In recent years, much effort has been devoted to find the "optimum impedance" i.e. the impedance that results in the maximum modal decay rate in flow duct acoustics. 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. Previous works have been concerned over the optimum impedance of higher order modes in rectangular ducts with uniform flow. In this work, the analysis is expanded to circular and rectangular ducts for both uniform and sheared inviscid flows. Focus is given on a typical aero-engine intake and flight conditions. It is shown that, in certain conditions, the optimum impedance is affected even by the presence of a small boundary layer thickness. It is also noted that for low Helmholtz numbers the optimum impedance may have a negative resistance.
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