# Numerical Simulation of Hydrogen Leakage from Fuel Cell Vehicle in an Outdoor Parking Garage

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Simulation

#### 2.1. FLACS-Hydrogen Code

_{v}is the volume porosity of the geometry, β

_{j}is the area porosity in the j direction, ρ is the density, $\tilde{{u}_{j}}$ is the mean velocity in the j direction, k is the turbulent kinetic energy, ε is the dissipation of turbulent kinetic energy, μ

_{eff}is the effective viscosity, μ

_{eff}= μ + μ

_{t}, μ

_{t}is the dynamic turbulent viscosity, σ is the Prandtl–Schmidt number, σ

_{k}= 1.0, σ

_{ε}= 1.0, P

_{k}is the production of turbulent kinetic energy, P

_{ε}is the production of dissipation of turbulent kinetic energy, C

_{2}

_{ε}is a model constant in transportation equation for dissipation with the default value of 1.92. δ

_{ij}is the Kronecker delta function, δ

_{ij}= 1 if i = j, δ

_{ij}= 0 if i ≠ j, and $\tilde{{u}_{i}^{\u2033}{u}_{j}^{\u2033}}$ is the mean velocity in the i and j directions.

_{1}is the effective nozzle area, γ is the isentropic ratio, c

_{p}is the specific heat at constant pressure, p

_{a}is the ambient pressure, and ${\dot{m}}_{1}$ is the mass flow rate. More detailed information about the model can be found in References [30,31].

#### 2.2. Geometry Configuration and Grids

#### 2.3. Grid Independency Validation

#### 2.4. Determination of Hydrogen Leakage Rate

## 3. Results and Discussions

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**2D plots showing impinging hydrogen-jet concentration predictions from three turbulent models (Standard, RNG, and Realizable k-ε). Reproduced with permission [27]. Copyright 2019, Elsvier.

**Figure 2.**Model of the outside parking garage; (

**a**) vertical parking configuration; (

**b**) leakage position in vertical parking configuration; (

**c**) parallel parking configuration; (

**d**) leakage position in parallel parking configuration.

**Figure 4.**Hydrogen mole fraction between 0.04 and 0.4 by volume for downward releases from 700 bar through 2 mm, 3 mm, and 4 mm in parallel (

**A**–

**C**) and vertical (

**D**–

**F**) parkingconfiguration after 2 s, 6 s, 10 s leakage.

Initial Reservoir Condition | Nozzle Conditions | Jet Conditions |
---|---|---|

Pressure: p_{0} | Effective nozzle area: A_{1} | Velocity: ${u}_{2}={u}_{1}+\frac{{p}_{1}-{p}_{2}}{{\rho}_{1}{u}_{1}}$ |

Temperature: T_{0} | Temperature: ${T}_{1}={T}_{0}\left(2/\left(\gamma +1\right)\right)$ | Enthalpy: ${h}_{2}={h}_{1}+\frac{1}{2}\left({u}_{1}^{2}-{u}_{2}^{2}\right)$ |

Volume: V_{0} | Pressure: ${p}_{1}={p}_{1}{\left({T}_{1}/{T}_{0}\right)}^{\gamma /\left(\gamma -1\right)}$ | Temperature: ${T}_{2}={T}_{1}+\frac{1}{2}\frac{{u}_{1}^{2}-{u}_{2}^{2}}{{c}_{p}}$ |

Density: ${\rho}_{0}=\frac{{p}_{0}}{R{T}_{0}}$ | Density: ${\rho}_{1}=\frac{{p}_{1}}{R{T}_{1}}$ | Pressure: ${p}_{2}={p}_{a}$ |

Total mass: ${m}_{0}={\rho}_{0}{V}_{0}$ | Sound speed: ${c}_{1}=\sqrt{\gamma R{T}_{1}}$ | Density: ${\rho}_{2}=\frac{{p}_{2}}{R{T}_{2}}$ |

Heat exchange coefficient: h_{wall} | Velocity: ${u}_{1}={c}_{1}$ | Effective outlet area: ${A}_{2}={A}_{1}\frac{{\rho}_{1}{u}_{1}}{{\rho}_{2}{u}_{2}}$ |

Enthalpy: ${h}_{1}={c}_{p}{T}_{1}$ | Mass flow: ${\dot{m}}_{1}={\rho}_{1}{u}_{1}{A}_{1}$ | |

Mass flow: ${\dot{m}}_{1}={\rho}_{1}{u}_{1}{A}_{1}$ |

**Table 2.**Scenarios considered varying release diameter and parking configurations for unignited hydrogen release.

Case Number | Parking Configuration | Release Diameter (mm) | Initial Hydrogen Leakage Rate (kg/s) | Leakage Time (s) | by HyRAM(s) |
---|---|---|---|---|---|

A | Parallel Parking | 2 | 0.126 | 166 | 164 (1.2%) |

B | Parallel Parking | 3 | 0.283 | 70.5 | 72.9 (3.3%) |

C | Parallel Parking | 4 | 0.428 | 44 | 41 (6.8%) |

D | Vertical Parking | 2 | 0.126 | 166 | 164 (1.2%) |

E | Vertical Parking | 3 | 0.283 | 70.5 | 72.9 (3.3%) |

F | Vertical Parking | 4 | 0.428 | 44 | 41 (6.8%) |

G | — | 4.2 mm, 171 L at 35 MPa | 102.5 | 100.66 (1.8%) |

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**MDPI and ACS Style**

Shen, Y.; Zheng, T.; Lv, H.; Zhou, W.; Zhang, C.
Numerical Simulation of Hydrogen Leakage from Fuel Cell Vehicle in an Outdoor Parking Garage. *World Electr. Veh. J.* **2021**, *12*, 118.
https://doi.org/10.3390/wevj12030118

**AMA Style**

Shen Y, Zheng T, Lv H, Zhou W, Zhang C.
Numerical Simulation of Hydrogen Leakage from Fuel Cell Vehicle in an Outdoor Parking Garage. *World Electric Vehicle Journal*. 2021; 12(3):118.
https://doi.org/10.3390/wevj12030118

**Chicago/Turabian Style**

Shen, Yahao, Tao Zheng, Hong Lv, Wei Zhou, and Cunman Zhang.
2021. "Numerical Simulation of Hydrogen Leakage from Fuel Cell Vehicle in an Outdoor Parking Garage" *World Electric Vehicle Journal* 12, no. 3: 118.
https://doi.org/10.3390/wevj12030118