The three-dimensional acoustic field in cylindrical and annular ducts with an axially varying mean temperature
File(s)
Accepted version
Author(s)
Li, Jingxuan
Morgans, Aimee S
Yang, Lijun
Type
Journal Article
Abstract
This paper presents analytical solutions for the three dimensional acoustic field in cylindrical and annular ducts with dependence of mean temperature on axial position. A wave equation for the pressure perturbation is constructed in cylindrical coordinates, applying a zero mean flow condition. Separation of variables is used to express the pressure perturbation as a product of functions which vary only axially, radially and circumferentially. The axial dependence of the mean temperature means that a general analytical solution for the axial second order ordinary differential equation (ODE) cannot be obtained. Variable transformation is applied, yielding a standard second order ODE with known solutions for linear and quadratic axial mean temperature dependence. The acoustic field and resonant frequencies for an annular duct with linear/quadratic axial mean temperature variation predicted using these solutions match perfectly with those calculated using the linearised Euler equations. The analytical solution for the linear mean temperature profile is applied to more complicated profiles in a piecewise linear manner, axially segmenting the temperature profile into regions that can be approximated as linear. The acoustic field and resonant frequency are predicted very accurately even when very few axial segments are used.
Date Issued
2020-01-27
Date Acceptance
2020-01-15
Citation
Aerospace Science and Technology, 2020, 99, pp.1-9
ISSN
1270-9638
Publisher
Elsevier BV
Start Page
1
End Page
9
Journal / Book Title
Aerospace Science and Technology
Volume
99
Copyright Statement
© 2020 Elsevier Ltd. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence http://creativecommons.org/licenses/by-nc-nd/4.0/
Sponsor
Commission of the European Communities
Identifier
https://www.sciencedirect.com/science/article/pii/S1270963819324630?via%3Dihub
Grant Number
FP7 - 305410
Subjects
Aerospace & Aeronautics
0901 Aerospace Engineering
0913 Mechanical Engineering
Publication Status
Published
Article Number
105712
Date Publish Online
2020-01-27