A comprehensive review of the modeling of transport phenomenon in the flow channels of polymer electrolyte membrane fuel cells

Abstract

Reactant gas and liquid water transport phenomena in the flow channels are complex and critical to the performance and durability of polymer electrolyte membrane fuel cells. The polymer membrane needs water at an optimum level for proton conductivity. Water management involves the prevention of dehydration, waterlogging, and the cell’s subsequent performance decline and degradation. This process requires the study and understanding of internal two-phase flows. Different experimental visualization techniques are used to study two-phase flows in polymer electrolyte membrane fuel cells. However, the experiments have limitations in in situ measurements; they are also expensive and time exhaustive. In contrast, numerical modeling is cheaper and faster, providing insights into the complex multiscale processes occurring across the components of the polymer electrolyte membrane fuel cells.

This paper introduces the recent design of flow channels. It reviews the numerical modeling techniques adopted for the transport phenomena therein: the two-fluid, multiphase mixture, volume of fluid, lattice Boltzmann, and pressure drop models. Furthermore, this work describes, compares, and analyses the models’ approaches and reviews the representative results of some selected aspects. Finally, the paper summarizes the modeling perspectives, emphasizing future directions with some recommendations.

Graphical abstract

Keywords

two-phase flows / numerical model / flow channel / polymer electrolyte membrane fuel cells / water management

References

[1] Çelik E , Karagöz İ . Polymer electrolyte membrane fuel cell flow field designs and approaches for performance enhancement. Proceedings of the Institution of Mechanical Engineers. Part A, Journal of Power and Energy, 2019, 234(8): 1189–1214

[2] Ebrahimzadeh A A , Khazaee I , Fasihfar A . Experimental and numerical investigation of obstacle effect on the performance of PEM fuel cell. International Journal of Heat and Mass Transfer, 2019, 141: 891–904

[3] Badduri S R , Srinivasulu G N , Rao S S . Influence of bio-inspired flow channel designs on the performance of a PEM fuel cell. Chinese Journal of Chemical Engineering, 2020, 28(3): 824–831

[4] Wang J . Theory and practice of flow field designs for fuel cell scaling-up: a critical review. Applied Energy, 2015, 157: 640–663

[5] Wang J . Barriers of scaling-up fuel cells: cost, durability and reliability. Energy, 2015, 80: 509–521

[6] Iranzo A , Arredondo C H , Kannan A M , Rosa F . Biomimetic flow fields for proton exchange membrane fuel cells: a review of design trends. Energy, 2020, 190: 116435

[7] Suárez C , Iranzo A , Toharias B , Rosa F . Experimental and numerical investigation on the design of a bioinspired PEM fuel cell. Energy, 2022, 257: 124799

[8] Zhao J , Li X , Shum C , McPhee J . A review of physics-based and data-driven models for real-time control of polymer electrolyte membrane fuel cells. Energy and AI, 2021, 6: 100–114

[9] Ferreira R B , Falcão D S , Oliveira V B , Pinto A M . Numerical simulations of two-phase flow in proton exchange membrane fuel cells using the volume of fluid method-review. Journal of Power Sources, 2015, 277: 329–342

[10] Ferreira R B , Falcão D S , Oliveira V B , Pinto A M . 1D + 3D two-phase flow numerical model of a proton exchange membrane fuel cell. Applied Energy, 2017, 203: 474–495

[11] AlbarbarAAlrweqM. Mathematical modelling and numerical simulation. In: Proton Exchange Membrane Fuel Cells: Design, Modelling and Performance Assessment Techniques. Cham: Springer, 2018, 77–99

[12] Mantzaras J , Freunberger S A , Büchi F N , Roos M , Brandstätter W , Prestat M , Gauckler L J , Andreaus B , Hajbolouri F , Senn S M . . Fuel cell modeling and simulations. Chimica, 2004, 58(12): 857–868

[13] YuanJFaghriMSundénB. On heat and mass transfer phenomena in PEMFC and SOFC and modeling approaches. In: Transport Phenomena in Fuel Cells. WIT Press, 2005, 133–174

[14] Kang S , Zhou B , Chin-Hsiang C , Huan-Ruei S , Lee C I . Liquid water flooding in a proton exchange membrane fuel cell cathode with an interdigitated design. International Journal of Energy Research, 2011, 35(15): 1292–1311

[15] Hu M , Cao G . Research on the performance differences between a standard PEMFC single cell and transparent PEMFC single cells using optimized transparent flow field unit. Part II: performance comparison and explanation. International Journal of Hydrogen Energy, 2016, 41(4): 2967–2980

[16] Cheddie D , Munroe N . Review and comparison of approaches to proton exchange membrane fuel cell modeling. Journal of Power Sources, 2005, 147(1-2): 72–84

[17] RahmanM A. Numerical simulation of interactive transport in a proton exchange membrane fuel cell. Dissertation for the doctoral degree. Carlifonia: University of California Merced, 2021, 13–24

[18] HisselDTurpinCAstierSBoulonLBouscayrolABultelYCandussoDCauxSChupinSColinartT, . A review on existing modeling methodologies for PEM fuel cell systems. In: Proceedings of the Fundamentals and Development of Fuel Cells. Nantes, France: 2008, 1–30

[19] Weber A Z , Borup R L , Darling R M , Das P K , Dursch T J , Gu W , Harvey D , Kusoglu A , Litster S , Mench M M . . A critical review of modeling transport phenomena in polymer-electrolyte fuel cells. Journal of the Electrochemical Society, 2014, 161(12): F1254–F1299

[20] Arif M , Cheung S C P , Andrews J . Different approaches used for modeling and simulation of polymer electrolyte membrane fuel cells: a review. Energy & Fuels, 2020, 34(10): 11897–11915

[21] Andersson M , Beale S B , Espinoza M , Wu Z , Lehnert W . A review of cell-scale multiphase flow modeling, including water management, in polymer electrolyte fuel cells. Applied Energy, 2016, 180: 757–778

[22] Kone J P , Zhang X , Yan Y , Hu G , Ahmadi G . Three-dimensional multiphase flow computational fluid dynamics models for proton exchange membrane fuel cell: a theoretical development. Journal of Computational Multiphase Flows, 2017, 9(1): 3–25

[23] Zhang G , Jiao K . Multi-phase models for water and thermal management of proton exchange membrane fuel cell: a review. Journal of Power Sources, 2018, 391: 120–133

[24] Anderson R , Zhang L , Ding Y , Blanco M , Bi X , Wilkinson D P . A critical review of two-phase flow in gas flow channels of proton exchange membrane fuel cells. Journal of Power Sources, 2010, 195(15): 4531–4553

[25] Chen L , Cao T F , Li Z H , He Y L , Tao W Q . Numerical investigation of liquid water distribution in the cathode side of proton exchange membrane fuel cell and its effects on cell performance. International Journal of Hydrogen Energy, 2012, 37(11): 9155–9170

[26] Wang J , Wang H . Flow-field designs of bipolar plates in PEM fuel cells: theory and applications. Fuel Cells, 2012, 12(6): 989–1003

