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Optimization design of trapezoidal flow field proton exchange membrane fuel cell combined with computational fluid dynamics, surrogate model, and multi-objective optimization algorithm

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Abstract

The flow field structure plays the key roles in the operating reliability and power output of proton exchange membrane fuel cell (PEMFC). This study investigates and compares two typical structural parameters of PEMFC with the trapezoidal flow channel (TFC) and the trapezoidal flow channel with block (TFCB). A three-dimensional (3-D) multiphase TFC model is first developed, and then the multi-objective optimization is performed by using the trained artificial neural network (ANN) surrogate model and non-dominated sorting genetic algorithm (NSGA-II). Finally, the technique for order preference by similarity to an ideal solution (TOPSIS) is used to investigate the optimized structural parameters of TFC. The results show the net power output and the oxygen uniformity index of the optimized TFC are increased by 19.77% and 21.92% compared with the straight flow channel (SFC). Furthermore, it is also found using block in the trapezoidal flow channel (TFCB) can increase the performance of PEMFC, and it exhibits a 25.10% improvement for the net power output and 27.88% for oxygen uniformity index, respectively.

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Abbreviations

a :

Water activity

ANN:

Artificial neural network

BP:

Bipolar plate

CFD:

Computational fluid dynamics

\({C}_{k}\) :

Species concentration (mol/m3)

CL:

Catalytic layer

\({c}_{p}\) :

Specific heat capacity at a constant pressure (J/(kg·K))

\({D}_{k}^{eff}\) :

Effective species diffusion coefficient (m2/s)

T :

Temperature (K)

FC:

Flow channel

GDL:

Gas diffusion layer

\(j\) :

Exchange current density (A/m3)

K :

Absolute permeability (m2)

\({k}^{eff}\) :

Effective thermal conductivity (W/(m·K))

LHS:

Latin hypercube sampling

PEM:

Proton exchange membrane

NSGA-II:

Non-dominated sorting genetic algorithm

p :

Pressure (Pa)

p c :

Capillary pressure (Pa)

PEMFC:

Proton exchange membrane fuel cell

R :

Universal gas constant (J/(kg·mol))

R m :

Proton current source term

R s :

Electron current source term

r w :

Phase transition source term

SFC:

Straight flow channel

S m :

Mass source term

S M :

Momentum source term

S k :

Concentration source term

S Q :

Energy source term

SVM:

Support vector machine

s :

Liquid water volume fraction

TFC:

Trapezoidal flow channel

TFCB:

Trapezoidal flow channel with block

TOPSIS:

Technique order preference by similarity to an ideal solution

\(\overrightarrow{u}\) :

Velocity vector (m/s)

\({V}_{\text{cell}}\) :

Operating voltage (V)

\({V}_{oc}\) :

Open circuit voltage (V)

\(\phi\) :

Electric potential (V)

\(\lambda\) :

Water content

\(\rho\) :

Density (kg/m3)

\(\mu\) :

Dynamic viscosity (Pa·s)

\(\alpha\) :

Transfer coefficient

\(\varepsilon\) :

Porosity

\(\nabla\) :

Hamiltonian operator

\(\theta\) :

Contact angle (◦)

\(\zeta\) :

Specific active surface area (1/m)

\(\eta\) :

Overpotential (V)

\(\sigma\) :

Electronic conductivity \(\left(1/\left(\Omega \cdot {\text{m}}\right)\right)\)

\({\sigma }_{t}\) :

Surface tension (N/m)

\(\chi\) :

Molar fraction

\(\gamma\) :

Concentration dependence

an :

Anode

cat :

Cathode

l :

Liquid water

m :

Membrane phase

ref :

Reference

s :

Solid phase

sat :

Saturation

wv :

Water vapor

References

  1. Ramirez D, Beites LF, Blazquez F, Ballesteros JC (2008) Distributed generation system with PEM fuel cell for electrical power quality improvement. Int J Hydrogen Energy 33:4433–4443. https://doi.org/10.1016/j.ijhydene.2008.06.002

    Article  CAS  Google Scholar 

  2. Z. Zhou, D. Qiu, S. Zhai, L. Peng, X. Lai. (2020) Investigation of the assembly for high-power proton exchange membrane fuel cell stacks through an efficient equivalent model. Applied Energy. 277. https://doi.org/10.1016/j.apenergy.2020.115532

