On the use of a stress-impedance model to describe sound propagation in a lined duct with grazing flow.

With flow, the acoustic effect of a locally reacting lined wall cannot be described by a single quantity independent of the incident wave, such as a wall impedance. At least two quantities, intrinsic to the liner and to the flow, are required to describe the effect of the lined wall regardless of the incident wave. In addition to the impedance, the unsteady tangential force exerted by the wall on the flow has to be taken into account. This force is due either to viscous effects or to the unsteady transfer of axial momentum from the flow into the lined wall. This paper describes a stress-impedance model, where the two variables used are the impedance and the friction factor that links the pressure to a tangential stress at the wall. The use of a wall stress helps to better understand the mechanisms of momentum transfer between the flow and the wall in the vicinity of an acoustic treatment.