[27] Deabate S , Gebel G , Huguet P , Morin A , Pourcelly G . In situ and operando determination of the water content distribution in proton conducting membranes for fuel cells: a critical review. Energy & Environmental Science, 2012, 5(10): 8824–8847

[28] Wang Y , Xu H , Wang X , Gao Y , Su X , Qin Y , Xing L . Multi-sub-inlets at cathode flow-field plate for current density homogenization and enhancement of PEM fuel cells in low relative humidity. Energy Conversion and Management, 2022, 252: 115069

[29] Kim J H , Kim W T . Numerical investigation of gas-liquid two-phase flow inside PEMFC gas channels with rectangular and trapezoidal cross sections. Energies, 2018, 11(6): 1403

[30] Li X , Sabir I . Review of bipolar plates in PEM fuel cells: flow-field designs. International Journal of Hydrogen Energy, 2005, 30(4): 359–371

[31] Porstmann S , Wannemacher T , Drossel W G . A comprehensive comparison of state-of-the-art manufacturing methods for fuel cell bipolar plates including anticipated future industry trends. Journal of Manufacturing Processes, 2020, 60: 366–383

[32] Sauermoser M , Kizilova N , Pollet B G , Kjelstrup S . Flow field patterns for proton exchange membrane fuel cells. Frontiers in Energy Research, 2020, 8: 13

[33] Hu G , Fan J , Chen S , Liu Y , Cen K . Three dimensional numerical analysis of proton exchange membrane fuel cells (PEMFCs) with conventional and interdigitated flow fields. Journal of Power Sources, 2004, 136(1): 1–9

[34] Wang Y , Yue L , Wang S . New design of a cathode flow-field with a sub-channel to improve the polymer electrolyte membrane fuel cell performance. Journal of Power Sources, 2017, 344: 32–38

[35] Wang Y , Wang S , Wang G , Yue L . Numerical study of a new cathode flow-field design with a sub-channel for a parallel flow-field polymer electrolyte membrane fuel cell. International Journal of Hydrogen Energy, 2018, 43(4): 2359–2368

[36] Rostami L , Haghshenasfard M , Sadeghi M , Zhiani M . A 3D CFD model of novel flow channel designs based on the serpentine and the parallel design for performance enhancement of PEMFC. Energy, 2022, 258: 124726

[37] Baik K D , Seo I S . Metallic bipolar plate with a multi-hole structure in the rib regions for polymer electrolyte membrane fuel cells. Applied Energy, 2018, 212: 333–339

[38] Chowdhury M Z , Akansu Y E . Novel convergent-divergent serpentine flow fields effect on PEM fuel cell performance. International Journal of Hydrogen Energy, 2017, 42(40): 25686–25694

[39] Chowdhury M Z , Timurkutluk B . Transport phenomena of convergent and divergent serpentine flow fields for PEMFC. Energy, 2018, 161: 104–117

[40] Timurkutluk B , Chowdhury M Z . Numerical investigation of convergent and divergent parallel flow fields for PEMFCs. Fuel Cells (Weinheim), 2018, 18(4): 441–448

[41] Wang Y , Wang X , Fan Y , He W , Guan J , Wang X . Numerical investigation of tapered flow field configurations for enhanced polymer electrolyte membrane fuel cell performance. Applied Energy, 2022, 306: 118021

[42] Ghasabehi M , Jabbary A , Shams M . Cathode side transport phenomena investigation and multi-objective optimization of a tapered parallel flow field PEMFC. Energy Conversion and Management, 2022, 265: 115761

[43] Girimurugan R , Anandhu K , Thirumoorthy A , Harikrishna N , Makeshwaran E , Prasanna S , Krishnaraj R . Performance studies on proton exchange membrane fuel cell with slightly tapered single flow channel for dissimilar cell potentials. Materials Today: Proceedings, 2023, 74: 602–610

[44] Huang H , Liu M , Li X , Guo X , Wang T , Li S , Lei H . Numerical simulation and visualization study of a new tapered-slope serpentine flow field in proton exchange membrane fuel cell. Energy, 2022, 246: 123406

[45] Wan Z , Quan W , Yang C , Yan H , Chen X , Huang T , Wang X , Chan S . Optimal design of a novel M-like channel in bipolar plates of proton exchange membrane fuel cell based on minimum entropy generation. Energy Conversion and Management, 2020, 205: 112386

[46] Yang C , Wan Z , Chen X , Kong X , Zhang J , Huang T , Wang X . Geometry optimization of a novel M-like flow field in a proton exchange membrane fuel cell. Energy Conversion and Management, 2021, 228: 113651

[47] Lin P , Wang H , Wang G , Li J , Sun J . Numerical study of optimized three-dimension novel key-shaped flow field design for proton exchange membrane fuel cell. International Journal of Hydrogen Energy, 2022, 47(8): 5541–5552

[48] Xie Q , Lian Y , Zheng M . CFD simulation and investigation of a new radial flow field structure on the PEMFC circular bipolar plate. International Journal of Electrochemical Science, 2021, 16(10): 211057

[49] Lian Y , Zheng M . Performance investigation on the radial flow channel of proton exchange membrane fuel cell. International Journal of Ambient Energy, 2021, 43(1): 4491–4498

[50] Zhang Z , Zheng M . Performance study and structure optimization of new type of radial flow field proton exchange membrane fuel cell. Energy Sources. Part A, Recovery, Utilization, and Environmental Effects, 2022, 44(3): 8266–8284

[51] Qu C , Zhang Y , Zhang Z , Zheng M . Design of radial flow channel proton exchange membrane fuel cell based on topology optimization. Processes, 2023, 11(8): 2482

[52] Wang B , Chen W , Pan F , Wu S , Zhang G , Park J W , Xie B , Yin Y , Jiao K . A dot matrix and sloping baffle cathode flow field of proton exchange membrane fuel cell. Journal of Power Sources, 2019, 434: 226741

[53] Zhang Y , He S , Jiang X , Xiong M , Ye Y , Yang X . Three-dimensional simulation of large-scale proton exchange membrane fuel cell considering the liquid water removal characteristics on the cathode side. International Journal of Hydrogen Energy, 2023, 48(27): 10160–10179

[54] Xie B , Zhang G , Jiang Y , Wang R , Sheng X , Xi F , Zhao Z , Chen W , Zhu Y , Wang Y . . “3D + 1D” modeling approach toward large-scale PEM fuel cell simulation and partitioned optimization study on flow field. eTransportation, 2020, 6: 100090

[55] Chen C , Wang C , Zhang Z . Numerical investigation of the water transport and performance of proton exchange membrane fuel cell with an imitating river flow field. Energy Conversion and Management, 2023, 276: 116532

[56] Atyabi S A , Afshari E . A numerical multiphase CFD simulation for PEMFC with parallel sinusoidal flow fields. Journal of Thermal Analysis and Calorimetry, 2018, 135(3): 1823–1833

[57] Chen X , Yu Z , Yang C , Chen Y , Jin C , Ding Y , Li W , Wan Z . Performance investigation on a novel 3D wave flow channel design for PEMFC. International Journal of Hydrogen Energy, 2021, 46(19): 11127–11139

