# Research on a Strategy for Prediction Methods of Submarine Self-Propulsion Hydrodynamic Performance
## 5 Propeller Excitation Force Calculation and Analysis under Different Computational Strategies  
To further compare the impact of different computational strategies on propeller excitation forces, four computational strategies were utilized to conduct numerical simulations of the submarine model's self-propulsion hydrodynamic performance at the self-propulsion point. The inflow velocity was set to \(V=3.051\) m/s, and the propeller rotational speed was set to \(n=10.145\) r/s. The analysis is presented as follows. Comparison and Analysis of Propeller Unsteady Bearing Forces under Different Computational Strategies  
Taking the results of the unsteady RBM method in computational strategy 1 as an example, the time-domain and frequency-domain curves of the three-directional forces T\({}_{X}\), T\({}_{Y}\), and T\({}_{Z}\), as well as the three-directional torques \(Q_{X}\), \(Q_{Y}\), and \(Q_{Z}\) of the propeller during the numerical simulation of the submarine model's self-propulsion hydrodynamic performance, are presented. Additionally, the time-domain and frequency-domain curves of the three-directional forces \(T_{Blade_{x}}\), \(T_{Blade_{x}}\), and \(T_{Blade_{x}}\), as well as the three-directional torques \(Q_{Blade_{x}}\), \(Q_{Blade_{x}}\), and \(Q_{Blude_{x}Z}\), for a single propeller blade, are also shown in Figures 18 and 19. Figure 17: Iso-surface vortex structure under different calculation strategies. Figure 18(a),b present the three-directional forces and torques of the propeller in an X-Y-YY format. The left side of the vertical axis represents the \(X\)-direction forces and torques, while the right side represents the \(Y\)- and \(Z\)-direction forces and torques. As shown in the figures, the forces and torques in all three directions exhibit periodic variations, with the forces and torques in the \(X\)-direction being the largest. In the \(Y\)- and \(Z\)-directions, the fluctuation ranges of forces and torques in the \(Y\)-direction are greater, with force fluctuations being particularly noticeable. In terms of load magnitude, the force in the \(Y\)-direction is larger, whereas the torque in the \(Z\)-direction is greater. By performing a fast Fourier transform (FFT) on the time-domain curves of load variations shown in Figure 18(a),b, the time-domain curves are transformed into frequency-domain curves, as shown in Figure 18(c). From the figures, it can be observed that the primary pulsation frequency of the propeller thrust and torque is the blade passage frequency (BPF = 71.015 Hz, calculated by multiplying the number of blades by the propeller rotational speed, where a 7-blade propeller at 10.145 r/s results in BPF = 10.145 \(\times\) 7 = 71.015 Hz). The fluctuating amplitude at the blade passage frequency is largest in the \(Y\)-direction forces and torques. Additionally, the magnitude of these amplitudes is related to the forces or torques; in terms of force, the fluctuating amplitude of BPF in the \(X\)-direction is slightly larger than in the \(Z\)-direction, while for torque, the fluctuating amplitude of BPF in the \(Z\)-direction is greater than in the \(X\)-direction, with a noticeable difference. This is primarily due to the uneven forces acting on the propeller in the non-uniform flow field at the submarine's stern. Moreover, in Figure 18, although the mean values of forces and torques in the \(Y\)- and \(Z\)-directions are smaller than in the \(X\)-direction, the fluctuating amplitude of BPF in the \(Y\)- and \(Z\)-directions is greater than or nearly equal to that in the \(X\)-direction. Therefore, when  
Figure 18: Time- and frequency-domain curves of propeller load (strategy 1). analyzing the propeller bearing forces, the influence of forces and torques in the \(Y\) and \(Z\) directions should not be overlooked. Based on the analysis results in Figure 18, the predicted hydrodynamic performance results at the self-propulsion point for the submarine model were extracted under four different computational strategies.