**3. Results and Discussions**

*3.1. The Influence of Wind Field on Leakage and Diffusion of LNG Storage Tank*

3.1.1. Numerical Simulation of Wind Field of LNG Storage Tank

The LNG storage tank will obstruct the flow of wind speed and thus affect the diffusion of LNG. In this study, the average wind speed at the height of 10 m is 4 m/s, and the wind speed of the inflow profile is implemented in a user-defined function (UDF) which is embedded in the numerical model as a boundary condition. Figure 5 shows the wind speed distribution in different planes of the calculation domain. As shown in Figure 5a, the wind speed at the boundary of the entire wind field is evenly distributed in the vertical plane of 0 m. The wind speed varied with height, forming gradient wind, which is the same as the wind field distribution law of the real atmospheric environment.

However, the atmospheric flow near the storage tank is affected by various factors, resulting in changes in wind speed and direction. When the wind flows from the top and

both sides of the storage tank, it causes a high wind speed zone with a speed of 7 m/s on top of the storage tank (shown in the black box, Figure 5 and a low wind speed zone with a speed of less than 1 m/s on both sides of the storage tank (shown in the red box, Figure 5). In Figure 5b, in the area away from the storage tank, the wind keeps up to 4 m/s; however, in the area near the storage tank, the wind speed is reduced because of obstruction. A detention zone is formed on the windward side of the tank due to the obstruction of the tank, so the wind speed decreases sharply. When the wind bypasses both sides of the tank, a certain length of a symmetrical bifurcated flow wake is formed downstream of the tank (shown in the red circle).

Figure 6 shows the distribution of the wind speed streamline near the storage tank. It shows that there are obvious vortices on the windward and leeward sides of the tank. In addition, two symmetrical vortices are formed at 70 m in the *x*-axis behind the horizontal of the tank after the atmosphere bypasses the tank (Figure 6a). In the process of the wind flowing downstream along both sides of the tank, the wind speed decreases continuously and the wind direction changes, thus producing backflow. When the wind reaches the central axis of the storage tank, the wind speed is close to zero, and a small cavity zone is formed on the back of the storage tank (Figure 6b). However, the vortex and low wind speed areas are very close to the storage tank. When the wind is away from the storage tank, the streamline returns to normal and the wind movement also stabilizes.

**Figure 6.** The distribution of wind speed streamlines near the storage tank.

3.1.2. Leakage and Diffusion Process of LNG Storage Tank under Wind Field

The average wind speed was assumed to be 4 m/s, and at the same time LNG was assumed to leak at a rate of 105.5 kg/s for 400 s. The expansion of LNG after leakage is shown in Figure 7. It can be seen that the pressure difference between the inside and outside of the tank causes the LNG to continue to spray from the leakage port to the ground in a parabolic form. The amount of LNG leakage is large, but the heat of the surrounding environment is limited, which makes it difficult to provide enough heat for the entire LNG to vaporize. Therefore, some LNG absorbs heat from the surrounding environment and then evaporates into a low-temperature gas cloud, and others form a liquid pool on the ground. During the landing process, some of the atomized LNG droplets absorb heat from the air and then evaporates into a gas state, resulting in a higher concentration of LNG leaking from the leakage hole and a lower concentration of LNG in the surface liquid pool (Figure 7c). Under the action of initial kinetic energy and gravity, the liquid LNG diffuses around the landing point, which is 7 m away from the storage tank and thus forming a thin "round" liquid pool (Figure 7b).

**Figure 7.** The distribution of LNG liquid pool. (**a**) Three-dimensional view of the liquid pool; (**b**) expansion of liquid pool at y = 0 m; (**c**) LNG injection at *z* = 0 m.

Figure 8 is a three-dimensional perspective view of gas clouds, which shows different methane volume fractions at different leakage moments, clearly showing the movement and diffusion process of low-temperature steam cloud containing leaking LNG. At the initial stage of leakage, the density of the low-temperature vapor cloud formed by flash evaporation is greater than that of the surrounding air, resulting in the extremely low gas cloud with methane volume fractions greater than 1%, 5%, and 15%. This phenomenon is also due to gravitational settling. As the leakage time increases to 120 s, the gas cloud with a volume fraction greater than 15% is still close to the ground with a "hole" inside, while the gas cloud with a volume fraction greater than 1% and 5% rises slightly. When the leakage time reaches 320 s, the whole gas cloud presents the phenomenon of "leaf-like bifurcation" on both sides. However, the height of gas clouds with 15% and more than 5% volume fraction is lower, while the height of gas cloud with volume fraction above 1% is relatively high, with a large amount of light methane floating over the tank (shown in the red box). The whole diffusion process fully reflects that LNG accumulates in the form of heavy gas cloud after leakage, mixes with air to absorb and transfer heat, resulting in the gradual narrowing of the difference between gas cloud density and air density. Finally, heavy methane turns into light methane in the periphery of the gas cloud.

