Acoustic of a perforated liner with grazing flow: Floquet-Bloch periodical approach versus impedance continuous approach

The effect of a shear flow on an acoustic liner consisting of a perforated plate backed by cavities is studied. Two different approaches are investigated: First, the duct and the liner are considered as a periodic system while in the second approach the liner is considered as homogeneous and described by an impedance. Those two approaches coincide perfectly without flow for a small hole spacing compared to the acoustic wavelength. This work demonstrates that those two approaches are not wholly consistent when a shear flow is present and reveals some problems in the use of the local impedance with flow. The no-flow impedance cannot be used to describe the liner when a shear flow is present. An equivalent impedance with flow can be defined but it depends on the direction of the incident waves and loses its local characteristic.