# Research on a Strategy for Prediction Methods of Submarine Self-Propulsion Hydrodynamic Performance
## 4 Analysis of Hydrodynamic Performance under Different Computational Strategies
### Comparison of the Pressure Field and Velocity Field under Different Strategic Approaches  
Based on Section 4.1, using the propeller rotational speed corresponding to the self-propulsion point, \(n=10.145\) r/s, as an example, the surface pressure distribution on the propeller blades and the submarine hull pressure distribution at the self-propulsion point during the numerical simulation of the submarine model's hydrodynamic performance were extracted and analyzed, as shown in Figures 13 and 14. Figures 13 and 14 show the pressure distribution on the submarine hull and the propeller blade's back, using the results of the submarine model's self-propulsion hydrodynamic performance numerical simulation from strategy 1, which employs a steady-state calculation method. From the pressure distribution contour maps, it can be seen that the four calculation strategies had almost no impact on the pressure distribution on the submarine hull and propeller surface during the numerical simulation. Combined with the submarine resistance, propeller thrust, and torque values from Section 4.1, the steady-state MRF method in strategy 1 accurately predicts the pressure distribution on the hull and propeller surface. Therefore, during the process of propeller optimization design and \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Propeller Rotational Speed \(n\) (r/s)**} & \multicolumn{2}{c}{**Submarine Resistance \(R\) Error**} & \multicolumn{2}{c}{**Propeller Thrust \(T\) Error**} & \multicolumn{2}{c}{**Propeller Torque \(Q\) Error**} \\ \cline{2-7}  & **Steady-State** & **Unsteady-State** & **Steady-State** & **Unsteady-State** & **Steady-State** & **Unsteady-State** \\ \hline
9 & 0.038\% & \(-\)0.017\% & \(-\)0.466\% & 0.110\% & \(-\)0.509\% & 0.110\% \\
10 & 0.078\% & 0.025\% & \(-\)0.519\% & 0.119\% & \(-\)0.638\% & 0.077\% \\
11 & \(-\)0.030\% & \(-\)0.044\% & \(-\)0.566\% & 0.098\% & \(-\)0.696\% & 0.101\% \\
12 & \(-\)0.055\% & \(-\)0.060\% & \(-\)0.392\% & 0.354\% & \(-\)0.506\% & 0.237\% \\
10.145 & 0.092\% & 0.090\% & \(-\)0.460\% & 0.065\% & \(-\)0.593\% & 0.038\% \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Error analysis between strategy 4 and strategy 1. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Propeller Rotational Speed \(n\) (r/s)**} & \multicolumn{2}{c}{**Submarine Hull Resistance \(R\) (N)**} & \multicolumn{2}{c}{**Propeller Thrust \(T\) (N)**} & \multicolumn{2}{c}{**Propeller Torque \(Q\) (N\(\cdot\)m)**} & \multicolumn{2}{c}{**Total Solver Actual Runtime \(t\) (h)**} \\ \hline
0 & 90.247 & & & 20.228 \\
12 & 124.325 & 192.493 & 8.968 & 37.771 \\
11 & 119.544 & 148.265 & 7.152 & 27.251 \\
10 & 115.026 & 109.195 & 5.506 & 29.599 \\
9 & 110.623 & 74.999 & 4.026 & 18.708 \\
10.145, self-propulsion point & 115.692 & 114.627 & 5.737 & 19.1624 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Analysis of load characteristics for submarine self-propulsion simulation in iterative mode (strategy 4). this area. In addition, it can be found that the sail and the tail rudder not only affect the flow field in the basin where they are located, but also generate wake flows that extend further to the rear of the submarine. The complexity of the flow field around the vertical submarine gradually decreases, and the flow field around the sail and the tail rudder has the richest layers. Comparing the simulation results of different strategy methods, it can be seen that the velocity field at the tail of the hub is more chaotic in strategy 1, while there is no difference between the other three strategy methods. As seen in Figure 16, there are differences in the velocity field between the propeller blades under different calculation strategies, particularly concentrated near the blade tips. These differences are mainly due to the interaction between the submarine hull, the tip vortices from the submarine hull and rudder, the horseshoe vortices, the irregular separation of the separated vortices, and the rotation of the propeller.