# Investigation on Characterization of Typical Characteristic in Compressor Based on Flat Plate Model
## 4 Acoustic Resonance in Pipe Cavity
### Computational Model and Parameter  
In the region of research on the mechanism of acoustic resonance, the Parker resonance introduced in the introduction is the research basis and focus of the majority of scholars. The model therefore established to study the acoustic resonance of rectangular ducts which are excited by the trailing wake of flat plates by [PERSON] is referenced, taking this to explore the characteristics law of acoustic resonance excited by shedding vortices from the trailing edge of the flat plates. The acoustic resonance experiment of the trailing edge of the flat plates, in which the cross-sectional dimension of the wind tunnel was 244 mm \(\times\) 244 mm, was completed in a low-speed wind tunnel by [PERSON] at a range of flow velocity from 0 to 40 m/s. In this rectangular plate with a semi-circular leading edge and a square trailing edge, the chord and thickness were 192 mm, 12 mm, and spanwise dimension was 244 mm, was locked in the center of the wind tunnel. In the processing of tests, the distribution characteristics and motion law of the region of wake vortex taking the flow display technology with discrete ranges of flow velocity were detected. A microphone above the flat plate near the tube wall was used to obtain the sound pressure spectrum, which indicated the correspondence between the frequency and amplitude of the sound pressure and the flow velocity, and captured the distribution characteristics of the sound pressure at the existence of acoustic resonance inside the tube. The sufficient and reliable experimental data above mean it is cited widely in the region of acoustic resonance, so the model mentioned above was taken to establish a computational model in the paper as shown in Figure 8. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Phase/\({}^{\circ}\)** & **IGV** & **IGV/Rotor1** & **Rotor1** & **Stator1** \\ \hline IGV & - & 115 & 142 & 242 \\ IGV/Rotor1 & –115 & - & 28 & 128 \\ Rotor1 & –142 & –28 & - & 99 \\ Stator1 & –242 & –128 & –99 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Phase difference of characteristic frequency of noise signal at different measurement positions. The wall of the rectangular tube and the flat plate is set to a no-slip boundary, and the inlet and outlet of the computational model are taken from the velocity inlet and the pressure outlet, respectively. The domain extracting the sound source covers the computational model. Structured grids are selected to divide the region of flow calculation. Further processing, in which the minimum and maximum grid are 0.5 mm and 2 mm, respectively, and the growth ratio of the grid is set to 1.2, is taken in the region near the flat plate. On the other region of the computational model, the grid size is set to 3 mm. The total number of grids in the calculation model is about 3,000,000. The computational model of the flow field is shown in Figure 9. Unstructured grids are taken to divide the source region in which the maximum grid is set to 8 mm. Acoustic non-reflection regions, i.e., the domains were referred to as free propagation domain 1 and domain 2, were applied to the inlet and outlet of the computational model to achieve the free propagation of the sound waves. The other walls of the computational model are set to acoustic hard walls to simulate the total reflection of sound waves. The computational model of the source field is shown in Figure 10.  
Initially, the flow field calculation under steady-state conditions is carried out with 100 iterations, and then the calculation results of this are used to initialize the transient flow field calculation. The calculation of the steady and transient flow field was applied with  
Figure 8: Diagram of calculation model. Figure 10: Sound field calculation model of plate wake. the RNG \(k-\varepsilon\) turbulence model and LES turbulence model, respectively. The standard wall function is taken to address the flow of information near the wall of the model. The second-order implicit regime is adopted in the transient equation.