# Optimization of Fuel Cell Performance Using Computational Fluid Dynamics

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

^{2}active area of a PEM fuel cell flow field channels was developed using SOLID WORKS 2016 version software and imported into ANSYS FLUENT 18.0 licensed software for simulation.

## 2. Geometry Design

^{2}; the channels are 2 mm in width and 2 mm in depth. The rib width is 2 mm. Table 1 and Table 2 shows the geometry properties and parameters for the simulation.

#### 2.1. Computational Domain

#### 2.2. Boundary Conditions

## 3. Mathematical Modelling

_{i}

_{,}

_{ϵ}of i species along ϵ direction is given by:

_{i}as:

_{sol}∇ø

_{sol}) + R

_{sol}= 0

_{mem}∇ø

_{mem}) + R

_{mem}= 0

_{sol}= -R

_{a}at the anode side of the solid phase and R

_{sol}= -R

_{c}at the cathode side. As for the membrane phase, R

_{mem}= +R

_{a}at the anode side and R

_{mem}= -R

_{c}at the cathode side.

_{a}and R

_{c}are the current exchange densities and they are calculated using the Butler–Volmer equation:

_{ref}is reference concentration, γ is concentration coefficient, α is transfer coefficient, ɳ is activation losses, F is Faraday constant. The anode and cathode over-potentials are related to the solid phase potential fields, and the membrane, ø

_{sol}and ø

_{mem}are given as:

_{a}= ø

_{sol}− ø

_{mem}

_{c}= ø

_{sol}− ø

_{mem}− V

_{oc}

_{oc}is open-circuit voltage, as stated by Um et al. [20]

_{oc}= 0.0025T + 0.2329

_{oc}= V

_{oc}− ɳ

_{act}− ɳ

_{ohm}− ɳ

_{conc}

_{act}is activation over-potential, which represents the irreversibility in the cell as a results of the energy losses during the chemical activation reactions; ɳ

_{ohm}is ohmic over-potential, this is the irreversibility caused from the flow of ions across the electrolyte, and electrons across the current collectors and electrodes; while the ɳ

_{conc}is mass transport or concentration over-potential, it occurs due to the high current density operation of the fuel cell [21]. When the energy demand conditions are high, then the electrochemical reactions consumption becomes faster.

Governing Equations | Mathematical Expressions | Ref. |
---|---|---|

Continuity | $\frac{\partial \left(\rho u\right)}{\partial x}$ + $\frac{\partial \left(\rho v\right)}{\partial y}$ + $\frac{\partial \left(\rho w\right)}{\partial z}$ = ${S}_{m}$ | [22] |

Momentum transport | $u\frac{\partial \left(\rho u\right)}{\partial x}$ + $v\frac{\partial \left(\rho v\right)}{\partial y}$ + $w\frac{\partial \left(\rho w\right)}{\partial z}$ = $-\frac{\partial P}{\partial x}+\frac{\partial}{\partial x}\left(\mu \frac{\partial u}{\partial x}\right)+$ $\frac{\partial}{\partial y}\left(\mu \frac{\partial u}{\partial y}\right)+\frac{\partial}{\partial z}\left(\mu \frac{\partial u}{\partial z}\right)+{S}_{px}$ $u\frac{\partial \left(\rho v\right)}{\partial x}$ + $v\frac{\partial \left(\rho v\right)}{\partial y}$ + $w\frac{\partial \left(\rho v\right)}{\partial z}$ = $-\frac{\partial P}{\partial y}+\frac{\partial}{\partial x}\left(\mu \frac{\partial v}{\partial x}\right)+$ $\frac{\partial}{\partial y}\left(\mu \frac{\partial v}{\partial y}\right)+\frac{\partial}{\partial z}\left(\mu \frac{\partial v}{\partial z}\right)+{S}_{py}$ $u\frac{\partial \left(\rho w\right)}{\partial x}$ + $v\frac{\partial \left(\rho w\right)}{\partial y}$ + $w\frac{\partial \left(\rho w\right)}{\partial z}$ = $-\frac{\partial P}{\partial z}+\frac{\partial}{\partial x}\left(\mu \frac{\partial w}{\partial x}\right)+$ $\frac{\partial}{\partial y}\left(\mu \frac{\partial w}{\partial y}\right)+\frac{\partial}{\partial z}\left(\mu \frac{\partial w}{\partial z}\right)+{S}_{pz}$ | [23] |