  3. Perng S-W, Wu H-W, Wang R-H (2014) Effect of modified flow field on non-isothermal transport characteristics and cell performance of a PEMFC. Energy Convers Manage 80:87–96. https://doi.org/10.1016/j.enconman.2013.12.044

    Article  CAS  Google Scholar 

  4. Raj A, Shamim T (2014) Investigation of the effect of multidimensionality in PEM fuel cells. Energy Convers Manage 86:443–452. https://doi.org/10.1016/j.enconman.2014.04.088

    Article  Google Scholar 

  5. An Z, Jian B, Du X, Lei C, Yao M, Zhang D (2023) Study on performance optimization of proton exchange membrane fuel cell with porous ridge flow channel. Ionics 29:4099–4113. https://doi.org/10.1007/s11581-023-05151-3

    Article  CAS  Google Scholar 

  6. Zhang Z, Fan X, Lu W, Yao J, Sui Z (2023) Investigation on the effect of transverse distribution obstacles on PEMFC performance. Ionics 29:4125–4145. https://doi.org/10.1007/s11581-023-05101-z

    Article  CAS  Google Scholar 

  7. Li XG, Sabir M (2005) Review of bipolar plates in PEM fuel cells: flow-field designs. Int J Hydrogen Energy 30:359–371. https://doi.org/10.1016/j.ijhydene.2004.09.019

    Article  CAS  Google Scholar 

  8. S. Zhang H. Xu Z. Qu S. Liu F.K. Talkhoncheh. (2022) Bio-inspired flow channel designs for proton exchange membrane fuel cells: a review. J Power Sources. 522. https://doi.org/10.1016/j.jpowsour.2022.231003

  9. Wang X, Zhao Y, Guo S, Lin F, Pan C (2023) Mass transfer analysis of improved serpentine flow field in fuel cells considering spatial traversal. Ionics. https://doi.org/10.1007/s11581-023-05308-0

    Article  PubMed  PubMed Central  Google Scholar 

  10. Marappan M, Palaniswamy K, Velumani T, Chul KB, Velayutham R, Shivakumar P et al (2021) Performance studies of proton exchange membrane fuel cells with different flow field designs - review. Chem Rec 21:663–714. https://doi.org/10.1002/tcr.202000138

    Article  CAS  PubMed  Google Scholar 

  11. Guo S, Zhao Y, Pan C, Wang X, Xu T (2023) Effect of structure parameters on internal mass transfer and performance of PEMFC with spider-web flow field using multi-physical simulation. Int J Hydrogen Energy 48:36937–36945. https://doi.org/10.1016/j.ijhydene.2023.06.133

    Article  CAS  Google Scholar 

  12. Xu C, Wang H, Cheng T (2023) Study on the net power density improvement of staggered trapezoidal baffle flow channel for PEMFC. Ionics 29:4775–4785. https://doi.org/10.1007/s11581-023-05198-2

    Article  CAS  Google Scholar 

  13. Wilberforce T, El Hassan Z, Ogungbemi E, Ijaodola O, Khatib FN, Durrant A et al (2019) A comprehensive study of the effect of bipolar plate (BP) geometry design on the performance of proton exchange membrane (PEM) fuel cells. Renew Sustain Energy Rev 111:236–260. https://doi.org/10.1016/j.rser.2019.04.081

    Article  CAS  Google Scholar 

  14. Fan L, Zhang G, Jiao K (2017) Characteristics of PEMFC operating at high current density with low external humidification. Energy Convers Manage 150:763–774. https://doi.org/10.1016/j.enconman.2017.08.034

    Article  CAS  Google Scholar 

  15. Owejan JP, Gagliardo JJ, Sergi JM, Kandlikar SG, Trabold TA (2009) Water management studies in PEM fuel cells, Part I: Fuel cell design and in situ water distributions. Int J Hydrogen Energy 34:3436–3444. https://doi.org/10.1016/j.ijhydene.2008.12.100

    Article  CAS  Google Scholar 

  16. K.-Q. Zhu, Q. Ding, B.-X. Zhang, J.-H. Xu, D.-D. Li, Y.-R. Yang, et al. (2024) Performance enhancement of air-cooled PEMFC stack by employing tapered oblique fin channels: experimental study of a full stack and numerical analysis of a typical single cell. Applied Energy. 358 122595. https://doi.org/10.1016/j.apenergy.2023.122595

