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On the impact of swirl on the growth of coherent structures

Published online by Cambridge University Press:  07 February 2014

K. Oberleithner ,
C. O. Paschereit  and
I. Wygnanski
K. Oberleithner*
Affiliation:
Laboratory for Turbulence Research in Aerospace and Combustion, Monash University, Clayton, VIC 3800, Australia
C. O. Paschereit
Affiliation:
Institut für Strömungsmechanik und Technische Akustik, HFI, Müller-Breslau Straße 8, D-10623 Berlin, Germany
I. Wygnanski
Affiliation:
Department of Aerospace and Mechanical Engineering, PO Box 210119, Tucson, AZ 85721, USA
*
†Email address for correspondence: [email protected]
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Abstract

Spatial linear stability analysis is applied to the mean flow of a turbulent swirling jet at swirl intensities below the onset of vortex breakdown. The aim of this work is to predict the dominant coherent flow structure, their driving instabilities and how they are affected by swirl. At the nozzle exit, the swirling jet promotes shear instabilities and, less unstable, centrifugal instabilities. The latter stabilize shortly downstream of the nozzle, contributing very little to the formation of coherent structures. The shear mode remains unstable throughout generating coherent structures that scale with the axial shear-layer thickness. The most amplified mode in the nearfield is a co-winding double-helical mode rotating slowly in counter-direction to the swirl. This gives rise to the formation of slowly rotating and stationary large-scale coherent structures, which explains the asymmetries in the mean flows often encountered in swirling jet experiments. The co-winding single-helical mode at high rotation rate dominates the farfield of the swirling jet in replacement of the co- and counter-winding bending modes dominating the non-swirling jet. Moreover, swirl is found to significantly affect the streamwise phase velocity of the helical modes rendering this flow as highly dispersive and insensitive to intermodal interactions, which explains the absence of vortex pairing observed in previous investigations. The stability analysis is validated through hot-wire measurements of the flow excited at a single helical mode and of the flow perturbed by a time- and space-discrete pulse. The experimental results confirm the predicted mode selection and corresponding streamwise growth rates and phase velocities.

JFM classification

Instability: Absolute/convective instability Turbulent Flows: Turbulent Flows Wakes/Jets: Wakes/Jets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 741 , 25 February 2014 , pp. 156 - 199
Copyright
© 2014 Cambridge University Press 

