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Feedback loop and upwind-propagating waves in ideally expanded supersonic impinging round jets

Published online by Cambridge University Press:  22 June 2017

Christophe Bogey Open the ORCID record for Christophe Bogey [Opens in a new window]  and
Romain Gojon Open the ORCID record for Romain Gojon [Opens in a new window]
Christophe Bogey*
Affiliation:
Laboratoire de Mécanique des Fluides et d’Acoustique, UMR CNRS 5509, Ecole Centrale de Lyon, Université de Lyon, 69134 Ecully CEDEX, France
Romain Gojon
Affiliation:
Laboratoire de Mécanique des Fluides et d’Acoustique, UMR CNRS 5509, Ecole Centrale de Lyon, Université de Lyon, 69134 Ecully CEDEX, France Department of Mechanics, Royal Institute of Technology (KTH), Linné FLOW Centre, Stockholm, Sweden
*
†Email address for correspondence: christophe.bogey@ec-lyon.fr
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Abstract

The aeroacoustic feedback loop establishing in a supersonic round jet impinging on a flat plate normally has been investigated by combining compressible large-eddy simulations and modelling of that loop. At the exit of a straight pipe nozzle of radius $r_{0}$, the jet is ideally expanded, and has a Mach number of 1.5 and a Reynolds number of $6\times 10^{4}$. Four distances between the nozzle exit and the flat plate, equal to $6r_{0}$, $8r_{0}$, $10r_{0}$ and $12r_{0}$, have been considered. In this way, the variations of the convection velocity of the shear-layer turbulent structures according to the nozzle-to-plate distance are shown. In the spectra obtained inside and outside of the flow near the nozzle, several tones emerge at Strouhal numbers in agreement with measurements in the literature. At these frequencies, by applying Fourier decomposition to the pressure fields, hydrodynamic-acoustic standing waves containing a whole number of cells between the nozzle and the plate and axisymmetric or helical jet oscillations are found. The tone frequencies and the mode numbers inferred from the standing-wave patterns are in line with the classical feedback-loop model, in which the loop is closed by acoustic waves outside the jet. The axisymmetric or helical nature of the jet oscillations at the tone frequencies is also consistent with a wave analysis using a jet vortex-sheet model, providing the allowable frequency ranges for the upstream-propagating acoustic wave modes of the jet. In particular, the tones are located on the part of the dispersion relations of the modes where these waves have phase and group velocities close to the ambient speed of sound. Based on the observation of the pressure fields and on frequency–wavenumber spectra on the jet axis and in the shear layers, such waves are identified inside the present jets, for the first time to the best of our knowledge, for a supersonic jet flow. This study thus suggests that the feedback loop in ideally expanded impinging jets is completed by these waves.

JFM classification

Acoustics: Acoustics Acoustics: Aeroacoustics Acoustics: Jet noise
Type
Papers
Information
Journal of Fluid Mechanics , Volume 823 , 25 July 2017 , pp. 562 - 591
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Copyright
© 2017 Cambridge University Press 

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Bogey and Gojon supplementary movie

Representation in the $(z,r)$ plane of density in the jet and near the flat plate and of pressure $p-p_0$ for (a) JetL6, (b) JetL8, (c) JetL10 and (d) JetL12. The colour scales range from $1$ to $2$~kg.m$^{-3}$ for density, from blue to red, and from $-5000$ to $5000$~Pa for pressure, from black to white. The nozzle is in black.

Download Bogey and Gojon supplementary movie(Video)
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