  17. H. Ashrafi, N. Pourmahmoud, I. Mirzaee, N. Ahmadi. (2022) Introducing a new serpentine configuration of gas channels to enhance the performance and reduce the water flooding in the PEMFC. IRANIAN JOURNAL OF CHEMISTRY & CHEMICAL ENGINEERING-INTERNATIONAL ENGLISH EDITION. https://doi.org/10.30492/IJCCE.2022.546616.5111

  18. Akbari MH, Rismanchi B (2008) Numerical investigation of flow field configuration and contact resistance for PEM fuel cell performance. Renew Energy 33:1775–83. https://doi.org/10.1016/j.renene.2007.10.009

    Article  CAS  Google Scholar 

  19. Chowdhury MZ, Genc O, Toros S (2018) Numerical optimization of channel to land width ratio for PEM fuel cell. Int J Hydrogen Energy 43:10798–809. https://doi.org/10.1016/j.ijhydene.2017.12.149

    Article  CAS  Google Scholar 

  20. H. Samanipour, N. Ahmadi, I. Mirzaee, M. Abbasalizadeh. (2019) The study of cylindrical polymer fuel cell’s performance and the investigation of gradual geometry changes’ effect on its performance. Periodica Polytechnica Chemical Engineering. 63. https://doi.org/10.3311/PPch.12793

  21. F. Zhao, Y. Zhao, X. Zhao, Y. Jia, Q. Huang, C. Zhang, et al. (2023) Numerical study on the influence of variable section-enhanced mass transfer flow field design on PEMFC performance based on underrib convection flow. International Journal of Energy Research. 2023. https://doi.org/10.1155/2023/5327387

  22. E. Fontana, E. Mancusi, A. da Silva, V.C. Mariani, A.A. Ulson de Souza, S.M.A. (2011) Guelli Ulson de Souza. Study of the effects of flow channel with non-uniform cross-sectional area on PEMFC species and heat transfer. International Journal of Heat and Mass Transfer. 54 4462–72. https://doi.org/10.1016/j.ijheatmasstransfer.2011.06.037

  23. Ahmed DH, Sung HJ (2006) Effects of channel geometrical configuration and shoulder width on PEMFC performance at high current density. J Power Sources 162:327–339. https://doi.org/10.1016/j.jpowsour.2006.06.083

    Article  CAS  Google Scholar 

  24. Freire LS, Antolini E, Linardi M, Santiago EI, Passos RR (2014) Influence of operational parameters on the performance of PEMFCs with serpentine flow field channels having different (rectangular and trapezoidal) cross-section shape. Int J Hydrogen Energy 39:12052–60. https://doi.org/10.1016/j.ijhydene.2014.06.041

    Article  CAS  Google Scholar 

  25. Liu HC, Yan WM, Soong CY, Chen FL (2005) Effects of baffle-blocked flow channel on reactant transport and cell performance of a proton exchange membrane fuel cell. J Power Sources 142:125–133. https://doi.org/10.1016/j.jpowsour.2004.09.037

    Article  CAS  Google Scholar 

  26. Y. Cai, D. Wu, J. Sun, B. Chen. (2021) The effect of cathode channel blockages on the enhanced mass transfer and performance of PEMFC. Energy. 222 119951. https://doi.org/10.1016/j.energy.2021.119951

  27. Chen H, Guo H, Ye F, Ma CF (2021) A numerical study of baffle height and location effects on mass transfer of proton exchange membrane fuel cells with orientated-type flow channels. Int J Hydrogen Energy 46(10):7528–7545. https://doi.org/10.1016/j.ijhydene.2020.11.226

  28. Bilgili M, Bosomoiu M, Tsotridis G (2015) Gas flow field with obstacles for PEM fuel cells at different operating conditions. Int J Hydrogen Energy 40:2303–11. https://doi.org/10.1016/j.ijhydene.2014.11.139

    Article  CAS  Google Scholar 

  29. Heidary H, Kermani MJ, Dabir B (2016) Influences of bipolar plate channel blockages on PEM fuel cell performances. Energy Convers Manage 124:51–60. https://doi.org/10.1016/j.enconman.2016.06.043

    Article  CAS  Google Scholar 

  30. Hu H, Xu X, Mei N, Li C (2021) Numerical analysis of wave-shaped flow field plate for proton-exchange membrane fuel cell. Int J Energy Res 45:6689–6697. https://doi.org/10.1002/er.6261

