# The Characteristics and Mechanisms of High-Intensity Sound in a High-Speed Multistage Compressor
## 1 Introduction
Experiments showed that the vortex shedding frequency of the wire wake was approximately equal to the sound frequency which occurred under specific wind speed conditions. The method, which combined computational fluid dynamics (CFD) technology with acoustic analogy, is taken by most researchers to solve problems when performing the numerical simulation of flow-induced acoustic problems in the development of computational aeroacoustics. The most famous Lighthill equation provides a good theoretical foundation for solving aeroacoustic problems, and is also an important technical mean for the development of numerical calculation methods [18]. [PERSON] extracted the sound source information from the turbulent shear layer with the Lighthill equation in the study of supersonic aircraft jet noise [19]. The final noise directivity prediction results showed good agreement with the experimental results. Taking the Reynolds-averaged Navier-Stokes (RANS) method to extract the sound source information from the flow field is impossible due to the fact that it is only suitable for average flow problems, which results in the failure of representing unsteady flow information effectively [20]. In order to solve that problem, a hybrid large eddy simulation (LES)/RANS method was developed to capture the velocity and pressure information of the unsteady flow field, using the acoustic analogy method to achieve the effective prediction of jet noise [21]. In dealing with the radiation noise prediction of the three-dimensional square cavity structures under complex flow conditions, [PERSON] completed the calculation of the acoustic radiation characteristics of the structure in the far field with a method combining the LES and The Ffowcs Williams and Hawkings Model. (FW-H) equations [22]. [PERSON] first achieved the simulation of the combustion reaction flow field at a low Mach number with LES, and loaded the sound source term and nonuniform flow field information caused by combustion into the acoustic wave equation with the acoustic analogy method, thereby realizing the prediction of combustion noise [23]. The combined use of the LES and the acoustic analogy method make a significant contribution to the noise prediction problem under the action of complex turbulence. A relevant adjustment should be made in the acoustic analogy equation according to the boundary conditions, flow characteristics and other factors. The influence of the solid wall was taken into context by [PERSON], who made a contribution to the calculation of the problem of the variable flow cross section and then improved the equation that had been established with the base of the Lighthill equation [24]. Thus, researchers try to rectify convection-induced sound sources by solving the flow field where the structure is located, then converting the aerodynamic force as the sound source term with the acoustic analogy equation. Some numerical simulations have been validated for this method [25; 26; 27]. The sound source arising from the action of the solid wall shows a relation between it and the force from the wall. Thus, there is a need to take this aerodynamic force resulting from the solid wall into account for flow-induced sound problems. [PERSON] established the relationship between aerodynamic force and vortices with theory, making it possible to exclude the force arising from the object, as verified by [PERSON] [28]. [PERSON] studied the reappearance of sound information in a structure through numerical simulation, but did not consider the influence of sound on flow [29]. Although numerous investigations have aimed to characterize this flow-induced sound issue, there is a huge gap in its application in engineering [30]. Therefore, there is urgent need for an accurate and reasonable numerical method to solve the coupling problem of sound and flow.