## 1 Introduction
The 0\({}^{\circ}\) VG is unacceptable because it not only raises the velocity fluctuation, but it also enhances the buffeting phenomenon [27]. The VGs' streamwise position, as well as the height and placement of the VG model, strongly affect the skin friction distribution [28]. [PERSON] found that the micro-ramp VG was most effective along its centerline [29]. On the other hand, the size of the VG is also believed to be a critical parameter. The vorticity from a dissymmetric micro-ramp VG is stronger than that from a standard micro-ramp VG [30]. A rod VG was proposed to enhance the stream-wise shear stresses and to effectively reduce flow separation [31]. [PERSON] found that the rectangular vane VGs seemed to be more effective than the triangular ones [32]. The listed references are mainly focused on the improvement of the flow field by VGs, and the work is mainly done in the aviation field. In the hydrodynamic field, only [PERSON] [33] found that mid-VGs could significantly reduce the cross-flow separation and the drag force, but the author did not consider the hydrodynamic noise. The utilization of a VG in underwater vehicles must be investigated in detail, especially the level change in the hydrodynamic noise. Since the physical difference between water and air is enormous, the results in the aviation field can only be considered as a reference. First, an object in the air, like an airplane, is running at high speed, at least 20 times faster than a submarine. The former encounters the problem of shock waves, while the latter encounters cavitation. The formation mechanism of the two problems is different. Second, air is a light medium, while water is a heavy medium. Therefore, the generation mechanism of aerodynamic noise and hydrodynamic noise is different, because the aerodynamic noise neglects the coupling between the shell and the air. Third, the source of aerodynamic noise is mainly from the boundary layer separation, while the boundary layer separation is only one of the hydrodynamic noise sources. Fourth, the boundary layer thickness of air is larger than that of water, and the Reynolds number in air is less than that in water. Therefore, the flow control reports on VGs in the air cannot be directly used to reduce the hydrodynamic noise. Since VGs can be used to redirect the flow in the aerodynamic field, we proposed the idea that mechanical VGs can be applied to reduce a submarine's flow-induced noise through the proper flow control. In this research, we placed VGs at the leading edge of the sail hull on a scaled SUBOFF model to inhibit the formation and development of the horseshoe vortex. We established the calculation process of the flow field and the sound field. The method of large eddy simulation (LES) was used to calculate the flow field. Then, the turbulent fluctuation pressure was extracted. The wavenumber-frequency spectrum method was used to estimate the sound radiation. We revealed the mechanism of mechanical VGs in rearranging the flow field and reducing the flow-induced noise. The VGs with the optimum noise reduction effect on the model were summarized and validated by experiments conducted in a water tunnel. The results from our study can provide a new way to reduce the hydrodynamic noise and enhance the acoustic stealth level of underwater vehicles, such as submarines, torpedoes, unmanned underwater vehicles (UUVs), etc.