    Article  CAS  Google Scholar 

  31. Guo H, Chen H, Ye F, Ma CF (2019) Baffle shape effects on mass transfer and power loss of proton exchange membrane fuel cells with different baffled flow channels. Int J Energy Res 43:2737–2755. https://doi.org/10.1002/er.4328

    Article  CAS  Google Scholar 

  32. H.-W. Li, J.-N. Liu, Y. Yang, W. Fan, G.-L. Lu. (2022) Research on mass transport characteristics and net power performance under different flow channel streamlined imitated water-drop block arrangements for proton exchange membrane fuel cell. Energy. 251. https://doi.org/10.1016/j.energy.2022.123983

  33. Z. Wan, W. Quan, C. Yang, H. Yan, X. Chen, T. Huang, et al. (2020) 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. 205. https://doi.org/10.1016/j.enconman.2019.112386

  34. C. Yang, Z. Wan, X. Chen, X. Kong, J. Zhang, T. Huang, et al. (2021) Geometry optimization of a novel M-like flow field in a proton exchange membrane fuel cell. Energy Conversion and Management. 228. https://doi.org/10.1016/j.enconman.2020.113651

  35. G. Cai, Y. Liang, Z. Liu, W. Liu. (2020) Design and optimization of bio-inspired wave-like channel for a PEM fuel cell applying genetic algorithm. Energy. 192. https://doi.org/10.1016/j.energy.2019.116670

  36. Li W-Z, Yang W-W, Wang N, Jiao Y-H, Yang Y, Qu Z-G (2020) Optimization of blocked channel design for a proton exchange membrane fuel cell by coupled genetic algorithm and three-dimensional CFD modeling. Int J Hydrogen Energy 45:17759–17770. https://doi.org/10.1016/j.ijhydene.2020.04.166

    Article  CAS  Google Scholar 

  37. M. Ghasabehi, M. Shams, H. Kanani. (2021) Multi-objective optimization of operating conditions of an enhanced parallel flow field proton exchange membrane fuel cell. Energy Conversion and Management. 230. https://doi.org/10.1016/j.enconman.2020.113798

  38. M. Ghasabehi, A. Jabbary, M. Shams. (2022) Cathode side transport phenomena investigation and multi-objective optimization of a tapered parallel flow field PEMFC. Energy Conversion and Management. 265. https://doi.org/10.1016/j.enconman.2022.115761

  39. M.A. Sadeghi, Z.A. Khan, M. Agnaou, L. Hu, S. Litster, A. Kongkanand, et al. (2024) Predicting PEMFC performance from a volumetric image of catalyst layer structure using pore network modeling. Applied Energy. 353 122004. https://doi.org/10.1016/j.apenergy.2023.122004

  40. B. Wang, B. Xie, J. Xuan, K. Jiao. (2020) AI-based optimization of PEM fuel cell catalyst layers for maximum power density via data-driven surrogate modeling. Energy Conversion and Management. 205. https://doi.org/10.1016/j.enconman.2019.112460

  41. G. Xu, Z. Yu, L. Xia, C. Wang, S. Ji. (2022) Performance improvement of solid oxide fuel cells by combining three-dimensional CFD modeling, artificial neural network and genetic algorithm. Energy Conversion and Management. 268 116026. https://doi.org/10.1016/j.enconman.2022.116026

  42. Guo Q, Zheng J, Qin Y (2022) Optimization of block structure parameters of PEMFC novel block channels using artificial neural network. Int J Hydrogen Energy 47:38386–94. https://doi.org/10.1016/j.ijhydene.2022.09.017

    Article  CAS  Google Scholar 

  43. Seyhan M, Akansu YE, Murat M, Korkmaz Y, Akansu SO (2017) Performance prediction of PEM fuel cell with wavy serpentine flow channel by using artificial neural network. Int J Hydrogen Energy 42:25619–29. https://doi.org/10.1016/j.ijhydene.2017.04.001

    Article  CAS  Google Scholar 

  44. Nam JH, Kaviany M (2003) Effective diffusivity and water-saturation distribution in single- and two-layer PEMFC diffusion medium. Int J Heat and Mass Transfer 46:4595–611. https://doi.org/10.1016/S0017-9310(03)00305-3

    Article  CAS  Google Scholar 

  45. Springer TE, Zawodzinski TA, Gottesfeld S (1991) Polymer electrolyte fuel-cell model. J Electrochem Soc 138:2334–2342. https://doi.org/10.1149/1.2085971

