On spatially varying acoustic impedance due to high sound intensity decay in a lined duct

Abstract

Direct numerical simulations (DNS) based on advanced computational aeroacoustic (CAA) methods are conducted to study the acoustic impedance of a uniformly distributed multi-slit liner under grazing incident sound waves at different frequencies and sound pressure levels (SPL), in the absence of mean-flow. The liner consists of a series of fifteen identical slit Helmholtz resonators. Numerical results show that a portion of the slit resonators in the upstream works in a non-linear regime and the others in the downstream work in a linear regime when high intense waves near the resonance are excited. It is a direct evidence that the acoustic impedance is non-uniform and spatially varying over the liner length due to the different local incident sound pressure levels. With the numerical data, two methodologies are adopted to determine the acoustic impedance of the liner, one is referred to as the Prony's method and the other one is based on an inverse method. The impedance value is validated by a time-domain linearized Euler equation (LEE) solver. Numerical results indicate that representing the liner with a homogenized impedance leads to considerable errors in the reconstructed sound fields when the liner experiences a transition from non-linear regime to linear regime. On the other hand, in cases where such a transition is absent, the homogenized constant impedance is adequate to estimate the acoustic response of the liner. Therefore, a spatially piece-wise function is derived and calibrated by the DNS results to take into consideration both the resistance and reactance variation in stream-wise direction. Comparison shows that the prediction of the sound field is improved by the space-dependent impedance boundary.