## 1 Introduction  
Torpedoes, submarines, and other underwater vehicles are the main combat tools of national navies and play an important role in assault operations, striking military targets, and reconnaissance owing to their high navigation speed, long range, and stealth. However, in the context of rapid development of soft and hard kill technologies such as sonar technology to combat underwater high-speed vehicles, how to improve the survivability of underwater vehicles has become a key technology in the military field. Underwater vehicles inevitably generate noise during their missions, and for every 5 dB increase in noise, the probability of hitting a target is reduced by 25%, thus directly affecting their stealth and deterrence. Therefore, underwater high-speed vehicles with silent characteristics have received much attention from various navies. The underwater noise is mainly generated by the pulsating pressure on the surface of vehicle and the disturbance within the turbulent boundary layer around the surface, and it is difficult to reduce the noise using general methods. Therefore, it is important to study the mechanism of underwater vehicle noise generation to improve its concealment. The study of noise begins with a focus on turbulence and pulsating pressure, which was usually studied by theoretical analysis and experimental verification. However, theoretical analysis is only applicable to a simplified model, which cannot describe the phenomenon of a complex flow; experimental verification is also not widely used because of its high cost, long cycle time, and small measurement range. With the development of computer technology and improvement of computer performance, computational fluid dynamics (CFD) has become an important tool for solving flow problems. After the SUBOFF submarine model was proposed in the United States in 1989 and a series of experimental data were obtained, many numerical simulation studies based on this model and data were also carried out [1]. [PERSON] analyzed a fully attached SUBOFF flow field variation usingUnsteady Reynolds Averaged Navier Stokes (URANS) [2], Detached Eddy Simulation (DES), and Large Eddy Simulation (LES) [3], discussed the accuracy of different numerical computational models, and finally found the advantages of DES and LES for solving the pulsation-related terms. [PERSON] [4] and [PERSON] [5] analyzed the viscous flow field and flow-separation phenomena in SUBOFF submarines using LES and verified the accuracy of LES in flow field simulations when compared with experimental values. [PERSON] and [PERSON] [6] directly used Direct Numerical Simulation (DNS) to calculate the pulsation pressure within the boundary layer of a two-dimensional model flow field. However, DNS is poorly applicable because of the high requirements of computer hardware. Therefore, to balance the computational resources and solution accuracy, it is gradually becoming a research trend to use LES to obtain turbulent flow field data. After separating the acoustic terms from the equations using the acoustic analogy theory proposed by [PERSON] [7; 8], the flow field calculations were successfully combined with the acoustic field calculations and numerical calculations on developing noise. [PERSON] et al. [9] simulated the complex flow field of a submarine with a propeller based on LES and analyzed the sound pressure spectrum and noise-pointing characteristics of the submarine using ACTRAN software. It was found that the noise of the submarine with a propeller was concentrated in the low-frequency band, and the high-pressure region of the propeller contributed the most to the noise. [PERSON] et al. [10] studied the effect of small-scale eddies on noise and found that the low-frequency part of the noise was better solved using the LES turbulence model. Both [PERSON] [11] and [PERSON] [12] studied flat plate noise.