# The Characteristics and Mechanisms of High-Intensity Sound in a High-Speed Multistage Compressor
## 5 Investigation on High-Intensity Sound in a Simplified Compressor Model
### Phenomenon of the Frequency-Locked Phase-Locked System  
The experimental results given by [PERSON] show that wake vortex frequency of the plate increases linearly with the velocity. The SPL in the pipe increases sharply over the velocity range of 28-30 m/s, and the phenomenon of high-intensity sound occurs in the pipe at this time. The frequency corresponding to high-intensity sound is 530 Hz, and SPL corresponding to this frequency is 145 dB. Additionally, the frequency of high-intensity sound stays constant at that velocity range, which is the phenomenon of the frequency-locked characteristic. The internal sound pressure spectrum of the pipe in the velocity range of 20-35 m/s is obtained by calculation, and the representative results of these are shown in Figure 22 at the velocities of 20 m/s, 29 m/s, 32 m/s and 35 m/s. The position of the sound pressure monitoring point is just above the middle of the plate and near the pipe wall, which is the same location as the measurement point in the experiment by [PERSON].  
Figure 21: Movement of plate wake vortex at different times. (**a**–**d**) represent the movement of wake vortex in the time of 0.1325 s, 0.0135 s, 0.014 s and 0.01425 s respectively.  
f\({}_{\rm zv}\), which is the frequency of the vortex, and f\({}_{\rm s}\), which is the frequency of the acoustic mode, presented in Figure 22, have pure tone and high amplitude. Additionally, f\({}_{\rm zv}\) dominates in the frequency spectrum as increasing velocities and harmonic components present themselves. The acoustic modal frequencies, i.e., the pure tone component f\({}_{\rm s}=511\) Hz, which is 3.6% different from the pipeline acoustic modal frequency 530 Hz given by Welsh, can be excited under discrete velocities. The wake vortex frequency increases close to the acoustic modal frequency of the pipeline with increasing flow velocity, which is dominant in the sound pressure spectrum in the pipe, and the SPL increases sharply. The SPL reaches up to 145 dB at the inlet velocity of 32 m/s, and the high-intensity sound occurs in the pipe at the same time. The vortex frequency grows sharply to beyond the acoustic mode frequency as flow velocity continues to increase and the SPL is greatly reduced. Figure 23 shows the evolution rhythm of character frequency and the SPL with increasing velocity, as well as the sound pressure distribution in the pipe with the frequency corresponding to high-intensity sound.  
Figure 23: Evolution rhythm of acoustic frequency and SPL with flow velocities.  
Figure 22: Sound pressure spectrum at discrete flow velocities.  
Figure 23 shows that the pure tone component f\({}_{\rm{v}}\), which is the frequency of the vortex, increases linearly as flow velocity increases. The velocity range where high-intensity sound occurs is 30-33 m/s, i.e., the frequency-locked area at character frequency 511 Hz. These characteristics are in line with the typical features of the Karman vortex street, so the vortex of plate is the source of the high SPL component. This also shows that the Strouhal number (St = f\({}_{\rm{v}}d/V\), where f\({}_{\rm{v}}\) is the frequency of vortex, \(d\) is the thickness of plate, and \(V\) is the flow velocity upstream of the plate) of the model always keeps constant at this flow velocity range, St = f\({}_{\rm{v}}d/V=0.212\), which is approximately consistent with the corresponding results in the literature [10]. The dark blue and dark red color of the sound pressure distribution in Figure 21 are high sound pressure regions, and the sign before the sound pressure value represents the phase. The sound pressure amplitudes on both sides of the plate are equal with the opposite phase of 180\({}^{\circ}\). The sound pressure distribution, when high-intensity sound appears in the model, presents the \(\beta\) mode form of the Parker model.