**Figure 8.** Three-dimensional perspectives of gas clouds with different methane volume concentrations at different leakage moments. (**a**) Three-dimensional image of the vapor cloud with volume fraction of methane in excess of 15%(upper flammability limit, UFL); (**b**) Three-dimensional image of vapor cloud with volume fraction of methane in excess of 5%(lower flammability limit, LFL); (**c**) Three-dimensional image of vapor cloud with methane fraction in excess of 1%.

In order to reveal the spatial distribution characteristics of the LNG vapor cloud near the storage tank, methane concentration contours are selected from the *x-y* plane, *x-z* plane, and *y-z* plane for analysis. Considering that the low height of the gas cloud and bifurcated gas cloud along the *z*-axis on both sides of the tank, *x* = 57 m, *z* = 30 m and *y* = 0.5 m are selected as the observation surface. Figure 9 shows that the distribution of methane gas cloud concentration is in different planes. As shown in Figure 9a, at the plane *y* = 0.5 m, the overall shape of the gas cloud is "fan-shaped" (shown in white box), accompanied by a cavity with a radius of about 17 m on the back. A high concentration of methane is deposited on both sides of the cloud, while a low concentration of methane is distributed in the middle of the cloud. As the leakage time increases, the low concentration methane in the middle is preferentially diluted by air, resulting in a "hole" in the middle of the gas cloud (shown in white box). As the leak continues for some time, the "hole" area expands from the middle to the tail, and the gas cloud splits into two parts. One part is a heavy gas cloud, which is stacked behind the storage tank in the form of "leaf-like bifurcation" (shown in white box), and the other part is a light gas cloud (shown in a white round frame), spreading further with the wind. During the whole leakage process, the gas cloud gradually develops from a complete "fan shape" to a front-end "leaf-shaped" bifurcation. Due to the disturbance effect of the storage tank on the atmospheric movement, the detention zone and low wind speed region behind the storage tank restrains the downwind expansion in the middle of the gas cloud in some sense. When the low-temperature LNG vapor mixes with the atmosphere, the movement of the vapor cloud also diverges laterally along the streamline development at the back of the tank, resulting in a large amount of methane accumulation on both sides and thus forming a leaf-shaped bifurcation.

In Figure 9b, it can be seen that the gas cloud is divided into different concentration layers along the vertical direction *z* = 30 m, and the methane volume fraction decreases with height. Among them, the methane concentration is high near the ground (shown in white box), and low far away from the ground (shown in white round frame). The reason is that a large amount of highly concentrated methane accumulates near the storage tank during the leakage process, which makes it difficult to dilute and dissipate. However, the heavy methane in the outermost part of the gas cloud continuously absorbs and transfers heat with air in order to form light methane with low concentration and then to spread to higher and farther places. In Figure 9c, the gas cloud after leakage is symmetrically distributed behind the storage tank at 57 m on the *x-*direction. As the leak progresses, the width and height of the vapor cloud in this area increase slightly. The vapor cloud appears as "low in the middle and high at both ends" (shown in a white circle).

According to the results of numerical simulation and relevant heavy gas diffusion theory [29], the macroscopic diffusion behavior of the LNG vapor cloud could be roughly divided into three stages according to the continuous leakage of the LNG tank studied in this paper.

(1) Initial stage of diffusion (heavy gas accumulation): This stage is a period of heavy gas accumulation and diffusion. As shown in Figure 9, from the beginning of the leakage to 50 s, the vapor cloud is in the shape of "fan leaf", and its internal concentration of the vapor cloud is in an unstable state.

(2) Mid-stage of diffusion (Transitional levitation): This stage is the period of heavy gas transiting to light gas. From 120 s to 160 s, the development of gas cloud is in a neutral state, and the whole gas cloud is still in a "fan leaf shape". The methane concentration inside the gas cloud increases to a peak.

(3) Post-diffusion stage (Light gas drift): this stage is the light gas into passive diffusion. After 210 s of leakage, the development of the vapor cloud is in a stable state, in which case the width of the gas cloud remains unchanged, but the length and height of the vapor cloud slowly increases. As the "hole" area inside the vapor cloud continues to expand, the contact area between the gas cloud and the surrounding air increases, which lead to the rise of temperature and the decrease of methane density at the tail of the gas cloud. Under

the influence of wind, methane in the outermost part of the cloud is diluted the fastest. As a result, the cloud still behaves as "low in the middle and high at both ends".

**Figure 9.** Distribution of methane concentration in different planes. (**a**) Distribution diagram of methane concentration at plane y = 0.5 m; (**b**) Distribution diagram of methane concentration at plane z = 30 m; (**c**) Distribution diagram of methane concentration at plane x = 57 m.
