## 7 The Mechanism of Noise Reduction by Triangular VGs  
When the triangular VGs are set up at the leading edge of the sail hull, a new flow disturbance will occur in the fluids. We observed the change of adverse pressure gradient.  
Figure 13 shows the pressure gradient of the leading edge at Plane B of the model with triangular VGs. Compared to Figure 4b, after the triangular VGs are placed, the change of the pressure gradient is not monotonous. Two eddies are at the bottom, which are the vortices from the corners of the triangular VGs. The pressure gradient of the eddies near the leading edge becomes small, which shows that the triangular VGs reduce the intensity of the adverse pressure gradient.  
Figure 14 shows the streamline of the leading edge of the sail hull between the original model and the model with triangular VGs. When the triangular VGs were placed, a clockwise eddy was formed at the origin of the horseshoe vortex, as shown in Figure 14b. From the comparison, the vortex area  
Figure 12: The wake flow field of the two models. (**a**) The original model; (**b**) the model with the mechanical VGs.  
was increased by 547% after the placement of the mechanical VGs. We can see that at the origin of the horseshoe vortex, the intensity of the eddies was significantly enhanced. That means the core area of the horseshoe vortex was expanded by the triangular VGs.  
Figure 15 shows the streamline comparison between the original model and the model with triangular VGs at Plane C. A counter-clockwise eddy on the surface of the original model ran in a longitudinal direction. That is the origin of the horseshoe vortex, which moves continuously in the downstream, as shown in Figure 15a. After the triangular VGs were set up, the counter-clockwise eddy still ran in the longitudinal direction along the sail hull, but the core became small. The vortex area was decreased by 52% after the placement of the mechanical VGs. The streamlines continue to increase, as shown in Figure 15b. The core of the horseshoe vortex moved close to the surface, which revealed that the boundary layer separation was inhibited by the triangular VGs. Therefore, the intensity of the horseshoe vortex was weakened.  
Figure 16 shows the diagram of the horseshoe vortex of the model with triangular VGs at \(Q=500\). Compared to Figure 5, the intensity of the horseshoe vortex at the origin becomes weak. The legs of the horseshoe vortex become shorter and are dissipated at the tail.  
Figure 14: The streamline near the leading edge of Plane B between the original model and the model with triangular VGs. (**a**) The original model; (**b**) the model with triangular VGs.  
Figure 13: The pressure gradient of the leading edge at Plane B of the model with triangular VGs. Two eddies from the triangular VGs can be clearly observed.  
There exists a pressure difference between the two sides of the triangular VGs, which makes the fluid move from a high pressure to low pressure along the flow direction. Then, the spiral vortices are generated, which are opposite to the rotation of the horseshoe vortex. If the intensity of the horseshoe vortex at the origin decreases more than that in the downstream, the sail hull's flow-induced noise will be reduced.  
From the above analysis, the mechanism of the mechanical VGs to control the horseshoe vortex and reduce the flow-induced noise was obtained. We achieved the shape and the angle of the triangular VGs, but other parameters still need to be studied to obtain an optimum noise reduction.