Effect of non-uniform perforation in the long concentric resonator on transmission loss and back pressure

It is known that the acoustical and, possibly, mechanical performance of the perforated resonator can be controlled by the porosity and distribution of holes. To analyze the effect of the porosity distribution pattern on resonator performance, in particular under the design condition of restricted volume, five typical perforation patterns of an acoustically long concentric resonator were investigated experimentally and numerically. Transmission loss and back pressure were used to represent the acoustic and mechanical performance indices, respectively. Prediction of transmission loss was made by segmental decoupling analysis with an empirical impedance model of orifices. Prediction of back pressure was done by computational fluid dynamics analysis. The overall trend of the calculated results matched well with the measured results. In terms of acoustic performance, it is noted that a specific frequency range was mostly influenced by the change of axial porosity pattern. For mechanical performance, a gradual change in porosity played a dominant role in stabilizing the flow field and static pressure distribution. It is concluded that an axial perforation pattern with a gradual change in porosity yields the best performance by forming a flow field with minimized loss and an acoustic field dominated by a quarter-wavelength resonance of equivalent extended pipes. In particular, the most preferred perforation pattern in terms of transmission loss and back pressure was the one with gradually increasing porosity from the upstream part and gradually decreasing porosity from the middle part as far as the downstream end.