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Mathematical models of aeroacoustics in boundary layers over acoustic linings
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King, Matthew John (2022) Mathematical models of aeroacoustics in boundary layers over acoustic linings. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b3911356
Abstract
Throughout this document we will study the linearised Euler equations within a cylindrical duct. We assume a mean flow that is uniform within most of the duct, except for a region near the wall, where the flow is sheared to retrieve a non-slip boundary. For these flow profiles, under Fourier series and transform, the linearised Euler equations become the Pridmore-Brown equation, which contains a regular sin gularity known as the critical layer.
When inverting the Fourier transform the resulting pressure perturbation consists of various contributions; the modal sum, the integration around a branch cut which occurs because of the critical layer, and a mode known as the hydrodynamic insta bility. The branch cut, which we refer to as the critical layer branch cut, is more commonly known as the continuous spectrum.
We consider a mean flow profile that has a boundary layer following a quadratic curve. It is found that in our case hydrodynamic instability mode can interact with the critical layer branch cut and be stabilised. As a result, the mode contributes as part of the critical layer branch cut and the far-field pressure perturbation changes considerably. This thesis is split into three main topics. Firstly, we solve the Pridmore-Brown equation for the mean flow profile mentioned above, including the appropriate an alytic continuations, to examine the behaviour of the critical layer branch cut. We make use of the Green’s function to understand the contributions to the Fourier in version.
This includes studying how the hydrodynamic instability may be stabilised, and the resulting far-field effects. This is followed by an extension to the Brambley boundary condition for a uniform mean flow to account for the sheared flow effects and observe similar behaviours. Finally, we examine the contributions of the critical layer under the scattering due to a change in the duct wall.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Aeroacoustics -- Mathematical models, Boundary layer, Fourier transformations, Fourier series, Shear flow, Hydrodynamics -- Mathematical models | ||||
Official Date: | October 2022 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Brambley, Edward James | ||||
Sponsors: | University of Warwick. Mathematics and Statistics Doctoral Training Centre | ||||
Format of File: | |||||
Extent: | xix, 200 pages : illustrations (some colour), charts | ||||
Language: | eng |
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