# A Computational Fluid Dynamics Analysis of Hydrogen Leakage and Nitrogen Purging of a Solid Oxide Fuel Cell Stack

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## Abstract

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## 1. Introduction

- Simulate the purging of the hot box with nitrogen and assess the amount of nitrogen required and how long it takes until the maximum oxygen concentration reaches 5%, given that it is filled with air at atmospheric pressure and initial temperatures of 800 °C and 300 °C, respectively.
- Assess the cooling effect of the purge on the hot box.
- Assess how long it takes for the hydrogen concentration to exceed 0.4% at the outlet if a leak occurs from the fuel-to-fuel heat exchanger during the OCV test.

## 2. Mathematical Model

#### 2.1. Main Assumptions

- The gases are assumed as ideal.
- The flow is assumed as incompressible.
- Buoyancy effects are neglected during the purge simulations.
- For the modelling of diffusive transport, both the laminar and turbulent Schmidt numbers are equal to one.

#### 2.2. Governing Equations

#### 2.3. Turbulence Models

#### 2.4. Boundary and Initial Conditions

#### 2.5. Numerical Verification

## 3. Results and Discussion

#### 3.1. Hot Purge

#### 3.2. Cold Purge

#### 3.3. OCV Leak

#### 3.4. Alternate Outlet

## 4. Conclusions

- Based on this study, the initial purge of the hot box, when it is still cold, should last a minimum of $t/{T}_{\mathrm{purge}}>1.58$ (94.8 s), corresponding to 3.0 kg of nitrogen. If the outlet is moved to the opposite side, the minimum initial purge period is $t/{T}_{\mathrm{purge}}>1.59$ (95.5 s), meaning the effect is negligible.
- If the hot box is filled with air at $T=1073$ K, the hot box should be purged for $t/{T}_{\mathrm{purge}}>0.58$ (35 s), corresponding to 1.1 kg of nitrogen. Moving the outlet to the opposite side would increase this period to 48 s. This means the original position is 37% more effective at purging compared to the new position.
- The leak at the original outlet would take 3.2 s to be detected if the leak was to occur during an OCV test. Moving the outlet to the opposite side would result in a reduction in the detection time by 1.2 s, meaning it is 39% faster.
- During periodic purges of the hot box, while it is operating, it can be expected that 72% of the purging nitrogen is heated from $T=300$ K to $T=1073$ K. During the purge, the average heat loss is 17.9 kW.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CAD | Computer Aided Design |

CFD | Computational Fluid Dynamics |

FC | Fuel Cell |

HB | Hot Box |

IMO | International Maritime Organization |

LEL | Lower Exlosive Level |

LFL | Lower Flammable Level |

LOC | Lower Oxygen Concentration |

OCV | Open Circuit Voltage |

RANS | Reynolds-averaged Navier-Stokes |

SOFC | Solid Oxide Fuel Cell |

SST | Shear Stress Transport |

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**Figure 1.**Production pathways for green ammonia [8].

**Figure 3.**Hot box with a hydrogen leak. The left figure is from the front and the right is zoomed in on the back. The hole diameter is 46.7 mm.

**Figure 4.**The hot box with a relocated outlet. The new outlet is marked in green, the original in red and the inlet in blue. The inlet has a diameter of 18.5 mm.

**Figure 6.**Histogram with ${x}_{{\mathrm{O}}_{2}}$ on the x-axis and probability on the y-axis. Bar width is 0.0005. Top left is at time $t/{T}_{\mathrm{purge}}=0.25$, top right is $t/{T}_{\mathrm{purge}}=0.5$, bottom left is $t/{T}_{\mathrm{purge}}=1$ and bottom right is in the steady state.

**Figure 7.**Molar fraction of oxygen at different time stamps in the hot box, with a threshold above 0.05, for the simulation using the standard $k-\epsilon $ model.

**Figure 8.**The left figure is the normalised energy of the system. The middle figure is the normalised mean outlet temperature. The right figure is the normalised gradient of the energy in the hot box.

**Figure 9.**The temperature distribution in the hot box at $t/{T}_{\mathrm{purge}}=0.083$ and $t/{T}_{\mathrm{purge}}=1.0$. The temperature scales are fixed to $0.79<T/{T}_{HB,initial}<0.93$ and $0.65<T/{T}_{HB,initial}<0.84$, respectively, to better visualise the distribution.

**Figure 10.**The mean and maximum molar oxygen fraction during the purge. The red dotted line represents the LOC at ${x}_{{\mathrm{O}}_{2}}=5\%$. The standard $k-\epsilon $ model uses $S{c}_{\mathrm{lam}}=0.76$ and $S{c}_{\mathrm{turb}}=0.9$ instead of $Sc=1$.

**Figure 11.**Molar oxygen fraction at different time steps in the hot box, with a threshold above 0.05%, for the simulation using the SST $k-\omega $ model.

**Figure 12.**The mean and maximum molar hydrogen fraction at the outlet in the time period $0<t<16$ s. The results are displayed for the three turbulence models, a laminar model and an unmodified $k-\epsilon $ model. The red dotted line is the minimum concentration for the sensor to detect hydrogen and the red line is when the sensor will give sound an alarm.

**Figure 13.**Distribution of hydrogen in the hot box, with a threshold of ${x}_{{\mathrm{H}}_{2}}>0.04$. The top left figure is at $t=2$ s, top right is at $t=4$ s, bottom left is at $t=8$ s and bottom right is at $t=16$ s.

**Figure 14.**Mean and max molar concentration of oxygen for the new and original outlet vs. normalised time for ${T}_{\mathrm{HB},\mathrm{initial}}=1073$ K.

**Figure 15.**Mean and max molar concentration of oxygen for the new and original outlet vs. normalised time for ${T}_{\mathrm{HB},\mathrm{initial}}=300$ K.

**Figure 16.**Mean and max molar concentration of hydrogen at the outlet for the original and new outlet. The sensors detects at ${x}_{{\mathrm{O}}_{2}}>0.4$% and the LFL is defined as ${x}_{{\mathrm{O}}_{2}}=4$%.

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**MDPI and ACS Style**

Sørensen, R.D.; Berning, T.
A Computational Fluid Dynamics Analysis of Hydrogen Leakage and Nitrogen Purging of a Solid Oxide Fuel Cell Stack. *Hydrogen* **2023**, *4*, 917-931.
https://doi.org/10.3390/hydrogen4040054

**AMA Style**

Sørensen RD, Berning T.
A Computational Fluid Dynamics Analysis of Hydrogen Leakage and Nitrogen Purging of a Solid Oxide Fuel Cell Stack. *Hydrogen*. 2023; 4(4):917-931.
https://doi.org/10.3390/hydrogen4040054

**Chicago/Turabian Style**

Sørensen, Rasmus Dockweiler, and Torsten Berning.
2023. "A Computational Fluid Dynamics Analysis of Hydrogen Leakage and Nitrogen Purging of a Solid Oxide Fuel Cell Stack" *Hydrogen* 4, no. 4: 917-931.
https://doi.org/10.3390/hydrogen4040054