 2643-2651.
[11] WANG C, NEHRIR M H. A physically based dynamic model for solid oxide fuel cells [J]. IEEE Transactions on Energy Conversion, 2007, 22(4): 887-897.
[12] SHIRATORI Y, TIETZ F, PENKALLA H, et al. Influence of impurities on the conductivity of composites in the system (3YSZ) 1− x–(MgO) x [J]. Journal of power sources, 2005, 148: 32-42.
[13] SRIRAMULU S, TARGOFF J, LASHER S, et al. Challenges and Opportunities for Fuel Cells in Stationary Power Generation [J]. Cogeneration and Distributed Generation Journal, 2005, 20(3): 31-42.
[14] OKAMOTO M, AKIMUNE Y, FURUYA K, et al. Phase transition and electrical conductivity of scandia-stabilized zirconia prepared by spark plasma sintering process [J]. Solid State Ionics, 2005, 176(7-8): 675-680.
[15] 曾潮流, 吴维. 熔融碳酸盐燃料电池材料的腐蚀与防护CORROSION AND PROTECTION FOR MOLTEN CARBONATE FUEL CELL [J]. 腐蚀科学与防护技术, 2001, 13(3): 147-151,161.
[16] MITSOS-MIT A, HENCKE-MIT M M, BARTON P I. Man-portable power generation based on fuel-cell systems [J]. American Institute of Chemical Engineers, 2004.
[17] 王强. 固水界面的电化学性质及其对PEMFC的意义 [D]; 武汉大学, 2010.
[18] 常国峰, 曾辉杰, 许思传. 燃料电池汽车热管理系统的研究 [J]. 汽车工程, 2015, 37(08): 959-963.
[19] 杨代军, 马建新, 徐麟, 等. 城市大气主要污染物对PEMFC性能的影响 [J]. 电源技术, 2006, (04): 269-273.
[20] JIAO K, XUAN J, DU Q, et al. Designing the next generation of proton-exchange membrane fuel cells [J]. Nature, 2021, 595(7867): 361-369.
[21] 何光伟. 质子交换膜传递通道理性构筑及其微环境调控研究 [D]; 天津大学, 2016.
[22] ADILBISH G, LEE J-W, JANG Y-S, et al. Preparation of Pt/C electrode with double catalyst layers by electrophoresis deposition method for PEMFC [J]. international journal of hydrogen energy, 2014, 39(7): 3381-3386.
[23] CLEEMANN L N, BUAZAR F, LI Q, et al. Catalyst degradation in high temperature proton exchange membrane fuel cells based on acid doped polybenzimidazole membranes [J]. Fuel Cells, 2013, 13(5): 822-831.
[24] KIM D-S, ZEID E F A, KIM Y-T. Additive treatment effect of TiO2 as supports for Pt-based electrocatalysts on oxygen reduction reaction activity [J]. Electrochimica Acta, 2010, 55(11): 3628-3633.
[25] KUMAR A, REDDY R G. Materials and design development for bipolar/end plates in fuel cells [J]. Journal of Power Sources, 2004, 129(1): 62-67.
[26] BERNARDI D M, VERBRUGGE M W. A mathematical model of the solid‐polymer‐electrolyte fuel cell [J]. Journal of the Electrochemical Society, 1992, 139(9): 2477.
[27] TOHIDI M, MANSOURI S, AMIRI H. Effect of primary parameters on the performance of PEM fuel cell [J]. International journal of hydrogen energy, 2010, 35(17): 9338-9348.
[28] SALVA J A, IRANZO A, ROSA F, et al. Experimental validation of the polarization curve and the temperature distribution in a PEMFC stack using a one dimensional analytical model [J]. International Journal of Hydrogen Energy, 2016, 41(45): 20615-20632.
[29] FALCãO D, GOMES P, OLIVEIRA V, et al. 1D and 3D numerical simulations in PEM fuel cells [J]. International Journal of Hydrogen Energy, 2011, 36(19): 12486-12498.
[30] SAHRAOUI M, KHARRAT C, HALOUANI K. Two-dimensional modeling of electrochemical and transport phenomena in the porous structures of a PEMFC [J]. international journal of hydrogen energy, 2009, 34(7): 3091-3103.
