## 9 The Experimental Validation
### The Description of the Experimental Measurement
We observed that when the frequency was less than 500 Hz, the radiated sound power from the two models was  
Figure 27: The turbulent fluctuation pressure measured by the fluctuation pressure sensor at different flow velocities: (**a**) 4.62 m/s; (**b**) 8.68 m/s. Figure 26: The diagram of the experimental measurement. (**a**) The composition of the vertical hydrophone array; (**b**) the spatial average method. especially low. This phenomenon clearly showed the measured limitation frequency, which was an intrinsic property of the reverberation tank. In Figure 28a, we can see that the fluctuation pressure in the low-frequency range was reduced by the triangular VGs. The radiated sound power was also decreased by the mechanical VGs. The radiated sound power was obviously reduced when \(f<1200\) Hz. Since the signal-to-noise ratio was too low, the radiated sound powers of the two models were very similar to each other when \(f>1200\) Hz. The radiated sound power from the model with the triangular VGs was even larger than that from the original model, due to the interference of the background noise. At a flow velocity of 4.62 m/s, the total radiated power reduction level by the mechanical VGs was 3.67 dB. Owing to the time limitation, we did not calculate the flow-induced noise from the models at the flow velocity of 4.62 m/s. In Figure 28b, if the frequency is less than 1200 Hz, the radiated sound power from the model with the mechanical VGs is less than the original model. Meanwhile, if the frequency was higher than 1200 Hz, the radiated sound power from the model with the mechanical VGs is larger than the original model. The trend of radiated sound power changing with the frequency in Figure 28b was the same as that in Figure 11.  
Through the statistical analysis, we found that the total radiated sound power of the two models was approximately proportional to the sixth power of the flow velocity. This phenomenon agreed well with the law of hydrodynamic noise. Through the comparison of the two models, the noise reduction of the radiated sound power by the mechanical VGs was 7.93 dB at a flow velocity of 8.68 m/s. However, the calculated noise reduction of the radiated sound power was 8.93 dB at a flow velocity of 8.68 m/s, as shown in Table 3. The reasons for the differences between the numerical simulation and the experiment measurement were as follows:  
First, the sail hull was welded on a part of the submarine body. The experimental model was not as smooth as that in the numerical simulation. The welded points can affect the formation of the horseshoe vortex. Second, the thickness of the models in the numerical simulation was identical. However, the thickness of the models in the experiment was not identical, due to issues relating to mechanical manufacture. Third, no background noise exists in the numerical simulation. In the experiment, we could not avoid background noise from the ground, the circular pipes, the power supply, etc., even if we did our best to reduce these background noise effects. Fourth, there were also some other interferences. For example, the water temperature, the flow velocity repetition, and the boundary conditions in the experiment were not considered to be rigid. Figure 28: The radiated sound power measured by the vertical hydrophone array in the reverberation tank at different flow velocities: (**a**) 4.62 m/s; (**b**) 8.68 m/s. However, the measured hydrodynamic noise suppression level was only 1 dB lower than the calculated noise suppression level. The models in the simulation and experiment were much smaller compared to real submarines, but the noise reduction effect was obvious. We may conclude that if the mechanical VGs are placed on a larger model, the noise reduction could be more considerable. Therefore, we believe that the proposed noise reduction method by the mechanical VGs in our research can be applied to enhance the acoustic stealth performance of underwater vehicles in the future.