# Investigation on Characterization of Typical Characteristic in Compressor Based on Flat Plate Model
## 1 Introduction
Combing with the unacceptable computational cost, it is very difficult to simulate the whole process of pressure disturbance in unsteady methods, and the directly coupling calculation between the three-dimensional flow field, sound field, and structure are merely impossible to achieve. Therefore, it is very necessary to establish a reasonably simplified physical model in the study of the acoustic resonance of the multistage compressor [9]. [PERSON] successfully constructed the first acoustic resonance model based on the flat blade cascade, confirmed the occurrence conditions of the resonant acoustic wave and its interfering effect on the shedding vortex in the flow field by experiments, and described the typical phenomenon of \"frequency locked\" [10]. The proposal of the Parker mode makes a further step to clarify that the internal relationship between the acoustic mode in the pipeline and the vibration mode of the plate structure directly determines the vibration of the plate [11; 12; 13]. [PERSON] built a two-dimensional rectangular plate wake model based on the plate cascade model, achieved the numerical calculation for the shear layer of the flow field, and described the physical process of the generation and development of the plate wake vortex in detail [14]. [PERSON] [15] obtained that the shedding vortex under parallel multi-plates exhibits an anti-phase mode by experiment. Research on the mechanism of acoustic resonance induced by plate wake flow in a hard-walled pipeline is conducted by [PERSON] and derived the key factors affecting the acoustic resonance, including the thickness of the plate, the chord length, the shape of the trailing edge of the plate, and the internal geometric dimensions of the pipeline [16]. [PERSON] indicated that the function of acoustic waves imposed on the flow field is mainly to affect the shedding of the wake vortices [17]. Taking the Parker \(\beta\) mode as a reference and ignoring the influence of airflow velocity, [PERSON] achieved the prediction of vortex shedding in the wake of the flat plate in the pipeline, derived the rhythm of the influence of acoustic waves on vortex shedding, and captured the characteristic phenomenon of the coupling between the acoustic wave frequency and the vortex frequency [18; 19]. [PERSON] discovered that the trailing edge shedding vortex is the main sound source through research with acoustic resonance [20]. [PERSON] completed the calculation of the acoustic wave transmission coefficient and reflection coefficient between the compressor blades with the definition of the internal flow field vortex of a four-stage compressor as a rigid body and thus established a simplified physical model [1]. At the same time, [PERSON] took this model to reveal the causes of acoustic resonance when discrete pure-tone components with a high amplitude appeared during the experiment [21]. An exciter disk model which can predict the acoustic resonance of aeroengines was established by [PERSON] based on the global stability theory and pointed out that the acoustic resonance phenomenon only occurs at special combined conditions of the rotor speed, the eddy current Mach number, the mass flow and other parameters [22]. The investigation of the failure of the blade in the aeroengine is conducted in detail [23; 24]. [PERSON]'s resonance mechanism established the physical model foundation for the study of structural destructive problems caused by acoustics and indicated the importance of the interaction between the sound waves and the wake vortex of the plate in acoustic resonance research. Considering the influence of the solid wall boundary on the acoustic propagation, [PERSON] established the [PERSON] acoustic analogy equation by further improving the Lighthill equation. The wake of the turbulent fluid in the flow channel develops along the direction of the incoming flow and spreads around, at the same time, the interaction of the force generated by the solid wall with it jointly affects the flow form of the entire flow field.