[31] WONG K, LOO K H, LAI Y, et al. A theoretical study of inlet relative humidity control in PEM fuel cell [J]. international journal of hydrogen energy, 2011, 36(18): 11871-11885.
[32] ZHANG Y, PITCHUMANI R. Numerical studies on an air-breathing proton exchange membrane (PEM) fuel cell [J]. International Journal of Heat and Mass Transfer, 2007, 50(23-24): 4698-4712.
[33] SAHRAOUI M, BICHIOUI Y, HALOUANI K. Three-dimensional modeling of water transport in PEMFC [J]. international journal of hydrogen energy, 2013, 38(20): 8524-8531.
[34] JIAO K, LI X. A Three‐Dimensional Non‐isothermal Model of High Temperature Proton Exchange Membrane Fuel Cells with Phosphoric Acid Doped Polybenzimidazole Membranes [J]. Fuel Cells, 2010, 10(3): 351-362.
[35] JOURDANI M, MOUNIR H, MARJANI A. Three-dimensional PEM fuel cells modeling using COMSOL multiphysics [J]. The International Journal of Multiphysics, 2017, 11(4): 427-442.
[36] JEON D H, KIM K N, BAEK S M, et al. The effect of relative humidity of the cathode on the performance and the uniformity of PEM fuel cells [J]. International Journal of Hydrogen Energy, 2011, 36(19): 12499-12511.
[37] 白世杰, 刘永峰, 裴普成, 等. 阳极压力降对质子交换膜燃料电池性能的影响 [J]. 电源技术, 2019, 43(05): 801-804.
[38] KANCHAN B K, RANDIVE P, PATI S. Implications of non-uniform porosity distribution in gas diffusion layer on the performance of a high temperature PEM fuel cell [J]. International Journal of Hydrogen Energy, 2021, 46(35): 18571-18588.
[39] JABER T J, JARALLA R, SULAIMAN M A, et al. Numerical Study on High Temperature PEM Fuel Cell (HTPEMFC); proceedings of the ICTEA: International Conference on Thermal Engineering, F, 2017 [C].
[40] KAHVECI E E, TAYMAZ I. Assessment of single-serpentine PEM fuel cell model developed by computational fluid dynamics [J]. Fuel, 2018, 217: 51-58.
[41] JHA V, HARIHARAN R, KRISHNAMURTHY B. A 3 dimensional numerical model to study the effect of GDL porosity on high temperature PEM fuel cells [J]. International Journal of Heat and Mass Transfer, 2020, 161: 120311.
[42] TURKMEN A C, CELIK C. The effect of different gas diffusion layer porosity on proton exchange membrane fuel cells [J]. Fuel, 2018, 222: 465-474.
[43] XIA L, NI M, HE Q, et al. Optimization of gas diffusion layer in high temperature PEMFC with the focuses on thickness and porosity [J]. Applied Energy, 2021, 300: 117357.
[44] LAI Y-W, LEE K-R, YANG S-Y, et al. Production of La0. 6Sr0. 4Co0. 2Fe0. 8O3-δ cathode with graded porosity for improving proton-conducting solid oxide fuel cells [J]. Ceramics International, 2019, 45(17): 22479-22485.
[45] CHUN J H, JO D H, KIM S G, et al. Development of a porosity-graded micro porous layer using thermal expandable graphite for proton exchange membrane fuel cells [J]. Renewable energy, 2013, 58: 28-33.
[46] WILKINSON D P, ST-PIERRE J. In-plane gradients in fuel cell structure and conditions for higher performance [J]. Journal of Power Sources, 2003, 113(1): 101-108.
[47] CHU H-S, YEH C, CHEN F. Effects of porosity change of gas diffuser on performance of proton exchange membrane fuel cell [J]. Journal of power sources, 2003, 123(1): 1-9.
[48] CHEN F, CHANG M-H, HSIEH P-T. Two-phase transport in the cathode gas diffusion layer of PEM fuel cell with a gradient in porosity [J]. International Journal of Hydrogen Energy, 2008, 33(10): 2525-2529.
[49] HUANG Y-X, CHENG C-H, WANG X-D, et al. Effects of porosity gradient in gas diffusion layers on performance of proton exchange membrane fuel cells [J]. Energy, 2010, 35(12): 4786-4794.
