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Bistability of bubble and conical forms of vortex breakdown in laminar swirling jets

  • Pradeep Moise (a1)

Abstract

Vortex breakdown (VB) in swirling jets can be classified as either a bubble (BVB) or a conical (CVB) form based on the shape of its recirculation zone. The present study investigates the hysteresis features of these forms in laminar swirling jets using direct numerical simulations. It is established here that BVB and CVB are bistable forms in a large swirl range and for a Reynolds number of 200 (based on jet radius and centreline velocity). Considerable differences were observed in the length scales associated with the two, with the approximate recirculation zone diameters of the BVB and CVB being 1 and 15 jet diameters, respectively. Additionally, two types of BVB were observed, identified as a two-celled BVB with spiral tail and an asymmetric BVB. The former is characterized by an almost steady bubble with a two-celled structure. By contrast, the entire bubble envelope oscillated in a non-axisymmetric fashion for the latter. These two types of BVB themselves were found to coexist in a small swirl range. A global linear stability analysis was used to show that two different unstable single helical modes are associated with these two types. In comparison to using the base flow, a stability analysis performed on the mean flow was found to predict the coherent features of asymmetric BVB observed in the simulations more precisely. This study highlights the rich variety of VB flow states that coexist in various ranges of swirl strengths and the significance of hysteresis effects in laminar swirling jets.

