# Modeling of Liquid Hydrogen Tank Cooled with Para-Orthohydrogen Conversion

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Modeling Details

^{3}is chosen for this study, as some experimental data are available from self-pressurization experiments [18]. The computational domain for the ullage space included a quarter of the actual volume occupied by gas, assuming two symmetry boundaries (Figure 2a,b). The tank wall was treated as a no-slip boundary with a prescribed heat flux. The bottom boundary was approximated as an inlet, with the evaporating hydrogen flow rate and temperature given by an empirical model described below. In simulations including the venting tube, the tube inlets were treated as mass flow outlets for the ullage domain, while the external tube wall acted as a no-slip boundary for the ullage space and the surface heat flux was determined by the amount of para-ortho-conversion.

## 3. Results

^{3}spheroid-type tank (similar to that shown in Figure 1a) at different fill levels of liquid hydrogen and heat leaks. A 49% fill level (by volume) and a wall heat flux (into the tank) of 3.5 W/m

^{2}were selected for the present validation study. The initial experimental conditions in the tank corresponded to a 103 kPa absolute pressure and a vertical temperature gradient in the ullage space of about 7.5 K/m.

^{2}and 10.5 W/m

^{2}, while a venting tube is added into the ullage space (as shown in Figure 1 and Figure 2). The heat flux of 3.5 W/m

^{2}is the same as in the validation study, whereas the larger heat leak is considered as a higher vent rate; therefore, a more drastic effect of para-orthohydrogen conversion cooling can be expected. (It can be noted that there are tanks with lower heat leaks, depending on insulation materials.)

_{2}, which amount to about 1.5% and 6% of hydrogen loss per day for smaller and larger heat leaks, respectively. To maintain constant pressure, the larger heat leak requires about a fourfold larger venting rate. The reduction of boil-off losses due to cooling induced by para-orthohydrogen conversion is about 10% for the tank with a smaller heat leak and close to 25% at a larger heat leak, which results in noticeable savings that can make this technique economically attractive. Moreover, most commercial tanks have cylindrical shapes (rather than spheroidal ones), with larger surface-to-volume ratios. This will produce a larger heat input per volume, thus increasing achievable hydrogen savings.

## 4. Conclusions

^{2}, assuming a hydrogen conversion down to an equilibrium value at a local temperature. The model can be further extended to model flow inside a catalyzed venting tube, account for finite hydrogen conversion rates, and include the modeling of heat conduction in the tank wall. The considered cooling method is expected to be even more effective in cylindrical tanks with a larger surface-to-volume ratio.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**(

**a**) Schematic illustration of internal space of LH2 tank with vent tube that can be used for cooling, and (

**b**) boundary heat fluxes, transfer rates and inlet/outlet mass flow rates.

**Figure 4.**Pressure evolution in a closed tank: blue circles, experimental data; red squares, numerical results.

Heat Leak | Venting Tube | Venting Rate | Boil-off Loss |
---|---|---|---|

3.5 W/m^{2} | Non-catalyzed | 0.034 g/s | 2.9 kg/day |

3.5 W/m^{2} | Catalyzed | 0.030 g/s | 2.6 kg/day |

10.5 W/m^{2} | Non-catalyzed | 0.121 g/s | 10.5 kg/day |

10.5 W/m^{2} | Catalyzed | 0.094 g/s | 8.2 kg/day |

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**MDPI and ACS Style**

Matveev, K.I.; Leachman, J.W.
Modeling of Liquid Hydrogen Tank Cooled with Para-Orthohydrogen Conversion. *Hydrogen* **2023**, *4*, 146-153.
https://doi.org/10.3390/hydrogen4010010

**AMA Style**

Matveev KI, Leachman JW.
Modeling of Liquid Hydrogen Tank Cooled with Para-Orthohydrogen Conversion. *Hydrogen*. 2023; 4(1):146-153.
https://doi.org/10.3390/hydrogen4010010

**Chicago/Turabian Style**

Matveev, Konstantin I., and Jacob W. Leachman.
2023. "Modeling of Liquid Hydrogen Tank Cooled with Para-Orthohydrogen Conversion" *Hydrogen* 4, no. 1: 146-153.
https://doi.org/10.3390/hydrogen4010010