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The University of Southampton
Engineering

Mode-matching techniques for duct acoustics (in collaboration with Jeremy Astley (ISVR))

Hard patches are small areas of a lined surface where the acoustic treatment has been removed either for design or for maintenance purposes. Hard patches are detrimental to the performance of liners as they reduce the area of treated surfaces. They also introduce significant modal scattering by redistributing the acoustic energy onto low-order modes which are less attenuated. A typical example is shown below.

Methods have been developed to predict the performance of acoustic treatments for ducts with flow. These methods use mode-matching techniques to build a semi-analytical model of the sound field in the duct. Compared to fully numerical methods, mode-matching techniques are much faster but limited to canonical geometries.

A finite element method has been develop to obtain the acoustic modes of a duct [1]. The use of finite element methods instead of purely analytical techniques allows for ducts with arbitrary cross sections, liner distributions and flow profiles. An eigenvalue problem based on Pridmore-Brown's equation is solved using standard finite elements.

At the interfaces between duct segments, the modes are matched using a weak variational formulation of the conservation of mass and momentum. This approach was shown to lead to a better description of the sound field near discontinuities of impedance under a grazing flow.

 

Finite element mesh representing the cross section of an annular duct.

 

 

 

 

 

 

Example of directivity of the insertion loss of a hard patch in a bypass duct.
 

 

 

 

 

[1] Gabard, G. and Astley, R.J. A computational mode-matching approach for sound propagation in three-dimensional ducts with flow. Journal of Sound and Vibration, 315, 2008, 1103-24.

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