## 5 Optimized Design of the Cooling Channel and Its Cooling Performance
### Steady-State Simulation Result Analysis  
As shown in Figure 16, a comparison of the temperature distribution along the rudder shaft at different flow rates revealed that, for both 0.1 m/s and 0.2 m/s inlet velocities, the new cooling structure exhibits a similar trend to the original design, with lower maximum temperatures as flow velocity increases. The enhanced convective heat transfer at higher fluid velocities results in better cooling performance at 0.2 m/s compared to 0.1 m/s. Based on the forced convection boiling heat transfer range and flow pattern in the vertical tube, the boiling in the tube under different inlet flow rates is analyzed and presented in Figure 17. When the inlet flow velocity is 0.1 m/s, the fluid near the wall at the upper flange reaches the vaporization threshold, forming floating vapor bubbles, while some of the central flow remains below the saturation temperature, leading to the condensation of bubbles as they move into the central flow. This region remains in the surface boiling zone. At the lower flange, the central flow exceeds the saturation temperature, with observable bubble, slug, and annular flows. The annular vapor reaches a superheated state, with a significant liquid film remaining, indicating the saturated nucleate boiling region. When the inlet velocity increases to 0.2 m/s, the wall fluid at the upper flange reaches the vaporization threshold, but when comparing to 0.1 m/s velocity, the central flow does not reach saturation, leading to the condensation of bubbles without the significant development of bubble flow. The flow remains in the surface boiling zone. At the lower flange, the central flow reaches saturation, with gradually growing vapor bubbles and observable bubble and slug flows, indicating the saturated nucleate boiling region, albeit with relatively lower intensity. Figure 16: Surface temperature distribution of the rudder shaft when the inlet flow velocity is (**a**) 0.1 and (**b**) 0.2 m/s. Figure 15: Schematic diagram of the physical model of the improved new cooling structure. Based on the above flow pattern analysis of the internal fluid, for both 0.1 and 0.2 m/s inlet velocities, the flow at the lower flange remains in the saturated nucleate boiling region, while the upper flange predominantly experiences surface boiling. Heat transfer at the lower flange relies on boiling in the annular water storage channel, whereas at the upper flange, boiling is less pronounced compared to the initial structure, leading to a significant role for forced convective heat transfer in the liquid phase. This suggests that the new cooling structure is safer, as it mitigates the risk of fluid boiling in the high-temperature region at the top of the rudder shaft. The average convective heat transfer coefficient at the rudder shaft's top is higher at 0.2 m/s inlet velocity compared to 0.1 m/s (see Table 9), with a pressure drop approximately 20% greater at the higher velocity. The 0.2 m/s inlet velocity offers better cooling efficiency with a moderate increase in pressure drop, making it advantageous. However, the 0.1 m/s inlet velocity also meets the cooling requirements without heat transfer deterioration, suggesting its advantage of halving the cooling water consumption and smaller pressure drop as shown in Table 10. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Flow Velocity (m/s)** & 0.1 & 0.2 \\ \hline
**Average convective heat transfer coefficient** & & \\
**(W/m\({}^{2}\cdot\)K)** & & 7729 & 10,335 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Average convective heat transfer coefficient at the rudder shaft’s top. Figure 17: **(a1,b1)** Phase fraction distribution and **(a2,b2)** temperature distribution of the fluid when the inlet flow rate is **(a)** 0.1 and **(b)** 0.2 m/s, respectively. The axial solid temperature distribution comparison between the new and old cooling structures, as shown in Figure 18, indicates that the new structure provides superior cooling performance at the same flow rate.