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Diffusion-flame flickering as a hydrodynamic global mode

Published online by Cambridge University Press:  15 June 2016

D. Moreno-Boza ,
W. Coenen ,
A. Sevilla ,
J. Carpio ,
A. L. Sánchez  and
A. Liñán
D. Moreno-Boza*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California at San Diego, La Jolla, CA 92093–0411, USA
W. Coenen
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California at San Diego, La Jolla, CA 92093–0411, USA
A. Sevilla
Affiliation:
Departamento de Ingeniería Térmica y de Fluidos, Universidad Carlos III de Madrid, 28911 Leganés, Spain
J. Carpio
Affiliation:
ETSI Industriales, Universidad Politécnica de Madrid, 28006 Madrid, Spain
A. L. Sánchez
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California at San Diego, La Jolla, CA 92093–0411, USA
A. Liñán
Affiliation:
ETSI Aeronáuticos, Universidad Politécnica de Madrid, 28006 Madrid, Spain
*
†Email address for correspondence: [email protected]
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Abstract

The present study employs a linear global stability analysis to investigate buoyancy-induced flickering of axisymmetric laminar jet diffusion flames as a hydrodynamic global mode. The instability-driving interactions of the buoyancy force with the density differences induced by the chemical heat release are described in the infinitely fast reaction limit for unity Lewis numbers of the reactants. The analysis determines the critical conditions at the onset of the linear global instability as well as the Strouhal number of the associated oscillations in terms of the governing parameters of the problem. Marginal instability boundaries are delineated in the Froude number/Reynolds number plane for different fuel jet dilutions. The results of the global stability analysis are compared with direct numerical simulations of time-dependent axisymmetric jet flames and also with results of a local spatio-temporal stability analysis.

JFM classification

Convection: Buoyancy-driven instability Reacting Flows: Flames Reacting Flows: Laminar reacting flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 798 , 10 July 2016 , pp. 997 - 1014
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Copyright
© Cambridge University Press 2016. This is a work of the U.S. Government and is not subject to copyright protection in the United States. 

