## 8 The Optimized Distance between the VGs and the Sail Hull
Therefore, the inhibition on the intensity of the horseshoe vortex is not apparent. Figure 20 shows the streamline of Plane C between the original model and the model with triangular VGs at a distance of 0.1c from the leading edge of the sail hull. In the original model, two vortex cores were formed near the bottom of the model and the rotation direction of the cores were contrary. The position of each core was not identical in the mirror. Compared to the model with triangular VGs, the position of the two cores was closer to the surface, and the dimension of the two cores was smaller. This phenomenon showed that the boundary layer separation was inhibited by the triangular VGs. The streamline was smoother than the original model. The excitation energy from the turbulence fluctuation pressure was less than the original model. Therefore, radiated sound power from the model with triangular VGs was less than that of the original model. Although the mechanical VGs are excited by the flow, the level of their radiated sound power is much less than the radiated sound power induced by the excitation of the horseshoe vortex in the original model. Since the dimension of the mechanical VGs was much less than the dimension of the model, the influence of the mechanical VGs on the flow-induced noise reduction from the excitation of the horseshoe vortex was the flow control. Figure 21 shows the vortex quanta from the model with triangular VGs at a distance of 0.1c from the leading edge of the sail hull. Compared with Figures 4 and 16, in the model with triangular VGs at a distance of 0.1c, the horseshoe vortex was split into two parts by the VGs. The two parts still surrounded the sail hull, that is, the head was in the leading edge, then the body, and the legs were  
Figure 19: The streamline of Plane B between the original model and the model with triangular VGs at different distances. (**a**) The original model; (**b**) VGs at 0.1c; (**c**) VGs at 0.15c; (**d**) VGs at 0.2c. Figure 20: The streamline of Plane C between the original model and the model with triangular VGs. (**a**) The original model; (**b**) the VGs at 0.1c. dissipated in the tail. Compared to the original model, the body became slim and the legs became short. Then, the intensity of the horseshoe vortex was weakened. When the triangular VGs were placed near the leading edge of the sail hull, the left corner of the VG was adjacent to the surface and the right corner was far away from the surface. Even if the left corner was close to the surface, the vortices were generated and developed at a short distance. The vortices from the right corner were not obvious, due to the influence of the horseshoe vortex. Since the dimension of the mechanical VGs was too small and the increased control of the flow was obvious, it was a good thing that achieved much while requiring limited change to the system. In Figure 22, after the triangular VGs are placed on the model, the peaks in the frequency range less than 500 Hz disappeared. This showed that the triangular VGs reduced the intensity of the horseshoe vortex. However, the peak at 595 Hz shifts, but does not disappear. This showed that the suppression of the horseshoe vortex by the triangular VGs could influence the vortices shedding from the tail of the sail hull. In Table 3, the level of noise reduction by the triangular VGs is mostly above 6 dB. This shows that the flow-induced noise from the model has been reduced by up to 50% in the distance of sound propagation. Therefore, it is possible to believe that the acoustic stealth performance of submarines would be enhanced if the mechanical VGs were set up. Figure 21: The vortex quanta from the model with triangular VGs at a distance of 0.1c from the leading edge of the sail hull. Figure 22: The comparison curve of radiated sound power from the original model and the models with triangular VGs at different distances. The black line denotes the radiated sound power from the original model.