[58] Zhu X , Zhou W , Zhu Z , Liu R , Lian Y , Chen R , Wu L , Ji D . Performance analysis of proton exchange membrane fuel cells with traveling-wave flow fields based on Grey-relational theory. International Journal of Hydrogen Energy, 2023, 48(2): 740–756

[59] Zhou Y , Meng K , Chen W , Deng Q , Chen B . Experimental performance of proton exchange membrane fuel cell with novel flow fields and numerical investigation of water-gas transport enhancement. Energy Conversion and Management, 2023, 281: 116865

[60] Zhang S , Xu H , Qu Z , Liu S , Talkhoncheh F K . Bio-inspired flow channel designs for proton exchange membrane fuel cells: a review. Journal of Power Sources, 2022, 522: 231003

[61] Li Y , Bi J , Tang M , Lu G . Snowflake bionic flow channel design to optimize the pressure drop and flow uniform of proton exchange membrane fuel cells. Micromachines, 2022, 13(5): 665

[62] Wen D H , Yin L Z , Piao Z Y , Lu C D , Li G , Leng Q H . A novel intersectant flow field of metal bipolar plate for proton exchange membrane fuel cell. International Journal of Energy Research, 2017, 41(14): 2184–2193

[63] Wen D H , Yin L Z , Piao Z Y , Lu C D , Li G , Leng Q H . Performance investigation of proton exchange membrane fuel cell with intersectant flow field. International Journal of Heat and Mass Transfer, 2018, 121: 775–787

[64] Atyabi S A , Afshari E . Three-dimensional multiphase model of proton exchange membrane fuel cell with honeycomb flow field at the cathode side. Journal of Cleaner Production, 2019, 214: 738–748

[65] Zhang S , Liu S , Xu H , Liu G , Wang K . Performance of proton exchange membrane fuel cells with honeycomb-like flow channel design. Energy, 2022, 239: 122102

[66] Cai G , Liang Y , Liu Z , Liu W . Design and optimization of bio-inspired wave-like channel for a PEM fuel cell applying genetic algorithm. Energy, 2020, 192: 116670

[67] Wang Y , Si C , Qin Y , Wang X , Fan Y , Gao Y . Bio-inspired design of an auxiliary fishbone-shaped cathode flow field pattern for polymer electrolyte membrane fuel cells. Energy Conversion and Management, 2021, 227: 113588

[68] Xie Q , Zheng M . CFD simulation and performance investigation on a novel bionic spider-web-type flow field for PEM fuel cells. Processes, 2021, 9(9): 1526

[69] Yao J , Yan F , Pei X . Design and analysis of spider bionic flow field for proton exchange membrane fuel cell. Journal of Electrochemical Science and Technology, 2023, 14(1): 38–50

[70] Li N , Wang W , Xu R , Zhang J , Xu H . Design of a novel nautilus bionic flow field for proton exchange membrane fuel cell by analyzing performance. International Journal of Heat and Mass Transfer, 2023, 200: 123517

[71] Tseng C J , Heush Y J , Chiang C J , Lee Y H , Lee K R . Application of metal foams to high temperature PEM fuel cells. International Journal of Hydrogen Energy, 2016, 41(36): 16196–16204

[72] Zhang G , Bao Z , Xie B , Wang Y , Jiao K . Three-dimensional multi-phase simulation of PEM fuel cell considering the full morphology of metal foam flow field. International Journal of Hydrogen Energy, 2021, 46(3): 2978–2989

[73] Awin Y , Dukhan N . Experimental performance assessment of metal-foam flow fields for proton exchange membrane fuel cells. Applied Energy, 2019, 252: 113458

[74] Suo M , Sun K , Chen R , Che Z , Zeng Z , Li Q , Tao X , Wang T . Oxygen transport in proton exchange membrane fuel cells with metal foam flow fields. Journal of Power Sources, 2022, 521: 230937

[75] Wan Z , Sun Y , Yang C , Kong X , Yan H , Chen X , Huang T , Wang X . Experimental performance investigation on the arrangement of metal foam as flow distributors in proton exchange membrane fuel cell. Energy Conversion and Management, 2021, 231: 113846

[76] Wu Y , Cho J I S , Whiteley M , Rasha L , Neville T P , Ziesche R , Xu R , Owen R , Kulkarni N , Hack J . . Characterization of water management in metal foam flow-field based polymer electrolyte fuel cells using in-operando neutron radiography. International Journal of Hydrogen Energy, 2020, 45(3): 2195–2205

[77] Bao Z , Niu Z , Jiao K . Numerical simulation for metal foam two-phase flow field of proton exchange membrane fuel cell. International Journal of Hydrogen Energy, 2019, 44(12): 6229–6244

[78] Park J E , Lim J , Kim S , Choi I , Ahn C Y , Hwang W , Lim M S , Cho Y H , Sung Y E . Enhancement of mass transport in fuel cells using three-dimensional graphene foam as flow field. Electrochimica Acta, 2018, 265: 488–496

[79] Jo A , Ju H . Numerical study on applicability of metal foam as flow distributor in polymer electrolyte fuel cells (PEFCs). International Journal of Hydrogen Energy, 2018, 43(30): 14012–14026

[80] Tseng C J , Tsai B T , Liu Z S , Cheng T C , Chang W C , Lo S K . A PEM fuel cell with metal foam as flow distributor. Energy Conversion and Management, 2012, 62: 14–21

[81] Jo A , Ahn S , Oh K , Kim W , Ju H . Effects of metal foam properties on flow and water distribution in polymer electrolyte fuel cells (PEFCs). International Journal of Hydrogen Energy, 2018, 43(30): 14034–14046

[82] Kang D G , Lee D K , Choi J M , Shin D K , Kim M S . Study on the metal foam flow field with porosity gradient in the polymer electrolyte membrane fuel cell. Renewable Energy, 2020, 156: 931–941

[83] Chen X , Yang C , Sun Y , Liu Q , Wan Z , Kong X , Tu Z , Wang X . Water management and structure optimization study of nickel metal foam as flow distributors in proton exchange membrane fuel cell. Applied Energy, 2022, 309: 118448

[84] Choi H , Kim O H , Kim M , Choe H , Cho Y H , Sung Y E . Next-generation polymer-electrolyte-membrane fuel cells using titanium foam as gas diffusion layer. ACS Applied Materials & Interfaces, 2014, 6(10): 7665–7671

[85] Zhang F Y , Advani S G , Prasad A K . Performance of a metallic gas diffusion layer for PEM fuel cells. Journal of Power Sources, 2008, 176(1): 293–298

[86] Tanaka S , Bradfield W W , Legrand C , Malan A G . Numerical and experimental study of the effects of the electrical resistance and diffusivity under clamping pressure on the performance of a metallic gas-diffusion layer in polymer electrolyte fuel cells. Journal of Power Sources, 2016, 330: 273–284

[87] Jiao K , Xuan J , Du Q , Bao Z , Xie B , Wang B , Zhao Y , Fan L , Wang H , Hou Z . . Designing the next generation of proton-exchange membrane fuel cells. Nature, 2021, 595(7867): 361–369

