## 10 Conclusions  
In the aviation field, mechanical VGs were successfully applied to control the flow separation. However, the noise reduction from the flow control by the VGs has not been fully considered, especially in water. We proposed a method whereby mechanical VGs were used to inhibit the formation of the horseshoe vortex and reduce the force from the horseshoe vortex. Then, the flow-induced noise can be suppressed. In our study, we created the model according to the structure of the SUROFF. The flow field was calculated by a combination between the large eddy simulation and the RNG \(k\)-e turbulent model. The flow-induced noise was estimated by the wavenumber-frequency spectrum. The flow-induced noise was calculated using [PERSON]'s acoustic analogy and the finite element method. Through the comparison, we investigated the change in the flow field and the sound field, when the mechanical VGs were placed at the leading edge of the sail hull. Through the investigation of the shapes of the VGs, the angles of the VGs to the direction of the flow, and the distances of the VGs to the leading edge of the sail hull, we summarized the optimum parameters of the VGs, based on comparisons with the original model. After that, we created a steel model according to the simulation. The experiment was carried out in a gravity water tunnel, based on the reverberation method. The simulation results were validated by the experiment. The conclusions of this research are as follows:  
First, the triangular VGs have a better effect in noise reduction. We found that the high corner of the triangular VGs will produce the vortices, which are opposite to the rotation of the horseshoe vortex. The vortices from the low corner can inject the outside energy into the boundary layer and reduce the pressure gradient. All these vortices can decrease the intensity of the horseshoe vortex.  
Second, the angle of the triangular VGs has an important influence on the noise reduction. Better noise reduction is achieved when the angle of the triangular VGs to the direction of the flow is 30\({}^{\circ}\).  
Third, the distance from the triangular VGs to the leading edge of the sail hull is related to the effect of the noise reduction. Better noise reduction can be achieved when the triangular VGs are placed at a distance of 0.1c, and the high corner of the VGs is placed at the origin of the horseshoe vortex, where c is the chord length.  
Fourth, we found that when the triangular VGs, with a length of 0.1c and the height of 0.1 \(H\), are placed at a distance of 0.1c and at an angle of 30\({}^{\circ}\) to the flow direction, the optimum reduction of the flow-induced noise is 8.93 dB, where \(H\) is the sail hull's height.  
Fifth, the noise reduction level of the flow-induced noise in the experimental measurement was in good accordance with that in the simulation. Therefore, the analysis of the numerical calculation was validated.  
The proposed method of flow-induced noise reduction by the mechanical VGs can be applied to reduce the hydrodynamic noise from underwater vehicles, such as the submarines, torpedoes, the UUV, etc.  
Writing--original draft preparation, [PERSON] ([PERSON]); writing--review and editing, [PERSON] ([PERSON]); visualization, [PERSON]; supervision, [PERSON] This research was funded by the steady support plan from the Acoustic Science and Technology Laboratory, grant number SSJSWDZC2018005, the project from Key Laboratory of Acoustic Stealth, grant number 614220405011706, and the project from Acoustic Science and Technology Laboratory, grant number 6142108011305. The authors would like to thank [PERSON] of the University of Alberta. The authors declare no conflict of interest.