# Collaborative Design for Uneven Physical Structures of Multi-Layers in PEMFC

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Model Description

#### 2.1. Numerical Simulation Model

#### 2.2. Governing Equations

- (1)
- The fuel cell operates under steady-state conditions.
- (2)
- The reactant gases introduced are all incompressible ideal gases.
- (3)
- The fuel cell works at a constant temperature.
- (4)
- The gas diffusion layer, catalyst layer and membrane are all isotropic porous media materials.
- (5)
- The fluid flow is laminar.

- (1)
- Mass conservation equation:$$\frac{\partial \rho}{\partial t}+\nabla \cdot \left(\rho \upsilon \right)=0$$
- (2)
- Momentum conservation equation:$$\frac{\partial \left(\rho \upsilon \right)}{\partial t}+\nabla \left(\rho \upsilon \upsilon \right)=-\nabla p+\nabla \left({\mu}^{eff}\nabla \upsilon \right)+{S}_{m}$$
^{eff}is the average viscosity of the mixture, and S_{m}is the momentum source term. For different regions of the fuel cell, the momentum source term is different.For the gas flow channel:$${S}_{m}=0$$For the gap between the support layer and the catalyst layer:$${S}_{m}=-\frac{\mu}{K}\epsilon \upsilon $$For water transport in the polymer phase, an additional momentum source term is electrokinetic permeability:$${S}_{m}=-\frac{\mu}{{K}_{p}}{\epsilon}_{m}{x}_{m}\upsilon +\frac{{K}_{\mathsf{\Phi}}}{{K}_{P}}{c}_{f}{n}_{f}F\nabla {\varphi}_{m}$$_{m}is the water porosity of the membrane, x_{m}is the volume fraction of ionomer in the catalyst layer, K_{f}is the electrokinetic permeability, K_{p}is the hydraulic permeability of the membrane, c_{f}is the fixed charge concentration, n_{f}is the number of sulfonic acid ion charges, F is the Faraday constant and Φ_{m}is the ionomer phase potential. - (3)
- Energy conservation equation:The energy conservation in any area of PEMFC can be described as:$${\left(\rho {c}_{p}\right)}_{eff}\frac{\partial T}{\partial t}+{\left(\rho {c}_{p}\right)}_{eff}\left(\upsilon \nabla T\right)=\nabla \left({k}_{eff}\nabla T\right)+{S}_{e}$$
_{p}is the average specific heat capacity of the mixture, T is the temperature, k is the thermal conductivity, S_{e}is the energy source term, and the subscript eff represents the effectiveness of the porous medium.$${\left(\rho {c}_{p}\right)}_{eff}=\left(1-\epsilon \right){\rho}_{s}{c}_{p,s}+\epsilon \rho {c}_{p}$$$${k}_{eff}=-2{k}_{s}+{\left[\frac{\epsilon}{2{k}_{s}+k}+\frac{1-\epsilon}{3{k}_{s}}\right]}^{-1}$$_{s}, c_{p,s}, and k_{s}respectively represent the temperature, specific heat capacity and thermal conductivity of the solid mixture.The energy source term in the energy conservation equation includes the heat generated by the reaction, resistance heating and (or) the heat generated by evaporation or condensation in the phase change. - (4)
- Constituent conservation equation:$$\frac{\partial \left(\epsilon \rho {x}_{i}\right)}{\partial t}+\nabla \left(\upsilon \epsilon \rho {x}_{i}\right)=\nabla \left(\rho {D}_{i}^{eff}\nabla {x}_{i}\right)+{S}_{s,i}$$
_{i}is the mass fraction of the gas component, and S_{s,i}is the component source or sink. In porous media, D_{i,eff}is a function of the porosity ε and tortuosity τ.$${D}_{i,eff}={D}_{i}{\epsilon}^{\tau}$$_{i}is the free flow mass diffusion coefficient.The source term S_{s,i}in the component conservation equation is all 0, except in the catalyst layer where the components are consumed or produced by the electrochemical reaction. In the catalyst layer, the source terms S_{s,i}of hydrogen, oxygen, water vapor, and liquid water are:$${S}_{s,{H}_{2}}=-{j}_{a}\frac{{M}_{{H}_{2}}}{2F}$$$${S}_{s,{O}_{2}}=-{j}_{c}\frac{{M}_{{O}_{2}}}{4F}$$$${S}_{s,{H}_{2}O\left(g\right)}=\sigma {A}_{fg}\left({x}_{sat}-{x}_{{H}_{2}O\left(g\right)}\right)$$$${S}_{s,{H}_{2}O\left(l\right)}=+{j}_{c}\frac{{M}_{{H}_{2}O}}{2F}-\sigma {A}_{fg}\left({x}_{sat}-{x}_{{H}_{2}O\left(g\right)}\right)$$In the water source term, it is assumed that water is produced in liquid form and will evaporate when the adjacent air or oxygen is not saturated. - (5)
- Charge conservation equation:The current transfer can be described by the governing equation of the conservation of charge; for the current, it is:$$\nabla \cdot \left({\kappa}_{s}^{eff}\nabla {\varphi}_{s}\right)={S}_{\varphi s}$$For the ion current, it is:$$\nabla \cdot \left({\kappa}_{m}^{eff}\nabla {\varphi}_{m}\right)={S}_{\varphi m}$$
_{s}is the solid phase potential, ϕ_{m}is the electrolytic liquid phase potential, and S_{ϕ}is the source term that refers to the transfer current. In the anode catalyst layer S_{ϕs}= −j_{a}and S_{ϕm}= −j_{a}, in the cathode catalyst layer S_{ϕs}= j_{c}and S_{ϕm}= −j_{c}, and for the rest S_{ϕ}= 0.

