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

TL;DR

This study investigates how different shear flow velocity profiles affect impedance measurements in a 2D duct, revealing that simplified profiles can cause significant deviations from realistic boundary layer effects.

Contribution

The paper compares traditional and realistic shear flow profiles in impedance eduction, demonstrating the importance of accurate boundary layer modeling for precise acoustic impedance measurements.

Findings

Simplified flow profiles can lead to significant impedance estimation errors.

The Ingard–Myers boundary condition remains valid for realistic turbulent boundary layers.

Realistic velocity profiles improve the accuracy of impedance eduction methods.

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.