The effects of thickness on the impedance of a rectangular aperture in the presence of a grazing flow

This paper presents an analytical investigation into the effect of a grazing mean flow upon the acoustic impedance of a rectangular aperture in a plate of finite thickness. Previous similar analytical works each made some simplifying approximation about the variation of the acoustic potential throughout the thickness of the aperture, such that they were valid only in either the thin or thick plate limits. In addition to providing a theoretical framework to correctly allow for a plate of any thickness, the results given here indicate the range of validity of the previous approximate theories.Two different forms of matching conditions across the shear layer have been proposed in previous works. Equations and boundary element method (BEM) solutions for both variants are given here. Results from both forms are compared against some existing measured results. As the approximations regarding aperture thickness have now been removed, it is possible to be definitive as to which form of matching conditions gives the most accurate results for a given application. The analysis is shown to predict the reactance of the aperture very well, although the results for resistance show greater discrepancy against experimental values.