Particle image velocimetry measurement of an instability wave over a porous wall in a duct with flow

The flow in a rectangular channel lined with a porous material and acoustically excited with an upstream loudspeaker has been investigated using particle image velocimetry. The measurements are phase-locked to the loudspeaker signal so that the phase-averaged velocity in the lined section is obtained during an excitation period. Most features of the phase-averaged velocity field in the lined section are found to be well described from the sum of three single duct modes: the hydrodynamic instability wave, a standing wave and an acoustic wave. The hydrodynamic instability wave travels at half the mean flow velocity, and its structure shows differences to the case of a locally reacting liner. The relative phase lag between the hydrodynamic and acoustic waves at the liner end dictates the interference between both waves, giving rise to the oscillations of the acoustical transmission coefficient as a function of the frequency. A detachment of the instability wave from the porous wall is observed in the vicinity of the liner downstream edge, together with the separation of the mean vorticity core.