# Research on a Strategy for Prediction Methods of Submarine Self-Propulsion Hydrodynamic Performance
## 4 Analysis of Hydrodynamic Performance under Different Computational Strategies  
Comparison of Submarine Resistance and Propeller Hydrodynamic Performance under Different Computational Strategies  
In computational strategy 1, the numerical simulation study of the submarine with propeller self-propulsion hydrodynamic performance was first conducted using the steady-state MRF method. After load convergence was achieved, the computation process was switched to the unsteady RBM method, and the simulation continued until the load converged. The numerical simulation results are shown in Tables 5-7. As shown in Tables 5-7, conducting the numerical simulation study of the submarine with propeller self-propulsion hydrodynamic performance using the steady-state MRF method takes very little time. It only takes 3.5 h to obtain the hydrodynamic performance data of the submarine model at a given propeller rotational speed, and 14.6 h to obtain the _T-n_ and _R-n_ curves needed to determine the self-propulsion point. When the unsteady hydrodynamic performance simulation is conducted based on the steady-state method, it takes approximately 5.0 h to achieve convergence of the unsteady state data, with the load converging very quickly. The calculation errors are also very small, with the submarine hull resistance error within 0.06%, and the propeller thrust and torque errors within 0.8%. Additionally, numerical simulations of the submarine model's self-propulsion hydrodynamic performance were conducted under both steady and unsteady conditions at the self-propulsion point. Tables 5-7, under steady-state conditions, show the submarine hull resistance \(R\) = 115.586 N, the propeller thrust \(T\) = 115.156 N, the propeller torque \(Q\) = 5.771 N\(\cdot\)m, and the total solver actual runtime \(t\) = 3.586 h. Under unsteady-state \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Propeller Rotational Speed _n_** & **Submarine Hull Resistance _R (N)_** & **Propeller Thrust _T (N)_** & **Propeller Torque (N\(\cdot\)m)** & **Total Solver Actual Runtime _t (h)_** \\ \hline
9 & 110.641 & 74.916 & 4.022 & 5.112 \\
10 & 114.997 & 109.065 & 5.502 & 5.073 \\
11 & 119.597 & 148.119 & 7.144 & 5.440 \\
12 & 124.399 & 191.812 & 8.946 & 5.111 \\
10.145, self-propulsion point & 115.588 & 114.552 & 5.735 & 5.122 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Analysis of load characteristics during simulation of submarine with propeller self-propulsion (strategy 1, RBM). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Propeller Rotational Speed** \(n\) & **Submarine Hull Resistance** & **Propeller Thrust** _T Error_ & **Propeller Torque (N\(\cdot\)m)** \\ \hline
9 & 0.054\% & \(-0.575\%\) & \(-0.618\%\) \\
10 & 0.053\% & \(-0.637\%\) & \(-0.713\%\) \\
11 & 0.014\% & \(-0.663\%\) & \(-0.797\%\) \\
12 & 0.005\% & \(-0.744\%\) & \(-0.741\%\) \\
10.145, self-propulsion point & 0.002\% & \(-0.525\%\) & \(-0.624\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Error analysis between steady MRF method and unsteady RBM method (strategy 1). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Propeller Rotational Speed** \(n\) & **Submarine Hull Resistance** & **Propeller Thrust** _T Error_ & **Propeller Torque (N\(\cdot\)m)** \\ \hline
9 & 110.581 & 75.350 & 4.047 & 3.508 \\
10 & 114.937 & 109.764 & 5.541 & 3.580 \\
11 & 119.580 & 149.109 & 7.202 & 3.865 \\
12 & 124.392 & 193.250 & 9.013 & 3.624 \\
10.145, self-propulsion point & 115.586 & 115.156 & 5.771 & 3.586 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Analysis of load characteristics during simulation of submarine with propeller self-propulsion (strategy 1, MRF). conditions, the submarine hull resistance \(R=115.588\) N, the propeller thrust \(T=114.552\) N, the propeller torque \(Q=5.735\) N\(\cdot\)m, and the total solver actual runtime \(t=5.122\) h. The errors in hull resistance, propeller thrust, and torque under unsteady conditions compared to steady conditions are \(0.002\%\), \(-0.525\%\), and \(-0.624\%\), respectively, indicating very small discrepancies.