## 3 Discussion and Analysis
### Influence of Environmental Parameters on the Temperature Field Evolution
#### 3.1.3 Ballast Water Height  
During the navigation of ships in the polar region, due to the complex and harsh environmental conditions in the polar region, the height of the ballast water level needs to be adjusted frequently to improve the stability of the ship. In order to explore the influence of the ballast water level height on temperature change, this section selects ballast water heights of 0.5 m, 0.45 m, 0.4 m, 0.3 m, and 0.2 m for sensitivity analysis. The ambient temperature is constant at \(-30\)\({}^{\circ}\)C, and the seawater temperature is constant at \(-2\)\({}^{\circ}\)C. Table 5 shows the environmental conditions under different working conditions, and Figure 13 shows the temperature field distribution cloud map of the freezing process at different liquid level heights.  
Figure 13: The temperature field evolution of the ballast tank under different ballast water heights.  
Figure 14 and 15 are shown as the curves of temperature change with time at points a and b at different liquid level heights.  
It can be observed from Figure 13 that as the height of the ballast water level decreases from 5 m to 2 m, the range and impact of the air domain on the ballast water gradually increase. This enhancement promotes convective heat transfer between the air domain and the ballast water, subsequently increasing the cooling rate of the ballast water. Additionally, when the ballast water level falls below the waterline, the air domain is influenced by both the cold air temperature and the seawater temperature. For instance, in cases B3 to B5, the temperature of the right bulkhead is lower than that of the air domain, resulting in a temperature hysteresis phenomenon. As the ballast water level decreases, the temperature  
Figure 14: The temperature change curve with time at point a under different ballast water heights.  
Figure 15: The temperature change curve with time at point c under different ballast water heights.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Case** & **Cold Air Temperature/\({}^{\circ}\)C** & **Sewater Temperature/\({}^{\circ}\)C** & **Ballast Water Height/m** \\ \hline B1 & \(-\)30 & \(-\)2 & 5 \\ B2 & \(-\)30 & \(-\)2 & 4.5 \\ B3 & \(-\)30 & \(-\)2 & 4 \\ B4 & \(-\)30 & \(-\)2 & 3 \\ B5 & \(-\)30 & \(-\)2 & 2 \\ \hline \end{tabular}
\end{table}
Table 5: Case of ballast water height analysis.  
hysteresis becomes more pronounced, and the range of temperatures that are not completely cooled becomes more evident. This occurs because both the seawater temperature and the cold air temperature are elevated, significantly affecting the air heat transfer rate. The lower the liquid level, the more pronounced the effect of seawater temperature becomes. Consequently, the temperature of the air domain decreases at a slower rate.  
Figures 14 and 15 illustrate the correlation between the height of the ballast water level and temperature changes. As the height of the ballast water level decreases, the minimum temperatures at points a and b also decline, albeit to varying degrees, with the overall change being relatively small. When the ballast water level is at 5 m, the volume of the air domain is limited, resulting in a shorter heat transfer time. Consequently, the temperature of the ballast water decreases rapidly, with the minimum temperature at point a reaching \(-1.14\)\({}^{\circ}\)C and at point b reaching \(-1.34\)\({}^{\circ}\)C. When the ballast water level is reduced to 2 m, the volume of the air domain increases, leading to a longer heat transfer time and a slower decrease in temperature. In this case, the minimum temperature at point a is \(-0.88\)\({}^{\circ}\)C, while at point b, it is \(-1.04\)\({}^{\circ}\)C.