Theoretical methods to predict the interaction of aero-engine fan tone radiation with the fuselage and its boundary layer

Abstract

The work in this thesis is focused on the acoustic installation effects of an aero-engine fan noise source adjacent to a cylindrical fuselage with a boundary layer running down its length. The main scope of this work is the development of theoretical methods to quantify scattering/diffraction by the fuselage and the refraction effect due to the presence of the boundary layer. The aim is to provide a faster and less computationally demanding alternative to high-fidelity numerical methods. The acoustic near-field of an installed fan noise source has been investigated before with the use of numerical methods to solve the problem of sound propagation through the shear layer. Therefore, in this work analytic expressions are derived that describe the acoustic pressure both in the near-field, in the form of a Fourier series and a Fourier integral, and in the far-field, in the form of a Fourier series. The use of numerical methods is avoided by utilising an asymptotic method for thin linear boundary-layer profiles. Additionally, a rudimentary step-function profile is investigated that avoids the solution to the Pridmore-Brown equation altogether. The capability of the two profiles to approximate the effects of more complex boundary layer profiles such as the quarter-sine and the 1/7th power-law profile is investigated. The analytic expressions are validated by comparing theoretical results to existing numerical results for the pressure on the fuselage surface. The two equivalent simplified profiles prove to be able to approximate the same effects as more realistic profiles especially for thin boundary layers. The linear profile accurately predicts shielding effects for thin boundary layers, but the step-function profile retains its accuracy regardless of the boundary-layer thickness. Both theoretical approaches are able to capture the pressure contour pattern and amplitude of shielding on the fuselage surface. The main advantage of this novel theoretical approach is the speed at which it can produce reliable results since there is no need for numerical schemes. Therefore, a multi-mode parametric study is conducted that identifies shielding trends on the fuselage surface and far-field directivity trends in various stages of flight. Multiple flow and source characteristics are examined with flight Mach number, cut-off ratio of the modal output of the fan, and boundary-layer thickness standing out as the major factors that affect shielding on the fuselage surface and directivity phase shifts in the far-field. The results of the multi-mode parameteric study highlight the capability of this novel theoretical approach to produce quick and reliable results that can serve as a preliminary analysis to a more in-depth numerical analysis.

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Identifiers

ORCID for Dionysios-Marios Rouvas: orcid.org/0009-0001-6646-4444

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

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