Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-29T10:26:43.227Z Has data issue: false hasContentIssue false
  • English
  • Français

Vortex breakdown in variable-density gaseous swirling jets

Published online by Cambridge University Press:  07 February 2022

Benjamin W. Keeton Open the ORCID record for Benjamin W. Keeton [Opens in a new window] ,
Jaime Carpio ,
Keiko K. Nomura Open the ORCID record for Keiko K. Nomura [Opens in a new window] ,
Antonio L. Sánchez Open the ORCID record for Antonio L. Sánchez [Opens in a new window]  and
Forman A. Williams
Benjamin W. Keeton*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA 92093–0411, USA
Jaime Carpio
Affiliation:
Departamento de Ingeniería Energética, E.T.S. Ingenieros Industriales, Universidad Politécnica de Madrid, 28006 Madrid, Spain
Keiko K. Nomura
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA 92093–0411, USA
Antonio L. Sánchez
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA 92093–0411, USA
Forman A. Williams
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA 92093–0411, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Theoretical predictions and numerical simulations are used to determine the transition to bubble and conical vortex breakdown in low-Mach-number laminar axisymmetric variable-density swirling jets. A critical value of the swirl number $S$ for the onset of the bubble ($S^*_B$) and the cone ($S^*_C$) is determined as the jet-to-ambient density ratio $\varLambda$ is varied, with the temperature dependence of the gas density and viscosity appropriate to that of air. The criterion of failure of the slender quasi-cylindrical approximation predicts $S^*_B$ that decreases with increasing values of $\varLambda$ for a jet in solid-body rotation emerging sharply into a quiescent atmosphere. In addition, a new criterion for the onset of conical breakdown is derived from divergence of the initial value of the radial spreading rate of the jet occurring at $S^*_C$, found to be independent of $\varLambda$, in an asymptotic analysis for small distances from the inlet plane. To maintain stable flow in the unsteady numerical simulations, an effective Reynolds number $Re_{eff}$, defined employing the geometric mean of the viscosity in the jet and ambient atmosphere, is fixed at $Re_{eff}=200$ for all $\varLambda$. Similar to the theoretical predictions, numerical calculations of $S^*_B$ decrease monotonically as $\varLambda$ is increased. The critical swirl numbers for the cone, $S^*_C$, are found to depend strongly on viscous effects; for $\varLambda =1/5$, the low jet Reynolds number (51) at $Re_{eff}=200$ delays the transition to the cone, while for $\varLambda =5$ at $Re_{eff}=200$, the large increase in kinematic viscosity in the external fluid produces a similar trend, significantly increasing $S^*_C$.

JFM classification

Vortex Flows: Vortex breakdown Wakes/Jets: Jets
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 936 , 10 April 2022 , A1
Check for updates
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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

