Optimum Impedance in the Presence of an Inviscid Sheared Flow

Abstract

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 for a given frequency, Mach number, and azimuthal mode order). Although such analysis can be carried out by means of numerical simulations, analytical expressions can also be derived to predict the optimum impedance. Previous works have been concerned with 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. Focus is given to typical operating conditions found in turbofan engine intakes and vehicle exhaust systems. 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.