BibTex format
@inproceedings{Li:2017,
author = {Li, J and Morgans, AS},
title = {Analytical solutions of the one-dimensional acoustic waves in a duct},
year = {2017}
}
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TY - CPAPER
AB - Wave-based models for one-dimensional duct acoustics are widely used in thermoacoustic network models. However, they currently assume a constant mean temperature and mean flow within each duct module, while in practice many ducts of relevance sustain a significant axial temperature gradient or mean flow gradient. This paper presents an analytical solution for the one-dimensional acoustic field in a duct with arbitrary mean temperature gradient and mean flow. A wave equation for the pressure perturbation is derived which relies on very few assumptions. An analytical solution for this is derived using an adapted WKB approximation. The proposed solution is applied to ducts with a mean temperature profile which varies axially with (i) a linear and (ii) a partial sine wave profile. The analytical solution reproduces the acoustic field very accurately across a wide range of flow conditions which span both low and moderate-to-high subsonic Mach numbers. It always performs well when the frequency exceeds a certain value; when the mean temperature profile is linear, it also performs well to very low frequencies. This increased frequency range for linear mean temperature profiles leads to its application 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 is predicted very accurately as long as enough segmentation points are used and the condition for the linear mean temperature profile is satisfied: |k0| > |α|, where k0 is the local wave number when there is no mean flow and α is the normalised mean density gradient.
AU - Li,J
AU - Morgans,AS
PY - 2017///
TI - Analytical solutions of the one-dimensional acoustic waves in a duct
ER -