## 3 Results and Discussion
### Flow Characteristics Under Different Storage Pressures
#### 3.2.2 Heat Transfer Analysis  
Figure 8 illustrates the temperature distribution at 0.6 MPa, 0.7 MPa, 1 MPa, 2 MPa, and 4 MPa. Figure 9 shows the temperature variation curves of the vapor and liquid phases over time under different pressures, along with temperature cloud plots at 50 s, 100 s, 200 s, and 300 s. The curves clearly illustrate the distinct thermal responses of the two phases under varying pressures. Quantitatively, the peak temperature difference (\(\Delta\)T) in the vapor phase after 300 s is significant at lower pressures (e.g., 3.42 K at 0.6 MPa) but diminishes considerably at higher pressures (e.g., 0.27 K at 4.0 MPa, as shown in Table 4). In contrast, the liquid phase exhibits minimal temperature changes, with peak \(\Delta\)T values remaining close to zero across all pressures (ranging from 0.03 K to 0.04 K). These quantitative metrics confirm that the efficiency of heat transfer, which primarily occurs in the gas phase, is significantly dependent on the storage pressure.  
Comparative analysis reveals that the temperature diffusion range under 4 MPa is significantly smaller than that under 0.6 MPa. This phenomenon can be attributed to the increase in the specific heat capacity of the fluid with rising pressure, enabling it to absorb more heat and resulting in weaker temperature transfer. Additionally, as shown in Figure 10, which depicts the variation of CO\({}_{2}\) Prandtl number and thermal diffusivity with pressure, the gas phase exhibits a larger thermal diffusion coefficient and a smaller Prandtl number compared to the liquid phase, leading to a faster thermal response speed. However, as the pressure increases, the thermal diffusion coefficient of the gas phase decreases, and the Prandtl number increases, causing the thermal response speed to slow down relative to  
\begin{table}
\begin{tabular}{c c c} \hline
**Pressure (MPa)** & **Vapor Peak \(\Delta\)T (K)** & **Liquid Peak \(\Delta\)T (K)** \\ \hline
0.6 & 3.42 & 0.03 \\
0.7 & 2.86 & 0.03 \\
1 & 2.05 & 0.03 \\
2 & 0.83 & 0.04 \\
4 & 0.27 & 0.04 \\ \hline \end{tabular}
\end{table}
Table 4: Peak temperature difference (\(\Delta\)T) after 300 s.  
Figure 8: The temperature cloud diagrams at 0.6 MPa, 0.7 MPa, 1 MPa,2 MPa, and 4 MPa.  
low-pressure conditions. Consequently, higher pressures result in a smaller temperature rise range and a more limited temperature distribution.  
In summary, the analysis of flow and heat transfer characteristics under varying storage pressures reveals distinct behaviors in the liquid and gas phases of carbon dioxide. The liquid phase consistently exhibits higher flow velocities compared to the gas phase, yet its thermal response speed is significantly slower. In contrast, the gas phase demonstrates  
Figure 10: The curves of CO\({}_{2}\) Prandtl number (**a**) and thermal diffusivity (**b**) variation with pressure.  
Figure 9: Temperature curves over time under different pressures. (**a**) 0.6 MPa, (**b**) 0.7 MPa, (**c**) 1 MPa, (**d**) 2 MPa, (**e**) 4 MPa.  
a more pronounced thermal stratification, with faster temperature propagation. As the storage pressure increases, the flow and heat transfer performance of liquid carbon dioxide gradually declines, manifested by reduced flow velocities and a smaller range of vortex formation. Similarly, in the gas phase, the heat transfer rate diminishes, resulting in a smaller temperature gradient. These trends are attributed to the combined effects of increasing specific heat capacity, decreasing thermal diffusivity, and rising Prandtl number with pressure, as illustrated in Figure 10.