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Three-dimensional coherent structures in a swirling jet undergoing vortex breakdown: stability analysis and empirical mode construction

Published online by Cambridge University Press:  17 May 2011

K. OBERLEITHNER ,
M. SIEBER ,
C. N. NAYERI ,
C. O. PASCHEREIT ,
C. PETZ ,
H.-C. HEGE ,
B. R. NOACK  and
I. WYGNANSKI
K. OBERLEITHNER*
Affiliation:
Hermann-Föttinger-Institut, Technische Universität Berlin, Müller-Breslau Str. 8, D-10623 Berlin, Germany
M. SIEBER
Affiliation:
Hermann-Föttinger-Institut, Technische Universität Berlin, Müller-Breslau Str. 8, D-10623 Berlin, Germany
C. N. NAYERI
Affiliation:
Hermann-Föttinger-Institut, Technische Universität Berlin, Müller-Breslau Str. 8, D-10623 Berlin, Germany
C. O. PASCHEREIT
Affiliation:
Hermann-Föttinger-Institut, Technische Universität Berlin, Müller-Breslau Str. 8, D-10623 Berlin, Germany
C. PETZ
Affiliation:
Abteilung Visualisierung und Datenanalyse, Bereich Numerische Mathematik, Zuse-Institut Berlin, Takustr. 7, D-14195 Berlin-Dahlem, Germany
H.-C. HEGE
Affiliation:
Abteilung Visualisierung und Datenanalyse, Bereich Numerische Mathematik, Zuse-Institut Berlin, Takustr. 7, D-14195 Berlin-Dahlem, Germany
B. R. NOACK
Affiliation:
Département Fluides, Thermique, Combustion, CEAT, Institut Pprime, CNRS – Université de Poitiers – ENSMA, UPR 3346, 43 rue de l'Aérodrome, F-86036 POITIERS CEDEX, France
I. WYGNANSKI
Affiliation:
Department of Aerospace and Mechanical Engineering, The University of Arizona, Tucson, AZ 85721, USA
*
†Email address for correspondence: [email protected]
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Abstract

The spatio-temporal evolution of a turbulent swirling jet undergoing vortex breakdown has been investigated. Experiments suggest the existence of a self-excited global mode having a single dominant frequency. This oscillatory mode is shown to be absolutely unstable and leads to a rotating counter-winding helical structure that is located at the periphery of the recirculation zone. The resulting time-periodic 3D velocity field is predicted theoretically as being the most unstable mode determined by parabolized stability analysis employing the mean flow data from experiments. The 3D oscillatory flow is constructed from uncorrelated 2D snapshots of particle image velocimetry data, using proper orthogonal decomposition, a phase-averaging technique and an azimuthal symmetry associated with helical structures. Stability-derived modes and empirically derived modes correspond remarkably well, yielding prototypical coherent structures that dominate the investigated flow region. The proposed method of constructing 3D time-periodic velocity fields from uncorrelated 2D data is applicable to a large class of turbulent shear flows.

JFM classification

Instability: Absolute/convective instability Wakes/Jets: Shear layers Vortex Flows: Vortex breakdown
Type
Papers
Information
Journal of Fluid Mechanics , Volume 679 , 25 July 2011 , pp. 383 - 414
Copyright
Copyright © Cambridge University Press 2011

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