# Optimizing Structural Parameters of PEMFC Based on Taguchi Method

^{*}

## Abstract

**:**

^{2}test is 0.915, and the F test is 53.508, indicating that the regression equation is significant and the optimal and worst structural parameter combinations are predicted. The current density reaches 14,190.18 $\mathrm{A}/{\mathrm{m}}^{2}$ under the optimal structure combination, which is 6.14% higher than the calibrated model. Single factor experiments are carried out on these three different structural parameters to verify the effectiveness of the Taguchi method, and the best combination of structural parameters is obtained.

## 1. Introduction

## 2. Constructing Simulation Model of PEMFC

#### 2.1. Mathematical Model of PEMFC

#### 2.1.1. Electrochemical Model

#### 2.1.2. Current Conservation Model

#### 2.2. Numerical Simulation Model of PEMFC

#### 2.2.1. Drawing Three-Dimensional Geometric Model

#### 2.2.2. Mesh Rendering

#### 2.2.3. Setting Physical Parameters

#### 2.3. Calibrating Model

## 3. Performance Analysis and Optimization of PEMFC

#### 3.1. Constructing Orthogonal Experiment Scheme

^{2}test is 0.915, indicating that there is a good linear correlation between the variables of the model and the current density. The F test is 53.508, which is much larger than the critical value F

_{0.01}(4,20) = 4.938. It shows that the regression result is significant, and the equation can be used to predict the current density as follows:

#### 3.2. Single Factor Simulation Experiment

## 4. Conclusions

^{2}, which is 6.14% higher than the calibration model.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

${\sigma}_{sol}$ | conductivity of the solid material | ${\varphi}_{sol}$ | potential of the solid material |

${R}_{sol}$ | volume current density of the solid material | ${M}_{w,{H}_{2}}$ | molecular weight of hydrogen |

${\sigma}_{mem}$ | conductivity in the catalytic layer and the membrane | ${M}_{w,{O}_{2}}$ | molecular weight of oxygen |

${\varphi}_{mem}$ | potential in the catalytic layer and the membrane | ${M}_{w,{H}_{2}O}$ | molecular weight of water |

${R}_{mem}$ | volume current density in the catalytic layer and membrane | ${a}_{an}^{an}$ | anode transfer coefficient of anode |

${R}_{an}$ | exchange current density of anode | ${a}_{cat}^{an}$ | cathodic transfer coefficient of anode |

${R}_{cat}$ | exchange current density of the cathode | ${a}_{an}^{cat}$ | anode transfer coefficient of cathode |

${j}_{an}\left(T\right)$ | reference exchange current density per active surface area of the anode | ${a}_{cat}^{cat}$ | cathodic transfer coefficient of cathode |

${j}_{cat}\left(T\right)$ | reference exchange current density per active surface area of the cathode | $F$ | Faraday constant |

${\zeta}_{an}$ | anode side specific effective surface area | $R$ | universal gas constant |

${\zeta}_{cat}$ | cathode side specific effective surface area | $T$ | temperature |

$\left[A\right]$ | local species concentration on the anode side | ${E}_{an}$ | anode activation energy |

$\left[C\right]$ | local species concentration on the cathode side | ${E}_{cat}$ | cathode activation energy |

${\left[A\right]}_{ref}$ | reference local species concentration on the anode side | ${j}_{an}^{ref}$ | reference exchange current density at the anode reference temperature |

${\left[C\right]}_{ref}$ | reference local species concentration on the cathode side | ${j}_{cat}^{ref}$ | reference exchange current density at the cathode reference temperature |

${T}_{an}^{ref}$ | anode reference temperature | $\epsilon $ | porosity |

${\gamma}_{an}$ | anode side concentration correlation coefficient | ${\gamma}_{cat}$ | cathode side concentration correlation coefficient |

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**Figure 2.**Mesh division of PEMFC. (

**a**) Mesh of overall structure; (

**b**) Mesh of catalytic layer and membrane.

**Figure 4.**Simulation results of PEMFC model after calibration. (

**a**) The current density distribution on the cathode side of the membrane; (

**b**) The water content distribution on the cathode side of the membrane.

**Figure 6.**Regression and simulation results of the best combination and the worst combination of factors and levels.

**Figure 7.**The influence of factors’ different levels on the current density. (

**a**) The influence of different anode wave channel distortion on current density; (

**b**) the influence of different gas diffusion layer thickness on current density; (

**c**) the influence of different porosity on current density.

Geometric Parameter | Value | Unit |
---|---|---|

Battery model length/width | 270/5.32 | mm |

Section parameters of anode and cathode flow channel upper bottom/lower bottom/height | 1.02/1.24/0.4 | mm |

Cross-section parameters of cathode and anode cooling channel upper bottom/lower bottom/high | 2.3/2.44/0.277 | mm |

Gas diffusion layer thickness of anode and cathode | 0.2 | mm |

Anode and cathode plate height | 1.5 | mm |

Thickness of Cathode and Anode Catalytic Layer | 0.01 | mm |

Membrane thickness | 0.03 | mm |

The distortion of the wave channel | 30 |

Parameter | Value | Unit |
---|---|---|

Reference exchange current density of anode and cathode | 0.5/10,000 | $\left({\mathrm{A}/\mathrm{m}}^{2}\right)$ |

Reference concentration of anode and cathode | 0.00339/0.0564 | $\left({\mathrm{kmol}/\mathrm{m}}^{3}\right)$ |

