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

Acoustic impedance is the most pivotal characteristic of acoustic liners. For an uniform locally reacting liner, the impedance spectrum over all the panel is usually assumed to be the same if the geometric parameters are fixed. 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 confront 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. For instance, in a grazing tube experiment, when acoustic waves propagate through the section where liner installed, acoustic scattering would happen, which will cause reflection and absorption. Accordingly, the acoustic energy distribution varies along the duct and the wavefront profile in the duct will be changed gradually comparing with the upstream, which would cause an impedance distinction between different zones of a liner. Furthermore, in a microcosmic scale, the perforated plate is a combination of spaced orifices and hard wall. Obviously, based on the definition of impedance, the values are actually discontinuous between walls and orifices. 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. Eight Helmholtz resonators in series with grazing incident waves were simulated by a two dimensional DNS solver based on computational aeroacoustic (CAA) method. Two disparate methodologies are adopted to determine the acoustic impedance which are the straightforward method and the definition of impedance. Numerical results show that representing the liner with an averaged impedance leads considerable errors of the reconstructed sound fields when the nonlinear effect is remarkable. 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.