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Theoretical analysis on the transient ignition of a premixed expanding flame in a quiescent mixture

Published online by Cambridge University Press:  11 August 2021

Dehai Yu  and
Zheng Chen Open the ORCID record for Zheng Chen [Opens in a new window]
Dehai Yu
Affiliation:
SKLTCS, CAPT, BIC-ESAT, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, PR China
Zheng Chen*
Affiliation:
SKLTCS, CAPT, BIC-ESAT, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, PR China
*
† Email address for correspondence: cz@pku.edu.cn
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Abstract

The ignition of a self-sustained premixed expanding flame constitutes a crucial problem in fundamental combustion research. In this work, a transient formulation on the forced ignition of a premixed expanding spherical flame in a quiescent mixture is proposed under the framework of the thermal-diffusive model. The present theory considers the unsteady evolution of the temperature and fuel mass fraction distributions subject to finite duration central heating. It can determine both critical heating power and minimum ignition energy for successful ignition. The transient flame initiation process is found to consist of four stages, including fast establishment of the ignition kernel, ignition-energy-supported flame kernel propagation, unsteady transition of the flame kernel, and quasi-steady spherical flame propagation. The unsteady effects lead to the observation of flame kernel establishing stage and considerably affect the subsequent flame kernel development by altering the flame propagation speed. Time scale analysis indicates that the transient formulation completely degenerates to the quasi-steady theory in the limits of both stationary flame ball and planar flame. Previous quasi-steady theory shows that the critical heating power for successful ignition is proportional to the cube of the critical flame radius. However, that scaling relation shall be revised in the transient formulation due to the unsteady thermal conduction from heating centre to flame front. The memory effect that persistently supports flame propagation subsequent to switching off the central heating is examined. It is found that as the heating power grows, the memory effect becomes increasingly important, and it can greatly reduce the predicted minimum ignition energy.

JFM classification

Reacting Flows: Combustion Reacting Flows: Flames
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 924 , 10 October 2021 , A22
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

