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Acoustic resonances and trapped modes in pipes and tunnels

Published online by Cambridge University Press:  23 May 2008

STEFAN HEIN  and
WERNER KOCH
STEFAN HEIN
Affiliation:
Institute of Aerodynamics and Flow Technology, DLR Göttingen, Germany
WERNER KOCH
Affiliation:
Institute of Aerodynamics and Flow Technology, DLR Göttingen, Germany
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Abstract

Acoustic resonances of simple three-dimensional finite-length structures in an infinitely long cylindrical pipe are investigated numerically by solving an eigenvalue problem. To avoid unphysical reflections at the finite grid boundaries placed in the uniform cross-sections of the pipe, perfectly matched layer absorbing boundary conditions are applied in the form of the complex scaling method of atomic and molecular physics. Examples of the structures investigated are sound-hard spheres, cylinders, cavities and closed side branches. Several truly trapped modes with zero radiation loss are identified for frequencies below the first cutoff frequency of the pipe. Such trapped modes can be excited aerodynamically by coherent vortices if the frequency of the shed vortices is close to a resonant frequency. Furthermore, numerical evidence is presented for the existence of isolated embedded trapped modes for annular cavities above the first cutoff frequency and for closed side branches below the first cutoff frequency. As applications of engineering interest, the acoustic resonances are computed for a ball-type valve and around a simple model of a high-speed train in an infinitely long tunnel.

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Papers
Information
Journal of Fluid Mechanics , Volume 605 , 25 June 2008 , pp. 401 - 428
Copyright
Copyright © Cambridge University Press 2008

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