Adzlan, A. & Gotoda, H. 2012 Experimental investigation of vortex breakdown in a coaxial swirling jet with a density difference. Chem. Engng Sci. 80, 174–181.CrossRefGoogle Scholar
Althaus, W., Brücker, C. & Weimer, M. 1995 Breakdown of slender vortices. In Fluid Vortices (ed. S.I. Green), pp. 373–426. Springer Netherlands.CrossRefGoogle Scholar
Benjamin, T. 1962 Theory of the vortex breakdown phenomenon. J. Fluid Mech. 14 (4), 593–629.CrossRefGoogle Scholar
Billant, P., Chomaz, J.-M. & Huerre, P. 1998 Experimental study of vortex breakdown in swirling jets. J. Fluid Mech. 376, 183–219.CrossRefGoogle Scholar
Brown, G.L. & Lopez, J.M. 1990 Axisymmetric vortex breakdown part 2. Physical mechanisms. J. Fluid Mech. 221, 553–576.CrossRefGoogle Scholar
Candel, S., Durox, D., Schuller, T., Bourgouin, J.-F. & Moeck, J.P. 2014 Dynamics of swirling flames. Annu. Rev. Fluid Mech. 46 (1), 147–173.CrossRefGoogle Scholar
Chapman, D.R. 1949 Laminar mixing of a compressible fluid. Tech. Note NACA-TN-1800. National Advisory Committee for Aeronautics.Google Scholar
Chigier, N.A. & Chervinsky, A. 1967 Experimental investigation of swirling vortex motion in jets. J. Appl. Mech. 34 (2), 443–451.CrossRefGoogle Scholar
Douglas, C., Emerson, B. & Lieuwen, T. 2021 Nonlinear dynamics of fully developed swirling jets. J. Fluid Mech. 924, A14.CrossRefGoogle Scholar
Escudier, M. 1988 Vortex breakdown: observations and explanations. Prog. Aerosp. Sci. 25 (2), 189–229.CrossRefGoogle Scholar
Farokhi, S., Taghavi, R. & Rice, E.J. 1989 Effect of initial swirl distribution on the evolution of a turbulent jet. AIAA J. 27 (6), 700–706.CrossRefGoogle Scholar
Fischer, P.F., Lottes, J.W. & Kerkemeier, S.G. 2008 Nek5000 web page. Available at: http://nek5000.mcs.anl.gov.Google Scholar
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. M. Behnia, W. Lin & G.D. McBain). The University of Sydney.Google Scholar
Gallaire, F., Rott, S. & Chomaz, J.-M. 2004 Experimental study of a free and forced swirling jet. Phys. Fluids 16 (8), 2907–2917.CrossRefGoogle Scholar
Gallardo-Ruiz, J.M., del Pino, C. & Fernandez-Feria, R. 2010 Quasicylindrical description of a swirling light gas jet discharging into a heavier ambient gas. Phys. Fluids 22 (11), 113601.CrossRefGoogle Scholar
Görtler, H. 1954 Decay of swirl in an axially symmetrical jet, far from the orifice. Rev. Mat. Hisp. Am. 14 (4), 143–178.Google Scholar
Hall, M.G. 1967 A new approach to vortex breakdown. In Proceedings of Heat Transfer and Fluid Mechanics Institute, pp. 319–340. Stanford University Press.Google Scholar
Hall, M.G. 1972 Vortex breakdown. Annu. Rev. Fluid Mech. 4 (1), 195–218.CrossRefGoogle 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
Leibovich, S. 1978 The structure of vortex breakdown. Annu. Rev. Fluid Mech. 10 (1), 221–246.CrossRefGoogle Scholar
Leibovich, S. 1984 Vortex stability and breakdown-survey and extension. AIAA J. 22 (9), 1192–1206.CrossRefGoogle Scholar
Lessen, M. 1950 On the stability of the laminar free boundary between parallel streams. Report NACA-R979. National Advisory Committee for Aeronautics.Google Scholar
Liang, H. & Maxworthy, T. 2005 An experimental investigation of swirling jets. J. Fluid Mech. 525, 115.CrossRefGoogle Scholar
Loitsianskii, L.G. 1953 Propagation of a whirling jet in an infinite space filled with the same fluid. Prikl. Mat. Mekh. 17 (3), 7.Google Scholar
Lucca-Negro, O. & O'Doherty, T. 2001 Vortex breakdown: a review. Prog. Energy Combust. Sci. 27 (4), 431–481.CrossRefGoogle Scholar
Manoharan, K., Frederick, M., Clees, S., O'Connor, J. & Hemchandra, S. 2020 A weakly nonlinear analysis of the precessing vortex core oscillation in a variable swirl turbulent round jet. J. Fluid Mech. 884, A29.CrossRefGoogle Scholar
Manoharan, K., Hansford, S., O'Connor, J. & Hemchandra, S. 2015 Instability mechanism in a swirl flow combustor: precession of vortex core and influence of density gradient. In ASME Turbo Expo 2015: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers.CrossRefGoogle Scholar
Moise, P. 2020 Bistability of bubble and conical forms of vortex breakdown in laminar swirling jets. J. Fluid Mech. 889, A31.CrossRefGoogle Scholar
Moise, P. & Mathew, J. 2019 Bubble and conical forms of vortex breakdown in swirling jets. J. Fluid Mech. 873, 322–357.CrossRefGoogle Scholar
Moise, P. & Mathew, J. 2021 Hysteresis and turbulent vortex breakdown in transitional swirling jets. J. Fluid Mech. 915, A94.CrossRefGoogle Scholar
Moreno-Boza, D., Coenen, W., Carpio, J., Sánchez, A.L. & Williams, F.A. 2018 On the critical conditions for pool-fire puffing. Combust. Flame 192, 426–438.CrossRefGoogle Scholar
Moreno-Boza, D., Coenen, W., Sevilla, A., Carpio, J., Sánchez, A.L. & Liñán, A. 2016 Diffusion-flame flickering as a hydrodynamic global mode. J. Fluid Mech. 798, 997–1014.CrossRefGoogle Scholar
Oberleithner, K., Paschereit, C., Seele, R. & Wygnanski, I. 2012 Formation of turbulent vortex breakdown: intermittency, criticality, and global instability. AIAA J. 50 (7), 1437–1452.CrossRefGoogle Scholar
Oberleithner, K., Sieber, M., Nayeri, C., Paschereit, C.O., Petz, C., Hege, H., 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.CrossRefGoogle Scholar
Panda, J. & McLaughlin, D.K. 1994 Experiments on the instabilities of a swirling jet. Phys. Fluids 6 (1), 263–276.CrossRefGoogle Scholar
Revuelta, A., Sánchez, A.L. & Liñán, A. 2004 The quasi-cylindrical description of submerged laminar swirling jets. Phys. Fluids 16 (3), 848–851.CrossRefGoogle Scholar
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), 1225–1250.CrossRefGoogle Scholar
Rukes, L., Sieber, M., Paschereit, C.O. & Oberleithner, K. 2016 The impact of heating the breakdown bubble on the global mode of a swirling jet: experiments and linear stability analysis. Phys. Fluids 28 (10), 104102.CrossRefGoogle Scholar
von Schlichting, H. 1933 Laminare strahlausbreitung. Z. Angew. Math. Mech. 13 (4), 260–263.CrossRefGoogle Scholar
Squire, H.B. 1960 Analysis of the vortex breakdown phenomenon: part I. Report 102. Aeronautical Department, Imperial College.Google Scholar
Tomboulides, A.G., Lee, J. & Orszag, S.A. 1997 Numerical simulation of low Mach number reactive flows. J. Sci. Comput. 12 (2), 139–167.CrossRefGoogle Scholar