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Turbulent mean reaction rates in the limit of large activation energies

Published online by Cambridge University Press:  20 April 2006

N. Peters ,
W. Hocks  and
G. Mohiuddin
N. Peters
Affiliation:
Institut für Allgemeine Mechanik, Rheinisch-Westfalische Technische Hochschule Aachen, D-5100 Aachen, Germany
W. Hocks
Affiliation:
Institut für Allgemeine Mechanik, Rheinisch-Westfalische Technische Hochschule Aachen, D-5100 Aachen, Germany
G. Mohiuddin
Affiliation:
Institut für Allgemeine Mechanik, Rheinisch-Westfalische Technische Hochschule Aachen, D-5100 Aachen, Germany
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Abstract

Closed-form expressions for the turbulent mean reaction rate and its covariance with the temperature are derived for premixed and non-premixed combustion. The limit of large activation energies is exploited for a chemical reaction rate that, by virtue of coupling functions, depends on the mixture fraction and a non-equilibrium progress variable only. The probability density function (p.d.f.) formulation with an assumed shape of the p.d.f. is used; a beta-function distribution is assumed for the progress variable. The mean reaction rate is expressed in terms of the mean and the variance of the temperature and, for non-premixed combustion, of the mixture fraction. The reaction kinetics are represented by the non-dimensional activation energy and the laminar flame velocity. For non-premixed systems the possibility of local extinction by flame stretch is considered.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 110 , September 1981 , pp. 411 - 432
Copyright
© 1981 Cambridge University Press

