Validation of an Impedance Education Method in Flow

This paper reports results of a research effort to validate a method for educing the normal incidence impedance of a locally reacting liner, located in a grazing incidence, nonprogressive acoustic wave environment with flow. The results presented in this paper test the ability of the method to reproduce the measured normal incidence impedance of a solid steel plate and two soft test liners in a uniform flow. The test liners are known to be locally react- ing and exhibit no measurable amplitude-dependent impedance nonlinearities or flow effects. Baseline impedance spectra for these liners were therefore established from measurements in a conventional normal incidence impedance tube. A key feature of the method is the expansion of the unknown impedance function as a piecewise continuous polynomial with undetermined coefficients. Stewart's adaptation of the Davidon-Fletcher-Powell optimization algorithm is used to educe the normal incidence impedance at each Mach number by optimizing an objective function. The method is shown to reproduce the measured normal incidence impedance spectrum for each of the test liners, thus validating its usefulness for determining the normal incidence impedance of test liners for a broad range of source frequencies and flow Mach numbers. Nomenclature