# The Effect of Liquid Hydrogen Tank Size on Self-Pressurization and Constant-Pressure Venting

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## Abstract

**:**

^{3}. Pressure and temperature growth rates are characterized in closed tanks, where the interfacial mass transfer manifests initial condensation followed by more pronounced evaporation. In tanks where pressure is kept fixed by venting some hydrogen from the vapor domain of the tank, the initial venting rate significantly exceeds evaporation rate, but after a settling period, magnitudes of both rates approach each other and continue evolving at a slower pace. The largest tank demonstrates a six-times-lower pressure rise than the smallest tank over a 100 h period. The relative boil-off losses in continuously vented tanks are found to be approximately proportional to the inverse of the tank diameter, thus generally following simple Galilean scaling with a few percent deviation due to scale effects. The model developed in this work is flexible for analyzing a variety of processes in liquid hydrogen storage systems, raising efficiencies, which is critically important for a future economy based on renewable energy.

## 1. Introduction

Authors | Modeling Methods | Focus Areas |
---|---|---|

Majumdar et al. [2] | Finite-volume network flow analysis | Self-pressurization; thermodynamic vent system (TVS). |

Bolshinskiy et al. [3] | Lumped, multi-node transient model | Locked-up tank; self-pressurization and pressure control venting; TVS operations. |

Al Ghafri et al. [4] | Two-element model | Validation for self-pressurization, densification, and venting. |

Wang et al. [5] | Multi-node model | Effects of fluid properties, initial conditions, and heat leakage on self-pressurization. |

Huerta and Vesovic [8] | Lumped model for liquid and 2D CFD ^{1} for ullage | Temperature and velocity fields in the ullage in isobaric venting. |

Matveev and Leachman [9] | Lumped model for liquid and CFD ^{1} model for ullage | Boil-off reduction using para-orthohydrogen conversion of vented gas. |

^{1}Computational fluid dynamics.

## 2. Mathematical Model

## 3. Results

#### 3.1. Validation Study

#### 3.2. Self-Pressurization Study

^{3}, ranging from small to large practical tanks for liquid hydrogen storage. The initial conditions include a 50% fill level of liquid hydrogen (i.e., when half of the tank is occupied by liquid phase), 1-bar pressure, the saturated state for both liquid and vapor inside the tanks, and an average surface heat leak of 1 W/m

^{2}. The same distribution factor is applied to access heat leaks into the ullage and liquid domains, so that external heat input to the liquid is roughly twice larger than that to the vapor. The process time is chosen as 100 h.

#### 3.3. Constant-Pressure Venting Study

^{2}tank in Figure 5d. Evaporated hydrogen not only needs to replace gas vented outside but also has to compensate for the reduction in liquid volume due to evaporation.

#### 3.4. Scaling Analysis

## 4. Conclusions

^{3}and with a heat leak of 1 W/m

^{2}were found to vary from about 1.8% to 0.2%, respectively. Simple Galilean scaling produced reasonable predictions for tanks of different sizes, but larger tanks still experience slightly lower scaled mass transfer rates.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**Modeling results for self-pressurization process in closed tanks of different scales: (

**a**) ullage pressure, (

**b**) ullage temperature, (

**c**) liquid temperature, (

**d**) relative tank volume occupied by liquid, (

**e**) evaporation rate, and (

**f**) evaporation rate normalized by total mass of fluid in the tank.

**Figure 5.**Modeling results for constant-pressure venting in tanks of different scales: (

**a**) ullage temperature, (

**b**) evaporation and vent rates in smaller tanks, (

**c**) evaporation and vent rates in bigger tanks, (

**d**) zoomed-in view of evaporation and vent rates in 2.3-m

^{3}tank during time interval from 60 to 80 h, (

**e**) normalized evaporation and vent rates in smaller tanks, (

**f**) normalized evaporation and vent rates in bigger tanks.

**Figure 6.**Scaled mass transfer rates for tanks of different sizes: (

**a**) normalized evaporation rates for self-pressurization scenarios, and (

**b**) normalized vent rates for constant-pressure venting processes.

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**MDPI and ACS Style**

Matveev, K.I.; Leachman, J.W.
The Effect of Liquid Hydrogen Tank Size on Self-Pressurization and Constant-Pressure Venting. *Hydrogen* **2023**, *4*, 444-455.
https://doi.org/10.3390/hydrogen4030030

**AMA Style**

Matveev KI, Leachman JW.
The Effect of Liquid Hydrogen Tank Size on Self-Pressurization and Constant-Pressure Venting. *Hydrogen*. 2023; 4(3):444-455.
https://doi.org/10.3390/hydrogen4030030

**Chicago/Turabian Style**

Matveev, Konstantin I., and Jacob W. Leachman.
2023. "The Effect of Liquid Hydrogen Tank Size on Self-Pressurization and Constant-Pressure Venting" *Hydrogen* 4, no. 3: 444-455.
https://doi.org/10.3390/hydrogen4030030