Energy | $u\frac{\partial \left(\rho CT\right)}{\partial x}$ + $v\frac{\partial \left(\rho CT\right)}{\partial y}$ + $w\frac{\partial \left(\rho CT\right)}{\partial z}$ = $\frac{\partial}{\partial x}\left(k\frac{\partial T}{\partial x}\right)+$ $\frac{\partial}{\partial y}\left(k\frac{\partial T}{\partial y}\right)+\frac{\partial}{\partial z}\left(k\frac{\partial T}{\partial z}\right)+{S}_{h}$ | [24] |

Hydrogen transport (anode region) | $u\frac{\partial \left(\rho {Y}_{{H}_{2}}\right)}{\partial x}$ + $v\frac{\partial \left(\rho {Y}_{{H}_{2}}\right)}{\partial y}$ + $w\frac{\partial \left(\rho {Y}_{{H}_{2}}\right)}{\partial z}=$ $\frac{\partial \left({J}_{x,{H}_{2}}\right)}{\partial x}$ + $\frac{\partial \left({J}_{y,{H}_{2}}\right)}{\partial y}$ + $\frac{\partial \left({J}_{z,{H}_{2}}\right)}{\partial z}$ $+{S}_{{H}_{2}}$ | [25] |

Water transport (anode region) | $u\frac{\partial \left(\rho {Y}_{aw}\right)}{\partial x}$ + $v\frac{\partial \left(\rho {Y}_{aw}\right)}{\partial y}$ + $w\frac{\partial \left(\rho {Y}_{aw}\right)}{\partial z}=$ $\frac{\partial \left({J}_{x,aw}\right)}{\partial x}$ + $\frac{\partial \left({J}_{y,aw}\right)}{\partial y}$ + $\frac{\partial \left({J}_{z,aw}\right)}{\partial z}$$+{S}_{aw}$ | [26] |

Oxygen transport (cathode region) | $u\frac{\partial \left(\rho {Y}_{{O}_{2}}\right)}{\partial x}$+$v\frac{\partial \left(\rho {Y}_{{O}_{2}}\right)}{\partial y}$+$w\frac{\partial \left(\rho {Y}_{{O}_{2}}\right)}{\partial z}=$ $\frac{\partial \left({J}_{x,{O}_{2}}\right)}{\partial x}$+$\frac{\partial \left({J}_{y,{O}_{2}}\right)}{\partial y}$+$\frac{\partial \left({J}_{z,{O}_{2}}\right)}{\partial z}$$+{S}_{{O}_{2}}$ | [27] |

Water transport (cathode region) | $u\frac{\partial \left(\rho {Y}_{cw}\right)}{\partial x}$+$v\frac{\partial \left(\rho {Y}_{cw}\right)}{\partial y}$+$w\frac{\partial \left(\rho {Y}_{cw}\right)}{\partial z}=$ $\frac{\partial \left({J}_{x,cw}\right)}{\partial x}$+$\frac{\partial \left({J}_{y,cw}\right)}{\partial y}$+$\frac{\partial \left({J}_{z,cw}\right)}{\partial z}$$+{S}_{cw}$ | [28] |

Source terms | S_{m} = ${S}_{{H}_{2}}+{S}_{aw}$ S_{m} = ${S}_{{O}_{2}}+{S}_{cw}$ | [29] |

S_{px} = −$\frac{\mu u}{k}$ S_{py} = −$\frac{\mu v}{k}$ S_{pz} = −$\frac{\mu w}{k}$ | [30] | |

$\overrightarrow{{\mathrm{J}}_{i}}$ = −$\rho \nabla \xb7{y}_{i}$ | [31] | |

S_{h} = I^{2}R_{ohm} + h_{react} + ${\mathsf{\u019e}}_{act}{R}_{an,ca}$ | [32] | |

