# CFD Model of Refuelling through the Entire HRS Equipment: The Start-Up Phase Simulations

^{*}

## Abstract

**:**

## 1. Introduction

#### The Start-Up Phase of Refuelling

## 2. Validation Experiment

## 3. CFD Model

#### 3.1. Calculation Domain and Parameters of HRS Components

_{d}= 0.65. The calculated values of an equivalent internal diameter of the PCV, 5 other valves, MFM and HE are shown in Table 1.

#### 3.2. Governing Equations and Numerical Details

_{μ}= 0.09, σ

_{k}= 1.0, σ

_{ε}= 1.3, C

_{1ε}= 1.44, C

_{2ε}= 1.92, ${C}_{3\epsilon}=\mathit{tanh}\left|{{u}_{y}/\left({u}_{x}^{2}+{u}_{z}^{2}\right)}^{0.5}\right|$, $S=\sqrt{2{S}_{ij}{S}_{ij}}$ is the mean rate of strain, ${S}_{ij}=\frac{1}{2}\left(\frac{\partial {u}_{i}}{\partial {x}_{j}}+\frac{\partial {u}_{j}}{\partial {x}_{i}}\right)$.

#### 3.3. Initial and Boundary Conditions

^{2}/K is used in line with the conclusions of the study [19].

#### 3.4. Modelling the PCV and the HE

## 4. Simulation Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

C | Specific heat [J/kg/K)] | S_{k}, S_{ε} | User-defined source terms for k [m^{2}/s^{2}] and ε [m^{3}/s^{3}] |

C_{1ε}, C_{2ε}, C_{3ε} | Standard k-ε model constants | t | Time [s] |

C_{d} | Discharge coefficient [-] | u_{i}, u_{j}, u_{k} | Velocity components [m/s] |

C_{p} | Specific heat at constant pressure [J/kg/K] | x_{i}, x_{j}, x_{k} | Cartesian coordinates [m] |

C_{v} | Flow coefficient [-] | Y_{M} | Contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate [-] |

D | Diameter of tank [m] | ||

D_{0} | Equivalent pipe diameter [m] | ||

$d{m}_{norm}$ | Normalised mass flow rate difference [-] | β | The ratio of the equivalent pipe diameter to the upstream pipe size [-] |

E | Total energy [J] | ||

g | Gravity acceleration [m/s^{2}] | γ | Ratio of specific heats [-] |

G_{b} | Generation of turbulence kinetic energy due to buoyancy [-] | δ | Thickness [mm] |

G_{k} | Generation of turbulence kinetic energy due to the mean velocity gradients [-] | δ_{ij} | Kronecker symbol [-] |

h_{ext} | External convection heat transfer coefficient [W/m^{2}/K] | ε | Dissipation rate of turbulent kinetic energy [m^{2}/s^{3}] |

k | Turbulent kinetic energy [J/kg] | λ | Thermal conductivity [W/m/K] |

${\dot{m}}_{sim}$ | Simulated mass flow rate [kg/s] | μ | Molecular dynamic viscosity [Pa·s] |

${\dot{m}}_{exp}$ | Experimental mass flow rate [kg/s] | μ_{t} | Turbulent dynamic viscosity [Pa·s] |

P | Pressure [Pa] | ρ | Density [kg/m^{3}] |

P_{initial} | Initial pressure in tanks [Pa] | σ_{k}, σ_{ε} | Turbulent Prandtl numbers for k and ɛ [-] |

Pr_{t} | Turbulent Prandtl number [-] | ||

Acronyms | |||

APRR | Average pressure ramp rate | CFRP | Carbon fibre-reinforced polymer |

CFD | Computational fluid dynamics | HE | Heat exchanger |

HDV | heavy-duty vehicles | HP | High pressure |

HRS | Hydrogen refuelling station | L/D | Length to diameter |

LDV | Light duty vehicles | MFM | Mass flow meter |

NREL | National Renewable Energy Laboratory | NWP | Nominal working pressure |

PCV | Pressure control valve | PID | Piping and instrumentation diagram |

STP | Standard temperature and pressure | TMA | Triple moving average |

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**Figure 1.**Start-up and overall hydrogen fuelling time representation by SAE J2601 [5].

**Figure 2.**Piping and instrumentation diagram (PID) of the NREL experimental facility [19].

**Figure 4.**The discretisation of hydrogen tanks: (

**top**) HP tanks and (

**bottom**) onboard tanks (scales are different).

**Figure 7.**(

**Left**): hydrogen mass flow rate at the PCV. (

**Right**): hydrogen temperature after the HE (TE4).

**Figure 8.**(

**Left**): Simulated versus experimental pressure in the onboard tanks. (

**Right**): simulated instantaneous temperature in the tank centre versus experimentally measured temperature in the two onboard tanks, and temperature dynamics in the assumption of the adiabatic process (blue line with diamonds).

**Figure 9.**Comparison of rolling average simulated temperature against experimentally measured temperature.

**Table 1.**Calculated equivalent internal diameter of 5 valves, PCV, HE, MFM using flow coefficient from [20] (C

_{d}= 0.65).

Parameter | Valve1 | Valve2 | MFM | PCV | Valve3 | HE | Valve4 | Valve5 |
---|---|---|---|---|---|---|---|---|

Flow coefficient, C_{v} [28] | 1.3 | 0.75 | 1.0 | 1.0 | 0.75 | 1.0 | 0.75 | 1.0 |

Calculated equivalent ID [mm] | 6.5 | 4.99 | 5.76 | 5.76 | 4.99 | 5.76 | 4.99 | 5.76 |

Upstream pipe diameter [mm] | 7.9 | 5.1 | 5.1 | 5.1 | 5.1 | 5.1 | 5.1 | 5.1 |

Downstream pipe diameter [mm] | 7.9 | 7.9 | 5.1 | 5.1 | 5.1 | 5.1 | 5.1 | 5.1 |

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**MDPI and ACS Style**

Molkov, V.; Ebne-Abbasi, H.; Makarov, D.
CFD Model of Refuelling through the Entire HRS Equipment: The Start-Up Phase Simulations. *Hydrogen* **2023**, *4*, 585-598.
https://doi.org/10.3390/hydrogen4030038

**AMA Style**

Molkov V, Ebne-Abbasi H, Makarov D.
CFD Model of Refuelling through the Entire HRS Equipment: The Start-Up Phase Simulations. *Hydrogen*. 2023; 4(3):585-598.
https://doi.org/10.3390/hydrogen4030038

**Chicago/Turabian Style**

Molkov, Vladimir, Hazhir Ebne-Abbasi, and Dmitriy Makarov.
2023. "CFD Model of Refuelling through the Entire HRS Equipment: The Start-Up Phase Simulations" *Hydrogen* 4, no. 3: 585-598.
https://doi.org/10.3390/hydrogen4030038