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References

Bilger, R. W. 1976 Turbulent jet diffusion flames. Prog. Energy Combust. Sci. 1, 87–109.Google Scholar
Borghi, R. 1975 Computational studies of turbulent flows with chemical reaction. Turbulent Mixing in Non-Reactive and Reactive Flows (ed. S. N. B. Murthy), pp. 163–188. Plenum.
Borghi, R. & Dutoya, D. 1979 On the scale of the fluctuations in turbulent combustion. 17th Symp. (Int.) on Combustion, pp. 235–244. Pittsburgh: The Combustion Institute.
Bray, K. N. C. 1979 The interaction between turbulence and combustion. 17th Symp. (Int.) on Combustion, The Combustion Institute, Pittsburgh, pp. 223–233.
Bray, K. N. C. & Libby, P. A. 1976 Interaction effects in turbulent premixed flames. Phys. Fluids 19, 1687–1701.Google Scholar
Bray, K. N. C. & Moss, J. B. 1977 A closure model for the turbulent premixed flame with sequential chemistry. Combust. & Flame 30, 125–131.Google Scholar
Buckmaster, J. & Ludford, G. S. S. 1981 Theory of Laminar Flames. (In preparation.)
Bush, W. B. & Fendell, F. E. 1970 Asymptotic analysis of laminar flame propagation for general Lewis numbers. Combust. Sci. Tech. 1, 421–428.Google Scholar
Clarke, J. F. 1978 Small amplitude gasdynamic disturbances in an exploding atmosphere. J. Fluid Mech. 89, 343–355.Google Scholar
Clarke, J. F. 1979 On the evolution of compression pulses in an exploding atmosphere: initial behaviour. J. Fluid Mech. 94, 195–208.Google Scholar
Clavin, P. & Williams, F. A. 1979 Theory of premixed-flame propagation in large-scale turbulence. J. Fluid Mech. 90, 589–604.Google Scholar
Damköhler, G. 1940 Der Einfluß der Turbulenz auf die Flammengeschwindigkeit in Gasgemischen. Z. Elektromech. 46, 601–626.Google Scholar
Fendell, F. E. 1972 Asymptotic analysis of premixed burning with large activation energies. J. Fluid Mech. 56, 81–95.Google Scholar
Janicka, J. 1979 Berechnung turbulenter Wasserstoff-Luft-Diffusionsflammen. Ph.D. thesis, Institut für Technische Thermodynamik, RWTH Aachen.
Janicka, J. & Kollmann, W. 1979 A two-variables formalism for the treatment of chemical reactions in turbulent H2-air diffusion flames. 17th Symp. (Int.) on Combustion, pp. 421–430. Pittsburgh: The Combustion Institute.
Kennedy, L. A. 1978 Turbulent Combustion, Progress in Astronautics and Aeronautics, vol. 58, A.I.A.A.
Libby, P. A. 1977 Studies in variable-density and reacting turbulent shear flows. In Studies in Convection, vol. 2, pp. 1–43. Academic.
Libby, P. A. & Bray, K. N. C. 1977 Variable density effects in pre-mixed turbulent flames. A.I.A.A.J. 15, 1186–1193.Google Scholar
Libby, P. A., Bray, K. N. C. & Moss, J. B. 1979 Effects of finite reaction rate and molecular transport in premixed turbulent combustion. Combust. & Flame 34, 285–301.Google Scholar
Libby, P. A. & Bray, K. N. C. 1980 Implications of the Laminar Flamelet Model in premixed turbulent combustion. Combust. & Flame 39, 33–41.Google Scholar
Libby, P. A. & Williams, F. A. 1976 Turbulent flows involving chemical reactions. Ann. Rev. Fluid Mech. 8, 351–376.Google Scholar
Liñán, A. 1974 The asymptotic structure of counterflow diffusion flames for large activation energies. Acta Astronautica 1, 1007–1039.Google Scholar
Lockwood, F. C. & Naguib, A. S. 1975 The prediction of the fluctuations in the properties of free, roundjet, turbulent diffusion flames. Combust. & Flame 24, 109–124.Google Scholar
Murthy, S. N. B. 1975 Turbulent Mixing in Non-reactive and Reactive Flows. Plenum.
Peters, N. 1978 On the stability of Liñán's premixed flame regime. Combust. & Flame 33, 315–318.Google Scholar
Peters, N. 1979 Premixed burning in diffusion flames — the flame zone model of Libby and Economos. Int. J. Heat Mass Transfer 22, 691–703.Google Scholar
Peters, N. 1980 Local quenching due to flame stretch and non premixed turbulent combustion. Western States Section of the Combustion Inst., Spring meeting, paper WSS 80–4.
Pope, S. P. 1979 The statistical theory of turbulent flames. Phil. Trans. Roy. Soc. A 291, 529–568.Google Scholar
Rhodes, R. P. 1975 A probability distribution function for turbulent flows. Turbulent Mixing in Non-Reactive and Reactive Flows (ed. S. N. B. Murthy), pp. 235–241. Plenum.
Rhodes, R. P. & Harsha, A. P. T. 1972 On putting the ‘turbulent’ in turbulent reacting flow. A.I.A.A. paper no. 72–68.Google Scholar
Richardson, J. M., Howard, H. C. & Smith, R. W. 1953 The relation between sampling-tube measurements and concentration fluctuations in a turbulent gas jet. 4th Symp. (Int.) on Combustion, pp. 814–817. Williams and Wilkins.
Sivashinsky, G. I. 1976 On a distorted flame front as a hydrodynamic discontinuity. Acta Astronautica 3, 889–918.Google Scholar
Sivashinsky, G. I. 1977 Diffusional-thermal theory of cellular flames. Combust. Sci. Tech. 15, 137–145.Google Scholar
Spalding, D. B. 1971a Mixing and chemical reaction in steady confined turbulent flames. 13th Symp. (int.) on Combustion, pp. 649–657. Pittsburgh: The Combustion Institute.
Spalding, D. B. 19716 Concentration fluctuations in a round turbulent free jet. Chem. Eng. Sci. 26, 95–107.Google Scholar
Spalding, D. B. 1976 Mathematical models of turbulent flames, a review. Combust. Sci. Tech. 13, 3–25.Google Scholar
Williams, F. A. 1971 Theory of combustion in laminar flows. Ann. Rev. Fluid Mech. 3, 171–188.Google Scholar
Williams, F. A. 1975a A review of some theoretical considerations of turbulent flame structure. AGARD Conf. Proc. 164, III 1-III 25.Google Scholar
Williams, F. A. 1975b Recent advances in theoretical descriptions of turbulent diffusion flames. Turbulent Mixing in Non-reactive and Reactive Flows (ed. S. N. B. Murthy), pp. 189–208. Plenum.
Zeldovich, Y. B. & Frank Kamenetskii, D. A. 1938 J. Phys. Chem. U.S.S.R. 12, 100 [cf. Zeldovich, Y. B. 1951 Theory of flame propagation. N.A.C.A. Tech. Memo. no. 1282].