Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-23T11:45:51.762Z Has data issue: false hasContentIssue false
  • English
  • Français

A vortex-dynamical scaling theory for flickering buoyant diffusion flames

Published online by Cambridge University Press:  24 September 2018

Xi Xia Open the ORCID record for Xi Xia [Opens in a new window]  and
Peng Zhang
Xi Xia
Affiliation:
Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
Peng Zhang*
Affiliation:
Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The flickering of buoyant diffusion flames is associated with the periodic shedding of toroidal vortices that are formed under gravity-induced shearing at the flame surface. Numerous experimental investigations have confirmed the scaling, $f\propto D^{-1/2}$, where $f$ is the flickering frequency and $D$ is the diameter of the fuel inlet. However, the connection between the toroidal vortex dynamics and the scaling has not been clearly understood. By incorporating the finding of Gharib et al. (J. Fluid Mech., vol. 360, 1998, pp. 121–140) that the detachment of a continuously growing vortex ring is inevitable and can be dictated by a universal constant that is essentially a non-dimensional circulation of the vortex, we theoretically established the connection between the periodicity of the toroidal vortices and the flickering of a buoyant diffusion flame with small Froude number. The scaling theory for flickering frequency was validated by the existing experimental data of pool flames and jet diffusion flames.

JFM classification

Reacting Flows: Flames Instability: Instability Vortex Flows: Vortex Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 855 , 25 November 2018 , pp. 1156 - 1169
Check for updates
Copyright
© 2018 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