[88] Tanaka S , Shudo T . Corrugated mesh flow channel and novel microporous layers for reducing flooding and resistance in gas diffusion layer-less polymer electrolyte fuel cells. Journal of Power Sources, 2014, 268: 183–193

[89] Tanaka S , Shudo T . Significant performance improvement in terms of reduced cathode flooding in polymer electrolyte fuel cell using a stainless-steel microcoil gas flow field. Journal of Power Sources, 2014, 248: 524–532

[90] Park J E , Lim J , Lim M S , Kim S , Kim O H , Lee D W , Lee J H , Cho Y H , Sung Y E . Gas diffusion layer/flow-field unified membrane-electrode assembly in fuel cell using graphene foam. Electrochimica Acta, 2019, 323: 134808

[91] Zhang G , Qu Z , Wang Y . Proton exchange membrane fuel cell of integrated porous bipolar plate-gas diffusion layer structure: entire morphology simulation. eTransportation, 2023, 17: 100250

[92] Zhang Y , He S , Jiang X , Wang Z , Yang X , Fang H , Li Q , Cao J . Investigation on performance of full-scale proton exchange membrane fuel cell: porous foam flow field with integrated bipolar plate/gas diffusion layer. Energy, 2024, 287: 129664

[93] Yoshida T , Kojima K . Toyota MIRAI fuel cell vehicle and progress toward a future hydrogen society. Electrochemical Society Interface, 2015, 24(2): 45–49

[94] Yumiya H , Kizaki M , Asai H . Toyota fuel cell system (TFCS). World Electric Vehicle Journal, 2015, 7(1): 85–92

[95] Kojima K , Fukazawa K . Current status and future outlook of fuel cell vehicle development in Toyota. ECS Transactions, 2015, 69(17): 213–219

[96] Kim J , Luo G , Wang C Y . Modeling two-phase flow in three-dimensional complex flow-fields of proton exchange membrane fuel cells. Journal of Power Sources, 2017, 365: 419–429

[97] Bao Z , Niu Z , Jiao K . Analysis of single- and two-phase flow characteristics of 3-D fine mesh flow field of proton exchange membrane fuel cells. Journal of Power Sources, 2019, 438: 226995

[98] Yan X , Guan C , Zhang Y , Jiang K , Wei G , Cheng X , Shen S , Zhang J . Flow field design with 3D geometry for proton exchange membrane fuel cells. Applied Thermal Engineering, 2019, 147: 1107–1114

[99] Shen J , Tu Z , Chan S H . Performance enhancement in a proton exchange membrane fuel cell with a novel 3D flow field. Applied Thermal Engineering, 2020, 164: 114464

[100] Sun F , Su D , Li P , Dong X . A novel 3D fine-mesh flow field design and performance analysis for proton exchange membrane fuel cells. Journal of Power Sources, 2023, 584: 233572

[101] Agyekum E B , Ampah J D , Wilberforce T , Afrane S , Nutakor C . Research progress, trends, and current state of development on PEMFC-new insights from a bibliometric analysis and characteristics of two decades of research output. Membranes, 2022, 12(11): 1103

[102] Tsuchiya H . Mass production cost of PEM fuel cell by learning curve. International Journal of Hydrogen Energy, 2004, 29(10): 985–990

[103] Thompson S T , James B D , Huya-Kouadio J M , Houchins C , DeSantis D A , Ahluwalia R , Wilson A R , Kleen G , Papageorgopoulos D . Direct hydrogen fuel cell electric vehicle cost analysis: system and high-volume manufacturing description, validation, and outlook. Journal of Power Sources, 2018, 399: 304–313

[104] Kampker A , Heimes H , Kehrer M , Hagedorn S , Reims P , Kaul O . Fuel cell system production cost modeling and analysis. Energy Reports, 2023, 9: 248–255

[105] Wang H , Wang R , Sui S , Sun T , Yan Y , Du S . Cathode design for proton exchange membrane fuel cells in automotive applications. Automotive Innovation, 2021, 4(2): 144–164

[106] YoshizumiTKuboHOkumuraM. Development of high-performance FC stack for the new MIRAI. SAE Technical Paper 2021–01-074, 2021

[107] Tanaka S , Nagumo K , Yamamoto M , Chiba H , Yoshida K , Okano R . Fuel cell system for Honda Clarity fuel cell. eTransportation, 2020, 3: 100046

[108] Yuan W , Tang Y , Yang X , Wan Z . Porous metal materials for polymer electrolyte membrane fuel cells: a review. Applied Energy, 2012, 94: 309–329

[109] Springer T E , Zawodzinski T A , Gottesfeld S . Polymer electrolyte fuel cell model. Journal of the Electrochemical Society, 1991, 138(8): 2334–2342

[110] Bernardi D M , Verbrugge M W . A mathematical model of the solid-polymer electrolyte. Journal of the Electrochemical Society, 1992, 139(9): 2477–2491

[111] Weber A Z , Newman J . Modeling transport in polymer-electrolyte fuel cells. Chemical Reviews, 2004, 104(10): 4679–4726

[112] Weber A Z , Newman J . Coupled thermal and water management in polymer electrolyte fuel cells. Journal of the Electrochemical Society, 2006, 153(12): A2205–A2214

[113] Nguyen T V , White R E . A water and heat management model for proton-exchange-membrane fuel cells. Journal of the Electrochemical Society, 1993, 140(8): 2178–2186

[114] Dutta S , Shimpalee S , Van Zee J W . Three-dimensional numerical simulation of straight channel PEM fuel cells. Journal of Applied Electrochemistry, 2000, 30(2): 135–146

[115] He W , Yi J S , Nguyen T V . Two-phase flow model of the cathode of PEM fuel cells using interdigitated flow fields. AIChE Journal. American Institute of Chemical Engineers, 2000, 46(10): 2053–2064

[116] WeberA ZBallietRGuntermanH PNewmanJ. Modeling water management in polymer-electrolyte fuel cells. In: Modelling and Numerical Simulations. Modern Aspects of Electrochemistry, vol 43. New York: Springer, 2008, 273–415

[117] Sridhar P , Perumal R , Rajalakshmi N , Raja M , Dhathathreyan K S . Humidification studies on polymer electrolyte membrane fuel cell. Journal of Power Sources, 2001, 101(1): 72–78

[118] Jiao K , Li X . Water transport in polymer electrolyte membrane fuel cells. Progress in Energy and Combustion Science, 2011, 37(3): 221–291

[119] Knights S D , Colbow K M , St-Pierre J , Wilkinson D P . Aging mechanisms and lifetime of PEFC and DMFC. Journal of Power Sources, 2004, 127(1–2): 127–134

[120] He G , Ming P , Zhao Z , Abudula A , Xiao Y . A two-fluid model for two-phase flow in PEMFCs. Journal of Power Sources, 2007, 163(2): 864–873

[121] IshiiMHibikiT. Two-fluid model. In: Thermo-Fluid Dynamics of Two-Phase Flow. Boston, MA: Springer, 2006, 155–216

