Validation of an impedance eduction method in flow

Results are reported for validating a method for educing the normal inciden ce impedance of a locally reacting liner in a grazing incidence, nonprogres sive acoustic wave environment with flow. The results demonstrate the abili ty of the method to reproduce the normal incidence admittance of a solid st eel plate and normal incidence impedance of two soft test liners in a unifo rm flow. The selected test liners are known to be locally reacting and exhi bit no amplitude-dependent impedance nonlinearities and only minimal how ef fects. Baseline results for these liners are, therefore, established from m easurements in a conventional normal Incidence impedance tube. A key featur e of the method is the expansion of the unknown impedance function as a pie cewise continuous polynomial with undetermined coefficients. Stewart's adap tation (Stewart, G, W., III, "A Modification of Davidon's Minimization Meth od to Accept Difference Approximations of Derivatives," Journal of ACM, Vol 14, No. 1, 1967, Dg. 72-83) of the Davidon-Fletcher-Powell optimization al gorithm is used to educe the normal incidence impedance at each Mach numbs by optimizing an objective function, The method very nearly reproduces the normal incidence impedance spectrum for each of the test liners; thus, its usefulness for determining the normal incidence impedance of test liners fo r a broad range of source frequencies and flow Mach numbers is demonstrated .