Efficient and secure refueling within the vehicle refueling systems exhibits a close correlation with the issues concerning fuel backflow and gasoline evaporation. This paper investigates the transient flow behavior in fuel hose refilling and simplified tank fuel replenishment using the volume of fluid method. The numerical simulation is validated with the simplified hose refilling experiment and the evaporation simulation of Stefan tube. The effects of injection flow rate and injection directions have been discussed in the fuel hose refilling part. For both the experiment and simulation, the pressure at the end of the refueling pipe in the lower located nozzle case is 30% higher than that in the upper located nozzle case at a high flow rate, and the backflow phenomenon occurs at the lower filling mode. The fluid will directly flush into the first pipe elbow, changing the flow pattern from bubble flow to slug flow, which results in low-frequency and high-amplitude flow pressure fluctuations. A hexane refueling system, consisting of a refueling pipe, fuel tank and a vapor return line, is analyzed, in which hexane evaporation is considered. At the early refueling period, a higher refueling rate will lead to more obvious splashing, which leads to a higher average mass of hexane vapor and pressure in the tank. Two optimized fuel tank designs are examined. The lower fuel tank filling port exhibits significantly lower vapor hexane in the fuel tank compared to the other design, resulting in a reduction of 200 Pa in the peak pressure in the tank, which contributes to a substantial reduction of gasoline loss during tank filling.

The fuel filling system plays a crucial role in the overall operation and safety of a vehicle [

Refueling is a complex process in unsteady multi-phase turbulent flow, and gasoline evaporation has a great influence on the gas-liquid two-phase flow. Researchers generally did several experimental studies with simplified tank models [

Matsui [

These experimental observations showed that the two-phase flow pressure drop is closely related to the flow pattern. However, the flow mechanism and explanations of the slug flow are still needed. Thaker et al. [

Evaporation of gasoline with complex components is a complicated process, and the empirical formula of fuel evaporation is summarized in the fuel evaporation experiment. Mackay et al. [

In order to solve the problems of fuel backflow and gasoline evaporation during automobile refueling and to understand the transient flow behavior during refueling, experiments and CFD numerical simulation studies were conducted on fuel hose refilling and simplified tank fuel replenishment. The numerical and experimental models are introduced in

In our study, we have chosen to utilize the volume of fluid (VOF) method for multi-phase flow simulation. In the VOF method, variations of the volume fraction,

where a cell with

The transport equation for

where

where

where

A vapor-liquid phase change model for VOF method is employed in the hexane refueling system using UDF in FLUENT. The energy equation is expressed as:

where _{0} = 298.15 K:

where

where ^{−1} [

With respect to a pipe’s internal flow, the family of the k

The momentum equation and energy dissipation equation are as follows:

where the dynamic turbulent viscosity is given by:

and

where

The simplified refuel pipe model and the simplified fuel tank model are depicted in ^{3}, respectively. The viscosity of water and air are 1.003 ^{−3} and 1.7984 ^{−5} kg

The simplified geometric model of the fuel filling system is shown in

The boundary conditions in our simulations were velocity inlet and pressure outlet. The RNG k-

The transient flow behavior in fuel pipe refilling and simplified tank refueling were discussed respectively. We focused on the influence of different filling forms on the pipeline flow pattern in the former part and on the influence of gasoline evaporation on the filling of the tank in the latter.

We selected two different positions for the gasoline nozzle assembly, as shown in

Case | Upper filling (Experiment) | Upper filling (Simulation) | Lower filling (Experiment) | Lower filling (Simulation) |
---|---|---|---|---|

_{small} (14.6 L/min) |
20.5 ± 0.5 | 20.8 | 19.5 ± 0.5 | 20.2 |

_{small} (14.6 L/min) |
28.5 ± 0.5 | 27.3 | 25.5 ± 0.5 | 24.3 |

_{large} (17.1 L/min) |
24.5 ± 0.5 | 24.8 | 27.5 ± 0.5 | 26.5 |

_{large} (17.1 L/min) |
30 ± 0.5 | 29.1 | 39 ± 0.5 | 39 |

To investigate the specific reasons for the pressure fluctuation patterns in the pipe, we analyzed the flow pattern of the refueling pipe.

During the refueling process in real life, gasoline evaporation is inevitable, which is a complex physicochemical process influenced by various factors. During refueling the tank, the fuel level rise rate varies with different refueling rates, making the refueling rate a crucial factor affecting gasoline evaporation. This section presented a simulation of the fuel refueling process using a simple refueling system to investigate the effects of refueling rate and fuel tank structure on gasoline evaporation. We considered the gasoline (hexane) evaporation process using the evaporative phase change model in

Property | Hexane | Vapor |
---|---|---|

Density (kg/m^{3}) |
659 | 2.86 |

Viscosity (kg |
5.4 ^{−4} |
1.72 ^{−5} |

Thermal conductivity (W/m |
0.125 | 0.012 |

Thermal capacity (J/kg |
2170 | 2220 |

To verify the accuracy of the phase change heat and mass transfer model in our UDF code, we adopted the initial conditions based on the analytical solution of Stephan’s problem [

The hexane volume fraction during the fuel refueling process at different refueling rates was shown in

1. The early refueling period: the vaporized hexane content significantly increased during the initial refueling stage [

2. The smooth refueling period: the vapor content remained relatively stable. As the fuel level rose, the splash phenomenon of fuel droplets was moderated, and the fuel flow tended to calm down. The hexane volatilization occurred on the fuel surface. Consequently, the vapor content inside the tank slightly decreased during the later stages of refueling. When filling at a rate of 50 L/min, fuel flow inside the tank was smooth, and the vapor content was stable.

