Sheared flow profile effects on acoustic impedance eduction in small 3D ducts

TL;DR

This work assesses how two- and three-dimensional mean-flow shear influences acoustic propagation and impedance eduction in small 3D rectangular ducts. By solving the Pridmore–Brown Equation for several cross-sectional velocity profiles and comparing against the CONVECTED Helmholtz Equation with the Ingard–Myers Boundary Condition, the study isolates when 2D or uniform-flow simplifications remain valid. It finds that realistic profiles such as the universal law-of-the-wall and CFD-derived shapes yield wavenumbers and impedances that align with CHE+IMBC predictions when the average Mach number is properly matched, while the hyperbolic-tangent profile can introduce errors. The results suggest that, for viscous effects neglected, traditional impedance eduction methods remain satisfactory provided the cross-sectional Mach number is consistently represented, guiding experimental design and interpretation in liner impedance studies.

Abstract

We investigate the influence of sheared grazing flow on acoustic propagation in three-dimensional rectangular ducts. We particularly focus on small ducts typical of most experimental impedance eduction facilities, for which the flow profile in the duct cross-section varies significantly. We assess the effect of simplifying this inherent two-dimensional flow profile to either a one-dimensional (2D duct) or uniform flow profile. Three flow profiles are considered, namely (i) the tensorised hyperbolic tangent, (ii) the law-of-the-wall, and (iii) one obtained from a RANS simulation. These flow profiles are used in numerical simulations, based on the solution of the Pridmore--Brown equation, to perform in silico impedance eduction experiments. Results show that realistic flow profiles can be approximated well in ducts by uniform or 2D-duct models provided the bulk Mach number is correctly accounted for, which contrasts with previous findings for more simplistic flow profiles. The key conclusion of this work is that if viscous effects are negligible and acoustic impedance is a good representation of a lined wall with grazing flow, then the simplification to a uniform flow is a reasonable approximation and traditional eduction methods are satisfactorily accurate.

Figures (8)

• Figure 1: Schematic duct and coordinates system adopted in this work.
• Figure 2: Flow profiles considered in this work. (a) Tensorized law of the wall; (b) CFD evaluated, and; (c) tensorized hyperbolic tangent. Isolines represent contour axial velocity.
• Figure 3: Reference impedance considered in the numerical experiment.
• Figure 4: Comparison of the wavenumbers obtained for the reference uniform impedance using different flow profile shapes. $(+)$ denotes downstream propagation, while $(-)$, upstream propagation.
• Figure 5: Comparison of the flow profiles considered on the analysis of the average flow profile effect when simplifying to a 2D duct.