Hostname: page-component-745bb68f8f-lrblm Total loading time: 0 Render date: 2025-01-08T20:45:35.881Z Has data issue: false hasContentIssue false
  • English
  • Français

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]
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Billant, P., Chomaz, J.-M. & Huerre, P. 1998 Experimental study of vortex breakdown in swirling jets. J. Fluid Mech. 376, 183–219.CrossRefGoogle Scholar
Cabral, B. & Leedom, L. C. 1993 Imaging vector fields using line integral convolution. In Proceedings of the 20th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH), Anaheim, CA, pp. 263–270.CrossRefGoogle Scholar
Cantwell, B. J. 1981 Organized motion in turbulent flow. Annu. Rev. Fluid Mech. 13, 457–515.CrossRefGoogle Scholar
Chigier, N. & Chervinsky, A. 1965 Experimental and theoretical study of turbulent swirling jets issuing from a round orifice. Isr. J. Technol. 4, 44–54.Google Scholar
Chomaz, J.-M. 2005 Global instabilities in spatially developing flows: non-normality and nonlinearity. Annu. Rev. Fluid Mech. 37, 357–392.CrossRefGoogle Scholar
Cohen, J., Marasli, B. & Levinski, V. 1994 Interaction between the mean flow and coherent structures in turbulent mixing layers. J. Fluid Mech. 260, 81–94.CrossRefGoogle Scholar
Cohen, J. & Wygnanski, I. 1987 The evolution of instabilities in the axisymmetric jet. Part I. The linear growth of disturbances near the nozzle. Part II. The flow resulting from the interaction between two waves. J. Fluid Mech. 176, 191–219.CrossRefGoogle Scholar
Crighton, D. G. & Gaster, M. 1976 Stability of slowly diverging jet flow. J. Fluid Mech. 77, 397–413.CrossRefGoogle Scholar
Depardon, S., Lasserre, J. J., Brizzi, L. E. & Borée, J. 2007 Automated topology classification method for instantaneous velocity fields. Exp. Fluids 42, 697–710.CrossRefGoogle Scholar
Duwig, C. & Fuchs, L. 2007 Large eddy simulation of vortex breakdown/flame interaction. Phys. Fluids 19, 5103.CrossRefGoogle Scholar
Escudier, M. P. & Keller, J. J. 1985 Recirculation in swirling flow. A manifestation of vortex breakdown. AIAA J. 23, 111–116.CrossRefGoogle Scholar
Faler, J. H. & Leibovich, S. 1978 An experimental map of the internal structure of a vortex breakdown. J. Fluid Mech. 86, 313–335.CrossRefGoogle Scholar
Freymuth, P. 1966 On transition in a separated laminar boundary layer. J. Fluid Mech. 25, 683–704.CrossRefGoogle Scholar
Gallaire, F. & Chomaz, J.-M. 2003 Mode selection in swirling jet experiments: a linear stability analysis. J. Fluid Mech. 494, 223–253.CrossRefGoogle Scholar
Gallaire, F., Chomaz, J.-M. & Huerre, P. 2004 Closed-loop control of vortex breakdown: a model study. J. Fluid Mech. 511, 67–93.CrossRefGoogle Scholar
Gallaire, F., Rott, S. & Chomaz, J.-M. 2004 Experimental study of a free and forced swirling jet. Phys. Fluids 16, 2907–2917.CrossRefGoogle Scholar
Gallaire, F., Ruith, M., Meiburg, E., Chomaz, J.-M. & Huerre, P. 2006 Spiral vortex breakdown as a global mode. J. Fluid Mech. 549, 71–80.CrossRefGoogle Scholar
Gaster, M. 1968 Growth of disturbances in both space and time. Phys. Fluids 11, 723–727.CrossRefGoogle Scholar
Gaster, M. 1974 On the effects of boundary-layer growth on flow stability. J. Fluid Mech. 66, 465–480.CrossRefGoogle Scholar
Gaster, M., Kit, E. & Wygnanski, I. 1985 Large-scale structures in a forced turbulent mixing layer. J. Fluid Mech. 150, 23–39.CrossRefGoogle Scholar
Ho, C.-M. & Huerre, P. 1984 Perturbed free shear layers. Annu. Rev. Fluid Mech. 16, 365–424.CrossRefGoogle Scholar
Holmes, P., Lumley, J. L. & Berkooz, G. 1998 Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge University Press.Google Scholar
Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22, 473–537.CrossRefGoogle Scholar
Hussain, A. K. M. F. & Reynolds, W. C. 1970 The mechanics of an organized wave in turbulent shear flow. J. Fluid Mech. 41, 241–258.CrossRefGoogle Scholar
Juniper, M. P., Li, L. K. & Nichols, J. W. 2009 Forcing of self-excited round jet diffusion flames. Proc. Combust. Inst. 32 (1), 1191–1198.CrossRefGoogle Scholar
Khorrami, M. R. 1991 On the viscous modes of instability of a trailing line vortex. J. Fluid Mech. 225, 197–212.CrossRefGoogle Scholar
Khorrami, M. R., Malik, M. R. & Ash, R. L. 1989 Application of spectral collocation techniques to the stability of swirling flows. J. Comput. Phys. 81 (1), 206–229.CrossRefGoogle Scholar
Lambourne, N. C. & Bryer, D. W. 1962 The bursting of leading-edge vortices: some observations and discussion of the phenomenon, Tech. Rep. Ministry of Aviation, Aeronautical Research Council, vol. 3282.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics. Pergamon.Google Scholar