${\mathrm{S}}_{{\mathrm{H}}_{2}}=-\frac{{\mathrm{M}}_{{\mathrm{H}}_{2}}}{2\mathrm{F}}{\mathrm{R}}_{\mathrm{an}}$ | [33] | |

${\mathrm{S}}_{\mathrm{aw}}$$=-\frac{{\mathrm{M}}_{{\mathrm{H}}_{2}}\mathrm{O}}{\mathrm{F}}{\mathrm{R}}_{\mathrm{an}}$ | [34] | |

${\mathrm{S}}_{{\mathrm{O}}_{2}}=-\frac{{\mathrm{M}}_{{\mathrm{O}}_{2}}}{4\mathrm{F}}{\mathrm{R}}_{\mathrm{ca}}$ | [35] | |

${\mathrm{S}}_{\mathrm{cw}}=-\frac{{\mathrm{M}}_{{\mathrm{H}}_{2}\mathrm{O}}}{2\mathrm{F}}{\mathrm{R}}_{\mathrm{ca}}$ | [36] | |

Charge transport | ∇·(σ_{sol} ∇ø_{sol}) + R_{sol} = 0∇·(σ _{mem} ∇ø_{mem}) + R_{mem}= 0 | [37] [38] |

## 4. Results and Discussion

#### 4.1. Effects of Operating Temperature Variation

#### 4.2. Effects of Operating Pressure Variation

#### 4.3. Mass Fraction

#### 4.4. Modeling Results Validation

^{2}. Some of these materials were integrated into Ansys software in order to simulate and find out the best material cell performance. In their experiment, a serpentine flow field plate was used with an anode and cathode parallel flow. A single cell with a serpentine flow channel with the co-counter flow was used in the model to represent their experimental setup.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Conflicts of Interest

## References

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**Figure 1.**Exploded view of a single PEM fuel cell [6].

**Figure 3.**A three-dimensional view of the single PEM fuel cell and its components. (

**a**) Inlet channel (

**b**) outlet channel.

**Figure 4.**Temperature distribution at the anode region (GDL/CL) for each material at 298K: (

**a**) Aluminum, (

**b**) Copper, (

**c**) Steel.

**Figure 5.**Temperature distribution at the cathode region (GDL/CL) for each material at 298K: (

**a**) Aluminum, (

**b**) Copper, (

**c**) Steel.

**Figure 6.**Temperature distribution at the anode region (GDL/CL) for each material at 323K: (

**a**) Aluminum, (

**b**) Copper, (

**c**) Steel.

**Figure 7.**Temperature distribution at the cathode region (GDL/CL) for each material at 323K: (

**a**) Aluminum, (

**b**) Copper, (

**c**) Steel.

**Figure 8.**Temperature distribution at the cathode region (GDL/CL) for each materials at 338K: (

**a**) Aluminum, (

**b**) Copper, (

**c**) Steel.

**Figure 9.**Temperature distribution at the cathode region (GDL/CL) for each material at 338K: (

**a**) Aluminum, (

**b**) Copper, (

**c**) Steel.

**Figure 10.**Pressure distribution at the anode region (GDL/CL) for each material with temperature 323 K at 1.5 bar: (

**a**) Aluminum, (

**b**) Copper, (

**c**) Steel.

**Figure 11.**Pressure distribution at the cathode region (GDL/CL) for each material with temperature 323 K at 1.5 bar: (

**a**) Aluminum, (

**b**) Copper, (

**c**) Steel.

**Figure 12.**Pressure distribution at the anode region (GDL/CL) for each material with temperature 323 K at 2.0 bar: (

**a**) Aluminum, (

**b**) Copper, (

**c**) Steel.

**Figure 13.**Pressure distribution at the cathode region (GDL/CL) for each material with temperature 323 K at 2.0 bar: (