[122] Zhang G , Jiao K . Three-dimensional multi-phase simulation of PEMFC at high current density utilizing Eulerian-Eulerian model and two-fluid model. Energy Conversion and Management, 2018, 176: 409–421

[123] Gurau V , Edwards R V , Mann J A , Zawodzinski T A . A look at the multiphase mixture model for PEM fuel cell simulations. Electrochemical and Solid-State Letters, 2008, 11(8): B132–B135

[124] He G , Yamazaki Y , Abudula A . A droplet size dependent multiphase mixture model for two phase flow in PEMFCs. Journal of Power Sources, 2009, 194(1): 190–198

[125] Wang C Y , Beckermann C . A two-phase mixture model of liquid-gas flow and heat transfer in capillary porous media—l. Formulation. International Journal of Heat and Mass Transfer, 1993, 36(11): 2747–2758

[126] Wang C Y , Cheng P . A multiphase mixture model for multiphase, multicomponent transport in capillary porous media. I. Model development. International Journal of Heat and Mass Transfer, 1996, 39(17): 3607–3618

[127] You L , Liu H . A two-phase flow and transport model for the cathode of PEM fuel cells. International Journal of Heat and Mass Transfer, 2002, 45(11): 2277–2287

[128] Perumal D A , Dass A K . A review on the development of lattice Boltzmann computation of macro fluid flows and heat transfer. Alexandria Engineering Journal, 2015, 54(4): 955–971

[129] Deng H , Jiao K , Hou Y , Park J W , Du Q . A lattice Boltzmann model for multi-component two-phase gas-liquid flow with realistic fluid properties. International Journal of Heat and Mass Transfer, 2019, 128: 536–549

[130] Han B , Yu J , Meng H . Lattice Boltzmann simulations of liquid droplets development and interaction in a gas channel of a proton exchange membrane fuel cell. Journal of Power Sources, 2012, 202: 175–183

[131] Liao J , Yang G , Li S , Shen Q , Jiang Z , Wang H , Li Z . Study of droplet flow characteristics on a wetting gradient surface in a proton exchange membrane fuel cell channel using lattice Boltzmann method. Journal of Power Sources, 2022, 529: 231–245

[132] Mortazavi M . Two-phase flow pressure drop in PEM fuel cell flow channel bends. International Journal of Multiphase Flow, 2021, 143: 103759

[133] Mortazavi M , Heidari M , Niknam S A . A discussion about two-phase flow pressure drop in proton exchange membrane fuel cells. Heat Transfer Engineering, 2020, 41(21): 1784–1799

[134] Zhou L X . Two-fluid models for simulating dispersed multiphase flows: a review. Journal of Computational Multiphase Flows, 2009, 1(1): 39–56

[135] YangCMaoZ S. Multiphase stirred reactors. In: Numerical Simulation of Multiphase Reactors with Continuous Liquid Pshase. Oxford: Academic Press, 2014, 75–151

[136] KuipersJ A Mvan SwaaijW P. Computational fluid dynamics applied to chemical reaction engineering. In: Advances in Chemical Engineering, vol 24. Academic Press, 1998, 227–328

[137] Ishii M , Mishima K . Two-fluid model and hydrodynamic constitutive relations. Nuclear Engineering and Design, 1984, 82(2–3): 107–126

[138] LitsterSDjilaliN. Two-phase transport in porous gas diffusion electrodes. In: Transport Phenomena in Fuel Cells. WIT Press, 2005, 175–213

[139] ColomboMFairweatherM. CFD simulation of boiling flows for nuclear reactor thermal hydraulic applications. In: Computer Aided Chemical Engineering, vol 38. Elsevier, 2016, 445–450

[140] Le A D , Zhou B , Shiu H R , Lee C I , Chang W C . Numerical simulation and experimental validation of liquid water behaviors in a proton exchange membrane fuel cell cathode with serpentine channels. Journal of Power Sources, 2010, 195(21): 7302–7315

[141] Spalding D . Numerical computation of multi-phase fluid flow and heat transfer. Recent Advances in Numerical Methods in Fluids, 1980, 1: 139–167

[142] Gurau V , Zawodzinski T A Jr , Mann J A Jr . Two-phase transport in PEM fuel cell cathodes. Journal of Fuel Cell Science and Technology, 2008, 5(2): 021009

[143] Natarajan D , Van Nguyen T . A two-dimensional, two-phase, multicomponent, transient model for the cathode of a proton exchange membrane fuel cell using conventional gas distributors. Journal of the Electrochemical Society, 2001, 148(12): A1324–A1335

[144] Dutta S S S . Numerical prediction of temperature distribution in PEM fuel cells. Numerical Heat Transfer Part A, 2000, 38(2): 111–128

[145] Berning T , Djilali N . Three-dimensional computational analysis of transport phenomena in a PEM fuel cell: a parametric study. Journal of Power Sources, 2003, 124(2): 440–452

[146] Berning T , Djilali N . A 3D, multiphase, multicomponent model of the cathode and anode of a PEM fuel cell. Journal of the Electrochemical Society, 2003, 150(12): A1589–A1598

[147] d’Adamo A , Haslinger M , Corda G , Höflinger J , Fontanesi S , Lauer T . Modelling methods and validation techniques for CFD simulations of PEM fuel cells. Processes, 2021, 9(4): 688

[148] FaghriAZhangY. Generalized governing equations for multiphase systems: averaging formulations. In: Transport Phenomena in Multiphase Systems. Boston: Academic Press, 2006, 238–330

[149] DingY. Numerical simulations of gas-liquid two-phase flow in polymer electrolyte membrane fuel cells. Dissertation for the doctoral degree. Vancouver: University of British Columbia, 2012, 17–22

[150] Wang Z H , Wang C Y , Chen K S . Two-phase flow and transport in the air cathode of proton exchange membrane fuel cells. Journal of Power Sources, 2001, 94(1): 40–50

[151] Mazumder S , Cole J V . Rigorous 3-D mathematical modeling of PEM fuel cells. II. Model predictions with liquid water transport. Journal of the Electrochemical Society, 2003, 150(11): A1510–A1517

[152] Sun H , Liu H , Guo L J . PEM fuel cell performance and its two-phase mass transport. Journal of Power Sources, 2005, 143(1): 125–135

[153] You L , Liu H . A two-phase flow and transport model for PEM fuel cells. Journal of Power Sources, 2006, 155(2): 219–230

[154] Wang Y , Basu S , Wang C Y . Modeling two-phase flow in PEM fuel cell channels. Journal of Power Sources, 2008, 179(2): 603–617

[155] Sun P . Modeling studies and efficient numerical methods for proton exchange membrane fuel cell. Computer Methods in Applied Mechanics and Engineering, 2011, 200(47–48): 3324–3340

[156] Sun P , Zhou S , Hu Q , Liang G . Numerical study of a 3D two-phase PEM fuel cell model via a novel automated finite element/finite volume program generator. Communications in Computational Physics, 2012, 11(1): 65–98

[157] KatopodesN D. Volume of fluid method. In: Free-Surface Flow. Computational Methods. Butterworth-Heinemann, 2018, 766–802