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References

Barkley, D. 2006 Linear analysis of the cylinder wake mean flow. EPL (Europhys. Lett.) 75, 750–756.Google Scholar
Billant, P., Chomaz, J.-M. & Huerre, P. 1998 Experimental study of vortex breakdown in swirling jets. J. Fluid Mech. 376, 183–219.Google Scholar
Carton, X. & McWilliams, J. 1989 Barotropic and baroclinic instabilties of axisymmetric vortices in a quasi-geostrophic model. In Mesoscale/Synoptic Coherent Structures in Geophysical Turbulence (ed. Nihoul, J. & Jamart, B.), pp. 225–244. Elsevier.CrossRefGoogle Scholar
Cohen, J. & Wygnanski, I. 1987a The evolution of instabilities in the axisymmetric jet. Part 1. The linear growth of disturbances near the nozzle. J. Fluid Mech. 176, 191–219.Google Scholar
Cohen, J. & Wygnanski, I. 1987b The evolution of instabilities in the axisymmetric jet. Part 2. The flow resulting from the interaction between two waves. J. Fluid Mech. 176, 221–235.Google Scholar
Cooper, A. J. & Peake, N. 2002 The stability of a slowly diverging swirling jet. J. Fluid Mech. 473, 389–411.CrossRefGoogle Scholar
Crighton, D. G. & Gaster, M. 1976 Stability of slowly diverging jet flow. J. Fluid Mech. 77, 397–413.Google Scholar
Cutler, A. D., Kraus, D. K. & Levey, B. S. 1995 Near-field flow of supersonic swirling jets. AIAA J. 33, 876–881.CrossRefGoogle Scholar
Delbende, I., Chomaz, J.-M. & Huerre, P. 1998 Absolute/convective instabilities in the Batchelor vortex: a numerical study of the linear impulse response. J. Fluid Mech. 355, 229–254.Google Scholar
Drazin, P. G. & Reid, W. H. 2004 Hydrodynamic Stability. Cambridge Mathematical Library.CrossRefGoogle Scholar
Escudier, M. & Keller, J. 1983 Vortex breakdown: a two-stage transition. In AGARD CP no.324: aerodynamics of vortical type flows in 3D. Paper 25.Google Scholar
Gallaire, F. & Chomaz, J.-M. 2003a Instability mechanisms in swirling flows. Phys. Fluids 15, 2622–2639.CrossRefGoogle Scholar
Gallaire, F. & Chomaz, J.-M. 2003b Mode selection in swirling jet experiments: a linear stability analysis. J. Fluid Mech. 494, 223–253.Google Scholar
Gaster, M. & Grant, I. 1975 An experimental investigation of the formation and development of a wave packet in a laminar boundary layer. Royal Soc. Lond. Proc. Ser. A 347, 253–269.Google Scholar
Gaster, M., Kit, E. & Wygnanski, I. 1985 Large-scale structures in a forced turbulent mixing layer. J. Fluid Mech. 150, 23–39.Google Scholar
Greenblatt, D. & Wygnanski, I. J. 2000 The control of flow separation by periodic excitation. Prog. Aeronaut. Sci. 36 (7), 487–545.Google Scholar
Gudmundsson, K. & Colonius, T. 2011 Instability wave models for the near-field fluctuations of turbulent jets. J. Fluid Mech. 689, 97–128.Google Scholar
Gutmark, E. J., Schadow, K. C. & Yu, K. H. 1995 Mixing enhancement in supersonic free shear flows. Annu. Rev. Fluid Mech. 27, 375–417.CrossRefGoogle Scholar
Herbert, T. 1997 Parabolized stability equations. Annu. Rev. Fluid Mech. 29, 245–283.CrossRefGoogle Scholar
Ho, C.-M. & Gutmark, E. 1987 Vortex induction and mass entrainment in a small-aspect-ratio elliptic jet. J. Fluid Mech. 179, 383–405.Google Scholar
Howard, L. N. & Gupta, A. S. 1962 On the hydrodynamic and hydromagnetic stability of swirling flows. J. Fluid Mech. 14, 463–476.Google Scholar
Hu, G.-H., Sun, D.-J. & Yin, X.-Y. 2001a A numerical study of dynamics of a temporally evolving swirling jet. Phys. Fluids 13, 951–965.CrossRefGoogle Scholar
Hu, G.-H., Sun, D.-J., Yin, X.-Y. & Binggang, T. 2001b Studies on stability and dynamics of a swirling jet. Acta Mechanica Sin. 17, 237–244.Google Scholar
Huang, Y. & Yang, V. 2009 Dynamics and stability of lean-premixed swirl-stabilized combustion. Prog. Energy Combust. Sci. 35 (4), 293–364.CrossRefGoogle 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.Google Scholar
Juniper, M. P., Tammisola, O. & Lundell, F. 2011 The local and global stability of confined planar wakes at intermediate Reynolds number. J. Fluid Mech. 686, 218–238.Google 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.Google Scholar
Knowles, K. & Saddington, A. J. 2006 A review of jet mixing enhancement for aircraft propulsion applications. Proc. IMechE G: J. Aerospace Engng 220 (2), 103–127.CrossRefGoogle Scholar
Leibovich, S. & Stewartson, K. 1983 A sufficient condition for the instability of columnar vortices. J. Fluid Mech. 126, 335–356.Google Scholar
Liang, H. & Maxworthy, T. 2005 An experimental investigation of swirling jets. J. Fluid Mech. 525, 115–159.Google Scholar
Liu, J. T. C. 1971 Nonlinear development of an instability wave in a turbulent wake. Phys. Fluids 14, 2251–2257.Google Scholar
