Numerical investigation on acoustic impedance variation along uniformly distributed multi-slit resonators

Acoustic impedance is the most important characteristic of acoustic liners. For an locally reacting liner, the impedance spectrum over all the panel is usually assumed to be the same. Under this assumption, the liner panel in a duct or a nacelle could be macroscopically treated as a single impedance value at each specific frequency. However, in real application, different parts of liner may encounter unequal acoustic and flow environment such as different acoustic modes and sound pressure levels, even if the liner structure is uniformly distributed. Consequently, the acoustic response could be varied at different locations. The main purpose of present paper is to investigate the impedance distribution of a uniform locally reacting liner in details and its relationship with incoming sound wave frequency and sound pressure level. A series of eight Helmholtz resonators with grazing incident waves were simulated by a two dimensional DNS solver. Two disparate methodologies are adopted to determine the acoustic impedance which are referred as to the straightforward method and the definition of impedance method. Numerical results show that representing the liner with an averaged impedance leads to considerable errors of the reconstructed sound fields when the nonlinear effect is important. Therefore, a piecewise function is derived and calibrated by the DNS results for accounting for the resistance variation over the liner length. Comparison shows the new model could achieve better results.