High-frequency sound transmission in flow ducts

Abstract

This dissertation considers sound transmission in axisymmetric, uniformly-lined ducts of constant cross-section, carrying a high speed, subsonic, parallel mean shear flow. Fast and efficient numerical and analytical methods that can be used with high-frequency sound are developed.

This is fundamentally theoretical work, but with a view to the specific engineering application of acoustic liner optimization in turbofan aero-engine ducts, as cylindrical and annular ducts are approximate models of inlet and bypass ducts, respectively. Focus has been given on applying those methods to problems for which the noise source, mean flow and duct geometry are representative of the turbofan aero-engine application.

A new numerical procedure to calculate the small-amplitude pressure perturbation in the frequency domain with arbitrary mean velocity profiles is developed and a computer code is implemented. The method is a problem-specific finite element solver which, owing to the axisymmetric geometry, enables the rapid computation of a large number of modes at very high frequencies (e.g., several harmonics of the fan’s blade passing frequency) at a modest computational cost. Because of its speed and accuracy, it may be suitable for application in practical design optimisation procedures for acoustic linings.

Examples of finite element solutions of the eigenvalue problem in cylindrical and annular ducts are provided and results, which show how the shape of the boundary-layer profile can affect the modal structure of the in-duct pressure perturbation field are presented.

In the special case of uniform core flow and thin boundary layers at duct walls, finite element solutions are compared with those obtained from an approximate perturbation method based on an asymptotic inner expansion valid in the boundary layer.

An investigation of the effect of boundary-layer shielding on high-frequency sound transmission is carried out. A new cost function, which provides a quantifiable measure of an acoustic liner’s performance for a multi-mode noise source is proposed.

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Identifiers

ORCID for Alan Mcalpine: orcid.org/0000-0003-4189-2167

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