Comparison of Two Waveguide Methods for Educing Liner Impedance in Grazing Flow

Abstract

Acoustic measurements taken with several liners in a flow impedance tube are used to assess two waveguide methods, the single mode method (SMM) and the finite element method (FEM), for impedance eduction in the presence of uniform grazing flow. Both methods use complex acoustic pressure data acquired over the liner length to educe the liner impedance. The SMM is based on the assumption that the sound pressure level and phase decay rates of a single progressive mode can be extracted from the measured complex acoustic pressures. No a priori assumptions are made in the FEM regarding the measured data. For no-flow conditions, the accuracy of each method is demonstrated by the excellent agreement between no-flow impedances educed in a grazing incidence tube and those acquired in a normal incidence tube. For grazing flow conditions (Mach numbers up to 0.5), the relative accuracy of the two waveguide methods is demonstrated by comparing the impedances educed with the FEM to the corresponding results for the SMM. Significant discrepancies occur for both methods for tests conducted at 0.5 kHz. Possible explanations for these discrepancies are explored with, as yet, no clear answer. Above 0.5 kHz, the results indicate the SMM can be used when the acoustic pressure profile is dominated by a single progressive mode, whereas the FEM can be used for all cases.