# Effect of Hydrogen Refueling Parameters on Final State of Charge

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## Abstract

**:**

## 1. Introduction

## 2. Model

## 3. Results and Discussions

#### 3.1. Effect of Inflow Temperature on SOC

#### 3.2. Effect of Mass Flow Rate on SOC

#### 3.3. Effects of Inflow Temperature and Mass Flow Rate on SOC

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

${a}_{f}$ | heat transfer coefficient between hydrogen and ambient fluid, kW/m^{2}/K | $T$ | (final) temperature of hydrogen, K |

${A}_{s}$ | internal surface area of tank, m^{2} | ${T}_{0}$ | initial temperature in tank, K |

${c}_{p}$ | constant-pressure specific heat, kJ/kg/K | ${T}_{f}$ | temperature of ambient fluid, K |

${c}_{v}$ | constant-volume specific heat, kJ/kg/K | ${T}_{\infty}$ | hydrogen inflow temperature, K |

$h$ | specific enthalpy of hydrogen, kJ/kg | ${T}^{*}$ | characteristic temperature, ${T}^{*}=\left(\gamma {T}_{\infty}+\alpha {T}_{f}\right)/\left(1+\alpha \right)$, K |

${k}_{m}$ | coefficient of $\alpha $, $\alpha ={K}_{m}/\dot{m}$ | $u$ | specific internal energy, kJ/kg |

$m$ | (final) hydrogen mass in tank, kg | Greek symbols | |

${m}_{0}$ | initial hydrogen mass in tank, kg | $\alpha $ | dimensionless heat transfer coefficient, $\alpha ={a}_{f}{A}_{s}/\left({c}_{v}\dot{m}\right)$ |

$\dot{m}$ | hydrogen mass flow rate, g/s or kg/s | $\mathsf{\gamma}$ | ratio of specific heats, $\mathsf{\gamma}={c}_{p}/{c}_{v}$ |

$p$ | (final) pressure, MPa | $\mu $ | initial mass fraction, $\mu ={m}_{0}/m$ |

${p}_{0}$ | initial pressure, MPa | ${\mu}^{\prime}$ | modified initial mass fraction, $\text{}{\mu}^{\prime}={\mu}^{1+\alpha}$ |

${R}_{{\mathrm{H}}_{2}}$ | hydrogen gas constant, ${R}_{{\mathrm{H}}_{2}}=4124\text{}\mathrm{J}/\mathrm{K}/\mathrm{kg}$ | $\pi $ | dimensionless pressure, $\pi =p/{p}_{0}$ |

$t$ | time variable or fill time, s | $\theta $ | dimensionless temperature, $\theta =T/{T}_{0}$ |

${t}^{*}$ | characteristic time, ${t}^{*}={m}_{0}/\dot{m}$, s | ${\theta}^{*}$ | dimensionless characteristic temperature, ${\theta}^{*}={T}^{*}/{T}_{0}$ |

## References

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**Figure 1.**Effect of inflow temperature (unit K is necessary for thermodynamic calculation) on SOC under different mass flow rates (unit g/s is used here only for simplifying the legends) for (

**a**) Type III tank and (

**b**) Type IV tank (Symbol: data [14], Line: fitting).

**Figure 2.**Effect of mass flow rate (unit g/s is used here for expressing source data of fitting) on SOC under different inflow temperatures (unit °C is used for expressing experimental condition) for (

**a**) Type III tank and (

**b**) Type IV tank (Symbol: data [14], Line: fitting).

**Figure 3.**Contours of SOC over inflow temperature (X) and mass flow rate (Y) for (

**a**) Type III tank and (

**b**) Type IV tank (Color fill and black line: data [14], white line: model fitting).

**Figure 4.**Contours of SOC over mass flow rate (X) and inflow temperature (Y) for (

**a**) Type III tank and (

**b**) Type IV tank (Color fill and black line: data [14], white line: model fitting).

Case of Mass Flow Rate | Parameter | Type III | Type IV | ||
---|---|---|---|---|---|

Value | Standard Error | Value | Standard Error | ||

2 g/s | $\alpha $ | 3.06895 | 0.09539 | 2.43893 | 0.21307 |

$\pi $ | 25.0915 | 0.03528 | 25.01956 | 0.10857 | |

4 g/s | $\alpha $ | 3.08553 | 0.27222 | 1.63482 | 0.07602 |

$\pi $ | 24.83858 | 0.0967 | 25.05608 | 0.06402 | |

6 g/s | $\alpha $ | 2.36404 | 0.22206 | 1.32689 | 0.07263 |

$\pi $ | 25.01534 | 0.1187 | 25.22366 | 0.07874 | |

8 g/s | $\alpha $ | 2.21015 | 0.39765 | 1.26377 | 0.23178 |

$\pi $ | 24.99006 | 0.23809 | 25.11684 | 0.26374 | |

10 g/s | $\alpha $ | 2.09046 | 0.28239 | 1.13221 | 0.14616 |

$\pi $ | 24.97778 | 0.17568 | 25.09859 | 0.18884 |

Case of Inflow Temperature | Parameter | Type III | Type IV | ||
---|---|---|---|---|---|

Value | Standard Error | Value | Standard Error | ||

Not precooled | $\pi $ | 30.52763 | 0.15174 | 28.76612 | 0.11574 |

${k}_{m}$ | 0.30976 | 0.08068 | 0.74662 | 0.08333 | |

0 °C | $\pi $ | 29.29102 | 0.10452 | 27.93052 | 0.14825 |

${k}_{m}$ | 0.39768 | 0.07708 | 0.88248 | 0.1438 | |

−20 °C | $\pi $ | 27.79269 | 0.12976 | 27.07205 | 0.23431 |

${k}_{m}$ | 0.49182 | 0.14135 | 0.8583 | 0.31881 | |

−40 °C | $\pi $ | 26.79338 | 0.06061 | 26.57885 | 0.09415 |

${k}_{m}$ | 0.24821 | 0.10236 | 0.16917 | 0.1507 |

Parameter | Type III | Type IV | ||
---|---|---|---|---|

Value | Standard Error | Value | Standard Error | |

$\pi $ | 25.0288 | 0.05962 | 25.15657 | 0.07491 |

${k}_{m}$ | 0.43528 | 0.07647 | 0.11065 | 0.02216 |

$A$ | 0.32364 | 0.03384 | 0.47913 | 0.03749 |

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## Share and Cite

**MDPI and ACS Style**

Xiao, J.; Ma, S.; Wang, X.; Deng, S.; Yang, T.; Bénard, P.
Effect of Hydrogen Refueling Parameters on Final State of Charge. *Energies* **2019**, *12*, 645.
https://doi.org/10.3390/en12040645

**AMA Style**

Xiao J, Ma S, Wang X, Deng S, Yang T, Bénard P.
Effect of Hydrogen Refueling Parameters on Final State of Charge. *Energies*. 2019; 12(4):645.
https://doi.org/10.3390/en12040645

**Chicago/Turabian Style**

Xiao, Jinsheng, Shuo Ma, Xu Wang, Shanshan Deng, Tianqi Yang, and Pierre Bénard.
2019. "Effect of Hydrogen Refueling Parameters on Final State of Charge" *Energies* 12, no. 4: 645.
https://doi.org/10.3390/en12040645