[50] MA X, ZHANG X, YANG J, et al. Impact of gas diffusion layer spatial variation properties on water management and performance of PEM fuel cells [J]. Energy Conversion and Management, 2021, 227: 113579.
[51] ZHAN N, WU W, WANG S. Pore network modeling of liquid water and oxygen transport through the porosity-graded bilayer gas diffusion layer of polymer electrolyte membrane fuel cells [J]. Electrochimica Acta, 2019, 306: 264-276.
[52] CARCADEA E, VARLAM M, ISMAIL M, et al. PEM fuel cell performance improvement through numerical optimization of the parameters of the porous layers [J]. International Journal of Hydrogen Energy, 2020, 45(14): 7968-7980.
[53] XING L, WANG Y, DAS P K, et al. Homogenization of current density of PEM fuel cells by in-plane graded distributions of platinum loading and GDL porosity [J]. Chemical Engineering Science, 2018, 192: 699-713.
[54] XING L, SHI W, SU H, et al. Membrane electrode assemblies for PEM fuel cells: A review of functional graded design and optimization [J]. Energy, 2019, 177: 445-464.
[55] LIM I S, PARK J Y, KANG D G, et al. Numerical study for in-plane gradient effects of cathode gas diffusion layer on PEMFC under low humidity condition [J]. International Journal of Hydrogen Energy, 2020, 45(38): 19745-19760.
[56] 王诚, 赵波, 张剑波. 质子交换膜燃料电池膜电极的关键技术 [J]. 科技导报, 2016, 34(06): 62-68.
[57] LIU Z, ZENG X, GE Y, et al. Multi-objective optimization of operating conditions and channel structure for a proton exchange membrane fuel cell [J]. International journal of heat and mass transfer, 2017, 111: 289-298.
[58] LIU Y, BAI S, WEI P, et al. Numerical and experimental investigation of the asymmetric humidification and dynamic temperature in proton exchange membrane fuel cell [J]. Fuel Cells, 2020, 20(1): 48-59.
[59] PAN W, CHEN X, WANG F, et al. Mass transfer enhancement of PEM fuel cells with optimized flow channel dimensions [J]. International Journal of Hydrogen Energy, 2021, 46(57): 29541-29555.
[60] SIVERTSEN B R, DJILALI N. CFD-based modelling of proton exchange membrane fuel cells [J]. Journal of Power Sources, 2005, 141(1): 65-78.
[61] BERNING T, DJILALI N. Three-dimensional computational analysis of transport phenomena in a PEM fuel cell—a parametric study [J]. Journal of Power Sources, 2003, 124(2): 440-452.
[62] GUVELIOGLU G H, STENGER H G. Computational fluid dynamics modeling of polymer electrolyte membrane fuel cells [J]. Journal of Power Sources, 2005, 147(1-2): 95-106.
[63] WISHART J, DONG Z, SECANELL M. Optimization of a PEM fuel cell system based on empirical data and a generalized electrochemical semi-empirical model [J]. Journal of Power Sources, 2006, 161(2): 1041-1055.
[64] 张洪霞, 沈承, 韩福江, 等. 质子交换膜燃料电池的水平衡 [J]. 化学通报, 2011, 74(11): 1026-1032.
[65] 张雪霞, 蒋宇, 孙腾飞, 等. 质子交换膜燃料电池水淹和膜干故障诊断研究综述 [J]. 西南交通大学学报, 2020, 55(04): 828-838+864.
[66] CHANG Y, QIN Y, YIN Y, et al. Humidification strategy for polymer electrolyte membrane fuel cells–A review [J]. Applied Energy, 2018, 230: 643-662.
[67] YANG X-G, YE Q, CHENG P. In-plane transport effects on hydrogen depletion and carbon corrosion induced by anode flooding in proton exchange membrane fuel cells [J]. International journal of heat and mass transfer, 2012, 55(17-18): 4754-4765.
[68] 涂正凯，余意. 质子交换膜燃料电池水热管理技术基础及应用 [M]. 北京: 科学出版社, 2017.
[69] TOMADAKIS M M, ROBERTSON T J. Viscous permeability of random fiber structures: comparison of electrical and diffusional estimates with experimental and analytical results [J]. Journal of Composite Materials, 2005, 39(2): 163-188.