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Acoustic emission of a vortex ring near a porous edge. Part 1: theory

Published online by Cambridge University Press:  27 April 2022

Huansheng Chen Open the ORCID record for Huansheng Chen [Opens in a new window] ,
Zachary W. Yoas ,
Justin W. Jaworski Open the ORCID record for Justin W. Jaworski [Opens in a new window]  and
Michael H. Krane Open the ORCID record for Michael H. Krane [Opens in a new window]
Huansheng Chen*
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18105, USA
Zachary W. Yoas
Affiliation:
Applied Research Laboratory, Penn State University, State College, PA 16802, USA
Justin W. Jaworski
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18105, USA
Michael H. Krane
Affiliation:
Applied Research Laboratory, Penn State University, State College, PA 16802, USA
*
†Email address for correspondence: huc216@lehigh.edu
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Abstract

The sound of a vortex ring passing near a semi-infinite porous edge is investigated analytically. A Green's function approach solves the associated vortex sound problem and determines the time-dependent pressure signal and its directivity in the acoustic far field as a function of a single dimensionless porosity parameter. At large values of this parameter, the radiated acoustic power scales on the vortex ring speed $U$ and the nearest distance between the edge and the vortex ring $L$ as $U^6 L^{-5}$, in contrast to the $U^5 L^{-4}$ scaling recovered in the impermeable edge limit. Results for the vortex ring configuration in a quiescent fluid furnish an analogue to scaling results from standard turbulence noise generation analyses, and permit a direct comparison to experiments described in Part 2 that circumvent contamination of the weak sound from porous edges by background noise sources that exist as a result of a mean flow.

JFM classification

Acoustics: Aeroacoustics Vortex Flows: Vortex dynamics Mathematical Foundations: General fluid mechanics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 941 , 25 June 2022 , A28
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Copyright
© The Author(s), 2022. Published by Cambridge University Press.

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References

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