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Three-dimensional density field of a screeching under-expanded jet in helical mode using multi-view digital holographic interferometry

Published online by Cambridge University Press:  30 August 2022

O. Léon Open the ORCID record for O. Léon [Opens in a new window] ,
D. Donjat Open the ORCID record for D. Donjat [Opens in a new window] ,
F. Olchewsky ,
J.-M. Desse Open the ORCID record for J.-M. Desse [Opens in a new window] ,
F. Nicolas Open the ORCID record for F. Nicolas [Opens in a new window]  and
F. Champagnat Open the ORCID record for F. Champagnat [Opens in a new window]
O. Léon*
Affiliation:
ONERA/DMPE, Université de Toulouse, 2 avenue Edouard Belin, 31055 Toulouse, France
D. Donjat
Affiliation:
ONERA/DMPE, Université de Toulouse, 2 avenue Edouard Belin, 31055 Toulouse, France
F. Olchewsky
Affiliation:
ONERA/DAAA, Laboratoire de Mécanique des Fluides de Lille – Kampé de Fériet, 59000 Lille, France
J.-M. Desse
Affiliation:
ONERA/DAAA, Laboratoire de Mécanique des Fluides de Lille – Kampé de Fériet, 59000 Lille, France
F. Nicolas
Affiliation:
ONERA/DAAA, Université Paris Saclay, 92190 Meudon, France
F. Champagnat
Affiliation:
ONERA/DTIS, Université Paris Saclay, 91123 Palaiseau, France
*
†Email address for correspondence: olivier.leon@onera.fr
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Abstract

A synchronised multi-axis digital holographic interferometry set-up is presented for the study of 3-D flow fields with large density gradients. This optical configuration provides instantaneous interferograms with fine spatial resolution in six directions of projection. A regularised tomographic approach taking into account the presence of possible shock waves is furthermore considered to reconstruct 3-D density fields. Applied to a screeching under-expanded supersonic jet with helical dynamics, this set-up is used to provide dense optical phase measurements in the initial region of the jet. The jet mean density field is shown to be satisfactorily estimated with sharply resolved density gradients. In addition, an approach based on azimuthal Fourier transform and snapshot proper orthogonal decomposition (POD) applied to the instantaneous flow observations is proposed to study the main coherent dynamics of the jet. Relying on a cluster analysis of the azimuthal POD mode coefficients, a reduced dynamical model in the POD mode phase space is used as an approximation of the two observed limit cycles. A clear 3-D representation of the density field of a helical instability associated with screech mode C is then evidenced, with two equally probable directions of rotation. Switching between the two directions is reported, highlighting intermittency in the feedback loop. This helical structure is particularly seen to extend to the jet core, driving its internal dynamics and inducing out-of-phase density fluctuations between the outer and inner shear layers. These out-of-phase motions are related to the non-uniform radial distribution of fluctuation phase associated with the outer-layer Kelvin–Helmholtz instability wave.

JFM classification

Compressible Flows: Supersonic flow Nonlinear Dynamical Systems: Low-dimensional models Wakes/Jets: Jets
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 947 , 25 September 2022 , A36
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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Léon et al. supplementary movie

Animation of the 3D density fields obtained by tomographic reconstruction of the 2 identified reduced dynamical models.

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