[158] Wu J , Li Y , Wang Y . Three-dimension simulation of two-phase flows in a thin gas flow channel of PEM fuel cell using a volume of fluid method. International Journal of Hydrogen Energy, 2020, 45(54): 29730–29737

[159] Owkes M , Desjardins O . A mesh-decoupled height function method for computing interface curvature. Journal of Computational Physics, 2015, 281: 285–300

[160] Vachaparambil K J , Einarsrud K E . Comparison of surface tension models for the volume of fluid method. Processes, 2019, 7(8): 542

[161] Ba geriA SGajbhiyeRAbdulraheemA. Evaluating the effect of surface tension on two-phase flow in horizontal pipes. In: SPE Kingdom of Saudi Arabia Annual Technical Symposium and Exhibition. Damman, Saudi Arabia: 2017, SPE-188009-MS

[162] He K , Wang S , Huang J . The effect of surface tension on phase distribution of two-phase flow in a micro-T-junction. Chemical Engineering Science, 2011, 66(17): 3962–3968

[163] WekingHSchlottkeJBogerMRauschenbergerPWeigandBMunzC D. DNS of rising bubbles using VOF and balanced force surface tension. In: High Performance Computing on Vector Systems. Berlin, Heidelberg: Springer, 2010, 171–184

[164] Brackbill J U , Kothe D B , Zemach C . A continuum method for modeling surface tension. Journal of Computational Physics, 1992, 100(2): 335–354

[165] KotheDRiderWMossoSBrockJHochsteinJ. Volume tracking of interfaces having surface tension in two and three dimensions. In: 34th Aerospace Sciences Meeting and Exhibit. Reno, USA: American Institute of Aeronautics and Astronautics, Inc., 1996, 859

[166] Golpaygan A , Ashgriz N . Multiphase flow model to study channel flow dynamics of PEM fuel cells: deformation and detachment of water droplets. International Journal of Computational Fluid Dynamics, 2008, 22(1–2): 85–95

[167] Ding Y , Bi X , Wilkinson D P . 3D simulations of the impact of two-phase flow on PEM fuel cell performance. Chemical Engineering Science, 2013, 100: 445–455

[168] Quan P , Zhou B , Sobiesiak A , Liu Z . Water behavior in serpentine micro-channel for proton exchange membrane fuel cell cathode. Journal of Power Sources, 2005, 152: 131–145

[169] Le A D , Zhou B . A general model of proton exchange membrane fuel cell. Journal of Power Sources, 2008, 182(1): 197–222

[170] Le A D , Zhou B . A generalized numerical model for liquid water in a proton exchange membrane fuel cell with interdigitated design. Journal of Power Sources, 2009, 193(2): 665–683

[171] Le A D , Zhou B . Fundamental understanding of liquid water effects on the performance of a PEMFC with serpentine-parallel channels. Electrochimica Acta, 2009, 54(8): 2137–2154

[172] Le A D , Zhou B . A numerical investigation on multi-phase transport phenomena in a proton exchange membrane fuel cell stack. Journal of Power Sources, 2010, 195(16): 5278–5291

[173] Bhatt T , Arumuga Perumal D . Application of lattice Boltzmann method for fluid flow modelling of FSLDR domain. Materials Today: Proceedings, 2020, 22: 2066–2073

[174] Espinoza M , Sundén B , Andersson M , Yuan J . Analysis of porosity and tortuosity in a 2D selected region of solid oxide fuel cell cathode using the lattice Boltzmann method. ECS Transactions, 2015, 65(1): 59–73

[175] Kim K N , Kang J H , Lee S G , Nam J H , Kim C J . Lattice Boltzmann simulation of liquid water transport in microporous and gas diffusion layers of polymer electrolyte membrane fuel cells. Journal of Power Sources, 2015, 278: 703–717

[176] Chen S , Doolen G D . Lattice Boltzmann method for fluid flows. Annual Review of Fluid Mechanics, 1998, 30(1): 329–364

[177] Han B , Ni M , Meng H . Three-dimensional lattice Boltzmann simulation of liquid water transport in porous layer of PEMFC. Entropy, 2015, 18(1): 17

[178] Han B , Meng H . Lattice Boltzmann simulation of liquid water transport in turning regions of serpentine gas channels in proton exchange membrane fuel cells. Journal of Power Sources, 2012, 217: 268–279

[179] Wang L P , Afsharpoya B . Modeling fluid flow in fuel cells using the Lattice-Boltzmann approach. Mathematics and Computers in Simulation, 2006, 72(2): 242–248

[180] Hao L , Cheng P . Lattice Boltzmann simulations of liquid droplet dynamic behavior on a hydrophobic surface of a gas flow channel. Journal of Power Sources, 2009, 190(2): 435–446

[181] Ben Amara M E A , Ben Nasrallah S . Numerical simulation of droplet dynamics in a proton exchange membrane (PEMFC) fuel cell micro-channel. International Journal of Hydrogen Energy, 2015, 40(2): 1333–1342

[182] Salah Y B , Tabe Y , Chikahisa T . Gas channel optimisation for PEM fuel cell using the lattice Boltzmann method. Energy Procedia, 2012, 28: 125–133

[183] Salah Y B , Tabe Y , Chikahisa T . Two phase flow simulation in a channel of a polymer electrolyte membrane fuel cell using the Lattice Boltzmann method. Journal of Power Sources, 2012, 199: 85–93

[184] Qin Y , Du Q , Yin Y , Jiao K , Li X . Numerical investigation of water dynamics in a novel proton exchange membrane fuel cell flow channel. Journal of Power Sources, 2013, 222: 150–160

[185] Zhu X , Sui P C , Djilali N . Three-dimensional numerical simulations of water droplet dynamics in a PEMFC gas channel. Journal of Power Sources, 2008, 181(1): 101–115

[186] Choi C , Yu D I , Kim M . Surface wettability effect on flow pattern and pressure drop in adiabatic two-phase flows in rectangular microchannels with T-junction mixer. Experimental Thermal and Fluid Science, 2011, 35(6): 1086–1096

[187] Hsieh S S , Huang Y J , Her B S . Pressure drop on water accumulation distribution for a micro PEM fuel cell with different flow field plates. International Journal of Heat and Mass Transfer, 2009, 52(23-24): 5657–5659

[188] Battrell L , Trunkle A , Eggleton E , Zhang L , Anderson R . Quantifying cathode water transport via anode relative humidity measurements in a polymer electrolyte membrane fuel cell. Energies, 2017, 10(8): 1222

[189] Mortazavi M , Tajiri K . Two-phase flow pressure drop in flow channels of proton exchange membrane fuel cells: review of experimental approaches. Renewable & Sustainable Energy Reviews, 2015, 45: 296–317

[190] Lockhart R W , Martinelli R C . Proposed correlation of data for isothermal two-phase, two-component flow in pipes. Chemical Engineering Progress, 1949, 45(1): 39–48

[191] English N J , Kandlikar S G . An experimental investigation into the effect of surfactants on air-water two-phase flow in minichannels. Heat Transfer Engineering, 2006, 27(4): 99–109