**a**) Aluminum, (

**b**) Copper, (

**c**) Steel.

**Figure 14.**Pressure distribution at the anode region (GDL/CL) for each material with temperature 323 K at 2.5 bar: (

**a**) Aluminum, (

**b**) Copper, (

**c**) Steel.

**Figure 15.**Pressure distribution at the cathode region (GDL/CL) for each material with temperature 323 K at 2.5 bar: (

**a**) Aluminum, (

**b**) Copper, (

**c**) Steel.

**Figure 16.**Contours of hydrogen mass fraction at the anode region (GDL/CL) for each material with temperature 323 K at pressure 1.5 bar: (

**a**) Aluminum, (

**b**) Copper, (

**c**) Steel.

**Figure 17.**Contours of oxygen mass fraction at the cathode region (GDL/CL) for each material with temperature 323 K at pressure 1.5 bar: (

**a**) Aluminum, (

**b**) Copper, (

**c**) Steel.

**Figure 18.**Water mass fraction at the membrane for (

**a**) Aluminum, (

**b**) Copper, (

**c**) Steel bipolar plate materials at 338 K, 1.5 bar.

**Figure 19.**Comparison between numerical and experimental results of various bipolar plate materials.

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

Current collector width (anode side) | 45 | mm |

Current collector width (cathode side) | 45 | mm |

Gas flow field channel width | 45 | mm |

Gas flow field channel depth | 2 | mm |

Cell electrode length | 65 | mm |

Gas diffusion layer thickness (anode region) | 0.39 | mm |

Gas diffusion layer thickness (cathode region) | 0.39 | mm |

Catalyst layer thickness (anode side) | 0.08 | mm |

Catalyst layer thickness (cathode side) | 0.08 | mm |

Active area | 25 | cm^{2} |

Membrane thickness | 0.6 | mm |

Gas diffusion layer porosity (anode side) | 0.5 | − |

Gas diffusion layer porosity (cathode side) | 0.5 | − |

Catalyst layer porosity (anode region) | 0.5 | − |

Catalyst layer porosity (cathode region) | 0.5 | − |

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

Operating temperature | 298/323/338 | K |

Operating pressure | 1.5/2/2.5 | Bar |

Mole fractions for hydrogen and water vapor (anode region) | 0.6/0.4 | − |

Mole fractions for oxygen and water vapor (cathode region) | 0.2/0.15 | − |

Relative humidity at anode side | 100 | % |

Relative humidity at cathode side | 100 | % |

Open circuit voltage | 0.7 | V |

**Table 4.**Peak power data is for simulation and experimental results for the three bipolar plate materials.

Materials | Peak Power (Simulation) | Peak Power (Experimental) | % Deviation b/w Simulation and Experimental Results |
---|---|---|---|

Aluminium | 0.36 | 0.33 | 8.33 |

Copper | 0.3 | 0.28 | 6.67 |

Steel | 0.25 | 0.23 | 8.00 |

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## Share and Cite

**MDPI and ACS Style**

Wilberforce, T.; Ijaodola, O.; Emmanuel, O.; Thompson, J.; Olabi, A.G.; Abdelkareem, M.A.; Sayed, E.T.; Elsaid, K.; Maghrabie, H.M.
Optimization of Fuel Cell Performance Using Computational Fluid Dynamics. *Membranes* **2021**, *11*, 146.
https://doi.org/10.3390/membranes11020146

**AMA Style**

Wilberforce T, Ijaodola O, Emmanuel O, Thompson J, Olabi AG, Abdelkareem MA, Sayed ET, Elsaid K, Maghrabie HM.
Optimization of Fuel Cell Performance Using Computational Fluid Dynamics. *Membranes*. 2021; 11(2):146.
https://doi.org/10.3390/membranes11020146

**Chicago/Turabian Style**

Wilberforce, Tabbi, Oluwatosin Ijaodola, Ogungbemi Emmanuel, James Thompson, Abdul Ghani Olabi, Mohammad Ali Abdelkareem, Enas Taha Sayed, Khaled Elsaid, and Hussein M. Maghrabie.
2021. "Optimization of Fuel Cell Performance Using Computational Fluid Dynamics" *Membranes* 11, no. 2: 146.
https://doi.org/10.3390/membranes11020146