# Numerical Investigation of Flow Channel Design and Tapered Slope Effects on PEM Fuel Cell Performance

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Model Description

#### 2.1. Mathematical Model

#### 2.2. Simulation Model

## 3. Results and Discussion

#### 3.1. Effects of Flow Channel Type

#### 3.2. Tapered Slope Effects of Flow Channel on PEM Fuel Cell Performance

#### 3.2.1. Different Tapered Slopes with the Same Inlet Depth

^{2}, respectively), it can be found that the current density of the cell with the largest flow channel tapered degree is increased by nearly 6.53%. Cases of 0.55 V are also chosen for further analysis in Figure 7.

#### 3.2.2. Different Inlet Depths with the Same Tapered Slope

^{2}). This can be also seen from Figure 9b, and it is obvious that the smallest channel depth makes the pressure in the flow channel significantly higher, which helps reactants diffuse to the CL easily and remove more reactant water. Further analysis is shown in Figure 10, and the voltage in all cases is 0.55 V.

#### 3.2.3. Different Flow Channel Widths with the Same Tapered Slope and Inlet Depth

^{2}, respectively). Figure 11b shows that a larger gas pressure drop can help reactant fuel easily diffuse to the CL and remove more reactant water. Cases of 0.55 V are also selected for further analysis in Figure 12.

## 4. Conclusions

- For the positive, negative, zero and hybrid tapered fuel cell flow channels, the positive tapered fuel cell flow channel is favorable for the high current density of a large fuel cell stack for automotive application, owing to high reactant gas diffusion with a large gas pressure drop and water removal capacity in the positive tapered flow channels.
- A certain positive tapered slope and a small depth of flow channel can amplify the advantageous effects of tapered flow channels. Their corresponding current densities are increased by a maximum of 6.53% and 12.72%.
- Channel width will significantly affect the diffusion of reactants; a small channel width will largely improve the diffusion of hydrogen and maintain a large gas pressure drop, thus facilitating reactant gas diffusion and water removal. Its corresponding current density is increased by a maximum of 61.13%.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Fuel cell polarization characteristics and pressure distribution of four fuel cells with different flow channels: (

**a**) polarization curves; (

**b**) pressure at the anode flow channel along the z-direction.

**Figure 4.**Species concentration at the electrode interface between the cathode GDL and CL of four fuel cells with different flow channels: (

**a**) molar concentration of hydrogen; (

**b**) molar concentration of oxygen; (

**c**) water vapor concentration.

**Figure 6.**Fuel cell polarization characteristics and pressure distribution of four fuel cells with different flow channel tapered slopes: (

**a**) polarization curves; (

**b**) pressure at the anode flow channel along the z-direction.

**Figure 7.**Species concentration at the electrode interface between the cathode GDL and CL of four fuel cells with different flow channel tapered slopes: (

**a**) molar concentration of hydrogen; (

**b**) molar concentration of oxygen; (

**c**) water vapor concentration.

**Figure 9.**Fuel cell polarization characteristics and pressure distribution of four fuel cells with different flow channel depths: (

**a**) polarization curves; (

**b**) pressure at the anode flow channel along the z-direction.

**Figure 10.**Species concentration at the electrode interface between the cathode GDL and CL of four fuel cells with different flow channel depths: (

**a**) molar concentration of hydrogen; (

**b**) molar concentration of oxygen; (

**c**) water vapor concentration.

**Figure 11.**Fuel cell polarization characteristics and pressure distribution of four fuel cells with different flow channel widths: (

**a**) polarization curves; (

**b**) pressure at the anode flow channel along the z-direction.

**Figure 12.**Species concentration at the electrode interface between the cathode GDL and CL of four fuel cells with different flow channel widths: (

**a**) molar concentration of hydrogen; (

**b**) molar concentration of oxygen; (

**c**) water vapor concentration.

Equation | Description * |
---|---|

mass conservation equation [44] | $\frac{\mathrm{\partial}\left(\mathsf{\epsilon}\mathsf{\rho}\right)}{\mathrm{\partial}\mathrm{t}}+\nabla \xb7\left(\mathsf{\epsilon}\mathsf{\rho}\overline{\mathrm{u}}\right){=\mathrm{S}}_{\mathrm{m}}$ ${\mathrm{S}}_{\mathrm{m},\text{}\mathrm{a}}=-\frac{{\mathrm{M}}_{{\mathrm{H}}_{2}}}{2\mathrm{F}}{\mathrm{i}}_{\mathrm{a}}^{\mathrm{v}}$$\text{}\mathrm{and}\text{}{\mathrm{S}}_{\mathrm{m},\text{}\mathrm{c}}=\frac{{\mathrm{M}}_{{\mathrm{H}}_{2}\mathrm{O}}}{2\mathrm{F}}{\mathrm{i}}_{\mathrm{c}}^{\mathrm{v}}-\frac{{\mathrm{M}}_{{\mathrm{O}}_{2}}}{4\mathrm{F}}{\mathrm{i}}_{\mathrm{c}}^{\mathrm{v}}$ |

