Perforated plates or sheets are widely used to decrease the noise in aero engines, exhaust mufflers, wind tunnels and other mechanical systems with or without flow. The acoustic impedance of an orifice without flow under low sound pressure level can be easily determined using the linear formulas. However, it is difficult to gain the acoustic impedance of the orifice in high sound pressure level and grazing flow by rigorous mathematical modeling.
To predict the sound absorption coefficient as well as investigate the influence of the parameters on the sound absorptive performance of double-layer perforated plates, researcher CHANG Daoqing from the Institute of Acoustics of the Chinese Academy of Sciences and his team propose a semi-empirical model to design double-layer perforated plates under grazing flow, revealing an interesting phenomenon that different from the case without flow, the sound absorption performance of a perforated plate under grazing flow is insensitive to the aperture of perforation and plate thickness.
Firstly, researchers measure the acoustic impedance of a double-layer perforated plate in a flow duct and calculate the sound absorption coefficient based the measured acoustic impedance.
Then, the research team presents an empirical model to predict the sound absorption coefficient, with comparing the predict result and the measured result.
Furthermore, researchers conduct a parametric study of double-layer perforated plate, and make discussion and conclusions at last.
In the experiment, researchers collect data by a 16-microphone array in the wall on the opposite side of a double-layer perforated plate, and then used it to calculate the acoustic impedance of the perforated plate. The double-layer perforated plate shown in Figure 1 is equivalent to an impedance series. The first-layer perforated plate is subject to a grazing flow, so an impedance model with flow is required. The linear impedance model of perforated plate can be applied to the second-layer perforated plate directly.
Figure1.The sample of the double-layer perforated plates (Image by CHANG Daoqing).
Referring to an empirical impedance model for perforated plates under grazing flow using the nonlinear regression analysis of various results, researchers obtain the specific acoustic impedance at the front surface of the double-layer perforated plate by applying the transfer matrix method.
Comparing the measured and calculated sound absorptive performance of the double-layer perforated plate under grazing flow at the speed of 50m/s, as shown in Figure 2, the prediction agrees well with the measured results except at the anti-resonant frequency.
Figure 2. Comparison of the measured and calculated results for double-layer perforated plate under flow at the speed 50m/s(Image by CHANG Daoqing).
Figure 3 exhibits the comparison of the measured and calculated sound absorptive performance of the single-layer perforated plate under grazing flow at the speed of 50m/s. The prediction also agrees well with the measured results. The double-layer perforated plate has a better sound absorbing performance in low and high frequency than the single-layer one. However, the double-layer perforated plate creates a sound absorption trough in the middle frequency due to the anti-resonance.
Figure 3. Comparison of the measured and calculated results for the single-layer perforated plate under flow at the speed of 50m/s(Image by CHANG Daoqing).
An empirical model is presented to predict the sound absorption coefficient and the prediction agrees well with the measured results. The grazing flow not only greatly influences the sound absorptive performance of the first-layer perforated plate, but also that of the second-layer perforated plate owing to the coupling effect.
Particularly, the sound absorptive performance of the perforated plate under grazing flow is not sensitive to the perforation aperture and plate thickness, which is very different from the case without flow.
In sum, the flow speed, perforation ratio and cavity depth are the key parameters to determine the sound absorptive performance of a perforated plate under grazing flow.
Funding for this research came from the National Natural Science Foundation of China (No. 11374326).
CHANG Daoqing, LU Fuan, JIN Weinan,LIU Bilong. Low-frequency sound absorptive properties of double-layer perforated plate under grazing flow. Applied Acoustics(Volume 130,January 2018, Pages 115–123).DOI: 10.1016/j.apacoust.2017.09.016.
Institute of Acoustics, Chinese Academy of Sciences, 100190 Beijing, China