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Theoretical model for sound radiation from annular jet pipes: Far- and near-field solutions

Theoretical model for sound radiation from annular jet pipes: Far- and near-field solutions
Theoretical model for sound radiation from annular jet pipes: Far- and near-field solutions
An analytical model is presented for sound radiation from a semi-infinite unflanged annular duct. The duct carries a jet which issues into a uniform mean flow while an inner cylindrical centre body extends downstream from the duct exit. This geometrical arrangement forms an idealized representation of a turbofan exhaust where noise propagates along the annular bypass duct, refracts through the external bypass stream and radiates to the far field. The instability wave of the vortex sheet and its interaction with the acoustic field are accounted for in an exact way in the current solution. Efficient numerical procedures are presented for evaluating near-field and far-field solutions, and these are used as the basis for a parametric study to illustrate the effect of varying the hub–tip ratio, and the ratio of jet velocity to external flow velocity. Since the ‘Kutta’ condition can be turned on and off in the current solution, this capability is used to assess the effect of vortex shedding on noise radiation. Far-field directivity patterns are presented for single modes and also for a multi-mode ‘broadband’ source model in which all cut-on modes are assumed to be present with equal modal power. Good agreement is found between analytical solutions and experimental data. Near-field pressure maps of the acoustic and instability portions of the solution are generated for selected tones.
0022-1120
315-341
Gabard, G.
bfd82aee-20f2-4e2c-ad92-087dc8ff6ce7
Astley, R.J.
cb7fed9f-a96a-4b58-8939-6db1010f9893
Gabard, G.
bfd82aee-20f2-4e2c-ad92-087dc8ff6ce7
Astley, R.J.
cb7fed9f-a96a-4b58-8939-6db1010f9893

Gabard, G. and Astley, R.J. (2006) Theoretical model for sound radiation from annular jet pipes: Far- and near-field solutions. Journal of Fluid Mechanics, 549, 315-341. (doi:10.1017/S0022112005008037).

Record type: Article

Abstract

An analytical model is presented for sound radiation from a semi-infinite unflanged annular duct. The duct carries a jet which issues into a uniform mean flow while an inner cylindrical centre body extends downstream from the duct exit. This geometrical arrangement forms an idealized representation of a turbofan exhaust where noise propagates along the annular bypass duct, refracts through the external bypass stream and radiates to the far field. The instability wave of the vortex sheet and its interaction with the acoustic field are accounted for in an exact way in the current solution. Efficient numerical procedures are presented for evaluating near-field and far-field solutions, and these are used as the basis for a parametric study to illustrate the effect of varying the hub–tip ratio, and the ratio of jet velocity to external flow velocity. Since the ‘Kutta’ condition can be turned on and off in the current solution, this capability is used to assess the effect of vortex shedding on noise radiation. Far-field directivity patterns are presented for single modes and also for a multi-mode ‘broadband’ source model in which all cut-on modes are assumed to be present with equal modal power. Good agreement is found between analytical solutions and experimental data. Near-field pressure maps of the acoustic and instability portions of the solution are generated for selected tones.

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Published date: 2006

Identifiers

Local EPrints ID: 28389
URI: https://eprints.soton.ac.uk/id/eprint/28389
ISSN: 0022-1120
PURE UUID: b4d15057-73d5-47ce-b9a7-68d4543c79db

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Date deposited: 02 May 2006
Last modified: 17 Jul 2017 16:01

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