Effects of the sheared flow velocity profile on impedance eduction in a 2D duct

Abstract

Impedance eduction methods are the current standard approach to measure the impedance of acoustic liner under sheared grazing flow. The dedicated facilities for these methods consists on a waveguide with rectangular cross-section, which implies a sheared grazing flow. A current debate in the literature is the effect of this sheared flow in the impedance eduction methods. We assess the impact of the flow profile shape on acoustic propagation in a two-dimensional duct within the typical operating range of impedance eduction facilities. Firstly, a numerical experiment is proposed in which the Pridmore--Brown equation is assumed to represent the true physical behaviour, and is used with both simplified flow profiles commonly used in the literature and a realistic representation of a turbulent boundary layer using a van Driest universal law of the wall model. The data from these numerical experiments are then used with a traditional impedance eduction process, and the resulting variation in obtained impedances are investigated. Secondly, we apply a less-traditional impedance eduction method that incorporates the sheared velocity profile to data obtained from real-world experiments. The results suggest that the Ingard--Myers boundary condition remains a good approximation to a realistic boundary layer profile, such as the universal law of the wall, at least in the two-dimensional case. However, it is also shown that the simplified flow profiles often used in the literature can lead to significant deviations from the results obtained using a realistic velocity distribution.