momentum conservation equation [44] | $\frac{\mathrm{\partial}\left(\overline{\mathrm{u}}\mathsf{\epsilon}\mathsf{\rho}\right)}{\mathrm{\partial}\mathrm{t}}+\nabla \xb7\left(\overline{\mathrm{u}}\overline{\mathrm{u}}\mathsf{\epsilon}\mathsf{\rho}\right)=-\nabla \mathrm{P}\mathsf{\epsilon}+\nabla \xb7\left(\mathsf{\epsilon}\mathsf{\mu}\nabla \text{}\overline{\mathrm{u}}\right){+\mathrm{S}}_{\mathrm{u}}$ |

energy conservation equation [44] | $\frac{\mathrm{\partial}\left({\mathsf{\rho}\mathsf{\epsilon}\mathrm{c}}_{\mathrm{k}}\mathrm{T}\right)}{\mathrm{\partial}\mathrm{t}}+\nabla \xb7\left({\mathsf{\rho}\overline{\mathrm{u}}\mathsf{\epsilon}\mathrm{c}}_{\mathrm{k}}\mathrm{T}\right)=\nabla \xb7\left({\mathrm{k}}^{\mathrm{eff}}\nabla \mathrm{T}\right){+\mathrm{S}}_{\mathrm{Q}}$ |

the Butler–Volmer equation [42] | ${\mathrm{S}}_{\mathrm{a}}{=\mathrm{j}}_{\mathrm{ref},\text{}\mathrm{a}\text{}}{\left(\frac{{\mathrm{C}}_{{\mathrm{H}}_{2}}}{{\mathrm{C}}_{{\mathrm{ref},\text{}\mathrm{H}}_{2}}}\right)}^{{\mathsf{\gamma}}_{\mathrm{a}}}\left({\mathrm{e}}^{\frac{{\mathrm{\alpha}}_{\mathrm{a}}{\mathrm{F}\mathsf{\eta}}_{\mathrm{a}}}{\mathrm{RT}}}{-\mathrm{e}}^{\frac{{-\mathrm{\alpha}}_{\mathrm{a}}{\mathrm{F}\mathsf{\eta}}_{\mathrm{a}}}{\mathrm{RT}}}\right)$ ${\mathrm{S}}_{\mathrm{c}}{=\mathrm{j}}_{\mathrm{ref},\text{}\mathrm{c}\text{}}{\left(\frac{{\mathrm{C}}_{{\mathrm{O}}_{2}}}{{\mathrm{C}}_{{\mathrm{ref},\text{}\mathrm{O}}_{2}}}\right)}^{{\mathsf{\gamma}}_{\mathrm{c}}}\left({\mathrm{e}}^{\frac{{\mathrm{\alpha}}_{\mathrm{c}}{\mathrm{F}\mathsf{\eta}}_{\mathrm{c}}}{\mathrm{RT}}}{-\mathrm{e}}^{\frac{{-\mathrm{\alpha}}_{\mathrm{c}}{\mathrm{F}\mathsf{\eta}}_{\mathrm{c}}}{\mathrm{RT}}}\right)$. |

current conservation equation [42] | $\nabla \xb7\left({\mathrm{\sigma}}_{\mathrm{s}}\nabla {\mathsf{\varphi}}_{\mathrm{s}}\right){+\mathrm{S}}_{\mathrm{i},\text{}\mathrm{s}}=0$$\text{}\mathrm{and}\text{}\nabla \xb7\left({\mathrm{\sigma}}_{\mathrm{m}}\nabla {\mathsf{\varphi}}_{\mathrm{m}}\right){+\mathrm{S}}_{\mathrm{i},\text{}\mathrm{m}}=0$ |

diffusion equation in the porous zone [10] | ${\mathrm{D}}_{\mathrm{k}}=\mathsf{\epsilon}{\left(1-\mathrm{s}\right)}^{\mathrm{b}}{\mathrm{D}}_{\mathrm{k}}^{0}{\left(\frac{{\mathrm{P}}_{0}}{\mathrm{P}}\right)}^{\mathsf{\gamma}}{\left(\frac{\mathrm{T}}{{\mathrm{T}}_{0}}\right)}^{1.5}$ |