## 3. Results and Discussion

#### 3.1. Effects of Uneven Design of Different Layers

_{2}concentration distribution in the diffusion layer in Table 5, it can be seen that the hydrogen concentration distribution of the model 2 is more uniform, which is more conducive to the penetration of hydrogen into the catalyst layer in order for it to participate in the reaction.

#### 3.2. Collaborative Design of Multilayers in PEMFC

^{2}), while the original model is 18,751.09 (A/m

^{2}). The optimized structure could reasonably adjust the concentration distribution of the reaction gas by integrating with the pressure drop distribution inside the flow channel. The setting of the uneven porosity increases the utilization rate of the membrane electrode and further improves the fuel cell performance.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Cai, Y.; Fang, Z.; Chen, B.; Yang, T.; Tu, Z. Numerical study on a novel 3D cathode flow field and evaluation criteria for the PEM fuel cell design. Energy
**2018**, 161, 28–37. [Google Scholar] [CrossRef] - Kanchan, B.K.; Randive, P.; Pati, S. Numerical investigation of multi-layered porosity in the gas diffusion layer on the performance of a PEM fuel cell. Int. J. Hydrog. Energy
**2020**, 45, 21836–21847. [Google Scholar] [CrossRef] - Manso, A.P.; Marzo, F.F.; Mujika, M.G.; Barranco, J.; Lorenzo, A. Numerical analysis of the influence of the channel cross-section aspect ratio on the performance of a PEM fuel cell with serpentine flow field design. Int. J. Hydrog. Energy
**2011**, 36, 6795–6808. [Google Scholar] [CrossRef] - Shimpalee, S.; Van Zee, J.W. Numerical studies on rib & channel dimension of flow-field on PEMFC performance. Int. J. Hydrog. Energy
**2007**, 32, 842–856. [Google Scholar] - Park, Y.C.; Chippar, P.; Kim, S.K.; Lim, S.; Jung, D.H.; Ju, H.; Peck, D.H. Effects of serpentine flow-field designs with different channel and rib widths on the performance of a direct methanol fuel cell. J. Power Source
**2012**, 205, 32–47. [Google Scholar] [CrossRef] - Zhou, P.; Wu, C.W. Numerical study on the compression effect of gas diffusion layer on PEMFC performance. J. Power Source
**2007**, 170, 93–100. [Google Scholar] [CrossRef] - Mahmoudi, A.H.; Ramiar, A.; Esmaili, Q. Effect of inhomogeneous compression of gas diffusion layer on the performance of PEMFC with interdigitated flow field. Energy Convers. Manag.
**2016**, 110, 78–89. [Google Scholar] [CrossRef] - Chi, P.H.; Chan, S.H.; Weng, F.B.; Su, A.; Sui, P.C.; Djilali, N. On the effects of non-uniform property distribution due to compression in the gas diffusion layer of a PEMFC. Int. J. Hydrog. Energy
**2010**, 35, 2936–2948. [Google Scholar] [CrossRef] - Shangguan, X.; Li, Y.; Qin, Y.; Cao, S.; Zhang, J.; Yin, Y. Effect of the porosity distribution on the liquid water transport in the gas diffusion layer of PEMFC. Electrochim. Acta
**2021**, 