## 4 Simulation Results and Analysis  
### Solidification Process  
In the solidification process, the most important information in this paper is that the time required for the phase change material to go from \(T(r,0)=T_{\rm a}\), \(f_{\rm l}=1\) to \(T(r,t)\leq T_{\rm m}\), \(f_{\rm l}=0\) under various working conditions and it must be shorter than the duration of the underwater monitoring device in cold water. The ocean surface-water temperature is taken as 26 \({}^{\circ}\)C [1] for calculation and analysis.  
4.1.1 Effect of Different Sizes of Cylindrical Phase-Change Heat Exchanger on Solidification Process  
It can be clearly seen from Figures 2 and 3 that as the outer diameter of the cylinder decreases (the thickness of the phase-change material decreases), the liquid-phase ratio decreases significantly at the same time, that is, the phase change condensation rate increases significantly. This is mainly because the thermal conductivity of the phase-change material n-hexadecane is very low even if 10% graphite is added. The smaller the thickness of the phase-change material, the smaller the thermal resistance and the stronger the heat transfer, so the condensation process is faster; in addition, under the premise that the total volume of the phase-change material and the inner diameter of the cylinder are the same, the smaller the outer diameter of the cylinder, the longer the cylinder, the larger the outer surface area, and the stronger the heat transfer, which is also the reason for the accelerated phase change rate. The numerical analysis results show that the time required for these two cylindrical phase change heat exchangers with different outer diameters to complete the solidification process is 18,290 and 4800 s, respectively.  
1.2 The Influence of Cylindrical Heat Exchanger and Cylindrical Heat Exchanger on the Solidification Process  
In order to compare the different effects of cylindrical phase change heat exchanger and cylindrical phase change heat exchanger on the solidification process, four cylindrical phase change heat exchangers with a diameter of 0.07 m were used to load phase-change materials, which were 0.95 m long and equivalent to the volume of cylindrical phase change heat exchanger. Because the working conditions of these four cylindrical phase change heat exchangers are exactly the same, only one is numerically analyzed.  
Comparing Figures 3 and 4, it can be clearly seen that under the same phase change time, the total liquid-phase ratio of the cylindrical phase change heat exchanger is significantly smaller than the total liquid-phase ratio of the cylindrical phase change heat exchanger. The reason is also that the cylindrical phase change heat exchanger has a larger thickness of the phase change material and a smaller total outer surface of the heat exchange, which is not conducive to the heat exchange between the phase change material and the outside world. The numerical analysis results show that the time required for the cylindrical phase change heat exchanger to complete the solidification process is as high as 27,800 s, which is much higher than any of the cylindrical phase change heat exchangers mentioned above. Of course, if we greatly increase the number of cylindrical phase change heat exchangers, the phase change rate will be greatly improved, but from the perspective of manufacturing and processing, this is obviously unfavorable.  
Figure 3: Liquid fraction distribution for the cylindrical heat exchanger with outer diameter of 0.26 m and height of 0.95 m.  
Figure 2: Liquid fraction distribution for the cylindrical heat exchanger with outer diameter of 0.3 m and height of 0.45 m.