Imperial College London
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DrOrySchnitzer

Faculty of Natural Sciences, Department of Mathematics

Reader in Applied Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 3833o.schnitzer Website

 
 
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Location

 

739Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Brandao:2020:10.1017/jfm.2020.187,
author = {Brandao, R and Schnitzer, O},
doi = {10.1017/jfm.2020.187},
journal = {Journal of Fluid Mechanics},
title = {Acoustic impedance of a cylindrical orifice},
url = {http://dx.doi.org/10.1017/jfm.2020.187},
volume = {892},
year = {2020}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - We use matched asymptotics to derive analytical formulae for the acoustic impedance of a subwavelength orifice consisting of a cylindrical perforation in a rigid plate. In the inviscid case, an end correction to the length of the orifice due to Rayleigh is shown to constitute an exponentially accurate approximation in the limit where the aspect ratio of the orifice is large; in the opposite limit, we derive an algebraically accurate correction, depending upon the logarithm of the aspect ratio, to the impedance of a circular aperture in a zero-thickness screen. Viscous effects are considered in the limit of thin Stokes boundary layers, where a boundary-layer analysis in conjunction with a reciprocity argument provides the perturbation to the impedance as a quadrature of the basic inviscid flow. We show that for large aspect ratios the latter perturbation can be captured with exponential accuracy by introducing a second end correction whose value is calculated to be in between two guesses commonly used in the literature; we also derive an algebraically accurate approximation in the small-aspect-ratio limit. The viscous theory reveals that the resistance exhibits a minimum as a function of aspect ratio, with the orifice radius held fixed. It is evident that the resistance grows in the long-aspect-ratio limit; in the opposite limit, resistance is amplified owing to the large velocities close to the sharp edge of the orifice. The latter amplification arrests only when the plate is as thin as the Stokes boundary layer. The analytical approximations derived in this paper could be used to improve circuit modelling of resonating acoustic devices.
AU  - Brandao,R
AU  - Schnitzer,O
DO  - 10.1017/jfm.2020.187
PY  - 2020///
SN  - 0022-1120
TI  - Acoustic impedance of a cylindrical orifice
T2  - Journal of Fluid Mechanics
UR  - http://dx.doi.org/10.1017/jfm.2020.187
UR  - http://hdl.handle.net/10044/1/78595
VL  - 892
ER  -
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