## 1 Introduction
Besides, with the fine grids of the model, the flow-induced noise from different flow phenomena can be investigated, and the noise generation mechanism can be analyzed in detail [17]. Furthermore, the characteristics of sub-boundary layer sound generation have been studied by [PERSON] et al., who have found that the rectangular steps produce more noise than the triangular steps, which is most likely due to the differences in the turbulent flow environment at the front surfaces of the steps [18]. After the analysis from the numerical calculation, the experimental measurement [10; 19] becomes essential to validate the calculated results, which can reveal the properties of the flow-induced noise, because the precision of the numerical calculation is limited by the number of the grids and the defects of the boundary element method [20]. To suppress the hydrodynamic noise from the submarines, we must know the exact noise sources from the excitation of different flow phenomena. One of the sources of the hydrodynamic noise is from the excitation by the horseshoe vortex. [PERSON] et al. have proposed the modified method of a vortex baffle to break the vortex core of the horseshoe vortex [6]. Since the horseshoe vortex is a giant vortex mass, from which the noise is in the low-frequency range, the control of the horseshoe vortex neglects the noise of high-frequency range. Aiming to describe the relationship between hydraulic and acoustic conditions, this research will provide a better understanding of noise source acoustical characteristics and show the influence of geometrical parameters on noise production and emission,just like what [PERSON] has done in a water installation system [21]. Furthermore, the exact understanding of the generation mechanism of the flow-induced noise can help us better separate the needed noise components from other noises with the disturbance of the hydrodynamic noise [22]. Although there are some mature studied reports in the airfoil [14; 19], which can be considered as similar to the sail hull and the stern of the submarine, these results can only be references. One difference of the results between the water and the air is the assumption that the feedback of the acoustic field to the flow is small for low Mach number flows [23] in the air. Because the water is the dense medium, of which the acoustic impedance is approximately equal to that of the submarine, the feedback of the acoustic field to the flow cannot be considered as small or neglected. Another difference in the results between the two is the experimental measurement. In the air experimental facilities, the model is placed at the outlet of the wind tunnel and the driven air can be dispersed everywhere. The third difference in the results between the water and the air is that the Reynolds number is lower and no cavitation occurs in the air, compared to that in the water. All these differences can be the obstacles when the results of the air are applied into the water. In our study, based on the theory of numerical simulation [24], we have proposed the method to calculate the flow-induced noise from the model of the sail hull with part of the submarine body. The flow field is calculated by the Large Eddy Simulation (LES), and the sound sources which are on the right-hand side of the acoustic equations are extracted from the computed flow field. After that, we have introduced the method of the wavenumber-frequency spectrum to calculate the flow-induced noise, to conquer the overestimate effect of the FW-H equation in the near sound field; at the same time, to avoid the problem that the solution is not unique in the characteristic frequency of the boundary element method. In the simulation, we have investigated the generation mechanism of the flow-induced noise from three kinds of the flow phenomena around the sail hull and part of the submarine body, which are the horseshoe vortex, the boundary layer separation, and the tail vortex shedding.