# Research on a Strategy for Prediction Methods of Submarine Self-Propulsion Hydrodynamic Performance
## 5 Propeller Excitation Force Calculation and Analysis under Different Computational Strategies
Based on the primary fluctuating frequencies of the forces and torques in different directions for a single propeller blade shown in Figure 19, the fluctuating amplitude at four times the APF and the APF were extracted, as presented in Table 15. As shown in Table 15, the differences in the fluctuating amplitudes of the bearing forces for a single propeller blade across the four different calculation strategies are not significant, with a maximum variation of 2.35%. Moreover, from Tables 14 and 15, it can be observed that in strategy 1, when steady-state calculations are conducted first followed by unsteady calculations, the fluctuating amplitudes of the propeller bearing forces do not exhibit the minimum values. Instead, they fall in the middle range among the four calculation strategies. Therefore, the combined steady-state and unsteady-state methods used in the submarine self-propulsion hydrodynamic performance simulations offer clear advantages in both accuracy and computational efficiency for determining the propeller-bearing forces. (\(R\) is the radius of the propeller). Using the results from the unsteady RBM method in calculation strategy 1 as an example, the time-domain and frequency-domain curves for the four monitoring points are presented in Figure 21.  
Figure 21: Fluctuating pressure curve around the propeller (Strategy 1). Figure 20: Schematic diagram of monitoring points for fluctuating pressure around the propeller. Figure 21a,b show the time-domain variation curves of the monitoring points. The fluctuating pressure at the monitoring points exhibits periodic changes, with 7 peaks occurring within 0.1 s. This is closely related to the 7-blade propeller and the fact that the propeller completes one rotation within 0.1 s. However, the magnitude of the 7 peaks varies, mainly due to the irregular separation of the submarine hull and rudder wing tip vortices, horseshoe vortices, and trailing vortices, as well as the rotation of the propeller. Additionally, there are slight differences in pressure values at the four monitoring points, with the order being Point 3 > Point 1 > Point 4 > Point 2, though the overall difference is not significant. The time-domain data were processed using FFT to obtain frequency-domain curves, as shown in Figure 21c,d. The figures reveal that the fluctuating amplitudes at the monitoring points occur at the BPF. Additionally, there are broadband spectral characteristics between three times and six times the BPF, and the amplitude of the pulsations within this broadband spectrum cannot be ignored. To compare the magnitude of the frequency-domain peaks at the monitoring points across the four different strategies, the BPF amplitudes were extracted from Figure 21 for a comparative analysis, as presented in Table 16.  
Table 16 shows that for the BPF fluctuating amplitudes, the order is Point 2 > Point 4 > Point 3 > Point 1, with a significant difference between Point 2 and Point 4, while the difference between Point 1 and Point 3 is not significant. Comparing the BPF fluctuating amplitudes across the four different calculation strategies, the differences among Point 2, Point 3, and Point 4 are very small, with a fluctuation range of 1.8%. The differences for Point 1 are larger, with a fluctuation range within 5%. Overall, the BPF amplitudes predicted by strategy 1, using both steady- and unsteady-state methods, are not the smallest and do not significantly differ from the maximum values. Therefore, strategy 1 can be used to predict the induced fluctuating pressure of the propeller.