# Investigation on Characterization of Typical Characteristic in Compressor Based on Flat Plate Model
## 3 Noise Experiments and Results
### Analysis of Noise Characteristics under Abnormal Vibration of Rotor Blades
According to the evolution rhythm of the noise spectrum inside the compressor operated over each typical speed condition of the engine in Figure 4, the corresponding relationship between the characteristic frequency in the noise spectrum and the engine speed is analyzed and plotted in Figure 6.  
It is clear that the characteristic frequency near 1402 Hz of the noise spectrum changes as the rotational speed increases. At the same time, the characteristic frequency of 1402 Hz remains constant over a specific speed range which presents no variation with the rotating speed, i.e., the phenomenon of \"frequency-locked\". This is consistent with the \"frequency locking and phase locking\" characteristics of the noise signal when the acoustic resonance phenomenon occurs inside the compressor [1]. In order to obtain the sound propagation characteristics of the characteristic frequency noise source in the compressor flow channel of the turbofan engine, the correlation analysis of the noise signal is carried out. When the high-amplitude vibration of Rotor1 of the high-pressure compressor of the engine occurs, the noise signal measured at different measuring points in the compressor flow channel at the characteristic frequency of 1402 Hz is subjected to cross-spectral analysis. The results of the cross-spectrum analysis are shown in Figure 7, the phase relationships of noise signals of characteristic frequency at different axial positions of the compressor are obtained. Thereby, the propagation rhythm of sound signals at a characteristic frequency in the compressor flow channel is investigated. The phase difference of the characteristic frequency of the noise signal at different measurement positions is shown in Table 2.  
Figure 5: Distribution of sound pressure level at 1402 Hz of noise signals at different measurement positions. Figure 6: Correspondence between characteristic frequency of noise spectrum and rotor speed. Figure 7: Cross-spectrum analysis about characteristic frequency noise. (**a**) The position of IGV and IGV/Rotor1. (**b**) The position of IGV and Rotor1. (**c**) The position of IGV and stator1. (**d**) The position of IGV/Rotor1 and Rotor1. (**e**) The position of IGV and Stator1. (**f**) The position of Rotor1 and Stator1. As shown above, the \"115\({}^{\circ}\) phase difference between IGV and IGV/Rotor1\" indicates the phase of the characteristic frequency 1402 Hz at IGV is ahead of the phase at IGV/Rotor1 about 115\({}^{\circ}\), i.e., the noise signal propagates from IGV/Rotor1 to IGV, and similar to others. The phase relationship of the noise signal of the characteristic frequency 1402 Hz at different measurement points is expounded as follows: (I-II) + (I-III) = (I-III), (II-III) + (III-IV) = (II-IV), and (I-II) + (II-III) + (III-IV) = (I-IV). The phase relation above is expressed as follows: characteristic frequency sound signal, which corresponds to the moment of Rotor1 of the high-pressure compressor vibrates with a high amplitude value, is the same sound wave at the different axial positions of the compressor. The phase relationship of the characteristic frequency noise signal which is transmitted from IGV through the first-stage rotor blade, and then to Sator1 is sequentially lagging. Therefore, the characteristic frequency noise signal origins after the cross-section of Sator1 of the high-pressure compressor, including the section itself. Combined with the circumferential rotational motion of the characteristic frequency noise source rotating around the rotor blade in the compressor flow channel [9], the propagation state of the characteristic frequency noise source in the compressor flow channel is a helix structure. This is consistent with the \"helix acoustic mode\" of the noise signal when the acoustic resonance occurs in the compressor [1].