Correlation coefficient of anode and cathode material concentration | 1/1 | |

Transfer coefficient of anode and cathode of anode electrode | 0.5/0.5 | |

The cathode and anode transfer coefficient of cathode electrode | 1.3; 1.3 | |

Open circuit voltage | 1.06 | $\left(\mathrm{V}\right)$ |

Porosity of diffusion layer | 0.5 | |

Absolute permeability of diffusion layer | 3 × 10^{−12} | $\left({\mathrm{m}}^{2}\right)$ |

Contact angle of diffusion layer | 150 | $\left(\xb0\right)$ |

Porosity of catalytic layer | 0.2 | |

Absolute permeability of catalytic layer | 3 × 10^{−12} | $\left({\mathrm{m}}^{2}\right)$ |

Contact angle of catalytic layer | 110 | $\left(\xb0\right)$ |

Working pressure | 11,325 | $\left(\mathrm{Pa}\right)$ |

Pressure of outlet | 0 | $\left(\mathrm{Pa}\right)$ |

Relative inlet humidity of cathode and anode | 100% | |

Working temperature | 353.15 | $\left(\mathrm{K}\right)$ |

Factor | Distortion of the Anode Wave Flow Channel | Thickness of the Gas Diffusion Layer | Porosity of the Gas Diffusion Layer |
---|---|---|---|

A | $\mathbf{B}/\mathbf{m}\mathbf{m}$ | C | |

Level 1 | 20 | 0.2 | 0.6 |

Level 2 | 25 | 0.3 | 0.65 |

Level 3 | 30 | 0.4 | 0.7 |

Level 4 | 35 | 0.5 | 0.75 |

Level 5 | 40 | 0.6 | 0.8 |

Case | Variable Factors and Calculation Results of Each Level Grouping | |||
---|---|---|---|---|

A | $\mathbf{B}/\mathbf{m}\mathbf{m}$ | C | $\mathbf{Current}\text{}\mathbf{Density}/\mathbf{A}/{\mathbf{m}}^{2}$ | |

Case 1 | 20 | 0.2 | 0.6 | 13,476.8 |

Case 2 | 20 | 0.3 | 0.65 | 13,944.893 |

Case 3 | 20 | 0.4 | 0.7 | 14,011.894 |

Case 4 | 20 | 0.5 | 0.75 | 13,733.151 |

Case 5 | 20 | 0.6 | 0.8 | 13,674.246 |

Case 6 | 25 | 0.2 | 0.65 | 13,575.083 |

Case 7 | 25 | 0.3 | 0.7 | 14,022.033 |

Case 8 | 25 | 0.4 | 0.75 | 14,087.25 |

Case 9 | 25 | 0.5 | 0.8 | 13,967.192 |

Case 10 | 25 | 0.6 | 0.6 | 13,471.345 |

Case 11 | 30 | 0.2 | 0.7 | 13,656.63 |

Case 12 | 30 | 0.3 | 0.75 | 14,083.23 |

Case 13 | 30 | 0.4 | 0.8 | 14,130.283 |

Case 14 | 30 | 0.5 | 0.6 | 13,754.372 |

Case 15 | 30 | 0.6 | 0.65 | 13,533.67 |

Case 16 | 35 | 0.2 | 0.75 | 13,828.567 |

Case 17 | 35 | 0.3 | 0.8 | 14,160.018 |

Case 18 | 35 | 0.4 | 0.6 | 13,934.971 |

Case 19 | 35 | 0.5 | 0.65 | 13,833.591 |

Case 20 | 35 | 0.6 | 0.7 | 13,722.57 |

Case 21 | 40 | 0.2 | 0.8 | 13,854.175 |

Case 22 | 40 | 0.3 | 0.6 | 13,978.937 |

Case 23 | 40 | 0.4 | 0.65 | 14,036.42 |

Case 24 | 40 | 0.5 | 0.7 | 13,919.343 |

Case 25 | 40 | 0.6 | 0.75 | 13,688.054 |

Level | A | B | C | |
---|---|---|---|---|

Average signal-to-noise ratio | 1 | 82.77 | 82.72 | 82.75 |

2 | 82.81 | 82.95 | 82.79 | |

3 | 82.81 | 82.95 | 82.84 | |

4 | 82.86 | 82.82 | 82.85 | |

5 | 82.86 | 82.68 | 82.89 | |

Range of signal-to-noise ratio | 0.09 | 0.27 | 0.14 | |

Contribution rate | 18% | 54% | 28% |

$\mathit{R}$ | ${\mathit{R}}^{2}$ | $\mathit{F}$ | Sig |
---|---|---|---|

0.956 | 0.915 | 53.508 | $2.1077\times {10}^{-10}$ |

Model | Coefficient | t | Sig |

constant | 11,613.26 | 63.0256 | 0.000 |

A | 6.51 | 3.4911 | 0.002 |

B | 7495.86 | 11.7542 | 0.000 |

C | 1134.23 | 6.0781 | 0.000 |

BB | −9765.88 | −12.3843 | 0.000 |

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## Share and Cite

**MDPI and ACS Style**

Yan, W.; Wang, J.; Li, J.; Wang, G.
Optimizing Structural Parameters of PEMFC Based on Taguchi Method. *World Electr. Veh. J.* **2023**, *14*, 76.
https://doi.org/10.3390/wevj14030076

**AMA Style**

Yan W, Wang J, Li J, Wang G.
Optimizing Structural Parameters of PEMFC Based on Taguchi Method. *World Electric Vehicle Journal*. 2023; 14(3):76.
https://doi.org/10.3390/wevj14030076

**Chicago/Turabian Style**

Yan, Wei, Jichuan Wang, Jiaqi Li, and Guihua Wang.
2023. "Optimizing Structural Parameters of PEMFC Based on Taguchi Method" *World Electric Vehicle Journal* 14, no. 3: 76.
https://doi.org/10.3390/wevj14030076