## 3 Discussion and Analysis
### Influence of Environmental Parameters on the Ice Shape Evolution  
#### 3.2.1 Cold Air Temperature  
This section primarily studies the impact of cold air temperature changes on the evolution of ice shape in the freezing process in ballast tanks. The temperature of cold air is selected as \(-40\)\({}^{\circ}\)C, \(-35\)\({}^{\circ}\)C, \(-30\)\({}^{\circ}\)C, \(-25\)\({}^{\circ}\)C and \(-20\)\({}^{\circ}\)C, while the other environmental conditions remain unchanged. This paper selected the volume fraction of ice phase (the proportion of ice to ballast water) as an index to measure the degree of freezing. Figure 16 shows the evolution of ice shape in the ballast tank at a typical time under different cold air temperatures. Figure 17 shows the variation curve of the ice volume fraction of the ballast tank with time under different cold air temperatures.  
Combined with Figures 7 and 16, it is evident that, under the influence of cold air temperatures, the freezing degree of the ballast tank increases over time. At a cold air temperature of \(-20\)\({}^{\circ}\)C, the temperature change at the ballast water level is relatively gradual, resulting in the formation of a thin ice layer at that level. However, when the cold air temperature drops to \(-25\)\({}^{\circ}\)C, the temperature near the center point 'a' of the ballast water level fluctuates slightly, which reduces the temperature of the ballast water and increases the ice thickness at that level. As the cold air temperature decreases further, the amplitude of these fluctuations increases slightly, and the fluctuation position gradually migrates toward the right bulkhead. At a cold air temperature of \(-40\)\({}^{\circ}\)C, temperature fluctuations are observed on the right bulkhead, extending to the inner depression of the  
Figure 16: Ice shape evolution under different cold air temperatures.  
ballast water, as illustrated in Figure 16a. A certain thickness of ice forms at the junction of the ballast water level and the right bulkhead.  
The temperature of the cold air decreased from \(-20\)\({}^{\circ}\)C to \(-40\)\({}^{\circ}\)C. The right bulkhead of the ballast water gradually transformed from a thin, strip-like cooling zone into a significant temperature gradient, as illustrated in Figure 16a-d. When the temperature of the cold air was higher, the ice layer formed on the right bulkhead was thinner. Conversely, when the temperature of the cold air dropped, the extent of freezing in the right bulkhead increased, gradually extending into the interior of the ballast water tank. As shown in Figure 17, when the ambient temperature is \(-20\)\({}^{\circ}\)C, the maximum volume fraction of the ice phase in the ballast water tank is approximately 42.05%. When the temperature decreases to \(-40\)\({}^{\circ}\)C, the maximum volume fraction of the ice phase in the ballast water tank rises to approximately 84.33%, indicating a relatively high degree of freezing in the ballast water tank. Therefore, the evolution of ice formation in ballast water tanks is primarily influenced by changes in the temperature field. The faster the rate of change in the temperature field, the more rapid the evolution of ice form evolution.