## 3 Results and Discussion
### Analysis of Evaporation Characteristics at Different Filling Ratios  
This section analyzes the differences in temperature and velocity fields at different filling ratios, studying the fluid dynamics, thermodynamics, and BOG generation characteristics of the fluid inside the tank at filling rates of 50%, 60%, 70%, 80%, and 90%. Figure 12 presents the temporal evolution of the velocity distribution within the tank at a filling rate of 50%. Consistent with prior observations, a velocity gradient initially develops near the wall surface. The heated fluid undergoes a reduction in density, inducing natural convection that drives the fluid upward toward the free surface and subsequently inward toward the central region of the tank. This flow behavior results in the formation of vortices at both ends of the tank. Under the influence of these vortices, multiple vortex  
Figure 11: The difference in BOG generated under different storage pressures. pairs are generated within the tank. The maximum velocity is observed at the interface where the liquid phase ascends and the gas phase descends, with the peak fluid velocity reaching 0.03 m/s. Figure 13 illustrates the variation of temperature distribution within the tank at a 50% filling rate. Over the studied time range, the temperature rise is predominantly observed in the gas phase. This phenomenon can be attributed to two factors: First, the gas phase exhibits a significantly lower specific heat capacity compared to the liquid phase, resulting in a more rapid temperature increase under identical heat input and consequently a steeper temperature gradient. Second, at this moderate filling level, the gas phase occupies a larger volume within the tank, enabling more extensive thermal diffusion throughout the vapor region when contrasted with higher filling rates. Figure 14 demonstrates the variations in velocity distribution under different filling rates. It is evident that the overall velocity within the fluid domain exhibits a decreasing trend as the filling rate increases. Specifically, at a 50% filling rate, the region where the velocity gradient forms at the liquid surface is more extensive compared to cases with higher filling rates. This behavior can be attributed to the greater degree of freedom of movement for both the gas and liquid phases at lower filling rates, facilitating their motion under the influence of wall-induced vortices. Conversely, at higher filling rates, the available space for the gas phase is reduced, limiting its freedom of movement, while the increased mass of the liquid phase results in slower fluid motion. Figure 12: The velocity distribution of a 50% filling rate. Figure 13: The temperature distribution of a 50% filling rate. Figures 15 and 16 present the temperature characteristics under different filling rates, with Figure 15 showing the spatial distribution and Figure 16 displaying the temporal evolution of gas and liquid phase temperatures. In the gas phase, lower filling rates (e.g., 50%) result in broader temperature distributions and higher peak temperatures, while higher filling rates (e.g., 90%) lead to more localized distributions. The liquid phase maintains near-uniform temperature distributions across all conditions, except at 70% filling rate, where temperatures are slightly lower. These observations are primarily attributed to (1) increased gas-phase interfacial area at lower filling rates, which enhances environmental heat influx into the system, and (2) reduced gas-liquid interfacial heat transfer at lower filling rates, causing greater heat retention and consequently higher gas-phase temperatures. Figure 14: The differences in velocity distribution under various filling rates. Figure 15: The differences in temperature distribution under various filling rates. Figure 17 illustrates the temporal evolution of the boil-off gas (BOG) generated under different filling rates. While these curves provide a visual comparison, a quantitative analysis of the average BOG generation rate offers further insight.