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Corresponding author

Email address for correspondence: pradeep890@gmail.com

References

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Adams, B., Jones, M., Hourigan, K. & Thompson, M. 1999 Hysteresis in the open pipe flow with vortex breakdown. In 2nd International Conference on CFD in the Minerals and Process Industries, pp. 311316.
Aguilar, M., Malanoski, M., Adhitya, G., Emerson, B., Acharya, V., Noble, D. & Lieuwen, T. 2015 Helical flow disturbances in a multinozzle combustor. Trans. ASME J. Engng Gas Turbines Power 137 (9), 091507.
Åkervik, E., Brandt, L., Henningson, D. S., Hœpffner, J., Marxen, O. & Schlatter, P. 2006 Steady solutions of the Navier–Stokes equations by selective frequency damping. Phys. Fluids 18 (6), 068102.
Balakrishna, N., Mathew, J. & Samanta, A. 2019 Inviscid and viscous global stability of vortex rings. J. Fluid Mech. (submitted).
Barkley, D. 2006 Linear analysis of the cylinder wake mean flow. Europhys. Lett. 75 (5), 750756.
Bayliss, A. & Turkel, E. 1992 Mappings and accuracy for Chebyshev pseudo-spectral approximations. J. Comput. Phys. 101 (2), 349359.
Beran, P. S. & Culick, F. E. C. 1992 The role of non-uniqueness in the development of vortex breakdown in tubes. J. Fluid Mech. 242, 491527.
Billant, P., Chomaz, J.-M. & Huerre, P. 1998 Experimental study of vortex breakdown in swirling jets. J. Fluid Mech. 376, 183219.
Brown, G. L. & Lopez, J. M. 1990 Axisymmetric vortex breakdown. Part 2. Physical mechanisms. J. Fluid Mech. 221, 553576.
Brücker, C. 1993 Study of vortex breakdown by particle tracking velocimetry (PTV). Part 2. Spiral-type vortex breakdown. Exp. Fluids 14 (1–2), 133139.
Brücker, C. & Althaus, W. 1992 Study of vortex breakdown by particle tracking velocimetry (PTV). Exp. Fluids 13 (5), 339349.
Burggraf, O. R. & Foster, M. R. 1977 Continuation or breakdown in tornado-like vortices. J. Fluid Mech. 80 (June 1976), 685703.
Darmofal, D. L. 1996 Comparisons of experimental and numerical results for axisymmetric vortex breakdown in pipes. Comput. Fluids 25 (4), 353371.
Escudier, M. 1984 Observations of the flow produced in a cylindrical container by a rotating endwall. Exp. Fluids 2 (4), 189196.
Escudier, M. 1988 Vortex breakdown: observations and explanations. Prog. Aerosp. Sci. 25 (2), 189229.
Faler, J. H. & Leibovich, S. 1977 Disrupted states of vortex flow and vortex breakdown. Phys. Fluids 20 (9), 13851400.
Faler, J. H. & Leibovich, S. 1978 An experimental map of the internal structure of a vortex breakdown. J. Fluid Mech. 86, 313335.
Falese, M., Gicquel, L. Y. M. & Poinsot, T. 2014 LES of bifurcation and hysteresis in confined annular swirling flows. Comput. Fluids 89, 167178.
Fitzgerald, A. J., Hourigan, K. & Thompson, M. C. 2004 Towards a universal criterion for predicting vortex breakdown in swirling jets. In Proceedings of the Fifteenth Australasian Fluid Mechanics Conference (ed. Behnia, M., Lin, W. & McBain, G. D.). The University of Sydney.
Gallaire, F. & Chomaz, J.-M. 2003 Mode selection in swirling jet experiments: a linear stability analysis. J. Fluid Mech. 494, 223253.
Gallaire, F., Rott, S. & Chomaz, J.-M. 2004 Experimental study of a free and forced swirling jet. Phys. Fluids 16 (8), 29072917.
Gore, R. W. & Ranz, W. E. 1964 Backflows in rotating fluids moving axially through expanding cross sections. AIChE J. 10 (1), 8388.
Grabowski, W. J. & Berger, S. A. 1976 Solutions of the Navier–Stokes equations for vortex breakdown. J. Fluid Mech. 75 (3), 525544.
Hall, M. G. 1972 Vortex breakdown. Annu. Rev. Fluid Mech. 4 (1), 195218.
Hernandez, V., Roman, J. E. & Vidal, V. 2005 SLEPc: a scalable and flexible toolkit for the solution of eigenvalue problems. ACM Trans. Math. Softw. 31 (3), 351362.
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 6994.
Jiang, T. L. & Shen, C. H. 1994 Numerical predictions of the bifurcation of confined swirling flows. Int. J. Numer. Meth. Fluids 19 (11), 961979.
Jordi, B. E., Cotter, C. J. & Sherwin, S. J. 2014 Encapsulated formulation of the selective frequency damping method. Phys. Fluids 26 (3), 034101.
Kurosaka, M., Kikuchi, M., Hirano, K., Yuge, T. & Inoue, H. 2003 Interchangeability of vortex-breakdown types. Exp. Fluids 34 (1), 7786.
Laizet, S. & Lamballais, E. 2009 High-order compact schemes for incompressible flows: a simple and efficient method with quasi-spectral accuracy. J. Comput. Phys. 228 (16), 59896015.
Laizet, S. & Li, N. 2011 Incompact3d, a powerful tool to tackle turbulence problems with up to O (105) computational cores. Intl J. Numer. Meth. Fluids 67, 17351757.
Lamballais, E., Fortuné, V. & Laizet, S. 2011 Straightforward high-order numerical dissipation via the viscous term for direct and large eddy simulation. J. Comput. Phys. 230 (9), 32703275.
Lambourne, N. C. & Bryer, D. W.1961 The bursting of leading-edge vortices – some observations and discussion of the phenomenon. Tech. Rep. ARC Reports and Memoranda No. 3282.
