arXiv subjects

Edward J. Brambley

Publications and source records attributed to Edward J. Brambley.

2 recordsLinked to original sources

arXiv2026

Realistic sheared flow profile effects on acoustic impedance eduction in small 3D-ducts

We investigate the influence of realistic sheared grazing flow on acoustic propagation in three-dimensional rectangular ducts. We show that conclusions reached in the literature about the effects of sheared grazing flow on acoustic propagation in lined ducts are dependent on the flow profiles used in those studies, and that significantly different conclusions are reached once a realistic flow profile is used. We particularly focus on small ducts typical of most experimental impedance eduction facilities, for which velocity gradients are relevant in a significant fraction of the duct cross-section. We assess the effect of simplifying the velocity distribution in the cross-section to either a one-dimensional (2D spanwise-infinite 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 as input in numerical simulations, based on the solution of the 3D Pridmore-Brown equation, to perform in silico impedance eduction experiments. Results show that realistic flow profiles can be well approximated for acoustic wave propagation in ducts by uniform or 1D flow profiles, provided the bulk Mach number is correctly accounted for, which contrasts with previous findings based on 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 sufficiently accurate.

physics.flu-dyn↗

arXiv2022

The critical layer in quadratic flow boundary layers over acoustic linings

A straight cylindrical duct is considered containing an axial mean flow that is uniform everywhere except within a boundary layer near the wall, which need not be thin. Within this boundary layer the mean flow varies parabolically. The linearized Euler equations are Fourier transformed to give the Pridmore-Brown equation, for which the Greens function is constructed using Frobenius series. Inverting the spatial Fourier transform, the critical layer contribution is given as the non-modal contribution from integrating around the continuous spectrum branch cut. This contribution is found to be the dominant downstream contribution to the pressure perturbation in certain cases, particularly for thicker boundary layers. The continuous spectrum branch cut is also found to stabilize what are otherwise convectively unstable modes by hiding them behind the branch cut. Overall, the contribution from the critical layer is found to give a neutrally stable non-modal wave with a phase velocity equal to the mean flow velocity at the source when the source is located within the sheared-flow region, and to decay algebraically along the duct as $O(x^{-5/2})$ for a source located with the uniform flow region. The Frobenius expansion, in addition to being numerically accurate close to the critical layer where other numerical methods loose accuracy, is also able to locate modal poles hidden behind the branch cut, which other methods are unable to find; this includes the stabilized hydrodynamic instability. Matlab code is provided to compute the Greens function.

physics.flu-dyn↗