# Research on a Strategy for Prediction Methods of Submarine Self-Propulsion Hydrodynamic Performance
## 4 Analysis of Hydrodynamic Performance under Different Computational Strategies
Furthermore, in the steady-state numerical simulation of the submarine model's self-propulsion hydrodynamic performance, the difference between submarine hull resistance and propeller thrust is \(0.43\) N, indicating that the self-propulsion point rotational speed obtained by adjusting four sets of propeller rotational speeds is highly accurate. Figure 12 presents the variation curves of submarine resistance, propeller thrust, torque, and total solver actual runtime with respect to iteration steps during the numerical simulation of the submarine model's self-propulsion hydrodynamic performance under steady and unsteady conditions. As shown in Figure 12, the load fluctuation range is much smaller under steady-state conditions compared to unsteady-state conditions, which is consistent with the actual behavior of the steady-state method. At the same time, the submarine's resistance is greater under unsteady conditions than under steady conditions, while the propeller thrust and torque are lower under unsteady conditions. Additionally, when performing unsteady calculations based on the steady-state conditions, the convergence speed of the propeller thrust and torque is very fast. In Figure 12d, the total solver time on the vertical axis is greater than the times shown in Tables 5 and 6. The main reason is that Figure 12d includes the time spent on continued calculations after the load is stabilized, whereas Tables 5 and 6 only reflect the total solver actual runtime corresponding to the load's periodic variation. Figure 12: The variation curve of load and total solver actual runtime with the iteration step. In computational strategy 2, the unsteady RBM method was used. Initially, the propeller rotational speed was set to \(n=0\) r/s to conduct a numerical simulation study of the submarine model's self-propulsion hydrodynamic performance. After the submarine hull resistance converged, the propeller rotational speeds were individually set to \(n=9\) r/s, 10 r/s, 11 r/s, 12 r/s, and 10.145 r/s to conduct numerical simulations of the submarine model's self-propulsion hydrodynamic performance at different propeller rotational speeds. The calculation results are shown in Tables 8 and 9. As shown in Table 8, using the unsteady RBM method for the numerical simulation of the submarine model's self-propulsion hydrodynamic performance is time-consuming. For example, the simulation of submarine hull resistance with a propeller rotational speed of \(n=0\) r/s alone takes 20.228 h. If this method were used to conduct numerical simulations at four different propeller rotational speeds to determine the propeller rotational speed corresponding to the self-propulsion point, it would take 174.012 h, which is 12 times longer than the time required for the steady-state method in strategy 1 (14.576 h) and 5 times longer than the time required for the steady-state + unsteady-state method (35.313 h). Therefore, the time required by the strategy 2 method to determine the propeller rotational speed corresponding to the self-propulsion point of the submarine model is significantly longer than that of the strategy 1 method. Table 9 provides an error analysis of the data obtained using the strategy 2 method, based on the predictions from strategy 1. As shown in Table 9, the maximum errors of submarine hull resistance, propeller thrust, and torque using the strategy 2 method compared to the steady-state results are \(-\)0.055%, \(-\)0.391%, and \(-\)0.579%, respectively. Compared to the unsteady-state results, the maximum errors are \(-\)0.070%, 0.543%, and 0.374%, respectively. The errors in the data obtained from both computational strategies are very small. In strategy 2, the submarine hull resistance obtained is slightly reduced compared to both the steady-state and unsteady-state methods, while the propeller thrust and torque are slightly reduced compared to the steady-state method and slightly increased compared to the unsteady-state method.