Barenblatt, G. 1985 The Mathematical Theory of Combustion and Explosions. Springer.Google Scholar
Bechtold, J. & Matalon, M. 1987 Hydrodynamic and diffusion effects on the stability of spherically expanding flames. Combust. Flame 67 (1), 77–90.CrossRefGoogle Scholar
Buckmaster, J., Clavin, P., Linan, A., Matalon, M., Peters, N., Sivashinsky, G. & Williams, F. 2005 Combustion theory and modeling. Proc. Combust. Inst. 30 (1), 1–19.CrossRefGoogle Scholar
Buckmaster, J. & Joulin, G. 1989 Radial propagation of premixed flames and t behavior. Combust. Flame 78 (3–4), 275–286.CrossRefGoogle Scholar
Champion, M., Deshaies, B. & Joulin, G. 1988 Relative influences of convective and diffusive transports during spherical flame initiation. Combust. Flame 74 (2), 161–170.CrossRefGoogle Scholar
Champion, M., Deshaies, B., Joulin, G. & Kinoshita, K. 1986 Spherical flame initiation: theory versus experiments for lean propane-air mixtures. Combust. Flame 65 (3), 319–337.CrossRefGoogle Scholar
Chen, Z. 2017 Effects of radiation absorption on spherical flame propagation and radiation-induced uncertainty in laminar flame speed measurement. Proc. Combust. Inst. 36 (1), 1129–1136.CrossRefGoogle Scholar
Chen, Z., Burke, M.P. & Ju, Y. 2011 On the critical flame radius and minimum ignition energy for spherical flame initiation. Proc. Combust. Inst. 33 (1), 1219–1226.CrossRefGoogle Scholar
Chen, Z. & Ju, Y. 2007 Theoretical analysis of the evolution from ignition kernel to flame ball and planar flame. Combust. Theor. Model. 11 (3), 427–453.CrossRefGoogle Scholar
Chen, Z. & Ju, Y. 2008 Combined effects of curvature, radiation, and stretch on the extinction of premixed tubular flames. Intl J. Heat Mass Transfer 51 (25–26), 6118–6125.CrossRefGoogle Scholar
Clavin, P. 2017 Quasi-isobaric ignition near the flammability limits. Flame balls and self-extinguishing flames. Combust. Flame 175, 80–90.CrossRefGoogle Scholar
Clavin, P. & Searby, G. 2016 Combustion Waves and Fronts in Flows: Flames, Shocks, Detonations, Ablation Fronts and Explosion of Stars. Cambridge University Press.CrossRefGoogle Scholar
Deshaies, B. & Joulin, G. 1984 On the initiation of a spherical flame kernel. Combust. Sci. Technol. 37 (3–4), 99–116.CrossRefGoogle Scholar
Fernández-Tarrazo, E., Sánchez-Sanz, M., Sánchez, A.L. & Williams, F.A. 2016 Minimum ignition energy of methanol–air mixtures. Combust. Flame 171, 234–236.CrossRefGoogle Scholar
He, L. 2000 Critical conditions for spherical flame initiation in mixtures with high Lewis numbers. Combust. Theor. Model. 4 (2), 159–172.CrossRefGoogle Scholar
Jackson, T., Kapila, A. & Stewart, D. 1989 Evolution of a reaction center in an explosive material. SIAM J. Appl. Maths 49 (2), 432–458.CrossRefGoogle Scholar
Joulin, G. 1985 Point-source initiation of lean spherical flames of light reactants: an asymptotic theory. Combust. Sci. Technol. 43 (1–2), 99–113.CrossRefGoogle Scholar
Kelley, A.P., Jomaas, G. & Law, C.K. 2009 Critical radius for sustained propagation of spark-ignited spherical flames. Combust. Flame 156 (5), 1006–1013.CrossRefGoogle Scholar
Kurdyumov, V., Blasco, J., Sánchez Pérez, A.L. & Liñán Martínez, A. 2004 On the calculation of the minimum ignition energy. Combust. Flame 136 (3), 394–397.CrossRefGoogle Scholar
Law, C.K. 2006 Combustion Physics. Cambridge University Press.CrossRefGoogle Scholar
Law, C. & Sirignano, W. 1977 Unsteady droplet combustion with droplet heating—II: conduction limit. Combust. Flame 28, 175–186.CrossRefGoogle Scholar
Maas, U. & Warnatz, J. 1988 Ignition processes in hydrogen-oxygen mixtures. Combust. Flame 74 (1), 53–69.CrossRefGoogle Scholar
Matalon, M., Cui, C. & Bechtold, J. 2003 Hydrodynamic theory of premixed flames: effects of stoichiometry, variable transport coefficients and arbitrary reaction orders. J. Fluid Mech. 487, 179–210.CrossRefGoogle Scholar
Ronney, P.D. 1989 On the mechanisms of flame propagation limits and extinguishment-processes at microgravity. Symp. Intl Combust. 22 (1), 1615–1623.CrossRefGoogle Scholar
Ronney, P.D. 1990 Near-limit flame structures at low Lewis number. Combust. Flame 82 (1), 4009.CrossRefGoogle Scholar
Ronney, P.D. & Sivashinsky, G.I. 1989 A theoretical study of propagation and extinction of nonsteady spherical flame fronts. SIAM J. Appl. Maths 49 (4), 1029–1046.CrossRefGoogle Scholar
Vázquez-Espí, C. & Liñán, A. 2001 Fast, non-diffusive ignition of a gaseous reacting mixture subject to a point energy source. Combust. Theor. Model. 5 (3), 485–498.CrossRefGoogle Scholar
Vázquez-Espı, C. & Linán, A. 2002 Thermal-diffusive ignition and flame initiation by a local energy source. Combust. Theory Modelling 6, 297–315.CrossRefGoogle Scholar
Veeraragavan, A. & Cadou, C.P. 2011 Flame speed predictions in planar micro/mesoscale combustors with conjugate heat transfer. Combust. Flame 158 (11), 2178–2187.CrossRefGoogle Scholar
Wu, Y.-C. & Chen, Z. 2012 Asymptotic analysis of outwardly propagating spherical flames. Acta Mech. Sin. 28 (2), 359–366.CrossRefGoogle Scholar
Yu, D. & Chen, Z. 2020 Theoretical analysis on droplet vaporization at elevated temperatures and pressures. Intl J. Heat Mass Transfer 164, 120542.CrossRefGoogle Scholar
Zhang, H. & Chen, Z. 2011 Spherical flame initiation and propagation with thermally sensitive intermediate kinetics. Combust. Flame 158 (8), 1520–1531.CrossRefGoogle Scholar
Zhang, H., Guo, P. & Chen, Z. 2013 Critical condition for the ignition of reactant mixture by radical deposition. Proc. Combust. Inst. 34 (2), 3267–3275.CrossRefGoogle Scholar