Leibovich, S. 1978 The structure of vortex breakdown. Annu. Rev. Fluid Mech. 10, 221246.
Leibovich, S. 1984 Vortex stability and breakdown – survey and extension. AIAA J. 22 (9), 11921206.
Leibovich, S. & Kribus, A. 1990 Large-amplitude wavetrains and solitary waves in vortices. J. Fluid Mech. 216, 459504.
Liang, H. & Maxworthy, T. 2005 An experimental investigation of swirling jets. J. Fluid Mech. 525, 115159.
Lopez, J. M. 1995 Unsteady swirling flow in an enclosed cylinder with reflectional symmetry. Phys. Fluids 7 (11), 27002714.
Lucca-Negro, O. & O’Doherty, T. 2001 Vortex breakdown: a review. Prog. Energy Combust. Sci. 27 (4), 431481.
Lumley, J. L. 1970 Stochastic Tools in Turbulence, 1st edn. Academic Press.
Meliga, P., Gallaire, F. & Chomaz, J.-M. 2012 A weakly nonlinear mechanism for mode selection in swirling jets. J. Fluid Mech. 699, 216262.
Moise, P. & Mathew, J. 2019 Bubble and conical forms of vortex breakdown in swirling jets. J. Fluid Mech. 873, 322357.
Mourtazin, D. & Cohen, J. 2007 The effect of buoyancy on vortex breakdown in a swirling jet. J. Fluid Mech. 571, 177189.
Ogus, G., Baelmans, M. & Vanierschot, M. 2016 On the flow structures and hysteresis of laminar swirling jets. Phys. Fluids 28 (12), 123604.
Pradeep, M.2019 Bubble and conical forms of vortex breakdown in swirling jets. PhD thesis, Indian Institute of Science.
Rajamanickam, K. & Basu, S. 2018 Insights into the dynamics of conical breakdown modes in coaxial swirling flow field. J. Fluid Mech. 853, 72110.
Reynolds, W. C., Parekh, D. E., Juvet, P. J. D. & Lee, M. J. D. 2003 Bifurcating and blooming jets. Annu. Rev. Fluid Mech. 35 (1), 295315.
Ruith, M. R., Chen, P. & Meiburg, E. 2004 Development of boundary conditions for direct numerical simulations of three-dimensional vortex breakdown phenomena in semi-infinite domains. Comput. Fluids 33 (9), 12251250.
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, 331378.
Santhosh, R. & Basu, S. 2015 Acoustic response of vortex breakdown modes in a coaxial isothermal unconfined swirling jet. Phys. Fluids 27 (3), 033601.
Sarpkaya, T. 1971 On stationary and travelling vortex breakdowns. J. Fluid Mech. 45 (3), 545559.
Sarpkaya, T. 1995 Turbulent vortex breakdown. Phys. Fluids 7 (10), 23012303.
Shtern, V. 2004 Bifurcation of conical magnetic field. Phys. Rev. E 69 (6), 065301.
Shtern, V. & Hussain, F. 1993 Hysteresis in a swirling jet as a model tornado. Phys. Fluids A Fluid Dyn. 5 (9), 21832195.
Shtern, V. & Hussain, F. 1999 Collapse, symmetry breaking, and hysteresis in swirling flows. Annu. Rev. Fluid Mech. 31 (1), 537566.
Sipp, D. & Lebedev, A. 2007 Global stability of base and mean flows: a general approach and its applications to cylinder and open cavity flows. J. Fluid Mech. 593, 333358.
Stevens, J. L., Lopez, J. M. & Cantwell, B. J. 1999 Oscillatory flow states in an enclosed cylinder with a rotating endwall. J. Fluid Mech. 389, 101118.
Syred, N. & Beer, J. M. 1974 Combustion in swirling flows: a review. Combust. Flame 23 (2), 143201.
Tammisola, O. & Juniper, M. P. 2016 Coherent structures in a swirl injector at Re = 4800 by nonlinear simulations and linear global modes. J. Fluid Mech. 792, 620657.
Towne, A., Schmidt, O. T. & Colonius, T. 2018 Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis. J. Fluid Mech. 847, 821867.
Vanierschot, M., Müller, J. S., Sieber, M., Percin, M., van Oudheusden, B. W. & Oberleithner, K. 2020 Single- and double-helix vortex breakdown as two dominant global modes in turbulent swirling jet flow. J. Fluid Mech. 883, A31.
Vanierschot, M. & Van den Bulck, E. 2007a Hysteresis in flow patterns in annular swirling jets. Exp. Therm. Fluid Sci. 31 (6), 513524.
Vanierschot, M. & Van den Bulck, E. 2007b Numerical study of hysteresis in annular swirling jets with a stepped-conical nozzle. Intl J. Numer. Meth. Fluids 54 (3), 313324.
Vanoverberghe, K. P., Van den Bulck, E. V., Tummers, M. J. & Hübner, W. A. 2002 Multiflame patterns in swirl-driven partially premixed natural gas combustion. Trans. ASME J. Engng Gas Turbines Power 125 (1), 4045.
Vishwanath, R. B., Tilak, P. M. & Chaudhuri, S. 2018 An experimental study of interacting swirl flows in a model gas turbine combustor. Exp. Fluids 59 (3), 38.
Wang, S. & Rusak, Z. 1997 The dynamics of a swirling flow in a pipe and transition to axisymmetric vortex breakdown. J. Fluid Mech. 340, 177223.
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JFM classification

Type Description Title
VIDEO
Movie

Moise supplementary movie
Contours of vorticity magnitude on the z = 0 plane at different times for the asymmetric type of BVB observed for S = 1.7, showing the oscillation of the entire bubble envelope, a characteristic of this BVB type.

 Video (13.1 MB)
13.1 MB

Bistability of bubble and conical forms of vortex breakdown in laminar swirling jets

  • Pradeep Moise (a1)

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