Investigation of straightforward impedance eduction in the presence of shear flow

Abstract

A straightforward impedance eduction method is proposed which combines Prony׳s method with the Pridmore-Brown equation to obtain the impedance of acoustic liners in the presence of shear flow. Particular attention is paid to the reported inconsistency problems associated with the boundary layer effect in the development of impedance eduction techniques. A kind of flow-insensitive acoustic liner is considered which is placed in a rectangular flow duct containing predominant grazing incidence mode. Three slip or no-slip flow profiles are examined, which are the parabola, the one-seventh power law and the uniform core flow with linear boundary layer. A shear-flow FEM model is also set up to simulate the duct acoustic field. The present impedance eduction method has been tested and validated using both the simulated and the published measured data. It is shown that, despite of their distinct boundary layers, the selected flow profiles lead to essentially the same impedance results. And also, for the impedance eduction the strict consideration of no-slip shear flow is very consistent with the use of the Ingard–Myers׳ boundary condition with the uniform flow assumption over the test conditions. Although not susceptible to the exact shape of flow profile, the impedance eduction critically depends on the determination of the cross-sectional average Mach number. The usual practice of approximately representing the duct flow with the midspan profile results in a slight overestimation of the average Mach number in the two-dimensional acoustic models, and thus can considerably affect the accuracy of the impedance eduction. To solve this problem, the average flow profile is introduced to account for the actual three-dimensional flow non-uniformity in the rectangular duct. It is further found that the effective Mach number, corresponding to a slightly modified average flow profile, can be used to achieve a considerable collapse of the impedance spectra educed at different Mach numbers. Based on the new evaluation of the influence of boundary layer profile, the FEM simulation using the straightforwardly educed impedance as the boundary condition can achieve an excellent agreement with the benchmark data for the complex sound pressure in the flow duct.