The absorption of axial acoustic waves by a perforated liner with bias flow

The effectiveness of a cylindrical perforated liner with mean bias flow in its absorption of planar acoustic waves in a duct is investigated. The liner converts acoustic energy into flow energy through the excitation of vorticity fluctuations at the rims of the liner apertures. A one-dimensional model that embodies this absorption mechanism is developed. It utilizes a homogeneous liner compliance adapted from the Rayleigh conductivity of a single aperture with mean flow. The model is evaluated by comparing with experimental results, with excellent agreement. We show that such a system can absorb a large fraction of incoming energy, and can prevent all of the energy produced by an upstream source in certain frequency ranges from reflecting back. Moreover, the bandwidth of this strong absorption can be increased by appropriate placement of the liner system in the duct. An analysis of the acoustic energy flux is performed, revealing that local differences in fluctuating stagnation enthalpy, distributed over a finite length of duct, are responsible for absorption, and that both liners in a double-liner system are absorbant. A reduction of the model equations in the limit of long wavelength compared to liner length reveals an important parameter grouping, enabling the optimal design of liner systems.