## 7 Conclusions  
We have taken the sail hull with part of the submarine body as the research model to investigate the generation mechanism of the hydrodynamic noise, especially the flow-induced noise from the sail hull. This complements the ignorance of the flow phenomenon of the horseshoe vortex in the isolated sail hull. The calculation of the flow field of the model is carried out by the method of LES. The unstable flow phenomena of the sail hull are analyzed. The turbulent fluctuation pressure is extracted as the excitation force from the flow field. Then, the sound radiation of the model is calculated by the wavenumber-frequency spectrum. After the simulation, the experimental validation has been done. Some conclusions can be drawn:  
Figure 19: Diagram of sound radiation power from the model in the experiments. The red line denotes the hydrodynamic noise from the model at a velocity of 8.68 m/s. The horizontal axis indicates the frequency range, while the vertical axis indicates the level of sound radiation power. (1) The horseshoe vortex, the boundary layer separation, and the tail vortex shedding are ascribed to the three kinds of unstable flow phenomena in the sail hull. (2) The flow-induced noise generated by the excitation of the horseshoe vortex is mainly in the low-frequency range. The flow-induced noise generated by the boundary layer separation exists in the whole frequency range. Only at the frequency of the tail vortex shedding, does the quasi-periodic excitation of the tail vortex produce the peaks of the flow-induced noise. (3) With the joint effect of the horseshoe vortex and the boundary layer separation, the frequency spectrum of the flow-induced noise has several peaks. As the frequency increases, the contribution from the excitation of the horseshoe vortex decreases, so that the level of the flow-induced noise decreases continuously. At the trailing edge of the sail hull, the strength of the horseshoe vortex decays. When the tail vortex passing through the model coincides with the characteristic frequency of the tail vortex shedding, a high peak of the flow-induced noise is formed in the frequency range. Therefore, the radiated noise spectrum of the sail hull is manifested by the tones and the continuous broadband. (4) The sound pressure on the surface of the sail hull is decreased from the leading edge to the trailing edge. Outside of the position of the horseshoe vortex, the fluctuation pressure generated by the boundary layer separation is relatively uniform, which makes the distribution of the flow-induced noise on the surface of the sail hull more uniform. The tail vortex shedding occurs at the trailing edge of the sail hull, which makes the distribution of the flow-induced noise on the surface of the sail hull further intensive. (5) In the low-frequency range, the sound radiation of the sail hull is approximately symmetrical to the direction of the chord, and the angle of horizontal directivity is more intensive in the range from \(45^{\circ}\) to \(135^{\circ}\). With the increase of the frequency, the distribution of the radiated sound field of the sail hull becomes complicated. However, the bow and the tail of the model are still the intensive positions of the flow-induced noise. (6) The measurement of the hydrodynamic noise is carried out in the gravity water tunnel, based on the reverberation method. The peaks of the frequency spectrum agree approximately with the simulation, which further validates the accuracy of the numerical calculation and the analysis from the numerical simulation. These results can provide reference for the design of flow control devices under various kinds of unstable flow phenomena and the reduction of flow-induced noise. At the same time, the results in this study compensate for the shortcomings of past research on the sound field properties of the isolated sail hull, providing a more accurate method for the calculation of the sail hull's flow-induced noise.