Albers, B. W. & Agrawal, A. K. 1999 Schlieren analysis of an oscillating gas-jet diffusion flame. Combust. Flame 119 (1–2), 84–94.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Baum, H. R. & McCaffrey, B. J. 1989 Fire induced flow field-theory and experiment. Fire Safety Sci. 2, 129–148.Google Scholar
Bejan, A. 1991 Predicting the pool fire vortex shedding frequency. Trans. ASME C: J. Heat Transfer 113 (1), 261–263.Google Scholar
Buckmaster, J. & Peters, N. 1988 The infinite candle and its stability a paradigm for flickering diffusion flames. Symp. Intl Combust. Proc. 21 (1), 1829–1836.Google Scholar
Burke, S. P. & Schumann, T. E. W. 1928 Diffusion flames. Ind. Engng Chem. 20 (10), 998–1004.Google Scholar
Byram, G. M. & Nelson, R. M. 1970 The modeling of pulsating fires. Fire Technol. 6 (2), 102–110.Google Scholar
Cantwell, B., Lewis, G. & Chen, J. 1989 Topology of three-dimensional, variable density flows. In 10th Australasian Fluid Mechanics Conference, Melbourne, Australia.Google Scholar
Carpio, J., Sánchez-Sanz, M. & Fernández-Tarrazo, E. 2012 Pinch-off in forced and non-forced, buoyant laminar jet diffusion flames. Combust. Flame 159 (1), 161–169.Google Scholar
Cetegen, B. M. 1997 Behavior of naturally unstable and periodically forced axisymmetric buoyant plumes of helium and helium–air mixtures. Phys. Fluids 9 (12), 3742–3752.Google Scholar
Cetegen, B. M. & Ahmed, T. A. 1993 Experiments on the periodic instability of buoyant plumes and pool fires. Combust. Flame 93 (1–2), 157–184.Google Scholar
Chamberlin, D. S. & Rose, A. 1948 The flicker of luminous flames. Symp. Intl Combust. Proc. 1, 27–32.Google Scholar
Chen, L. D. & Roquemore, W. M. 1986 Visualization of jet flames. Combust. Flame 66 (1), 81–86.Google Scholar
Chen, L. D., Seaba, J. P., Roquemore, W. M. & Goss, L. P. 1989 Buoyant diffusion flames. Symp. Intl Combust. Proc. 22 (1), 677–684.Google Scholar
Coats, C. M. 1996 Coherent structures in combustion. Prog. Energy Combust. Sci. 22 (5), 427–509.Google Scholar
Cox, G. 1995 Combustion Fundamentals of Fire. Academic Press.Google Scholar
Dabiri, J. O. & Gharib, M. 2005 Starting flow through nozzles with temporally variable exit diameter. J. Fluid Mech. 538, 111–136.Google Scholar
Davis, R. W., Moore, E. F., Santoro, R. J. & Ness, J. R. 1990 Isolation of buoyancy effects in jet diffusion flame experiments. Combust. Sci. Technol. 73 (4–6), 625–635.Google Scholar
Detriche, P. H. & Lanore, J. C. 1980 An acoustic study of pulsation characteristics of fires. Fire Technol. 16 (3), 204–211.Google Scholar
Didden, N. 1979 On the formation of vortex rings: rolling-up and production of circulation. Z. Angew. Math. Phys. 30 (1), 101–116.Google Scholar
Durox, D., Yuan, T., Baillot, F. & Most, J. M. 1995 Premixed and diffusion flames in a centrifuge. Combust. Flame 102 (4), 501–511.Google Scholar
Fang, J., Wang, J.-W., Guan, J.-F., Zhang, Y.-M. & Wang, J.-J. 2016 Momentum- and buoyancy-driven laminar methane diffusion flame shapes and radiation characteristics at sub-atmospheric pressures. Fuel 163, 295–303.Google Scholar
Gharib, M., Rambod, E. & Shariff, K. 1998 A universal time scale for vortex ring formation. J. Fluid Mech. 360, 121–140.Google Scholar
Ghoniem, A. F., Lakkis, I. & Soteriou, M. 1996 Numerical simulation of the dynamics of large fire plumes and the phenomenon of puffing. Symp. Intl Combust. Proc. 26 (1), 1531–1539.Google Scholar
Glezer, A. 1988 The formation of vortex rings. Phys. Fluids 31 (12), 3532–3542.Google Scholar
Hamins, A., Yang, J. C. & Kashiwagi, T. 1992 An experimental investigation of the pulsation frequency of flames. Symp. Intl Combust. Proc. 24 (1), 1695–1702.Google Scholar
Jiang, X. & Luo, K. H. 2000 Combustion-induced buoyancy effects of an axisymmetric reactive plume. Proc. Combust. Inst. 28 (2), 1989–1995.Google Scholar
Joulain, P. 1998 The behavior of pool fires: state of the art and new insights. Symp. Intl Combust. Proc. 27 (2), 2691–2706.Google Scholar
Katta, V. R., Goss, L. P. & Roquemore, W. M. 1994 Numerical investigations of transitional H2/N2 jet diffusion flames. AIAA J. 32 (1), 84–94.Google Scholar
Katta, V. R. & Roquemore, W. M. 1993 Role of inner and outer structures in transitional jet diffusion flame. Combust. Flame 92 (3), 274–282.Google Scholar
Klimenko, A. Y. & Williams, F. A. 2013 On the flame length in firewhirls with strong vorticity. Combust. Flame 160, 335–339.Google Scholar
Kolhe, P. S. & Agrawal, A. K. 2007 Role of buoyancy on instabilities and structure of transitional gas jet diffusion flames. Flow Turbul. Combust. 79 (4), 343–360.Google Scholar
Krieg, M. & Mohseni, K. 2013 Modelling circulation, impulse, and kinetic energy of starting jets with non-zero radial velocity. J. Fluid Mech. 719, 488–526.Google Scholar