[192] Zhang L , Bi X T , Wilkinson D P , Anderson R , Stumper J , Wang H . Gas-liquid two-phase flow behavior in minichannels bounded with a permeable wall. Chemical Engineering Science, 2011, 66(14): 3377–3385

[193] Anderson R , Eggleton E , Zhang L . Development of two-phase flow regime specific pressure drop models for proton exchange membrane fuel cells. International Journal of Hydrogen Energy, 2015, 40(2): 1173–1185

[194] MortazaviMTajiriK. Interaction between liquid droplet growth and two-phase pressure drop in PEM fuel cell flow channels. In: Proceedings of the 4th International Conference of Fluid Flow, Heat and Mass Transfer. Toronto, Canada: 2017, 133

[195] Niknam S A , Mortazavi M , Santamaria A D . Signature analysis of two-phase flow pressure drop in proton exchange membrane fuel cell flow channels. Results in Engineering, 2020, 5: 100071

[196] MortazaviMShannonR CAbdollahpourA. Retrofitting a two-phase flow pressure drop model for PEM fuel cell flow channel bends. In: 20th IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems. San Diego, USA: IEEE, 2021, 1114–1122

[197] Sookprasong P , Brill J , Schmidt Z . Two-phase flow in piping components. Journal of Energy Resources Technology, 1986, 108(3): 197–201

[198] Banerjee R , Howe D , Mejia V , Kandlikar S G . Experimental validation of two-phase pressure drop multiplier as a diagnostic tool for characterizing PEM fuel cell performance. International Journal of Hydrogen Energy, 2014, 39(31): 17791–17801

[199] Kandlikar S G , See E J , Banerjee R . Modeling two-phase pressure drop along PEM fuel cell reactant channels. Journal of the Electrochemical Society, 2015, 162(7): F772–F782

[200] Pham T Q D , Jeon J , Choi S . Quantitative comparison between volume-of-fluid and two-fluid models for two-phase flow simulation using OpenFOAM. Journal of Mechanical Science and Technology, 2020, 34(3): 1157–1166

[201] ManninenMTaivassaloV. On the mixture model for multiphase flow. Technical Research Centre of Finland, Espoo, VTT Publications 288, 1996: 67

[202] Eghbalzadeh A , Javan M . Comparison of mixture and VOF models for numerical simulation of air-entrainment in skimming flow over stepped spillways. Procedia Engineering, 2012, 28: 657–660

[203] Hirt C W , Nichols B D . Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics, 1981, 39(1): 201–225

[204] Zhang L , Liu S , Wang Z , Li R , Zhang Q . Numerical simulation of two-phase flow in a multi-gas channel of a proton exchange membrane fuel cell. International Journal of Hydrogen Energy, 2022, 47(40): 17713–17736

[205] Yin Y , Li Y , Qin Y , Li M , Liu G , Zhang J , Zhao J . Ex-situ experimental study on dynamic behaviors and detachment characteristics of liquid water in a transparent channel of PEMFC. Renewable Energy, 2022, 187: 1037–1049

[206] Ding Y , Bi X T , Wilkinson D P . Numerical investigation of the impact of two-phase flow maldistribution on PEM fuel cell performance. International Journal of Hydrogen Energy, 2014, 39(1): 469–480

[207] Ding Y , Bi H T , Wilkinson D P . Three-dimensional numerical simulation of water droplet emerging from a gas diffusion layer surface in micro-channels. Journal of Power Sources, 2010, 195(21): 7278–7288

[208] Jiao K , Ni M . Challenges and opportunities in modelling of proton exchange membrane fuel cells (PEMFC). International Journal of Energy Research, 2017, 41(13): 1793–1797

[209] Niu Z , Wang R , Jiao K , Du Q , Yin Y . Direct numerical simulation of low Reynolds number turbulent air-water transport in fuel cell flow channel. Science Bulletin, 2017, 62(1): 31–39

[210] Wu M L , Li R R , Lang X J , Song M . Lattice Boltzmann method development of PEMFC in mesoscopic scale. IOP Conference Series. Earth and Environmental Science, 2021, 680(1): 012089

[211] Jithin M , Siddharth S , Das M K , De A . Simulation of coupled heat and mass transport with reaction in PEM fuel cell cathode using lattice Boltzmann method. Thermal Science and Engineering Progress, 2017, 4: 85–96

[212] Molaeimanesh G R , Akbari M H . A three-dimensional pore-scale model of the cathode electrode in polymer-electrolyte membrane fuel cell by lattice Boltzmann method. Journal of Power Sources, 2014, 258: 89–97

[213] Yu Z , Hemminger O , Fan L S . Experiment and lattice Boltzmann simulation of two-phase gas-liquid flows in microchannels. Chemical Engineering Science, 2007, 62(24): 7172–7183

[214] SucciS. LBE in the framework of computational fluid dynamics. In: The Lattice Boltzmann Equation for Fluid Dynamics and Beyond (Numerical Mathematics and Scientific Computation). New York: Oxford University Press, 2001, 175–213

[215] Chai Z , Guo Z , Shi B . lattice Boltzmann simulation of mixed convection in a driven cavity packed with porous medium. In: Computational Science–ICCS 2007: 7th International Conference, Beijing, China. Berlin: Springer, 2007, 4487: 802–809

[216] MortazaviM. Water transport through porous media and in flow channels of proton exchange membrane fuel cell. Dissertation for the doctoral degree. Michigan, USA: Michigan Technological University, 2014, 81–84

[217] Triplett K A , Ghiaasiaan S M , Abdel-Khalik S I , Sadowski D L . Gas-liquid two-phase flow in microchannels Part I: two-phase flow patterns. International Journal of Multiphase Flow, 1999, 25(3): 377–394

[218] Ding Y , Bi H T , Wilkinson D P . Three dimensional numerical simulation of gas-liquid two-phase flow patterns in a polymer-electrolyte membrane fuel cells gas flow channel. Journal of Power Sources, 2011, 196(15): 6284–6292

[219] Wang Y . Porous-media flow fields for polymer electrolyte fuel cells. II. Analysis of channel two-phase flow. Journal of the Electrochemical Society, 2009, 156(10): B1134–B1141

[220] Theodorakakos A , Ous T , Gavaises M , Nouri J M , Nikolopoulos N , Yanagihara H . Dynamics of water droplets detached from porous surfaces of relevance to PEM fuel cells. Journal of Colloid and Interface Science, 2006, 300(2): 673–687

[221] Grimm M , See E J , Kandlikar S G . Modeling gas flow in PEMFC channels: Part I—flow pattern transitions and pressure drop in a simulated ex situ channel with uniform water injection through the GDL. International Journal of Hydrogen Energy, 2012, 37(17): 12489–12503

[222] Zhou Y , Chen B , Chen W , Deng Q , Shen J , Tu Z . A novel opposite sinusoidal wave flow channel for performance enhancement of proton exchange membrane fuel cell. Energy, 2022, 261: 125383

