# Experimental and Numerical Research on Temperature Evolution during the Fast-Filling Process of a Type III Hydrogen Tank

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. CFD Simulation

#### 2.1. Governing Equation

- (1)
- The temperature in the hydrogen tank is evenly distributed and the same as the ambient temperature.
- (2)
- The thermodynamic properties of the solid materials are isotropic, and mechanical deformation of the solid parts is neglected.
- (3)
- Heat transfer between the tank and the ambiance could happen during the filling process, and the heat transfer coefficient is assumed to be a constant, 6 W·m
^{−2}·K^{−1}[30]. - (4)
- The temperature and pressure of the inflow in the hydrogen refueling station are constant.
- (5)
- The hydrogen velocity of the injector is high during the fast-filling process, and the buoyance induced by the gravity can be neglected [31].

#### 2.2. Meshes and Mesh Independence Check

#### 2.3. Conditions and Solving Procedure

^{−2}·K

^{−1}. The thermodynamic properties of the liner and carbon fiber was listed in Table 3.

## 3. Experimental Set-Up

#### 3.1. Test Rig

#### 3.2. Temperature Evolution during the Air Filling Process

^{−1}by using a two-stage storage system. The two-stage air storage system was equipped with two tanks storing two different levels of pressure. Consequently, the filling procedure was divided into two steps. First, the pressure of the hydrogen tank increased from initial pressure to middle pressure by using the low-pressure tank. Second, the high-pressure tank continued to fill the hydrogen tank to the designed pressure.

^{−1}. The temperatures increased from 297 K to an average value of 336 K, and the final temperatures of TC1~TC7 were different from each other and showed a non-uniform distribution inside the tank. Otherwise, the filling temperature of air began to decrease with the increase in filling time which was caused by the throttling effect of the pressure regulating valve. Despite the filling temperature being decreased due to the throttling effect, the temperature inside the tank continued to increase. During the filling process, pressure fluctuation occurred around 125 s and 150 s which was contributed by the switching of the storage tank and the automatic adjusting of the pressure regulating valve.

## 4. Discussion

#### 4.1. Predicting the Temperature Evolution of the Air Filling Process

^{−1}, it would be too complex to conduct the CFD simulation of the filling process if directly taken into consideration the motion of the regulating valve. However, adopting the mass flow rate as the inlet boundary conditions would make the CFD model much simpler. Therefore, the mass flow rate during the air filling process was calculated based on Equation (4) and pressure-temperature evolution curves shown in Figure 3. The calculated mass flow rate and the filling temperature were shown in Figure 4, and the boundary condition for the inlet of the CFD model was set accordingly.

#### 4.2. Temperature Distribution and Evolution during the Hydrogen Filling Process

^{−1}with a temperature of 243 K. The filling process was 150 s with an expected filling mass of 3 kg. The temperature distribution acquired at the filling time of 10 s, 80 s, and 150 s were shown in Figure 6. As can be seen, the highest temperatures were 316 K, 378 K, and 403 K in Figure 5a–c located in the tailer of the tank, and the temperature gradients increased with obvious thermal stratification in the axial direction. The thermal stratification was induced by the injection of the hydrogen around the inlet, and the hydrogen in the tailer was heated due to the compression effect.

^{−1}.

#### 4.3. Effects of Filling Parameters on the Temperature Evolution

#### 4.3.1. Effect of Initial Pressure in the Tank

^{−1}, the ambient temperature is 273 K, and the filling time is 180 s. The calculated initial pressures are 2 MPa, 5 MPa, 8 MPa, and 10 MPa, respectively. The results were shown in Figure 8. As can be seen, the temperature increased from 31.6 K to 34.9 K with the decrease of initial pressure from 10 MPa to 2 MPa. In the first 30 s of the filling stage, the smaller the initial pressure, the greater the temperature rise. Then the rate of temperature rise tended to be parallel. This was mainly because the lower pressure meant a smaller residual mass in the tank, and a certain amount of heat was generated due to the filling, the smaller residual mass consequently was heated to a higher temperature. With the increase of the hydrogen temperature and the mass in the tank, the heat flowing out of the system gradually increases, and the influence of the initial mass on the temperature rise rate gradually disappears, resulting in a consistent temperature rise rate in the later stage of filling. It can be seen from Figure 8, that under different initial pressure conditions, the hydrogen pressure in the tank increase almost linearly and the higher initial pressure led to a higher final temperature.

#### 4.3.2. Effect of Ambient Temperature

#### 4.3.3. Effect of Filling Mass Flow Rate

^{−1}, 12 g·s

^{−1}, 16 g·s

^{−1}, and 20 g·s

^{−1}, and the results were shown in Figure 10. As can be seen, the temperature increased rapidly at the beginning of the filling process, and both the final temperature and pressure increased obviously with the increase in mass flow rate. The final temperatures were 294.4 K, 301.2 K, 306.6 K, and 310.9 K while the acquired final pressures were 19.36 MPa, 27.99 MPa, 37.66 MPa, and 48.5 MPa. Despite the final temperatures being lower than 358 K, the pressures at the mass flow rate of 20 g·s

^{−1}were higher than the 42 MPa, i.e., 1.2 times the NWP of the 145 L type III tank. Therefore, the duration of the filling time should be limited in this case.

#### 4.3.4. Effect of Filling Temperature

#### 4.3.5. Fitting Formula to Predict the Final Temperature

^{2}of the two fitting results is greater than 0.999, indicating that the fitting degree is high, and the results are reliable. Therefore, the relationship between the hydrogen final temperature and the filling parameters during the rapid filling process of the 145 L type III bottle can be obtained as follows:

#### 4.4. Effects of Injector Length of Tanks on the Characteristics of the Filling Process

## 5. Conclusions

- (1)
- 2D axisymmetric CFD model was built to reveal the temperature evolution during the fast-filling process, and a test rig was carried out to measure the gas temperature distribution and evolution along the axial direction inside the tank during the fast-filling process. Despite the filling temperature of the air was cooled down by the throttling effect cooled down, a significant temperature rises in the tank occurred during the fast-filling process of air, as a consequence of the compression effect.
- (2)
- Axial thermal stratification during the fast-filling process was observed in the 145 L type III hydrogen tank, with a ratio of length to diameter of 4.72, and the region of the highest temperature was located at the opposite end of the injector.
- (3)
- Effects of multiple filling parameters, such as initial pressure, ambient temperature, filling rate, and filling temperature on the temperature evolution were examined and a formula was fitted to predict the final temperature of the hydrogen, based on the predicted results.
- (4)
- The effect of injector length on the temperature distribution and evolution during the fast-filling process was examined. The result showed increasing the length of the injector contributed to decreasing both the maximal temperature and mass averaged temperature during the fast-filling process.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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