An investigation on the modelling of a finite porous liner for the sound propagation in a rectangular duct

Acoustic liners take an essential role in the noise attenuation in ducts. In this work, the multimodal method based on the finite-difference method is extended to predict the acoustic field in a rectangular duct lined with a finite porous material and validated by the experiment. A modified immersed interface method is developed for the air–porous interface problem in the extended multimodal method without flow. When the flow exists, the treatments of the air–porous interface problem and the continuity of pressure between the wall and liner are also given. Three ways of describing the porous liner using the surface impedance at normal incidence named normal impedance, the surface impedance at grazing incidence named shear impedance and a cavity filled with the equivalent fluid of porous material are introduced. The comparison among the three ways reveals that the extended method of treating liners using a cavity filled with the equivalent fluid is more accurate for the acoustic evaluation of porous liners. The analysis finds that the shear impedance can reasonably present the influence of porous material during the comparisons of transmission loss curves of the liners with different lengths and depths at different Mach numbers. In most cases, the prediction by the shear impedance is closer to that simulated by the cavity filled with porous material than the normal impedance. Normal impedance is hardly utilized to describe the porous material and is only reliable when the cavity is very short and deep.