Smeared Impedence Model for Variable Depth Liners

Noise from modern aircraft engines has a significant broadband component, which has motivated the need for broadband acoustic engine liners. A promising broadband design, called a variable depth liner, is composed of groups of resonators tuned for different frequencies. The accuracy of commonly used smeared impedance models, however, has not been thoroughly assessed for this type of liner. Therefore, the purpose of this study is to assess, and if necessary develop, semi-analytical impedance models for variable depth designs. The impedance prediction is complicated by the fact that the radiation loading on individual resonators within the array can be different. While the radiation loading can be neglected on conventional engine liners that consist of a dense array of uniform resonators, the same is not true for variable depth liners. To better understand and model this effect, nine liner samples are tested in the NASA Langley normal incidence tube. Comparisons of predicted and measured data for relatively simple non-uniform samples confirm that the radiation loading can be approximated using mass end correction terms. Semi-analytical impedance models that incorporate the proposed end corrections provide favorable comparisons with measured impedance spectra for variable depth liner samples.