# A Simulation Tool for Geometrical Analysis and Optimization of Fuel Cell Bipolar Plates: Development, Validation and Results

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Solution Method and Model Description

^{2}, with ten channels in a serpentine flow field configuration. The channels are 2 mm in width and 1 mm in depth. The width of the rib is 2 mm. The thickness of the porous zones is 0.354 mm, which is equivalent to the thickness of the gas diffusion layer and the catalytic layer according to [7].

#### 2.1. Model Assumptions

#### 2.2. Governing Transport Equations

_{i}, which is the mass fraction of specie i representing the water vapour content in the reactant gases.

_{2}is the inertial resistance of the zone and v

_{i}is the flow velocity in the i-direction.

^{12}m

^{-2}.

#### 2.3. Anode Compartment Model

#### 2.4. Cathode Compartment Model

#### 2.5. Boundary Conditions

^{2}and 7,000 A/m

^{2}. In order to determine the consumption an average current density of 5,000 A/m

^{2}is imposed, and using an experimental polarization curve a voltage of 0.64 V has then been established. The power density of the cell is therefore 3.78 kW/m

^{2}. Currently a typical PEM fuel cell requires around 1.0 Nm

^{3}of pure hydrogen to produce 1.8–1.9 kW, while around 30% or 40% is lost in the operation. Thus, a hydrogen consumption of 1.05 × 10

^{-7}kg/s is considered. It is established that all the hydrogen entering in the cell is consumed, so 1.05 × 10

^{-7}kg/s of hydrogen must be introduced. By using a psychometric chart of the hydrogen-water vapour mixture the absolute humidity depending on the inlet temperature is obtained, obtaining the gas mixture mass flow at the anode inlet, 2.36 × 10

^{-7}kg/s.

## 3. Model Validation

_{e}is the current density (A/m

^{2}), v

_{z}is the mixture velocity in the z-direction (m/s), z

_{0}is the coordinate in the z axis related to the anode catalytic layer (through-plane coordinate).

_{e}and the gas velocity in the consumption direction v

_{z}. Therefore K(x,y) should be constant for all the points (x,y) on the working surface of the electrode:

_{m}) is represented in Figure 3. An important dependency of K(x,y) with the location is observed, especially at the inlet zone. Therefore it is not possible to affirm that the assumption is valid, but as can be seen in Figure 3, velocities over the consumption surface are in general an excellent parameter to analyse the utilisation of the whole area of MEA.

_{e.a}is the local current density over the anode electrode and i

_{e,c}is the local current density over the cathode electrode. In order to verify this, the current densities in both surfaces are calculated using the PEMFC Module of FLUENT, and the function h(x,y) is created and defined as the ratio between the anode current density and the cathode current density:

## 4. Model Results

#### 4.1. Sensitivity Analysis of Channel Dimensions

#### 4.2. Sensitivity Analysis of Different Geometrical Configurations

## 5. Conclusions

## Acknowledgments

## References and Notes

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**2005**, 30, 359–371. [Google Scholar] [CrossRef] - Sun, W.; Peppley, B.A.; Karan, K. Modeling the Influence of GDL and flow-field plate parameters on the reaction distribution in the PEMFC cathode catalyst layer. J. Power Sources
**2005**, 144, 42–53. [Google Scholar] [CrossRef] - FLUENT 6.2 Documentation; Fluent Inc.: Lebanon, NH, USA, 2005.
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**2003**, 113, 11–18. [Google Scholar] [CrossRef] - Martínez, J.J.; Pino, F.J. Sensitivity analysis of the design parameters of cathode side of the bipolar plates. In Proceedings of the 16th World Hydrogen Energy Conference, Lyon, France, June 2006; p. 117.
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**Figure 2.**Distribution of current density (left) and z-velocity (right) over the anode electrode surface. Results from the FLUENT PEMFC Module.

**Figure 3.**Distribution of K(x,y)/K

_{m}over the anode electrode surface. Results from the FLUENT PEMFC Module.

**Figure 4.**Distribution of h(x,y) over the anode electrode surface. Results from the FLUENT PEMFC Module.

**Figure 5.**Contours lines of q(x,y) over the electrode surface. Results from the FLUENT PEMFC Module.

Equation | Variable φ |
---|---|

Continuity | 1 |

x-momentum | U |

y-momentum | V |

z-momentum | W |

Chemical species i | y_{i} |

Case ID | Flow field design | Channel width (mm) | Channel depth (mm) | Number of channels |
---|---|---|---|---|

Base case | Serpentine | 1 | 1 | 20 |

Case 2 | Serpentine | 0.5 | 1 | 27 |

Case 3 | Serpentine | 1.5 | 1 | 16 |

Case 4 | Serpentine | 2 | 1 | 13 |

Case 5 | Serpentine | 1 | 0.5 | 20 |

Case 6 | Serpentine | 1 | 1.5 | 20 |

Case 7 | Serpentine | 1 | 2 | 20 |

Case 8 | Serpentine | 1 | 1 | 20 |

Case 9 | Parallel | 1 | 1 | 20 |

Case 10 | Parallel with various inlet/outlets | 1 | 1 | 40 |

Case 11 | Various serpentine zones | 1 | 1 | - |

Case 12 | “Pin” type | 1 | 1 | - |

Case | Flow field design | Pressure drop (bar) |
---|---|---|

Base case | Serpentine | 0.0510 |

Case 9 | Parallel | 0.0031 |

Case 10 | Parallel with various inlet/outlets | 0.0029 |

Case 11 | Various serpentine zones | 0.0628 |

Case 12 | “Pin” type | 0.00057 |

Case | Flow field design | Removed water (kg/s) |
---|---|---|

Base case | Serpentine | 4.77 × 10^{-9} |

Case 9 | Parallel | 1.19 × 10^{-10} |

Case 10 | Parallel with various inlet/outlets | 9.57 × 10^{-10} |

Case 11 | Various serpentine zones | 5.13 × 10^{-10} |

Case 12 | “Pin” type | 1.58 × 10^{-8} |

© 2009 by the authors. Licensee Molecular Diversity Preservation International, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license ( http://creativecommons.org/licenses/by/3.0/).

## Share and Cite

**MDPI and ACS Style**

Iranzo, A.; Rosa, F.; Pino, J.
A Simulation Tool for Geometrical Analysis and Optimization of Fuel Cell Bipolar Plates: Development, Validation and Results. *Energies* **2009**, *2*, 582-594.
https://doi.org/10.3390/en20300582

**AMA Style**

Iranzo A, Rosa F, Pino J.
A Simulation Tool for Geometrical Analysis and Optimization of Fuel Cell Bipolar Plates: Development, Validation and Results. *Energies*. 2009; 2(3):582-594.
https://doi.org/10.3390/en20300582

**Chicago/Turabian Style**

Iranzo, Alfredo, Felipe Rosa, and Javier Pino.
2009. "A Simulation Tool for Geometrical Analysis and Optimization of Fuel Cell Bipolar Plates: Development, Validation and Results" *Energies* 2, no. 3: 582-594.
https://doi.org/10.3390/en20300582