Validation of an Impedance Eduction Method in Flow

Abstract

Results are reported for validating a method for educing the normal incidence impedance of a locally reacting liner in a grazing incidence, nonprogressive acoustic wave environment with flow. The results demonstrate the ability of the method to reproduce the normal incidence admittance of a solid steel plate and normal incidence impedance of two soft test liners in a uniform flow. The selected test liners are known to be locally reacting and exhibit no amplitude-dependent impedance nonlinearities and only minimal flow effects. Baseline results for these liners are, 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 (Stewart, G. W., III, A Modification of Davidon's Minimization Method to Accept Difference Approximations of Derivatives, Journal of ACM, Vol. 14, No. 1, 1967, pp. 72-83) 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 very Marly reproduces the normal incidence impedance spectrum for each of the test liners; thus, its usefulness for determining the normal incidence impedance of test liners for a broad range of source frequencies and flow Mach numbers is demonstrated.