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Nozzle dynamics and wavepackets in turbulent jets

Published online by Cambridge University Press:  28 July 2021

Oğuzhan Kaplan Open the ORCID record for Oğuzhan Kaplan [Opens in a new window] ,
Peter Jordan Open the ORCID record for Peter Jordan [Opens in a new window] ,
André V.G. Cavalieri Open the ORCID record for André V.G. Cavalieri [Opens in a new window]  and
Guillaume A. Brès Open the ORCID record for Guillaume A. Brès [Opens in a new window]
Oğuzhan Kaplan*
Affiliation:
Département Fluides, Thermique et Combustion, Institut Pprime, CNRS – Université de Poitiers – ENSMA, 86036 Poitiers, France Univ. Lille, CNRS, ONERA, Arts et Métiers Institute of Technology, Centrale Lille, UMR 9014 – LMFL – Laboratoire de Mécanique des fluides de Lille – Kampé de Fériet, F-59000 Lille, France
Peter Jordan
Affiliation:
Département Fluides, Thermique et Combustion, Institut Pprime, CNRS – Université de Poitiers – ENSMA, 86036 Poitiers, France
André V.G. Cavalieri
Affiliation:
Divisão de Engenharia Aeronautica, Instituto Tecnologico de Aeronautica, 12228-900São Jose dos Campos, SP, Brazil
Guillaume A. Brès
Affiliation:
Cascade Technologies Inc., Palo Alto, CA94303, USA
*
†Email address for correspondence: oguzhankpln@gmail.com
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Abstract

We study a turbulent jet issuing from a cylindrical nozzle to characterise coherent structures evolving in the turbulent boundary layer. The analysis is performed using data from a large-eddy simulation of a Mach 0.4 jet. Azimuthal decomposition of the velocity field in the nozzle shows that turbulent kinetic energy predominantly resides in high azimuthal wavenumbers; the first three azimuthal wavenumbers, that are important for sound generation, contain much lower, but non-zero amplitudes. Using two-point statistics, low azimuthal modes in the nozzle boundary layer are shown to exhibit significant correlations with modes of the same order in the free-jet region. Spectral proper orthogonal decomposition is used to distill a low-rank approximation of the flow dynamics. This reveals the existence of tilted coherent structures within the nozzle boundary layer and shows that these are coupled with wavepackets in the jet. The educed nozzle boundary-layer structures are modelled using a global resolvent analysis of the mean flow inside the nozzle to determine the most amplified flow responses using the linearised Navier–Stokes system. It is shown that the most-energetic nozzle structures can be successfully described with optimal resolvent response modes, whose associated forcing modes are observed to tilt against the nozzle boundary layer, suggesting that the Orr mechanism underpins these organised, turbulent, boundary-layer structures.

JFM classification

Acoustics: Jet noise Boundary Layers: Boundary layer stability Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 923 , 25 September 2021 , A22
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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Kaplan at al. Supplementary Movie

Cross-spectral-density of axisymmetric streamwise velocity fluctuations with the correlation point indicated indicated by `+' for St = 0:6.

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