## 6 The Optimized Angle of Mechanical VGs to the Flow Direction  
To reveal the optimum effect of the flow-induced noise suppression by mechanical VGs, we investigated the radiated sound power from the model with triangular VGs at different angles to the flow direction: \(0^{\circ}\), \(15^{\circ}\), \(30^{\circ}\), \(45^{\circ}\), and \(60^{\circ}\). Figure 9 shows the curves of the radiated sound power from the original model and the model with triangular VGs at different angles to the flow direction. The curve of the radiated sound power from the original model was similar to that from the model with triangular VGs. With the frequency increase, some peaks were observed. The level of the radiated sound power from the model with triangular VGs was higher than that of the original model in some frequencies. To better evaluate the noise reduction effect by the VGs, the total levels of radiated sound power from the original model and that with the triangular VGs are shown in Table 2.  
From Table 2, we see that with the increase in the angle, the total level of radiated sound power from the model with triangular VGs firstly decreased, and then increased. Therefore, to obtain a better noise reduction, there exists an optimum angle of VGs to the flow direction. The optimum angle is \(30^{\circ}\), as shown in Table 2. When the angle of triangular VGs to the flow direction was \(15^{\circ}\), \(30^{\circ}\), and \(45^{\circ}\), the flow-induced noise reduction could be \(2.07\) dB, \(5.23\) dB, and \(1.48\) dB, respectively. Meanwhile, at the angles of \(0^{\circ}\) and \(60^{\circ}\), the noise reduction was negative. Therefore, the improper placement of triangular VGs increases the radiated sound power. The reason is that when the triangular VGs are placed at the angle of \(0^{\circ}\) to the flow direction, the VGs blockage strengthens the dimension of the lateral vortices, so that the intensity of the horseshoe vortex is enhanced. When the triangular VGs are placed at the angle of \(45^{\circ}\) or \(60^{\circ}\), the VGs also strengthen the dimension of the lateral vortices and enhance the intensity of the horseshoe vortex. Figure 10 shows the curves of radiated sound power from the original model and the model with triangular VGs at the angle of \(0^{\circ}\) to the flow direction. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Model** & **Total Level of Radiated Sound Power/dB 1** & **Noise Reduction/dB 1** \\ \hline Original & 113.51 & 0 \\ \(0^{\circ}\) VGs & 130.54 & \(-17.03\) \\ \(15^{\circ}\) VGs & 111.44 & 2.07 \\ \(30^{\circ}\) VGs & 108.23 & 5.23 \\ \(45^{\circ}\) VGs & 112.03 & 1.48 \\ \(60^{\circ}\) VGs & 119.71 & \(-6.20\) \\ \hline \hline \end{tabular}  
* dB The reference is \(0.67\times 10^{-18}\).  
\end{table} 
Table 2: The total level of radiated sound power from the original model and the models with triangular VGs at different angles. Figure 9: The comparison curve of radiated sound power from the original model and the model with triangular VGs at different angles to the flow direction. The \(0^{\circ}\) VG’ means that the triangular VGs are at the angle of \(0^{\circ}\) to the flow direction. The other meanings are the same as ’The \(0^{\circ}\) VG’. At the initial frequency range shown in Figure 10, the level of radiated sound power from the model with triangular VGs is 124 dB and is much larger than that of the original model, where the latter is 102 dB. A high peak at the frequency of 40 Hz was observed, which was caused by the horseshoe vortex excitation, not by the VGs. The dimension of VGs was too minimal compared to the wavelength of sound waves in the water; the efficiency of radiated sound power was too low. Therefore, the radiated sound power from the VGs themselves can be ignored. The triangular VGs had strengthened the lateral vortices, which were the origin of the horseshoe vortex. Then, the flow-induced noise from the shell excited by the horseshoe vortex was enhanced. In addition, the peak's position in Figure 10 is not changed, even after the triangular VGs are placed.