Optimum acoustic impedance in circular ducts with inviscid sheared flow: Application to turbofan engine intake

Abstract

Acoustic liners are widely employed in turbofan aero-engines as acoustic treatment. Their performance is determined by its acoustic impedance in the presence of flow. In recent years, much effort has been devoted to find the “optimum impedance” i.e. the impedance that results in the maximum attenuation. Although such analysis can be carried out by means of numerical simulations, analytical expressions can also be derived in order to predict the optimum impedance based on exceptional points i.e. when two modes coalesce, resulting in a maximum modal decay rate. Previous works focus on the optimum impedance of higher order modes in rectangular ducts with uniform flow. In this work, the analysis is expanded to circular ducts for both uniform and sheared inviscid flows. Typical turbofan engine intake geometry and flight conditions are considered, corresponding to certification points: sideline, cut-back and approach. It is shown that, for sideline and cut-back conditions, the optimum impedance and the maximum attenuation are affected even by the presence of a small boundary layer. For approach condition, uniform and shear flows lead to essentially the same results. Limitations of the analytical expression in the presence of multi-modal propagation is also discussed.