Parameters | Units | Description |
---|---|---|

$\mathsf{\epsilon}$ | porosity | |

$\mathsf{\rho}$ | kg·m^{−3} | gas density |

$\overline{\mathrm{u}}$ | m·s^{−1} | gas velocity |

${\mathrm{S}}_{\mathrm{m}}$ | kmol·m^{−3} | mass source term |

$\mathrm{M}$ | kg·kmol^{−1} | molar mass |

$\mathrm{F}$ | C·mol^{−1} | Faraday constant |

${\mathrm{i}}^{\mathrm{v}}$ | A·m^{−3} | volumetric current density |

$\mathrm{P}$ | Pa | pressure |

${\mathrm{S}}_{\mathrm{u}}$ | kg·m^{−2}·s^{−1} | momentum source term |

$\mathsf{\mu}$ | Pa·s | viscosity |

$\mathrm{c}$ | J·kg^{−1}·K^{−1} | specific heat at constant pressure |

$\mathrm{T}$ | K | temperature |

${\mathrm{k}}^{\mathrm{eff}}$ | W·m^{−1}·K^{−1} | effective thermal conductivity |

${\mathrm{S}}_{\mathrm{Q}}$ | W·m^{−3} | energy source term |

$\mathsf{\eta}$ | V | overpotential |

${\mathrm{j}}_{\mathrm{ref}}$ | A·m^{−2} | reference exchange current density |

$\mathrm{C}$ | kmol·m^{−3} | molar concentration |

${\mathrm{C}}_{\mathrm{ref}}$ | kmol·m^{−3} | reference molar concentration |

$\mathsf{\gamma}$ | concentration index | |

$\mathsf{\alpha}$ | charge transfer coefficient | |

$\mathsf{\sigma}$ | s·m^{−1} | charge or electron conductivity |

$\mathsf{\varphi}$ | V | phase potential |

${\mathrm{S}}_{\mathrm{i}}$ | A·m^{−3} | current source term |

$\mathrm{s}$ | liquid water saturation | |

$\mathrm{b}$ | liquid water saturation index | |

$\mathrm{D}$ | m^{2}·s^{−1} | diffusion coefficient |

${\mathrm{D}}^{0}$ | m^{2}·s^{−1} | $\mathrm{diffusion}\text{}\mathrm{coefficient}\text{}\mathrm{at}\text{}{\mathrm{T}}_{0}$$\text{}\mathrm{and}\text{}{\mathrm{P}}_{0}$ |

$\mathsf{\gamma}$ | pressure index | |

${\mathrm{T}}_{0}$ | K | reference temperature |

${\mathrm{P}}_{0}$ | Pa | reference pressure |

к | m^{−2} | viscous resistance in the porous zone |

${\mathrm{M}}_{\mathrm{PEM}}$ | kg·kmol^{−1} | molar mass of proton exchange membrane |

${\mathsf{\zeta}}_{\mathrm{CL}}$ | m^{−1} | specific surface area of the catalyst layer |

Component | Height/mm | Width/mm | Length/mm |
---|---|---|---|

BPP | 1.5 | 1.8 | 50 |

GDL | 0.2 | 1.8 | 50 |

CL | 0.01 | 1.8 | 50 |

PEM | 0.03 | 1.8 | 50 |

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

${\mathrm{j}}_{\mathrm{ref},\text{}\mathrm{a}}$ [42] | 10,000 |

${\mathrm{j}}_{\mathrm{ref},\text{}\mathrm{c}}$ [42] | 20 |

${\mathsf{\epsilon}}_{\mathrm{GDL}}$ [29] | 0.5 |

${\mathsf{\epsilon}}_{\mathrm{CL}}$ [29] | 0.5 |

${\mathsf{\u043a}}_{\mathrm{GDL}}$ [29] | 1.76 × 10^{−11} |

${\mathsf{\u043a}}_{\mathrm{CL}}$ [29] | 1.76 × 10^{−11} |

${\mathsf{\alpha}}_{\mathrm{a}}$ [43] | 1 |

${\mathsf{\alpha}}_{\mathrm{c}}$ [43] | 1 |

${\mathsf{\gamma}}_{\mathrm{a}}$ [10] | 0.5 |

${\mathsf{\gamma}}_{\mathrm{c}}$ [10] | 0.5 |

${\mathrm{M}}_{\mathrm{PEM}}$ [42] | 1100 |

${\mathsf{\zeta}}_{\mathrm{CL}}$ [33] | 4.5 × 10^{7} |

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## Share and Cite

**MDPI and ACS Style**

Zhang, Z.; Wu, S.; Miao, H.; Zhang, T.
Numerical Investigation of Flow Channel Design and Tapered Slope Effects on PEM Fuel Cell Performance. *Sustainability* **2022**, *14*, 11167.
https://doi.org/10.3390/su141811167

**AMA Style**

Zhang Z, Wu S, Miao H, Zhang T.
Numerical Investigation of Flow Channel Design and Tapered Slope Effects on PEM Fuel Cell Performance. *Sustainability*. 2022; 14(18):11167.
https://doi.org/10.3390/su141811167

**Chicago/Turabian Style**

Zhang, Zhiming, Sai Wu, Huimin Miao, and Tong Zhang.
2022. "Numerical Investigation of Flow Channel Design and Tapered Slope Effects on PEM Fuel Cell Performance" *Sustainability* 14, no. 18: 11167.
https://doi.org/10.3390/su141811167