# Analysis of Acoustic Flow Field Characteristics of Key Components of High-Speed Train Bogies
## 1 Introduction
### Calculation Current Status of Research on the Effect of Flow Field on Sound Field  
Any fluid motion must obey the three laws of conservation, i.e., the law of conservation of mass, the law of conservation of momentum, and the law of conservation of energy [9]. The conservation of momentum for viscous incompressible fluids is described by the Navier-Stokes equation, also referred to as the N-S equation. This equation was established by [PERSON] and [PERSON] in 1827 and 1845, respectively, on the basis of the equation of motion of an ideal fluid, which reflects the basic mechanical laws of real fluids. Later, with the development of Reynolds theorem, boundary layer theory, and turbulence theory, the development of fluid mechanics and aerodynamics was promoted. In the field of acoustics, [PERSON] summarized the results of a large number of past acoustic studies in 1877 and published _The Theory of Sound_, which marked the establishment of the classical acoustic theoretical system and the beginning of modern acoustics [10]. In 1952, the British scientist [PERSON] decouple the flow field and acoustic field from a set of equations, including the Navier-Stokes equations, and derived the Lighthill equation [11; 12], which establishes the connection between the flow field parameters and acoustic fluctuation quantities. The equations point out that the flow-causing noise in free space is equivalent to the noise generated by the perturbation of quadrupole sources, which can effectively solve the jet noise problem, and is widely regarded as the beginning of aerodynamic acoustics research with great theoretical significance. In 1955, [PERSON] applied the Kirchhoff method in the [PERSON] aerodynamic acoustics theory based on the existence of the static solid boundary influence of the flow field noise radiation integral solution. [PERSON]'s [13] theory shows that the solid boundary of the influence of the flow noise can be seen as a dipole source dispersed in the flow field on the solid boundary, and the strength of the source is directly proportional to the surface of the object of the fluid force. In addition, the quadrupole source action constitutes an acoustic field. [PERSON]'s theory effectively solves the problems of cylindrical flow noise and windblown sound in turbulent flows with stationary objects. However, it is not possible to solve the noise problems of the moving solid boundary coupled with the flow field, such as rotor noise, propeller noise, and other complex streaming noise. In 1964, [PERSON] [14] adopted the vortex volume term to describe the unknown source term of [PERSON]'s equation to form the vortex acoustic equation, which was used to study the acoustic-fluid interactions and the noise problems caused by pulsating heat sources. In 1969, based on [PERSON]'s theory, [PERSON] and [PERSON] used the generalized function method [15; 16] to effectively solve the flow sounding problem influenced by the existence of a moving solid boundary and obtained the famous Ffowcs Williams-Hawkings equation (FW-H equation for short) [17]. This equation states that the flow field noise in the presence of moving solids includes three kinds of sound sources: monopole, dipole and quadrupole sources [18]. Subsequently, after continuous refinement, the equation has been widely used for the far-field and near-field prediction of noise. However, both [PERSON]'s theory and the FW-H equation are obtained under the condition of propagation in a stationary flow field medium. Therefore, in 1975, [PERSON] [19] applied the Green (Green) function method to generalize the theory of aerodynamic acoustics to the problem of sound generation of moving objects in a uniformly moving medium, such as the aerodynamic noise of turbulent shear flow, turbulent jet noise, and so on. His results are known as the generalized Lighthill equation.