An improved impedance eduction technique based on impedance models and the mode matching method

The problem of determining the acoustic impedance of liners used in turbofan engines of commercial aircraft has been a point of interest for the scientific community for decades, especially in the presence of grazing flows, similar to operational conditions. Different techniques have been developed to determine liner acoustic impedance under grazing flow. More recent research have been focused on inverse methods, which consist of two steps: (i) measurement of the acoustic field in a rectangular duct with flow and a liner sample located at one or two walls of the duct and (ii) modelling of the acoustic field and application of an optimization procedure to find the impedance that minimize the difference between experimental and analytic results. The process is usually carried on using optimization techniques and performed at each frequency step, which can lead to discontinuous impedance curves and large computational costs. In this work, the mode matching method is discussed in detail, and a new technique for impedance determination is proposed, which incorporates a mathematical impedance model to the optimization process as a mean to improve the impedance curve, therefore suppressing measurements error and convergence issues at single frequencies. The impedance models considered here are given in the frequency domain and satisfy passivity, reality and causality conditions, which allows the use of the educed impedance in time domain simulations. Three models are considered and compared regarding different liner samples, flow velocities and wave propagation direction. The results show that the impedance models can successfully suppress convergence errors close to the liner resonance frequency.