Loiseleux, T. & Chomaz, J.-M. 2003 Breaking of rotational symmetry in a swirling jet experiment. Phys. Fluids 15, 511–523.Google Scholar
Loiseleux, T., Chomaz, J. M. & Huerre, P. 1998 The effect of swirl on jets and wakes: linear instability of the Rankine vortex with axial flow. Phys. Fluids 10, 1120–1134.Google Scholar
Loiseleux, T., Delbende, I. & Huerre, P. 2000 Absolute and convective instabilities of a swirling jet/wake shear layer. Phys. Fluids 12, 375–380.CrossRefGoogle Scholar
Long, T. A. & Petersen, R. A. 1992 Controlled interactions in a forced axisymmetric jet. Part 1. The distortion of the mean flow. J. Fluid Mech. 235, 37–55.Google Scholar
Lu, G. & Lele, S. K. 1999 Inviscid instability of compressible swirling mixing layers. Phys. Fluids 11, 450–461.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
Marasli, B., Champagne, F. H. & Wygnanski, I. J. 1991 On linear evolution of unstable disturbances in a plane turbulent wake. Phys. Fluids 3, 665–674.CrossRefGoogle Scholar
Martin, J. E. & Meiburg, E. 1994 On the stability of the swirling jet shear layer. Phys. Fluids 6, 424–426.Google Scholar
Martin, J. E. & Meiburg, E. 1996 Nonlinear axisymmetric and three-dimensional vorticity dynamics in a swirling jet model. Phys. Fluids 8 (7), 1917–1928.CrossRefGoogle Scholar
Martin, J. E. & Meiburg, E. 1998 The growth and nonlinear evolution of helical perturbations in a swirling jet model. Eur. J. Mech. (B/Fluids) 17, 639–651.Google Scholar
McManus, K. R., Poinsot, T. & Candel, S. M. 1993 A review of active control of combustion instabilities. Prog. Energy Combust. Sci. 19, 1–29.Google Scholar
Mehta, R. D., Wood, D. H. & Clausen, P. D. 1991 Some effects of swirl on turbulent mixing layer development. Phys. Fluids 3, 2716–2724.Google Scholar
Meliga, P., Pujals, G. & Éric, S. 2012 Sensitivity of 2-D turbulent flow past a D-shaped cylinder using global stability. Phys. Fluids 24 (6), 061701.Google Scholar
Michalke, A. 1965 On spatially growing disturbances in an inviscid shear layer. J. Fluid Mech. 23, 521–544.Google Scholar
Monkewitz, P. A. & Sohn, K. D. 1988 Absolute instability in hot jets. AIAA J. 26, 911–916.Google Scholar
Müller, S. B. & Kleiser, L. 2008 Viscous and inviscid spatial stability analysis of compressible swirling mixing layers. Phys. Fluids 20 (11), 114103.Google Scholar
Naughton, J. W., Cattafesta, L. N. III & Settles, G. S. 1997 An experimental study of compressible turbulent mixing enhancement in swirling jets. J. Fluid Mech. 330, 271–305.Google 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.Google Scholar
Oberleithner, K., Paschereit, C. O., Seele, R. & Wygnanski, I. 2012 Formation of turbulent vortex breakdown: intermittency, criticality, and global instability. AIAA J. 50, 1437–1452.Google Scholar
Oberleithner, K., Paschereit, C. O. & Wygnanski, I. 2007 Vortex breakdown in a swirling jet with axial forcing. In 18eme Congres Francais de Mechanique, colloquium: Stratified and Rotating Flows. AFM.Google Scholar
Oberleithner, K., Sieber, M., Nayeri, C. N., Paschereit, C. O., Petz, C., Hege, H.-C., Noack, B. R. & Wygnanski, I. 2011 Three-dimensional coherent structures in a swirling jet undergoing vortex breakdown: stability analysis and empirical mode construction. J. Fluid Mech. 679, 383–414.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.Google Scholar
Paschereit, C. O., Wygnanski, I. & Fiedler, H. E. 1995 Experimental investigation of subharmonic resonance in an axisymmetric jet. J. Fluid Mech. 283, 365–407.Google Scholar
Pier, B. 2002 On the frequency selection of finite-amplitude vortex shedding in the cylinder wake. J. Fluid Mech. 458, 407–417.CrossRefGoogle Scholar
Raffel, M., Willert, C., Wereley, S. & Kompenhans, J. 2007 Particle Image Velocimetry, A Practical Guide. 2nd edn. Springer.Google Scholar
Reau, N. & Tumin, A. 2002 Harmonic Perturbations in Turbulent Wakes. AIAA J. 40, 526–530.Google Scholar
Sarpkaya, T. 1971 On stationary and travelling vortex breakdowns. J. Fluid Mech. 45, 545–559.Google Scholar
Semaan, R., Naughton, J. W. & Ewing, D. 2009 Approach toward similar behaviour of a swirling jet flow. In 47th AIAA Aerospace Sciences Meeting. AIAA.CrossRefGoogle Scholar
Townsend, A. 1956 The Structure of Turbulent Shear Flow. Cambridge University Press.Google Scholar
Trefethen, ; 2000 Spectral Methods in Matlab. SIAM.Google Scholar
Wu, C., Farokhi, S. & Taghavi, R. 1992 Spatial instability of a swirling jet — theory and experiment. AIAA J. 30, 1545–1552.Google Scholar
Wu, J.-Z., Ma, H.-Y. & Zhou, M.-D. 2006 Vorticity and Vortex Dynamics. Springer.Google Scholar
Zhou, M. D., Heine, C. & Wygnanski, I. 1996 The effects of excitation on the coherent and random motion in a plane wall jet. J. Fluid Mech. 310, 1–37.Google Scholar