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Axisymmetric superdirectivity in subsonic jets

Cavalieri, André V. G. and Jordan, Peter and Colonius, Tim and Gervais, Yves (2012) Axisymmetric superdirectivity in subsonic jets. Journal of Fluid Mechanics, 704 . pp. 388-420. ISSN 0022-1120. doi:10.1017/jfm.2012.247.

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We present experimental results for the acoustic field of jets with Mach numbers between 0.35 and 0.6. An azimuthal ring array of six microphones, whose polar angle, θ, was progressively varied, allows the decomposition of the acoustic pressure into azimuthal Fourier modes. In agreement with past observations, the sound field for low polar angles (measured with respect to the jet axis) is found to be dominated by the axisymmetric mode, particularly at the peak Strouhal number. The axisymmetric mode of the acoustic field can be clearly associated with an axially non-compact source, in the form of a wavepacket: the sound pressure level for peak frequencies is found be superdirective for all Mach numbers considered, with exponential decay as a function of (1 – M_c cos θ)^2, where M_c is the Mach number based on the phase velocity U_c of the convected wave. While the mode m = 1 spectrum scales with Strouhal number, suggesting that its energy content is associated with turbulence scales, the axisymmetric mode scales with Helmholtz number – the ratio between source length scale and acoustic wavelength. The axisymmetric radiation has a stronger velocity dependence than the higher-order azimuthal modes, again in agreement with predictions of wavepacket models. We estimate the axial extent of the source of the axisymmetric component of the sound field to be of the order of six to eight jet diameters. This estimate is obtained in two different ways, using, respectively, the directivity shape and the velocity exponent of the sound radiation. The analysis furthermore shows that compressibility plays a significant role in the wavepacket dynamics, even at this low Mach number. Velocity fluctuations on the jet centreline are reduced as the Mach number is increased, an effect that must be accounted for in order to obtain a correct estimation of the velocity dependence of sound radiation. Finally, the higher-order azimuthal modes of the sound field are considered, and a model for the low-angle sound radiation by helical wavepackets is developed. The measured sound for azimuthal modes 1 and 2 at low Strouhal numbers is seen to correspond closely to the predicted directivity shapes.

Item Type:Article
Related URLs:
URLURL TypeDescription ItemConference Paper
Cavalieri, André V. G.0000-0003-4283-0232
Jordan, Peter0000-0001-8576-5587
Colonius, Tim0000-0003-0326-3909
Additional Information:© 2012 Cambridge University Press. Received 7 October 2011; revised 12 April 2012; accepted 23 May 2012; first published online 3 July 2012. This work was partially supported by CNPq, National Council of Scientific and Technological Development – Brazil, and through the EU–Russian program ORINOCO (FP7-AAT-2010-RTD-Russia; project number 266103). The authors thank J. Delville and C. Fourment-Cazenave for their work during the experiments.
Funding AgencyGrant Number
European Research Council (ERC)266103
Subject Keywords:aeroacoustics; jet noise; hydrodynamic noise
Record Number:CaltechAUTHORS:20120817-102356325
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Official Citation:André V. G. Cavalieri, Peter Jordan, Tim Colonius and Yves Gervais (2012). Axisymmetric superdirectivity in subsonic jets. Journal of Fluid Mechanics,704, pp 388420 doi:10.1017/ jfm.2012.247
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:33289
Deposited By: Tony Diaz
Deposited On:17 Aug 2012 18:47
Last Modified:09 Nov 2021 21:33

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