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Reconciling turbulent burning velocity with flame surface area in small-scale turbulence

Published online by Cambridge University Press:  05 November 2018

G. V. Nivarti*
University Engineering Department, Trumpington Street, Cambridge CB2 1PZ, UK
R. S. Cant
University Engineering Department, Trumpington Street, Cambridge CB2 1PZ, UK
S. Hochgreb
University Engineering Department, Trumpington Street, Cambridge CB2 1PZ, UK
Email address for correspondence:


A discrepancy between the enhancement in overall burning rate and the enhancement in flame surface area measured for high-intensity turbulence is addressed. In order to reconcile the two quantities, an additional contribution from the effective turbulent diffusivity is considered. This contribution is expected to arise in sufficiently intense turbulence from eddies smaller than the flamelet thickness. In the present work, the enhancement in diffusivity arising from these eddies is estimated based on a model energy spectrum; individual contributions from all turbulence length scales smaller the flamelet thickness are integrated over the corresponding portion of the spectrum. It is shown that diffusivity enhancement, estimated in this manner, is able to account for the measured discrepancy between the overall burning rate enhancement and flame surface area enhancement. The factor quantifying this discrepancy is formalized as a closed-form function of the Karlovitz number.

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© 2018 Cambridge University Press 

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Abdel-Gayed, R. G., Bradley, D. & Lawes, M. 1987 Turbulent burning velocities: a general correlation in terms of straining rates. Proc. R. Soc. Lond. A 414, 421444.Google Scholar
Aspden, A., Woosley, S. & Bell, J. B. 2010 Turbulence-flame interactions in type Ia supernovae. Astrophys. J. 689, 11731185.Google Scholar
Bradley, D. 1992 How fast can we burn? In 24th Symposium (International) on Combustion, pp. 247262. The Combustion Institute.Google Scholar
Bray, K. N. C. & Cant, R. S. 1991 Some applications of Kolmogorovs turbulence research in the field of combustion. Proc. R. Soc. Lond. A 434, 217240.Google Scholar
Damköhler, G. 1940 Der einfluss der turbulenz auf die flammengeschwindigkeit in gasgemschen. Zeitschrift für Elektrochemie und angewandte physikalische Chemie 46, 601652. (English translation: The effect of turbulence on the flame velocity in gas mixtures, NACA TM 1112, 1947).Google Scholar
Driscoll, J. F. 2008 Turbulent premixed combustion: flamelet structure and its effect on turbulent burning velocities. Progress in Combustion and Energy Science 34, 91134.Google Scholar
Gülder, Ö. 2007 Contribution of small scale turbulence to burning velocity of flamelets in the thin reaction zones regime. Proc. Combust. Inst. 31, 13691375.Google Scholar
von Karman, T. 1948 Progress in the statistical theory of turbulence. Proc. Natl Acad. Sci. USA 34, 530539.Google Scholar
Kraichnan, R. H. 1959 The structure of isotropic turbulence at very high Reynolds numbers. J. Fluid Mech. 5, 497543.Google Scholar
Lee, D. & Huh, K. Y. 2012 Validation of analytical expressions for turbulent burning velocity in stagnating and freely propagating turbulent premixed flames. Combust. Flame 159, 15761591.Google Scholar
Lee, J., Lee, G. G. & Huh, K. Y. 2014 Asymptotic expressions for turbulent burning velocity at the leading edge of a premixed flame brush and their validation by published measurement data. Phys. Fluids 26, 125103, 1–19.Google Scholar
Peters, N. 1999 The turbulent burning velocity for large-scale and small-scale turbulence. J. Fluid Mech. 384, 107132.Google Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.Google Scholar
Ronney, P. D. & Yakhot, V. 1992 Flame broadening effects on premixed turbulent flame speed. Combust. Sci. Technol. 86, 3143.Google Scholar
Shepherd, I. G. 1996 Flame surface density and burning rate in premixed turbulent flames. Symposium (International) on Combustion 26, 373379.Google Scholar
Taylor, G. I. 1935 Statistical theory of turbulence. Proc. R. Soc. Lond. A 151, 421444.Google Scholar
Veynante, D., Lodato, G., Domingo, P., Vervisch, L. & Hawkes, E. R. 2010 Estimation of three-dimensional flame surface densities from planar images in turbulent premixed combustion. Exp. Fluids 49, 267278.Google Scholar
Wabel, T. M.2017 An experimental investigation of premixed combustion in extreme turbulence. PhD thesis, University of Michigan, USA.Google Scholar
Wabel, T. M., Skiba, A. W. & Driscoll, J. F. 2017 Turbulent burning velocity measurements: extended to extreme levels of turbulence. Proc. Combust. Inst. 36, 18011808.Google Scholar
Wang, G.-H., Clemens, N. T., Barlow, R. S. & Varghese, P. L. 2007 A system model for assessing scalar dissipation measurement accuracy in turbulent flows. Meas. Sci. Technol. 18, 12871303.Google Scholar
Wang, H., Hawkes, E. R. & Chen, J. H. 2016 Turbulence-flame interactions in DNS of a laboratory high Karlovitz premixed turbulent jet flame. Phys. Fluids 28, 095107, 1–20.Google Scholar
Williams, F. A. 1985 Combustion Theory, 3rd edn. The Benjamin/Cummings Publishing Company, Inc.Google Scholar
Yuen, F. T. C.2009 Experimental investigation of the dynamics and structure of lean-premixed turbulent combustion. PhD thesis, University of Toronto, Canada.Google Scholar
Yuen, F. T. C. & Gülder, Ö. 2013 Turbulent premixed flame front dynamics and implications for limits of flamelet hypothesis. Proc. Combust. Inst. 34, 13931400.Google Scholar
Zel’dovich, Y. B. & Frank-Kamenetskiĭ, D. A. 1938 Teoriĭa teplovogo rasprostraneniĭa plameni. Zhurnal Fizicheskoi Khimii 12, 100105. (English translation: 1992 A theory of flame propagation. In Selected Works of Yakov Borisovich Zeldovich, Volume I. Princeton University Press).Google Scholar
Zimont, V. L. 1979 Theory of turbulent combustion of a homogeneous fuel mixture at high Reynolds numbers. Combust. Explos. Shock Waves 15, 305311.Google Scholar