# Investigation on Characterization of Typical Characteristic in Compressor Based on Flat Plate Model
## 1 Introduction  
Since the 1950s, research institutions represented by the National Aeronautics and Space Administration (NASA) in the United States, Deutsches Zentrum fur Luft-und Raumfahrt (DLR) in Germany, have encountered many cases of vibration damage to the engine casing, rotor blades, and other structures caused by acoustic resonance during the development and use of aeroengines [1, 2]. At the same time, the \"Engine Structural Integrity Plan\" proposed that numerous acoustic modes presented in a closed cavity simultaneously weaken the energy of a single mode and reduce the interaction with surrounding structures [3], which causes difficulties in verifying the strength of acoustic resonance on aeroengines. The phenomenon of acoustic resonance that occurs in the compressor has been presented in many studies. Although it has similar characteristics, there are differences in the explanations of its mechanism. [PERSON] presented the first report on acoustic resonance in a low-speed single-stage compressor in 1968 [4]. The problem of compressor blade breakage caused by acoustic resonance was captured in a multi-stage high-speed axial compressor, which was not publicly reported due to technical confidentiality. The problem of acoustic resonance has been investigated by [PERSON] withthe full-scale compressor developed by Rolls Royce, and proposed that the problem of acoustic resonance may widely exist in other types of aeroengines [5]. The annular cascade experiment conducted by [PERSON] indicated that, when the Ma of flow is 0.482, the acoustic mode with a helical structure occurs in the annular cascade flow channel and the blade vibration frequency corresponding to the acoustic mode frequency, which is related to the excitation sources of the high amplitude of blade vibration is obtained [6]. Stator blade damage had appeared in the rear stage of the Alstom gas turbine compressor, [PERSON] measured the pressure pulsation in the compressor flow channel with a pneumatic pressure probe and found that asynchronous pressure pulsation occurred in the rear stage of this compressor. The frequency of the asynchronous pressure pulsation is basically consistent with the natural frequency of vibration of the damaged blade, and it is believed that acoustic resonance plays a role in it [7]. The experimental research conducted by [PERSON] on the C106 low-speed and high-pressure axial flow compressor at the University of Cambridge presented a helical acoustic mode very similar to the acoustic resonance. So, [PERSON] concluded there must be three frequencies closed when the acoustic resonance occurs, i.e., the frequency of the shedding vortex, the acoustic modal frequency of the cavity (including the blade row), and the natural frequency of the blade vibration are very close, thus the blade vibrates with a high amplitude [8]. [PERSON] discovered the phenomenon of acoustic resonance at a four-stage compressor running near the off-design conditions and summarized the typical characteristics of the acoustic resonance of an axial-flow compressor, i.e., the frequency of the helical acoustic mode in the pipeline is consistent with the frequency of the blade vortex shedding, the vortex shedding frequency and the acoustic mode frequency present the phenomenon of \"frequency locked\", and the characteristic frequency of the noise signal has a change sharp [1]. Most of the above research studies the characteristics of acoustic resonance by experiment because there are too many influencing factors in the compressor, including the non-uniform swirl, the changing pipe geometry, the reflection and transmission of acoustic waves between multi-stage blade rows, and high-intensity aerodynamic loads, which lead to significant difficulty in constructing theoretical models to predict the occurrence of acoustic resonances.