Experimentally testing impedance boundary conditions for acoustic liners with flow: Beyond upstream and downstream

Abstract

Impedance eduction experiments on acoustic liners with flow have systematically shown the educed impedance depending on the direction of the incident wave. Recent attempts to model this dependence include impedance boundary conditions with an additional degree of freedom. In this case, both upstream and downstream acoustic sources must be used to educe both the liner impedance and the extra degree of freedom of the model, which implies two different axial wavenumber conditions are used, and always result in a perfect collapse of the educed impedances; this would be true whether or not the model itself is correct. In this work, we describe a novel experimental setup that allows for four different axial wavenumbers per frequency to be measured: two upstream and two downstream. We use this experiment to investigate three different impedance boundary conditions, namely inviscid sheared, viscous, and momentum transfer conditions, in addition to the classical Ingard–Myers boundary condition, using an inverse eduction technique based on the mode matching method. The additional degree of freedom in each of the first three models is best fitted to experimental data, and then compared to the theoretically predicted values. Unphysical or unrealistic values are found at certain frequencies for each model, and therefore the validity of such models is questionable. The predictive capabilities of the models are tested and compared by means of the plane-wave scattering matrix, and no model is found to be truly predictive. Under certain conditions, educed impedances using the Ingard–Myers boundary condition show similar accuracy in terms of transmission coefficients when compared to the other models.