Krueger, P., Dabiri, J. & Gharib, M. 2006 The formation number of vortex rings formed in a uniform background co-flow. J. Fluid Mech. 556, 147–166.Google Scholar
Lawson, J. M. & Dawson, J. R. 2013 The formation of turbulent vortex rings by synthetic jets. Phys. Fluids 25 (10), 105113.Google Scholar
Liñán, Vera, M. & Sánchez, A. L. 2015 Ignition, liftoff, and extinction of gaseous diffusion flames. Annu. Rev. Fluid Mech. 47, 293–314.Google Scholar
Liñán, A., Fernández-Tarrazo, E., Vera, M. & Sánchez, A. L. 2005 Lifted laminar jet diffusion flames. Combust. Sci. Technol. 177 (5–6), 933–953.Google Scholar
Lingens, A., Neemann, K., Meyer, J. & Schreiber, M. 1996 Instability of diffusion flames. Symp. Intl Combust. Proc. 26 (1), 1053–1061.Google Scholar
Malalasekera, W. M. G., Versteeg, H. K. & Gilchrist, K. 1996 A review of research and an experimental study on the pulsation of buoyant diffusion flames and pool fires. Fire Mater. 20 (6), 261–271.Google Scholar
Maxworthy, T. 1972 The structure and stability of vortex rings. J. Fluid Mech. 51 (1), 15–32.Google Scholar
Maxworthy, T. 1977 Some experimental studies of vortex rings. J. Fluid Mech. 81 (3), 465–495.Google Scholar
Maxworthy, T. 1999 The flickering candle: transition to a global oscillation in a thermal plume. J. Fluid Mech. 390, 297–323.Google Scholar
McCamy, C. S. 1956 A five-band recording spectroradiometer. J. Res. Natl Bur. Stand. 56 (5), 293–299.Google Scholar
Mell, W. E., McGrattan, K. B. & Baum, H. R. 1996 Numerical simulation of combustion in fire plumes. Symp. Intl Combust. Proc. 26 (1), 1523–1530.Google Scholar
Mohseni, K. & Gharib, M. 1998 A model for universal time scale of vortex ring formation. Phys. Fluids 10 (10), 2436–2438.Google Scholar
Nitsche, M. & Krasny, R. 1994 A numerical study of vortex ring formation at the edge of a circular tube. J. Fluid Mech. 276, 139–161.Google Scholar
Portscht, R. 1975 Studies on characteristic fluctuations of the flame radiation emitted by fires. Combust. Sci. Technol. 10 (1–2), 73–84.Google Scholar
Roquemore, W. M., Chen, L. D., Seaba, J. P., Tschen, P. S., Goss, L. P. & Trump, D. D. 1987 Jet diffusion flame transition to turbulence. Phys. Fluids 30 (9), 2600.Google Scholar
Saffman, P. G. 1978 The number of waves on unstable vortex rings. J. Fluid Mech. 84 (4), 625–639.Google Scholar
Sato, H., Amagai, K. & Arai, M. 2000 Diffusion flames and their flickering motions related with Froude numbers under various gravity levels. Combust. Flame 123 (1), 107–118.Google Scholar
Schönbucher, A., Arnold, B., Banhardt, V., Bieller, V., Kasper, H., Kaufmann, M., Lucas, R. & Schiess, N. 1988 Simultaneous observation of organized density structures and the visible field in pool fires. Symp. Intl Combust. Proc. 21 (1), 83–92.Google Scholar
Shariff, K. & Leonard, A. 1992 Vortex rings. Annu. Rev. Fluid Mech. 24 (1), 235–279.Google Scholar
Sibulkin, M. & Hansen, A. G. 1975 Experimental study of flame spreading over a horizontal fuel surface. Combust. Sci. Technol. 10 (1–2), 85–92.Google Scholar
Tieszen, S. R. 2001 On the fluid mechanics of fires. Annu. Rev. Fluid Mech. 33 (1), 67–92.Google Scholar
Tieszen, S. R., Nicolette, V. F., Gritzo, L. A., Moya, J., Holen, J. & Murray, D.1996 Vortical structures in pool fires: observation, speculation, and simulation. Tech. Rep. SAND-96-2607. Sandia National Labs., Albuquerque, NM (USA).Google Scholar
Trefethen, L. M. & Panton, R. L. 1990 Some unanswered questions in fluid mechanics. Appl. Mech. Rev. 43 (8), 153–170.Google Scholar
Weckman, E. J. & Sobiesiak, A. 1989 The oscillatory behaviour of medium-scale pool fires. Symp. Intl Combust. Proc. 22 (1), 1299–1310.Google Scholar
Wu, J. Z., Ma, H. Y. & Zhou, M. D. 2007 Vorticity and Vortex Dynamics. Springer.Google Scholar
Xia, X. & Mohseni, K. 2015 Far-field momentum flux of high-frequency axisymmetric synthetic jets. Phys. Fluids 27 (11), 115101.Google Scholar
Yoshihara, N., Ito, A. & Torikai, H. 2013 Flame characteristics of small-scale pool fires under low gravity environments. Proc. Combust. Inst. 34 (2), 2599–2606.Google Scholar
Yu, D. & Zhang, P. 2017a On flame height of circulation-controlled firewhirls with variable physical properties and in power-law vortices: a mass-diffusivity-ratio model correction. Combust. Flame 182, 36–47.Google Scholar
Yu, D. & Zhang, P. 2017b On the flame height of circulation-controlled firewhirls with variable density. Proc. Combust. Inst. 36 (2), 3097–3104.Google Scholar
Zhu, X., Xia, X. & Zhang, P. 2018 Near-field flow stability of buoyant methane/air inverse diffusion flames. Combust. Flame 191, 66–75.Google Scholar
Zukoski, E. E., Cetegen, B. M. & Kubota, T. 1985 Visible structure of buoyant diffusion flames. Symp. Intl Combust. Proc. 20 (1), 361–366.Google Scholar