## 1 Introduction  
With excellent concealment, submarines are one of the most critical naval weapons in the ocean. However, the noise radiated by the submarines during movement is a direct threat to their safety, and noise control of submarines has become a hot issue nowadays. Generally speaking, the noise radiated by a submarine can be divided into three categories: hydrodynamic noise, mechanical vibration noise, and propeller noise. If the submarine runs over a speed of 12 knots, the hydrodynamic noise will be the dominant noise source, compared to the mechanical vibration noise and propeller noise, of which the mechanisms have been sufficiently investigated [1; 2; 3]; the other two noises have been efficiently controlled [4] by modern technology. When the fluid flows around the submarine, two kinds of noises will be generated. The turbulent fluctuation pressure in the flow radiates a noise, which is called the flow noise. The elastic shell of the submarine is excited by the turbulent fluctuation pressure, and radiates the flow-induced noise. The hydrodynamic noise is the summation of the flow noise and the flow-induced noise. Since the sound pressure level of the flow noise is much lower than that of the flow-induced noise, the flow noise is usually negligible. In some conditions, the flow-induced noise can be described as the hydrodynamic noise. Recently, some phenomena of the flow-induced noise from underwater elastic structures similar to the submarines have been revealed, and the techniques of the flow control to reduce the hydrodynamic noise have been investigated [5; 6]. However, these researches are only concerned in the optimization of the shape, which is probably not suitable for the submarines, because the optimization of the shape will squeeze some space of the submarines and is hardly to be carried out in practical engineering. As we know, the hydrodynamic noise of the submarines comes from the bow, the sail hull, the stern, and the propeller, which is mentioned earlier. The noise generation mechanism of the submarine is complicated because of its complex structure. The previous studies on the flow-induced noise of the submarines stem from the cylinder for its simple structure [7], and some analytical equations are obtained. However, the bow, the sail hull and the stern of the submarine are not symmetric, and the exact analytic solutions of the flow-induced noise cannot be reached like what [PERSON] et al. [8] have done. Therefore, the direct experimental observation is also another commonly adopted method [9; 10]. After that, with the development of computational capability, the numerical calculation has become a powerful tool to analyze the flow-induced noise from these complicated structures [11; 12]. The numerical calculation is usually done by coupling a Reynolds-averaged Navier-Stokes hydrodynamic solver to a hydroacoustic code implementing different resolution forms of the Ffowcs Williams-Hawkings (FW-H) equation [13]. From numerical simulation, we can draw some results of the flow-induced noise from the structures, which is similar to part of the submarines. [PERSON] et al. has studied the characteristics of flow field and hydrodynamic noise of trapezoidal rudder wing under different rudder angles by the simulation, and have found that the sound pressure level spectrum band of the flow noise is full and there is no apparent dominant frequency [14]. [PERSON] et al. has proposed the mutual coupling method between the vulcanized rubber layer and the flow around to solve the flow field and the noise field for an axisymmetric body in water, and have found that noise power levels in the peak of the axisymmetric body are lower than those in the other positions [15]. [PERSON] et al. has numerically calculated the propeller noise from the INSEAN E1619 submarine propeller in open water and have found that noise propagation in the study is a spherical spreading model [16].