Slow sound in lined flow ducts

The acoustic propagation in lined flow duct with purely reactive impedance at the wall is considered. This reacting liner has the capability to reduce the speed of sound, and thus to enhance the interaction between the acoustic propagation and the low Mach number flow ( M≃0.3). At the lower frequencies, there are typically four acoustic or hydrodynamic propagating modes, with three of them propagating in the direction of the flow. Above a critical frequency, there are only two propagating modes that all propagate in the direction of the flow. From the exact two-dimensional formulation an approximate one-dimensional model is developed to study the scattering of acoustic waves in a straight duct with varying wall impedance. This simple system, with a uniform flow and with non-uniform liner impedance at the wall, permits to study the scattering between regions with different wave characteristics. Several situations are characterized to show the importance of negative energy waves, strong interactions between acoustic and hydrodynamic modes, or asymmetric scattering.