A three-dimensional straightforward method for liner impedance eduction in uniform grazing flow

Abstract

There are increasing demands for a more efficient acoustic liner design in measuring liner impedance over a broad frequency range in a large-sized duct. But few impedance eduction methods can be applied when the sound pressure field in the flow duct is three-dimensional as frequency or duct size increases. To solve this issue, a 3-D straightforward method has been developed by combining the traditional mode decomposition method with the original 2-D straightforward method. The unknown impedance is straightforwardly determined by using the measured pressure data at the measuring microphones which are flush mounted on the rigid wall opposite to the test liner in the form of an evenly spaced rectangular array. By conducting the numerical simulation experiments and Monte-Carlo-method-based uncertainty analysis, the efficiency and feasibility of the present 3-D method are validated in a wide Helmholtz number range through comparing the educed and imposed impedances for both flow-off and flow-on cases. It is found that this method performs quite well even with measured data polluted by random perturbations. A solution selection process is proposed to completely solve the multi-solution problem existing in all straightforward methods. The optimized layout of the measuring microphone array has been investigated and greater sound pressure difference between adjacent measuring points results in a narrower uncertainty range. The present method is found to have several obvious advantages such as practicability in real experiments and significantly saving the measurement time and consumption.