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References

Batchelor, G. & Gill, A. E. 1962 Analysis of the stability of axisymmetric jets. J. Fluid Mech. 14, 529–551.Google Scholar
Boulanger, J. 2010 Laminar round jet diffusion flame buoyant instabilities: study on the disappearance of varicose structures at ultra-low Froude number. Combust. Flame 157, 757–768.CrossRefGoogle Scholar
Buckmaster, J. & Peters, N. 1986 The infinite candle and its stability – a paradigm for flickering diffusion flames. Proc. Combust. Inst. 21, 1829–1836.Google Scholar
Burke, S. P. & Schumann, T. E. W. 1928 Diffusion flames. Ind. Engng Chem. 20, 998–1004.CrossRefGoogle Scholar
Carpio, J., Prieto, J. L. & Vera, M. 2016 Local anisotropic adaptive algorithm for the solution of low-Mach transient combustion problems. J. Comput. Phys. 306, 19–42.Google Scholar
Cetegen, B. M. & Dong, Y. 2000 Experiments on the instability modes of buoyant diffusion flames and effects of ambient atmosphere on the instabilities. Exp. Fluids 28, 546–558.CrossRefGoogle Scholar
Chamberlin, D. S. & Rose, A. 1948 The flicker of luminous flames. Proc. Combust. Inst. 1–2, 27–32.Google Scholar
Chen, L. D., Seaba, J. P., Roquemore, W. M. & Goss, L. P. 1988 Buoyant diffusion flames. Proc. Combust. Inst. 22, 677–684.Google Scholar
Coenen, W., Lesshafft, L., Garnaud, X. & Sevilla, A. 2016 Global instability in low-density jets: physical eigenmodes and spurious feedback effects. J. Fluid Mech. (submitted).Google Scholar
Coenen, W. & Sevilla, A. 2012 The structure of the absolute unstable regions in the near field of low-density jets. J. Fluid Mech. 713, 123–149.CrossRefGoogle Scholar
Coenen, W., Sevilla, A. & Sánchez, A. L. 2008 Absolute instability of light jets emerging from circular injector tubes. Phys. Fluids 20, 074104.Google Scholar
Deissler, R. J. 1987 The convective nature of instability in plane poiseuille flow. Phys. Fluids 30, 2303–2305.CrossRefGoogle Scholar
Durox, D., Yuan, T. & Villermaux, E. 1997 The effect of buoyancy on flickering in diffusion flames. Combust. Sci. Technol. 124, 277–294.Google Scholar
Garnaud, X., Lesshafft, L., Schmid, P. J. & Huerre, P. 2013a Modal and transient dynamics of jet flows. Phys. Fluids 25, 044103.Google Scholar
Garnaud, X., Lesshafft, L., Schmid, P. J. & Huerre, P. 2013b The preferred mode of incompressible jets: linear frequency response analysis. J. Fluid Mech. 716, 189–202.CrossRefGoogle Scholar
Giannetti, F. & Luchini, P. 2007 Structural sensitivity of the first instability of the cylinder wake. J. Fluid Mech. 581, 167–197.Google Scholar
Hallberg, M. P. & Strykowski, P. J. 2006 On the universality of global modes in low-density axisymmetric jets. J. Fluid Mech. 569, 493–507.Google Scholar
Hecht, F. 2012 New development in FreeFem++. J. Numer. Math. 20 (3–4), 251–265.Google Scholar
Huerre, P. 2000 Open shear flow instabilities. In Perspectives in Fluid Dynamics (ed. Batchelor, G., Moffatt, K. & Worster, G.), pp. 159–229. 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
Jiang, X. & Luo, K. H. 2000 Combustion-induced buoyancy effects of an axisymmetric reactive plume. Proc. Combust. Inst. 28, 1989–1995.Google Scholar
Juniper, M. P., Li, L. K. B. & Nichols, J. W. 2009 Forcing of self-excited round jet diffusion flame. Proc. Combust. Inst. 32, 1191–1198.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, 206–229.CrossRefGoogle Scholar
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics, 3rd edn. Pergamon.Google Scholar
Lehoucq, R. B., Sorensen, D. C. & Yang, C. 1998 ARPACK Users’ Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods. SIAM.CrossRefGoogle Scholar
Lesshafft, L., Coenen, W., Garnaud, X. & Sevilla, A. 2015 Modal instability analysis of light jets. In Procedia IUTAM, vol. 14, pp. 137–140. Elsevier.Google Scholar
Lesshafft, L. & Huerre, P. 2007 Linear impulse response in hot round jets. Phys. Fluids 19, 024102.Google Scholar
Lesshafft, L., Huerre, P. & Sagaut, P. 2007 Frequency selection in globally unstable round jets. Phys. Fluids 19 (5), 054108.Google Scholar
Lesshafft, L. & Marquet, O. 2010 Optimal velocity and density profiles for the onset of absolute instability in jets. J. Fluid Mech. 662, 398–408.Google Scholar
Liñán, A. 1991 The structure of diffusion flames. In Fluid Dynamical Aspects of Combustion Theory (ed. Onofri, M. & Tesev, A.), pp. 11–29. Longman Scientific & Technical.Google Scholar
Liñán, A., Vera, M. & Sánchez, A. L. 2015 Ignition, liftoff, and extinction of gaseous diffusion flames. Annu. Rev. Fluid Mech. 47, 293–314.Google Scholar
Lingens, A., Neemann, K., Meyer, J. & Schreiber, M. 1996a Instability of diffusion flames. Proc. Combust. Inst. 26, 1053–1061.Google Scholar
Lingens, A., Reeker, M. & Schreiber, M. 1996b Instability of buoyant diffusion flames. Exp. Fluids 20, 241–248.Google Scholar
Mahalingam, S., Cantwell, B. J. & Ferziger, J. H. 1991 Stability of low-speed reacting flows. Phys. Fluids A 3, 1533–1543.CrossRefGoogle Scholar
Marquet, O., Sipp, D. & Jacquin, L. 2008 Sensitivity analysis and passive control of cylinder flow. J. Fluid Mech. 615, 221–252.CrossRefGoogle Scholar
Maxworthy, T. 1999 The flickering candle: transition to a global oscillation in a thermal plume. J. Fluid Mech. 390, 297–323.Google Scholar
Nichols, J., Chomaz, J.-M. & Schmid, P. J. 2009 Twisted absolute instability in lifted flames. Phys. Fluids 21, 015110.Google Scholar
Nichols, J. R. & Lele, S. K. 2011 Global modes and transient response of a cold supersonic jet. J. Fluid Mech. 669, 225–241.CrossRefGoogle Scholar
Nichols, J. W. & Schmid, P. J. 2008 The effect of a lifted flame on the stability of round fuel jets. J. Fluid Mech. 609, 275–284.CrossRefGoogle Scholar
Pier, B., Huerre, P. & Chomaz, J.-M. 1998 Steep nonlinear global modes in spatially developing media. Phys. Fluids 10, 2433–2435.Google Scholar
Qadri, U. A., Chandler, G. J. & Juniper, M. P. 2015 Self-sustained hydrodynamic oscillations in lifted jet diffusion flames: origin and control. J. Fluid Mech. 775, 201–222.Google Scholar
Sato, H., Amagai, K. & Arai, M. 2000 Flickering frequencies of diffusion flames observed under various gravity fields. Proc. Combust. Inst. 28, 1981–1987.Google Scholar
See, Y. C. & Ihme, M. 2014 Effects of finite-rate chemistry and detailed transport on the instability of jet diffusion flames. J. Fluid Mech. 745, 647–681.CrossRefGoogle Scholar
Shvab, V. A. 1948 The relationship between the temperature and velocity fields in a gaseous flame. In Research on Combustion Processes in Natural Fuel (ed. Knorre, G. F.), pp. 231–248. Gosenergoizdat.Google Scholar
Soteriou, M. C. & Ghoniem, A. F. 1995 Effects of the free-stream density ratio on free and forced spatially developing shear layers. Phys. Fluids 7, 2036.Google Scholar
Toong, T.-Y., Salant, R. F., Stopford, J. M. & Anderson, G. Y. 1965 Mechanisms of combustion instability. Proc. Combust. Inst. 10, 1301–1313.Google Scholar
Trefethen, L. N. & Embree, M. 2005 Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators. Princeton University Press.Google Scholar
Zel’dovich, Y. B. 1949 Teorii gorenia neperemeshannykh gazov. Zh. Tekh. Fiz. 19, 1199–1210.Google Scholar