371, 137814. [Google Scholar] [CrossRef] - Rabissi, C.; Zago, M.; Gazdzicki, P.; Guétaz, L.; Escribano, S.; Grahl-Madsen, L.; Casalegno, A. A locally resolved investigation on direct methanol fuel cell uneven components fading: Local cathode catalyst layer tuning for homogeneous operation and reduced degradation rate. J. Power Source
**2018**, 404, 135–148. [Google Scholar] [CrossRef] [Green Version] - Jiang, J.; Li, Y.; Liang, J.; Yang, W.; Li, X. Modeling of high-efficient direct methanol fuel cells with order-structured catalyst layer. Appl. Energy
**2019**, 252, 113431. [Google Scholar] [CrossRef] - Havaej, P.; Kermani, M.J.; Abdollahzadeh, M.; Heidary, H.; Moradi, A. A numerical modeling study on the influence of catalyst loading distribution on the performance of Polymer Electrolyte Membrane Fuel Cell. Int. J. Hydrog. Energy
**2018**, 43, 10031–10047. [Google Scholar] [CrossRef] - Ebrahimi, S.; Roshandel, R.; Vijayaraghavan, K. Power density optimization of PEMFC cathode with non-uniform catalyst layer by Simplex method and numerical simulation. Int. J. Hydrog. Energy
**2016**, 41, 22260–22273. [Google Scholar] [CrossRef] - Ebrahimi, S.; Ghorbani, B.; Vijayaraghavan, K. Optimization of catalyst distribution along PEMFC channel through a numerical two-phase model and genetic algorithm. Renew. Energy
**2017**, 113, 846–854. [Google Scholar] [CrossRef] - Zheng, Z.; Yang, F.; Lin, C.; Zhu, F.; Shen, S.; Wei, G.; Zhang, J. Design of gradient cathode catalyst layer (CCL) structure for mitigating Pt degradation in proton exchange membrane fuel cells (PEMFCs) using mathematical method. J. Power Source
**2020**, 451, 227729. [Google Scholar] [CrossRef] - Yin, K.M.; Cheng, B.S.; Chiang, K.W. Non-uniform agglomerate cathode catalyst layer model on the performance of PEMFC with consideration of water effect. Renew. Energy
**2016**, 95, 191–201. [Google Scholar] [CrossRef] - Soler, J.; Hontanon, E.; Daza, L. Electrode permeability and flow-field configuration: Influence on the performance of a PEMFC. J. Power Source
**2003**, 118, 172–178. [Google Scholar] [CrossRef]

Parameters | Value |
---|---|

Channel width | 1 mm |

Channel height | 1 mm |

Rib width | 1 mm |

GDL thickness | 0.2 mm |

Catalyst layer thickness | 0.026 mm |

Membrane thickness | 0.05 mm |

Parameters | Value | Parameters | Value |
---|---|---|---|

Operating temperature | 353 K | Operating pressure | 1 atm |

Anode stoichiometric flow rate | 1.5 | Cathode stoichiometric flow rate | 2 |

Anode relative humidity | 30% | Cathode relative humidity | 30% |

GDL porosity | 0.5 | CL porosity | 0.5 |

Anode concentration exponent | 0.5 | Cathode concentration exponent | 1 |

Anode exchange coefficient | 2 | Cathode exchange coefficient | 2 |

Rib Width | Anode Gas Diffusion Layer | Cathode Gas Diffusion Layer | Anode Catalyst Layer | Cathode Catalyst Layer |
---|---|---|---|---|

