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Wavepackets in the velocity field of turbulent jets

Published online by Cambridge University Press:  02 August 2013

André V. G. Cavalieri ,
Daniel Rodríguez ,
Peter Jordan ,
Tim Colonius  and
Yves Gervais
André V. G. Cavalieri*
Affiliation:
Département Fluides, Thermique, Combustion, Institut PPrime, CNRS–Université de Poitiers–ENSMA, Poitiers, France Divisão de Engenharia Aeronáutica, Instituto Tecnológico de Aeronáutica, São José dos Campos, SP, Brazil
Daniel Rodríguez
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA School of Aeronautics, Universidad Politécnica de Madrid, Madrid, Spain
Peter Jordan
Affiliation:
Département Fluides, Thermique, Combustion, Institut PPrime, CNRS–Université de Poitiers–ENSMA, Poitiers, France
Tim Colonius
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
Yves Gervais
Affiliation:
Département Fluides, Thermique, Combustion, Institut PPrime, CNRS–Université de Poitiers–ENSMA, Poitiers, France
*
†Email address for correspondence: andre@ita.br
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Abstract

We study the velocity fields of unforced, high Reynolds number, subsonic jets, issuing from round nozzles with turbulent boundary layers. The objective of the study is to educe wavepackets in such flows and to explore their relationship with the radiated sound. The velocity field is measured using a hot-wire anemometer and a stereoscopic, time-resolved PIV system. The field can be decomposed into frequency and azimuthal Fourier modes. The low-angle sound radiation is measured synchronously with a microphone ring array. Consistent with previous observations, the azimuthal wavenumber spectra of the velocity and acoustic pressure fields are distinct. The velocity spectrum of the initial mixing layer exhibits a peak at azimuthal wavenumbers $m$ ranging from 4 to 11, and the peak is found to scale with the local momentum thickness of the mixing layer. The acoustic pressure field is, on the other hand, predominantly axisymmetric, suggesting an increased relative acoustic efficiency of the axisymmetric mode of the velocity field, a characteristic that can be shown theoretically to be caused by the radial compactness of the sound source. This is confirmed by significant correlations, as high as 10 %, between the axisymmetric modes of the velocity and acoustic pressure fields, these values being significantly higher than those reported for two-point flow–acoustic correlations in subsonic jets. The axisymmetric and first helical modes of the velocity field are then compared with solutions of linear parabolized stability equations (PSE) to ascertain if these modes correspond to linear wavepackets. For all but the lowest frequencies close agreement is obtained for the spatial amplification, up to the end of the potential core. The radial shapes of the linear PSE solutions also agree with the experimental results over the same region. The results suggests that, despite the broadband character of the turbulence, the evolution of Strouhal numbers $0. 3\leq St\leq 0. 9$ and azimuthal modes 0 and 1 can be modelled as linear wavepackets, and these are associated with the sound radiated to low polar angles.

JFM classification

Instability: Absolute/convective instability Acoustics: Hydrodynamic noise Acoustics: Jet noise
Type
Papers
Information
Journal of Fluid Mechanics , Volume 730 , 10 September 2013 , pp. 559 - 592
Copyright
©2013 Cambridge University Press 

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