[223] Cao Y , Ayed H , Jafarmadar S , Abdollahi M A A , Farag A , Wae-hayee M , Hashemian M . PEM fuel cell cathode-side flow field design optimization based on multi-criteria analysis of liquid-slug dynamics. Journal of Industrial and Engineering Chemistry, 2021, 98: 397–412

[224] Hou Y , Deng H , Du Q , Jiao K . Multi-component multi-phase lattice Boltzmann modeling of droplet coalescence in flow channel of fuel cell. Journal of Power Sources, 2018, 393: 83–91

[225] Bao Z , Wang Y , Jiao K . Liquid droplet detachment and dispersion in metal foam flow field of polymer electrolyte membrane fuel cell. Journal of Power Sources, 2020, 480: 229150

[226] Yang D , Garg H , Andersson M . Numerical simulation of two-phase flow in gas diffusion layer and gas channel of proton exchange membrane fuel cells. International Journal of Hydrogen Energy, 2023, 48(41): 15677–15694

[227] Zhang G , Xie X , Xie B , Du Q , Jiao K . Large-scale multi-phase simulation of proton exchange membrane fuel cell. International Journal of Heat and Mass Transfer, 2019, 130: 555–563

[228] Khazaee I , Sabadbafan H . Effect of humidity content and direction of the flow of reactant gases on water management in the 4-serpentine and 1-serpentine flow channel in a PEM (proton exchange membrane) fuel cell. Energy, 2016, 101: 252–265

[229] Zhang Z , Zhao J , Ling X , Ma J . Numerical study on dynamic behaviours of a micro-droplet impacting on a vertical wall in PEMFC. International Journal of Hydrogen Energy, 2021, 46(35): 18557–18570

[230] Hou Y , Deng H , Zamel N , Du Q , Jiao K . 3D lattice Boltzmann modeling of droplet motion in PEM fuel cell channel with realistic GDL microstructure and fluid properties. International Journal of Hydrogen Energy, 2020, 45(22): 12476–12488

[231] Kotaka T , Tabuchi Y , Pasaogullari U , Wang C Y . Impact of interfacial water transport in PEMFCs on cell performance. Electrochimica Acta, 2014, 146: 618–629

[232] Lu Z , Rath C , Zhang G , Kandlikar S G . Water management studies in PEM fuel cells, Part IV: effects of channel surface wettability, geometry and orientation on the two-phase flow in parallel gas channels. International Journal of Hydrogen Energy, 2011, 36(16): 9864–9875

[233] Ding Y , Xu L , Zheng W , Hu Z , Shao Y , Li J , Ouyang M . Characterizing the two-phase flow effect in gas channel of proton exchange membrane fuel cell with dimensionless number. International Journal of Hydrogen Energy, 2023, 48(13): 5250–5265

[234] Liao P , Yang D , Pan X , Li B , Ming P , Li Z . Enhancing the dynamic performance of proton exchange membrane fuel cells through two-phase flow experimental investigation. International Journal of Hydrogen Energy, 2023, 48(82): 32093–32109

[235] Andersson M , Beale S B , Reimer U , Lehnert W , Stolten D . Interface resolving two-phase flow simulations in gas channels relevant for polymer electrolyte fuel cells using the volume of fluid approach. International Journal of Hydrogen Energy, 2018, 43(5): 2961–2976

[236] Lu Z , Kandlikar S G , Rath C , Grimm M , Domigan W , White A D , Hardbarger M , Owejan J P , Trabold T A . Water management studies in PEM fuel cells, part II: ex situ investigation of flow maldistribution, pressure drop and two-phase flow pattern in gas channels. International Journal of Hydrogen Energy, 2009, 34(8): 3445–3456

[237] Kandlikar S G , Lu Z , Domigan W E , White A D , Benedict M W . Measurement of flow maldistribution in parallel channels and its application to ex-situ and in-situ experiments in PEMFC water management studies. International Journal of Heat and Mass Transfer, 2009, 52(7–8): 1741–1752

[238] Malhotra S , Ghosh S . Effects of channel diameter on flow pattern and pressure drop for air-water flow in serpentine gas channels of PEM fuel cell–an ex situ experiment. Experimental Thermal and Fluid Science, 2019, 100: 233–250

[239] Fan L , Tu Z , Chan S H . Technological and engineering design of a megawatt proton exchange membrane fuel cell system. Energy, 2022, 257: 124728

[240] Razmjooy N . A survey on parameters estimation of the proton exchange membrane fuel cells based on the swarm-inspired optimization algorithms. Frontiers in Energy Research, 2023, 11: 1148323

[241] Badra J A , Khaled F , Tang M , Pei Y , Kodavasal J , Pal P , Owoyele O , Fuetterer C , Mattia B , Aamir F . Engine combustion system optimization using computational fluid dynamics and machine learning: a methodological approach. Journal of Energy Resources Technology, 2021, 143(2): 1–36

[242] Maionchi D O , Ainstein L , dos Santos F P , de Souza Júnior M B . Ainstein L, dos Santos F P, de Souza Júnior M B. Computational fluid dynamics and machine learning as tools for optimization of micromixers geometry. International Journal of Heat and Mass Transfer, 2022, 194: 123110

[243] Ranade R , Hill C , Pathak J . DiscretizationNet: a machine-learning based solver for Navier-Stokes equations using finite volume discretization. Computer Methods in Applied Mechanics and Engineering, 2021, 378: 113722

[244] Erichson N B , Mathelin L , Yao Z , Brunton S L , Mahoney M W , Kutz J N . Shallow neural networks for fluid flow reconstruction with limited sensors. Proceedings-Royal Society. Mathematical, Physical and Engineering Sciences, 2020, 476(2238): 20200097

[245] Chauhan V , Mortazavi M , Benner J Z , Santamaria A D . Two-phase flow characterization in PEM fuel cells using machine learning. Energy Reports, 2020, 6: 2713–2719

[246] Santamaria A D , Mortazavi M , Chauhan V , Benner J , Philbrick O , Clemente R , Jia H , Ling C . Machine learning applications of two-phase flow data in polymer electrolyte fuel cell reactant channels. Journal of the Electrochemical Society, 2021, 168(5): 054505

[247] Santamaria A D , Mortazavi M , Chauhan V , Benner J , Philbrick O , Clemente R , Ling C , Jia H . Applications of artificial intelligence for analysis of two-phase flow in PEM fuel cell flow fields. ECS Transactions, 2020, 98(9): 279–290

[248] Wang Y , Seo B , Wang B , Zamel N , Jiao K , Adroher X C . Fundamentals, materials, and machine learning of polymer electrolyte membrane fuel cell technology. Energy and AI, 2020, 1: 100014

[249] Shen J , Tu Z , Chan S H . Evaluation criterion of different flow field patterns in a proton exchange membrane fuel cell. Energy Conversion and Management, 2020, 213: 112841

[250] Gao W , Li Q , Sun K , Chen R , Che Z , Wang T . Mass transfer and water management in proton exchange membrane fuel cells with a composite foam-rib flow field. International Journal of Heat and Mass Transfer, 2023, 216: 124595

RIGHTS & PERMISSIONS

Higher Education Press