# Reducing Hydrogen Boil-Off Losses during Fuelling by Pre-Cooling Cryogenic Tank

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## Abstract

**:**

## 1. Introduction

## 2. Materials and methods

#### 2.1. EcoSimPro

#### 2.2. Fuelling Model

#### 2.2.1. Mesh Study

#### 2.2.2. Boundary and Initial Conditions

#### 2.3. Analytical Validation

## 3. Results

#### 3.1. Analytical Validation Results

#### 3.2. Fuelling Model Results

## 4. Sensitivity Study

#### 4.1. Tank Size

#### 4.2. Tank Geometry

#### 4.3. Mass Flow

#### 4.4. Insulation thickness

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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Boundary Condition | Value |
---|---|

$L{H}_{2}$ storage pressure | 10 bar |

$L{H}_{2}$ storage temperature | 27 K |

Cryotank Volume | 0.1134 m${}^{3}$ |

Cryotank liquid hydrogen mass (full) | 6.85 kg |

Cryotank lower dome radius | 0.3 m |

Cryotank upper dome radius | 0.3 m |

Cryotank wall thickness | 0.005 m |

VIP insulation thickness | 0.1 m |

Maximum Cryotank pressure | 5.02 bar |

Target mass flow | 30 g/s |

Initial Condition | Value |
---|---|

Cryotank pressure | 1 bar |

Cryotank fill level | 5 % |

Cryotank liquid temperature | 20 K |

Fuelling Pipe pressure | 5 bar |

Fuelling Pipe temperature | 20 K |

Relief Pipe pressure | 1 bar |

Relief pipe temperature | 293 K |

Measuring tank pressure | 1 bar |

Measuring tank temperature | 293 K |

${\overline{\mathit{T}}}_{0,\phantom{\rule{3.33333pt}{0ex}}\mathit{ins}}$ before Fuelling | ${\overline{\mathit{T}}}_{\mathit{ins}}$ after Fuelling | $\mathbf{\Delta}{\mathit{T}}_{\mathit{ins}}$ | |
---|---|---|---|

Standard fuelling process | 293 K | 240 K | 53 K |

Pre-cooling method | 250 K | 210 K | 40 K |

Constants and Variables | Value |
---|---|

${\overline{cp}}_{SS,\phantom{\rule{0.222222em}{0ex}}293-94K}$ | 0.415 kJ/kgK |

${\overline{cp}}_{SS,\phantom{\rule{0.222222em}{0ex}}293-27K}$ | 0.375 kJ/kgK |

${\overline{cp}}_{SS,\phantom{\rule{0.222222em}{0ex}}94-27K}$ | 0.130 kJ/kgK |

${\overline{cp}}_{AL,\phantom{\rule{0.222222em}{0ex}}293-94K}$ | 0.830 kJ/kgK |

${\overline{cp}}_{AL,\phantom{\rule{0.222222em}{0ex}}293-27K}$ | 0.745 kJ/kgK |

${\overline{cp}}_{AL,\phantom{\rule{0.222222em}{0ex}}94-27K}$ | 0.172 kJ/kgK |

${\overline{cp}}_{Insulation\phantom{\rule{0.222222em}{0ex}}\left(VIP\right)}$ | 0.586 kJ/kgK |

${\overline{cp}}_{{H}_{2}}$ | 13 kJ/kgK |

${\overline{cp}}_{{N}_{2}}$ | 1.2 kJ/kgK |

$\Delta {h}_{vap,{H}_{2}}$ | 446 kJ/kg |

$\Delta {h}_{vap,{N}_{2}}$ | 199 kJ/kg |

${\rho}_{SS}$ | 8000 kg/m${}^{3}$ |

${\rho}_{AL}$ | 2650 kg/m${}^{3}$ |

${\rho}_{Insulation\phantom{\rule{0.222222em}{0ex}}\left(VIP\right)}$ | 160 kg/m${}^{3}$ |

Cryotank wall thickness t | 5 mm |

Vacuum Insulation Panel thickness ${t}_{VIP}$ | 50 mm |

Cryotank radius r | 0.3 m |

Steel cryotank mass ${m}_{SS}$ | 45.24 kg |

Aluminium cryotank mass ${m}_{Al}$ | 15 kg |

Insulation mass ${m}_{Insulation\phantom{\rule{0.222222em}{0ex}}\left(VIP\right)}$ | 9.05 kg |

Boil-Off Losses Fuelling Model | Value |
---|---|

${m}_{{H}_{2},\phantom{\rule{0.222222em}{0ex}}SS,\phantom{\rule{0.222222em}{0ex}}293\phantom{\rule{0.222222em}{0ex}}K}$ | 4.14 kg |

${m}_{{H}_{2},\phantom{\rule{0.222222em}{0ex}}AL,\phantom{\rule{0.222222em}{0ex}}293\phantom{\rule{0.222222em}{0ex}}K}$ | 2.58 kg |

${m}_{{H}_{2},\phantom{\rule{0.222222em}{0ex}}SS,\phantom{\rule{0.222222em}{0ex}}94\phantom{\rule{0.222222em}{0ex}}K}$ | 0.65 kg |

${m}_{{H}_{2},\phantom{\rule{0.222222em}{0ex}}AL,\phantom{\rule{0.222222em}{0ex}}94\phantom{\rule{0.222222em}{0ex}}K}$ | 0.34 kg |

Tank Radius | Mass Flow | Filling Time |
---|---|---|

0.1 m | 5 g/s | 150 s |

0.3 m (reference case) | 0.03 kg/s | 196 s |

1 m | 0.5 kg/s | 9 min |

3 m | 3 kg/s | 37 min |

30 m | 30 kg/s | 2.58 days |

Radius | Length of Cylindrical Section |
---|---|

0.3 m (reference case) | 0.001 m |

0.17 m | 1 m |

0.15 m | 1.3 m |

Mass Flow ($\dot{\mathit{m}}$) | $\dot{\mathit{m}}/{\dot{\mathit{m}}}_{\mathit{ref}}$ |
---|---|

0.003 kg/s | 0.1 |

0.006 kg/s | 0.2 |

0.03 kg/s (reference case) | 1 |

0.06 kg/s | 5 |

0.3 kg/s | 10 |

Insulation Thickness |
---|

0.5 m |

0.05 m (reference case) |

0.01 m |

0.001 m |

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**MDPI and ACS Style**

Ghaffari-Tabrizi, F.; Haemisch, J.; Lindner, D.
Reducing Hydrogen Boil-Off Losses during Fuelling by Pre-Cooling Cryogenic Tank. *Hydrogen* **2022**, *3*, 255-269.
https://doi.org/10.3390/hydrogen3020015

**AMA Style**

Ghaffari-Tabrizi F, Haemisch J, Lindner D.
Reducing Hydrogen Boil-Off Losses during Fuelling by Pre-Cooling Cryogenic Tank. *Hydrogen*. 2022; 3(2):255-269.
https://doi.org/10.3390/hydrogen3020015

**Chicago/Turabian Style**

Ghaffari-Tabrizi, Fardin, Jan Haemisch, and Daniela Lindner.
2022. "Reducing Hydrogen Boil-Off Losses during Fuelling by Pre-Cooling Cryogenic Tank" *Hydrogen* 3, no. 2: 255-269.
https://doi.org/10.3390/hydrogen3020015