# Research on Characteristics of Flow Noise and Flow-Induced Noise
## 4 Noise Calculation of Cylindrical Shell Model
### Flow-Induced Noise Calculation  
The calculation of flow noise regards the shell as a rigid body, but in actual situations, the shell will vibrate when subjected to surface pressure. Flow-induced noise takes structural vibrations into consideration, and it can be regarded as a composite of vibration noise generated by fluctuating pressures from the flow field and vibration-induced noise from the shell surface. When calculating flow-induced noise, the vibration displacement of the shell surface must be considered, so fluid\(-\)structure interaction analysis is required. Because of the very small deformation in the shell structure, the volume change in the fluid domain could be neglected. So, we adopted a one-way fluid\(-\)structure interaction, considering only the influence of the fluid on the structure. The CGNS file containing flow field fluctuation information solved by Fluent was imported as the initial condition for the acoustic solution into the acoustic simulation software. The fluctuating pressure at each time step was applied as an external load to the shell structure to solve the structural dynamics equation and to obtain the displacement at each time step. Taking the derivative of displacement with respect to time could obtain the vibration velocity of the shell structure under the action of fluctuating pressure. The vibration velocities at each time node were the velocity boundary conditions when using the boundary element method to solve for flow-induced noise. After completing the acoustic field simulation, we analyze the sound pressure nephogr am at various cross-sections. The sound pressure nephogram provided us with an intuitive understanding of the spatial distribution of the acoustic field, enabling us to analyze the distribution of sound pressure at corresponding frequencies. The variations of the acoustic field around the shell are shown in Figure 8.  
Figure 8: Acoustic field around the shell. Figure 7: Flow noise acoustic directivity diagram: (**a**) vertical section and (**b**) horizontal section. We conducted a comparative analysis of the longitudinal sectional sound pressure nephogram of flow-induced noise at 200 Hz, 244 Hz, 300 Hz, and 450 Hz, with results as follows:  
From Figure 9, it can be observed that at frequencies of 201 Hz, 244 Hz, 302 Hz, and 450 Hz, the maximum sound pressure levels of flow-induced noise were 137 dB, 165 dB, 108 dB, and 89.2 dB, respectively. Notably, at a frequency of 244 Hz, the vibration displacement of the shell structure was significantly higher than at other frequencies. This was attributed to resonance between the shell structure and the fluid at this frequency. In comparison with other frequencies, changes in the sound pressure nephogram were observed in the near-field region. Except for 244 Hz, the sound pressure distribution near the wall was lower at the bow and stern due to the \"masking effects\" of the incoming flow, while the numerical values were smaller at the bow and stern than in the middle section. Overall, the sound pressure nephogram exhibited a symmetric \"butterfly\" pattern. As the frequency increased from 201 Hz to 302 Hz, the flow-induced noise decreased by 29 dB, and as the frequency increased from 302 Hz to 450 Hz, the flow-induced noise decreased by 19 dB. Evidently, with increasing frequency, the rate of flow-induced noise attenuation gradually decreased, and the reduction became less pronounced as the distance from the shell surface increased. The spatial distribution characteristics of flow-induced noise are illustrated in Figure 10, with the detection points positioned in alignment with the flow noise locations. From Figure 10, it is evident that the spatial directivity of flow-induced noise in the vertical section was consistent with that of the flow noise--both were circular in shape. It can be seen from the horizontal section that the flow-induced noise was smaller at both ends of the shell, and because there were two slots on both sides of the shell, it presented a \"butterfly\" shape.