Numerical models for predicting sound propagation in ducts

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Numerical models for predicting sound propagation in ducts


Author: Chan, Chi-lung
Title: Numerical models for predicting sound propagation in ducts
Degree: M.Phil.
Year: 2003
Subject: Hong Kong Polytechnic University -- Dissertations
Air ducts -- Noise -- Measurement
Air ducts -- Noise -- Mathematical models
Department: Dept. of Mechanical Engineering
Pages: vii, 137 leaves : ill. ; 30 cm
Language: English
Abstract: The prediction of sound propagation in a duct has been a topic of research for many years because lined ducts have an important role in commercial markets. To date, most of theoretical and empirical models cannot accurately predict the acoustic performance of a duct silencer. In the present study, several numerical models for the propagation of sound in a lined duct with different features are presented. These numerical schemes include a ray model, a wavenumber integration technique (also known as the Fast Field Program, FFP) and the parabolic equation (PE) model. With appropriate boundary conditions, different situations of noise propagation in ducts are investigated. The goal for the present study is to explore the suitability of various numerical schemes for the analyses of the noise attenuation in duct silencers. This, in turn, will improve the design of a duct silencer by providing a better model for an accurate numerical simulation. Since the basic ray model is a well-known method for studying the physical phenomenon of sound propagation, it has been applied initially for the calculation of the sound fields in a region bounded by two parallel planes in the current study. The numerical solutions had been validated by experimental measurements in a homogeneous plane-parallel system of a constant cross-sectional area with no fluid flow. It is used to simulate the condition of a two-dimensional duct. The analytical solution of the ray model can then be used as a reference for comparisons with other numerical schemes such as the FFP formulation and PE model. The FFP formulation is introduced next because it is rather complicated to apply the classic ray model for studying the effect of stratified flow fields of the duct. Indeed, the FFP formulation has long been used in the study of sound propagation in stratified media, for example, long range sound propagation in underwater and outdoor acoustics. However, it has never been applied in the field of duct acoustics. In the current study, the FFP formulation has been modified for modelling sound propagation in ducts. The computational results agree well with the ray model. However, due to range-independent nature of the fast field formulation, its application has only been limited to ducts with a relatively simple geometry. In studying the acoustic performance of duct silencer, it is important to investigate the effect of impedance and area discontinuities on the propagation of sound in ducts. In a related study, an integral method, which is based on the approximation of the Boundary Element formulation, has provided a useful method to predict the effect of impedance discontinuity for outdoor sound propagation. This integral method has been adapted in the ray model to predict the sound attenuation in a duct with discontinuities. Finally, the PE model has been applied to evaluate the Sound field in a duct with a silencer because it has a remarkable applicability in computational acoustics for range dependent conditions. The presented numerical results have shown that PE is a good model for predicting noise propagation in a duct when comparing with classical ray model. It is also found that the PE model has the ability to describe the silencer performance more precisely due to its range-dependent property. Therefore, it is concluded that PE model is the most suitable numerical scheme for the investigation of silencer attenuation in ducts.

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