Laufer, J. 1975 New trends in experimental turbulence research. Annu. Rev. Fluid Mech. 7, 307–326.CrossRefGoogle Scholar
Liang, H. & Maxworthy, T. 2005 An experimental investigation of swirling jets. J. Fluid Mech. 525, 115–159.CrossRefGoogle Scholar
Liu, J. 1989 Coherent structures in transitional and turbulent free shear flows. Annu. Rev. Fluid Mech. 21, 285–315.CrossRefGoogle Scholar
Ludwieg, H. 1961 Ergänzung zu der Arbeit: Stabilität der Strömung in einem zylindrischen Ringraum. Z. Flugwiss. 9, 359.Google Scholar
Lumley, J. L. 1967 Atmospheric Turbulence and Radio Wave Propagation. Elsevier.Google Scholar
Malik, M. R., Zang, T. A. & Hussaini, M. Y. 1985 A spectral collocation method for the Navier–Stokes equations. J. Comput. Phys. 61, 64–88.CrossRefGoogle Scholar
Martinelli, F., Olivani, A. & Coghe, A. 2007 Experimental analysis of the precessing vortex core in a free swirling jet. Exp. Fluids 42, 841–841.CrossRefGoogle Scholar
Michalke, A. 1965 On spatially growing disturbances in an inviscid shear layer. J. Fluid Mech. 23, 521–544.CrossRefGoogle Scholar
Michalke, A. 1999 Absolute inviscid instability of a ring jet with back-flow and swirl. Eur. J. Mech. 18, 3–12.CrossRefGoogle Scholar
Monkewitz, P. A., Huerre, P. & Chomaz, J.-M. 1993 Global linear stability analysis of weakly non-parallel shear flows. J. Fluid Mech. 251, 1–20.CrossRefGoogle Scholar
Monkewitz, P. A. & Sohn, K. D. 1988 Absolute instability in hot jets. AIAA J. 26, 911–916.CrossRefGoogle Scholar
Noack, B. R., Afanasiev, K., Morzyński, M., Tadmor, G. & Thiele, F. 2003 A hierarchy of low-dimensional models for the transient and post-transient cylinder wake. J. Fluid Mech. 497, 335–363.CrossRefGoogle Scholar
Oberleithner, K., Lück, M., Paschereit, C. O. & Wygnanski, I. 2009 Control of vortex breakdown in critical swirl regime using azimuthal forcing. In Minnowbrook VI, Syracuse University.Google Scholar
Olendraru, C. & Sellier, A. 2002 Viscous effects in the absolute convective instability of the Batchelor vortex. J. Fluid Mech. 459, 371–396.CrossRefGoogle Scholar
Panda, J. & McLaughlin, D. K. 1994 Experiments on the instabilities of a swirling jet. Phys. Fluids 6, 263–276.CrossRefGoogle Scholar
Parras, L. & Fernandez-Feria, R. 2007 Spatial stability and the onset of absolute instability of Batchelor's vortex for high swirl numbers. J. Fluid Mech. 583, 27.CrossRefGoogle Scholar
Pier, B. & Huerre, P. 2001 Nonlinear self-sustained structures and fronts in spatially developing wake flows. J. Fluid Mech. 435, 145–174.CrossRefGoogle Scholar
Plaschko, P. 1979 Helical instabilities of slowly divergent jets. J. Fluid Mech. 92, 209–215.CrossRefGoogle Scholar
Provansal, M., Mathis, C. & Boyer, L. 1987 Benard-von Karman instability: transient and forced regimes. J. Fluid Mech. 182, 1–22.CrossRefGoogle Scholar
Rajaratnam, N. 1976 Turbulent Jets (Developments in Water Science, vol 5). Elsevier.Google Scholar
Roshko, A. 1977 Errata: structure of turbulent shear flows: a new look. AIAA J. 15, 768–768.CrossRefGoogle Scholar
Rowley, C. 2005 Model reduction for fluids using balanced proper orthogonal decomposition. Intl J. Bifurcation Chaos 15 (3), 997–1013.CrossRefGoogle Scholar
Rowley, C. W., Mezić, I., Bagheri, S., Schlatter, P. & Henningson, D. S. 2009 Spectral analysis of nonlinear flows. J. Fluid Mech. 641, 115.CrossRefGoogle Scholar
Ruith, M. R., Chen, P., Meiburg, E. & Maxworthy, T. 2003 Three-dimensional vortex breakdown in swirling jets and wakes: direct numerical simulation. J. Fluid Mech. 486, 331–378.CrossRefGoogle Scholar
Sarpkaya, T. 1971 On stationary and travelling vortex breakdowns. J. Fluid Mech. 45, 545–559.CrossRefGoogle Scholar
Schmid, P. J. 2010 Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656, 5–28.CrossRefGoogle Scholar
Sirovich, L. 1987 Turbulence and the dynamics of coherent structures. Part I. Coherent structures. Q. Appl. Math. XLV, 561–571.CrossRefGoogle Scholar
Sreenivasan, K. R., Raghu, S. & Kyle, D. 1989 Absolute instability in variable density round jets. Exp. Fluids 7, 309–317.CrossRefGoogle Scholar
Stalling, D. & Hege, H.-C. 1995 Fast and resolution independent line integral convolution. In Proceedings of the 22nd annual conference on Computer graphics and interactive techniques (SIGGRAPH), Los Angeles, CA, pp. 249–256.Google Scholar
Stuart, J. 1958 On the non-linear mechanics of hydrodynamic stability. J. Fluid Mech. 4, 1–21.CrossRefGoogle Scholar
Townsend, A. 1956 The Structure of Turbulent Shear Flow. Cambridge University Press.Google Scholar
VanDyke, M. Dyke, M. 1975 Perturbation Methods in Fluid Mechanics, annotated edn. The Parabolic Press.Google Scholar
Weisbrot, I. & Wygnanski, I. 1988 On coherent structures in a highly excited mixing layer. J. Fluid Mech. 195, 137.CrossRefGoogle Scholar