The flow pattern of fuel inside a tank is significantly impacted by the tank’s structure. Due to the varying shapes of tank structures, several factors related to these structures can influence the fuel flow, such as the tank refueling port location and slotting treatment. Thus, we explore these two factors. One is that we lower the height of the fuel filler to 100 mm from the bottom, and the other is that we introduce a slotting treatment at the bottom of the tank. Here, only 60 L/min flow rate is selected.

The pressure fluctuation plays a crucial role in the oil refueling system. By monitoring pressure fluctuations, the effects of the nozzle flow rate and direction on the refueling pipe and the effects of the flow rate and tank structures on the entire tank have been discussed. The following conclusions can be drawn:

(1) The experimental and simulation results indicate that the likelihood of backflow in the refueling pipe rises with the refueling rate. Direct liquid flow into the inclined pipe results in a bubbly flow formation inside the refueling pipe. In the bubbly flow, the gas phase is distributed in the form of dispersed bubbles that continuously generate and collapse and have minimal influence on the pressure difference fluctuation. Besides, the stable liquid seal is formed inside the fuel pipe, which enhances filling smoothness.

(2) When the liquid flushes to the elbow near the inlet, it will intensify the gas-liquid mixing. The pressure at the end of the refueling pipe in the lower located nozzle case is 30% higher than that in the upper located nozzle case at a high flow rate. Due to the high-speed flow of the fuel and the curvature of the pipeline, intense vortices and turbulence will form, leading to an increased degree of gas-liquid mixing, which causes a change of flow pattern in the inclined pipe from bubbly flow to slug flow. The FFT analysis shows that the pressure fluctuation of the slug flow is more severe than that of the bubble flow, and the differential pressure fluctuation exhibits low frequency and high amplitude, which results in a backflow phenomenon. Thus, the slug flow during the refueling process should be avoided.

(3) Both filling efficiency and pressure fluctuations should be concerned in the fueling process. For the entire tank refueling, hexane evaporation is considered. As the filling rate increases, it is an indication of higher filling efficiency. When refueling the fuel tank at a rate of 70 L/min, the pressure peak within the tank exhibited an increase of 800 Pa compared to the pressure peak recorded during refueling at the other two rates. Nevertheless, this can lead to an intensified splashing phenomenon at the beginning of fueling, causing a significant increase not only in the hexane content of the fuel vapor but also in the tank pressure fluctuations. Injected fuel directly contacting the liquid surface or forming liquid seal for the refueling port can decrease the pressure fluctuations. It is essential to choose a moderate filling flow rate for the gasoline refueling with reasonable pressure fluctuations and take into account the balance of the filling efficiency and safety.

(4) The study analyzes the structural parameters of the fuel tank, including the location of the refueling port and slotting treatment. The results show that the vapor hexane content inside the tank increases sharply in all three structures due to fuel splashing. However, for the tank structure with a lower refueling port, the occurrence of a liquid seal in the early stages of refueling leads to the evaporation rates of vapor hexane lower than 0.004 kg/s during the middle and final stages. In contrast, the tank structure with a slotted bottom exhibits high vapor hexane content throughout the refueling process, likely due to the increased impact area of the fuel in the tank wall. Nevertheless, the peak pressure of the fuel tank and vapor return line is reduced by about 200 Pa relative to the initial tank structure, which is favorable for refueling safety.

Gas phase specific heat, Jkg^{−1}K^{−1}

Liquid phase specific heat, Jkg^{−1}K^{−1}

Force, N

Turbulence kinetic energy, W/m^{3}

_{large}

Height of liquid column in vertical pipe under large flow condition, cm

_{small}

Height of liquid column in vertical pipe under small flow condition, cm

_{large}

Length of liquid seal along the inclined pipe under large flow condition, cm

_{small}

Length of liquid seal along the inclined pipe under small flow condition, cm

Pressure, Pa

_{l}

Liquid temperature, K

_{sat}

Saturation temperature, K

Interfacial mass-transfer rates for vapor phase

Interfacial mass-transfer rates for liquid phase

Velocity vector

Gravitational force, m/s^{2}

_{lh}

Latent heat of fuel oil gasification, J/g

Computational fluid dynamic

Renormalization group

Reid vapor pressure

User defined function

Volume of fluid

Coefficients

Volume fraction

Mass transfer time relaxation factor

Interface curvature, m^{−1}

Thermal conductivity, W/mK

Dynamic viscosity, Pa

Linearly weighted averages for the bulk density, kg/m^{3}

Density of gas phase, kg/m^{3}

Density of liquid phase, kg/m^{3}

Interface tension, N/m

Turbulent dissipation rate

Apparent energy

Liquid

Gas

Saturation

Not applicable.

This work was supported by the National Natural Science Foundation of China with Grant No. 12002334 for C.Z., Zhejiang Provincial Natural Science Foundation (Grant No. LQ21A020004 for C.Z.) and the Excellent Youth Natural Science Foundation of Zhejiang Province, National Science Foundation of Anhui Province (2108085QE226), China (No. LR21E060001 for L.Q. and C.Z.). C.Z. acknowledges the China Scholarship Council (No. 202108330166) for providing him with a visiting scholarship at NUS, Singapore.

The authors confirm contribution to the paper as follows: study conception and design: Chenlin Zhu,Yan Zhao; data collection: Yan Zhao, Lifang Zeng; analysis and interpretation of results: Yan Zhao, Chenlin Zhu, Lifang Zeng, Lijuan Qian; draft manuscript preparation: Yan Zhao, Zhitao Jiang, Jiafeng Xie. All authors reviewed the results and approved the final version of the manuscript.

All data generated or analysed during this study are included in this published article.

The authors declare that they have no conflicts of interest to report regarding the present study.