    Article  CAS  Google Scholar 

  46. Yu Z, Xia L, Xu G, Wang C, Wang D (2022) Improvement of the three-dimensional fine-mesh flow field of proton exchange membrane fuel cell (PEMFC) using CFD modeling, artificial neural network and genetic algorithm. Int J Hydrogen Energy 47:35038–35054. https://doi.org/10.1016/j.ijhydene.2022.08.077

    Article  CAS  Google Scholar 

  47. L. Xia, Z. Yu, G. Xu, S. Ji, B. (2021) Sun. Design and optimization of a novel composite bionic flow field structure using three-dimensional multiphase computational fluid dynamic method for proton exchange membrane fuel cell. Energy Conversion and Management. 247. https://doi.org/10.1016/j.enconman.2021.114707

  48. Wang L, Husar A, Zhou TH, Liu HT (2003) A parametric study of PEM fuel cell performances. Int J Hydrogen Energy 28:1263–1272. https://doi.org/10.1016/s0360-3199(02)00284-7

    Article  CAS  Google Scholar 

  49. S. Maharudrayya, S. Jayanti, A.P. Deshpande. Pressure drop and flow distribution in multiple parallel-channel configurations used in proton-exchange membrane fuel cell stacks. Journal of Power Sources. 157 (2006) 358-67. https://doi.org/10.1016/j.jpowsour.2005.07.064

  50. E. Bulut, E.I. Albak, G. Sevilgen, F. Ozturk. (2021) A new approach for battery thermal management system design based on grey relational analysis and Latin hypercube sampling. Case Studies in Thermal Engineering. 28. https://doi.org/10.1016/j.csite.2021.101452

  51. S.K. Sarangi, D.P. Mishra, H. Ramachandran, N. Anand, V. Masih, L.S. Brar. (2021) Analysis and optimization of the curved trapezoidal winglet geometry in a compact heat exchanger. Applied Thermal Engineering. 182. https://doi.org/10.1016/j.applthermaleng.2020.116088

  52. G. Xu, Z. Yu, L. Xia, C. Wang, S. Ji. (2022) Performance improvement of solid oxide fuel cells by combining three-dimensional CFD modeling, artificial neural network and genetic algorithm. Energy Conversion and Management. 268. https://doi.org/10.1016/j.enconman.2022.116026

  53. F.S. Nanadegani, E.N. Lay, A. Iranzo, J.A. Salva, B. Sunden. (2020) On neural network modeling to maximize the power output of PEMFCs. Electrochimica Acta. 348 136345. https://doi.org/10.1016/j.electacta.2020.136345

  54. H. Li, B. Xu, G. Lu, C. Du, N. (2021) Huang. Multi-objective optimization of PEM fuel cell by coupled significant variables recognition, surrogate models and a multi-objective genetic algorithm. Energy Conversion and Management. 236 114063. https://doi.org/10.1016/j.enconman.2021.114063

  55. H. Li, B. Xu, G. Lu, C. Du, N. (2021) Huang. Multi-objective optimization of PEM fuel cell by coupled significant variables recognition, surrogate models and a multi-objective genetic algorithm. Energy Conversion and Management. 236. https://doi.org/10.1016/j.enconman.2021.114063

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Funding

This work was supported by the National Natural Science Foundation of China (No. 62192753).

National Natural Science Foundation of China,62192753

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Authors and Affiliations

  1. School of Energy and Power Engineering, Shandong University, Jinan, 250061, People’s Republic of China

    Changjiang Wang, Zeting Yu & Haonan Wu

  2. School of Electrical Engineering, Shandong University, Jinan, 250061, People’s Republic of China

    Daohan Wang

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  1. Changjiang Wang
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Contributions

Changjiang Wang: methodology, software, data curation, validation, writing—original draft. Zeting Yu: funding acquisition, project administration, writing—review and editing. Haonan Wu: writing—review and editing. Daohan Wang: writing—review and editing.

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Correspondence to Zeting Yu.

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Wang, C., Yu, Z., Wu, H. et al. Optimization design of trapezoidal flow field proton exchange membrane fuel cell combined with computational fluid dynamics, surrogate model, and multi-objective optimization algorithm. Ionics (2024). https://doi.org/10.1007/s11581-024-05494-5

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