This thesis contains original research into the propagation of sound in acoustically lined ducts with flow. The motivation for this work is the requirement to predict the sound attenuation of acoustic liners in the bypass duct of modern turbofan aeroengines. The liners provide the most effective means with which to suppress the rear fan noise. It is therefore important to make the best possible use of the available lined area by optimising the liner configuration. A set of analytic and numerical methods for predicting the liner attenuation performance have been developed, which are suitable for use in intensive liner optimisation studies, or as preliminary design tools. Eigenvalue solvers have been developed to find modal solutions in rectangular ducts with uniform flow and annular ducts with sheared flow. The solvers are validated by replicating results from the scientific literature and the Finite Element method. The effect of mean core flow radial profile and boundary layers on the mode eigenfunctions and axial decay rates are considered. It is shown that solutions for thin boundary layer flows converge to those based on the commonly used slip flow boundary condition. It is demonstrated that realistic flow profiles should be used to assess acoustic mode propagation in bypass ducts. The flow profile can have strong effects upon low order modes and surface waves, and in fact at high frequencies, the profile can affect all the modes. Mode-matching schemes are developed to assess the power attenuation performance and modal scattering of finite length liners. The results of the schemes are used to show that refraction of sound by boundary layers increases attenuation at high frequency. Power attenuation is higher where the mean core flow gradient refracts sound towards the liner. It is found that asymmetric liners can provide improved attenuation, depending on the direction of the mean flow shear gradient. The optimisation of axially-segmented liners for single and multi-mode sources is demonstrated. It is found that potentially large improvements in the attenuation of tonal noise is possible, whilst benefits for broadband noise are more difficult to achieve.
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