## 3 Discussion and Analysis
### Influence of Environmental Parameters on the Ice Shape Evolution
#### 3.2.3 Ballast Water Height  
The height of the ballast water is selected as 0.5 m, 0.45 m, 0.4 m, 0.3 m and 0.2 m, respectively, while the other environmental conditions remain unchanged. The influence of a change in the height of the ballast water level on the evolution of ice shape during the freezing process in ballast tanks is analyzed. Figure 20 shows the evolution of the ice phase in ballast tanks at different liquid level heights, and Figure 21 shows the change curve of the ice volume fraction in ballast tanks at different liquid level heights.  
Figure 19: The variation curve of the ice phase volume fraction in the ballast tank under different seawater temperatures.  
Figure 18: Ice shape evolution under different seawater temperatures.  
As illustrated in the ice shape evolution depicted in Figure 20, the freezing rate and degree of freezing of ballast water vary with different liquid level heights. As the liquid level of the ballast water decreases, the degree of freezing increases correspondingly. Combined with the analysis of Figure 13, it can be concluded that at positions with a significant temperature variation range, the freezing rate of ballast water fluctuates considerably. As shown in Figure 20a-d, when the liquid level height is 5 m, the ice layer first appears on the left and right sides of the ballast water surface near the bulkhead, gradually evolving into the interior of the ballast water as the liquid level decreases. When the liquid level height reaches 2 m, the volume of the air domain is larger, significantly enhancing the effect of cold air temperature on the ballast water. Consequently, the ice layer formed by the freezing of ballast water is relatively thick and exhibits a high degree of freezing.  
The influence of the ballast water height on the freezing rate differs from that of temperature. When the ballast water height is elevated, the volume of the air space in the ballast water tank decreases. Due to the low specific heat capacity of air, the heat transfer rate increases, leading to a faster freezing rate in the ballast water. Conversely, when the ballast water height is lower, the volume of the ballast water is also diminished, requiring less heat for complete freezing. As a result, the ballast water demonstrates a relatively high degree of freezing.  
Figure 21 clearly illustrates the change in the ice volume fraction over time at varying liquid levels. When the ballast water height is 5 m and the time is 14,400 s, the ice phase volume fraction in the ballast tank is approximately 63.17%. Conversely, when the ballast water height is reduced to 2 m, the ice phase volume fraction in the ballast tank increases to approximately 92.35%, indicating a greater degree of freezing. Therefore, the change in the  
Figure 21: The variation curve of the ice phase volume fraction in the ballast tank under different ballast water heights.  
Figure 20: Ice shape evolution under different ballast water heights.  
liquid level of the ballast water significantly impacts the heat transfer rate. As the height of the ballast water decreases, the heat transfer rate diminishes, while the relative degree of freezing increases.