A systematic uncertainty analysis for liner impedance eduction technology

The so-called impedance eduction technology is widely used for obtaining acoustic properties of liners used in aircraft engines. The measurement uncertainties for this technology are still not well understood though it is essential for data quality assessment and model validation. A systematic framework based on multivariate analysis is presented in this paper to provide 95 percent confidence interval uncertainty estimates in the process of impedance eduction. The analysis is made using a single mode straightforward method based on transmission coefficients involving the classic Ingard-Myers boundary condition. The multivariate technique makes it possible to obtain an uncertainty analysis for the possibly correlated real and imaginary parts of the complex quantities. The results show that the errors in impedance results at low frequency mainly depend on the variability of transmission coefficients, while the mean Mach number accuracy is the most important source of error at high frequencies. The effect of Mach numbers used in the wave dispersion equation and in the Ingard-Myers boundary condition has been separated for comparison of the outcome of impedance eduction. A local Mach number based on friction velocity is suggested as a way to reduce the inconsistencies found when estimating impedance using upstream and downstream acoustic excitation.