- | - | - | - | - |

uneven (↑↓) | uneven (↑↓) | - | - | - |

uneven (↑↓) | - | uneven (↑↓) | - | - |

uneven (↑↓) | uneven (↑↓) | uneven (↑↓) | - | - |

uneven (↑↓) | - | - | uneven (↑↓) | - |

uneven (↑↓) | - | - | - | uneven (↑↓) |

uneven (↑↓) | - | - | uneven (↑↓) | uneven (↑↓) |

uneven (↑↓) | uneven (↑↓) | - | uneven (↑↓) | - |

uneven (↑↓) | - | uneven (↑↓) | - | uneven (↑↓) |

uneven (↑↓) | uneven (↑↓) | uneven (↑↓) | uneven (↑↓) | uneven (↑↓) |

Model | Rib Width /(mm) | Porosity (Anode GDL) | Porosity (Cathode GDL) | Porosity (Anode CL) | Porosity (Cathode CL) | Growth Rate |
---|---|---|---|---|---|---|

1 | 0.6 1 1.4 | 0.5 | 0.5 | 0.5 | 0.5 | −6.59% |

2 | 1.4 1 0.6 | 0.5 | 0.5 | 0.5 | 0.5 | 8.10% |

3 | 1 | 0.3 0.5 0.7 | 0.5 | 0.5 | 0.5 | −0.21% |

4 | 1 | 0.5 | 0.3 0.5 0.7 | 0.5 | 0.5 | 2.40% |

5 | 1 | 0.5 | 0.5 | 0.3 0.5 0.7 | 0.5 | −0.03% |

6 | 1 | 0.5 | 0.5 | 0.5 | 0.3 0.5 0.7 | 0.19% |

7 | 1 | 0.7 0.5 0.3 | 0.5 | 0.5 | 0.5 | 0.09% |

8 | 1 | 0.5 | 0.7 0.5 0.3 | 0.5 | 0.5 | −2.80% |

9 | 1 | 0.5 | 0.5 | 0.7 0.5 0.3 | 0.5 | 0.01% |

10 | 1 | 0.5 | 0.5 | 0.5 | 0.7 0.5 0.3 | −0.22% |

11 | 1 | 0.3 0.5 0.7 | 0.3 0.5 0.7 | 0.5 | 0.5 | 2.09% |

12 | 1 | 0.5 | 0.5 | 0.3 0.5 0.7 | 0.3 0.5 0.7 | 0.16% |

13 | 1 | 0.5 | 0.3 0.5 0.7 | 0.5 | 0.3 0.5 0.7 | 2.61% |

14 | 1 | 0.3 0.5 0.7 | 0.3 0.5 0.7 | 0.3 0.5 0.7 | 0.3 0.5 0.7 | 2.24% |

15 | 1.4 1 0.6 | 0.5 | 0.3 0.5 0.7 | 0.5 | 0.3 0.5 0.7 | 10.60% |

Regular Even Design Model | Model 1 | Model 2 | |
---|---|---|---|

Standard deviation | 0.00223376 | 0.00232341 | 0.00204100 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Yang, Q.; Chen, S.; Xiao, G.; Li, L.
Collaborative Design for Uneven Physical Structures of Multi-Layers in PEMFC. *World Electr. Veh. J.* **2021**, *12*, 148.
https://doi.org/10.3390/wevj12030148

**AMA Style**

Yang Q, Chen S, Xiao G, Li L.
Collaborative Design for Uneven Physical Structures of Multi-Layers in PEMFC. *World Electric Vehicle Journal*. 2021; 12(3):148.
https://doi.org/10.3390/wevj12030148

**Chicago/Turabian Style**

Yang, Qinwen, Shujun Chen, Gang Xiao, and Lexi Li.
2021. "Collaborative Design for Uneven Physical Structures of Multi-Layers in PEMFC" *World Electric Vehicle Journal* 12, no. 3: 148.
https://doi.org/10.3390/wevj12030148