## 6 The Optimized Angle of Mechanical VGs to the Flow Direction
This phenomenon also shows that the high level at 40 Hz is not from the vibration of the VGs themselves. In the other frequency range, the radiated sound powers of the two models were similar to each other. As we know, the evaluation of noise reduction is based on the total level of radiated sound power. Since the level difference of the two models at the initial frequency reached up to 22 dB, the total level of radiated sound power was mostly influenced by the difference, and the placement of the triangular VGs did not achieved the goal of noise reduction. Figure 11 shows the level of radiated sound power from the original model and the model with triangular VGs at the angle of 30\({}^{\circ}\) to the direction of the flow. In the low-frequency range (\(f<500\)Hz), the radiated sound power from the model with triangular VGs was lower than that from the original model. This phenomenon showed that the flow-induced noise was strongly weakened by the flow control of the triangular VGs. Therefore, the low-frequency hydrodynamic noise can be suppressed by the triangular VGs. The vortices generated by the mechanical VGs could change the structure of the horseshoe vortex. Specifically, the cluster of large-scale vortices could be changed into small-scale vortices. Figure 11: The curve of radiated sound power from the original model and the model with triangular VGs at the angle of 30\({}^{\circ}\) to the flow direction. Figure 10: The comparison curve of radiated sound power between the original model and the model with triangular VGs at the angle of 0\({}^{\circ}\) to the flow direction. At 650 Hz, a high peak was observed compared to the other frequencies. The frequency of the tail vortex shedding is  
\[f=\frac{S_{t}\times U}{C}, \tag{24}\]  
where \(S_{t}\) is the Strouhal number, \(U\) is the incoming flow velocity, and \(C\) is the feature length of the model. According to Equation (24), the frequency of the tail vortex shedding was 595 Hz, just as the black dotted line in Figure 11 indicates. This phenomenon indicated that the triangular VGs also changed the formation of the tail vortex shedding. Figure 12 shows the turbulent kinetic energy contour at Plane A from the two models. In the wake flow field of the model with mechanical VGs, the area of intensive turbulence was somewhat larger than that of the original model. This phenomenon showed that the vortices produced by the mechanical VGs could influence the tail vortex shedding from the tail. The vortices could enhance the intensity of the wake. Meanwhile, these vortices were in the small-scale vortices. The flow-induced noise in the high-frequency range could be increased, because the flow-induced noise from the excitation of the small-scale vortices was mainly in the high-frequency range. Since small-scale vortices from the triangular VGs can excite the shell of the model and generate the radiated sound power, more peaks were observed at the high-frequency range. Therefore, the utilization of the triangular VGs can shift the hydrodynamic noise from the low-frequency range to the high-frequency range through the flow control. As we know, the sound absorption in seawater is approximately proportional to the squared frequency. The low-frequency noise can propagate over a long distance and can be an efficient signal to detect underwater vehicles, while the high-frequency noise can be quickly absorbed by the seawater. Therefore, the triangular VGs provide a feasible method to suppress the low-frequency flow-induced noise.