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Asymptotic analysis of premixed burning with large activation energy

Published online by Cambridge University Press:  29 March 2006

Francis E. Fendell
Affiliation:
Fluid Mechanics Laboratory, TRW Systems, Redondo Beach, California

Abstract

The structure and propagation rates of premixed flames are determined by singular perturbation in the limit where the activation temperature is large relative to other flow temperatures for several basic flows. Specifically, the simple kinetics of an exothermic first-order monomolecular decomposition under Arrhenius kinetics is studied for one-dimensional laminar flame propagation, spherically symmetric quasi-steady monopropellant droplet burning, and other simple geometries. Results elucidate Lewis-number effects, losses owing to fuel gasification processes, and conditions under which the thin-flame approximation is a limit of finite-rate Arrhenius kinetics.

Type
Research Article
Copyright
© 1972 Cambridge University Press

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References

Adler, J. & Spalding, D. B. 1961 One-dimensional laminar flame propagation with an enthalpy gradient. Proc. Roy, Soc. A 261, 5378.Google Scholar
Burke, S.P. & Schumann, T. E. W. 1928 Diffusion flames. Indust. Eng. Chem. 20, 9981004.Google Scholar
Bush, W. B. & Fendell, F. E. 1970 Asymptotic analysis of laminar flame propagation for general Lewis numbers. Combustion Sci. Tech. 1, 421428.Google Scholar
Bush, W. B. & Fendell, F. E. 1971 Asymptotic analysis of the structure of a steady planar detonation. Combustion Sci. Tech. 2, 271285.Google Scholar
Cole, J. D. 1968 Perturbation Methods in Applied Mathematics. Blaisdell.
Faeth, G. M., Karhan, B. L. & Yanyecic, G. A. 1968 Ignition and combustion of monopropellant droplets. A.I.A.A. J. 4, 684689.Google Scholar
Fendell, F. E. 1965 Ignition and extinction in combustion of initially unmixed reactants. J. Fluid Mech. 21, 281303.Google Scholar
Fendell, F. E. 1969 Quasi-steady sphericosymmetric monopropellant decomposition in inert and reactive environments. Combustion Sci. Tech. 1, 131145.Google Scholar
Jain, V. K. 1963 The theory of burning of monopropellant droplets in an atmosphere of inerts. Combustion & Flame, 1, 1727.Google Scholar
Jain, V. K. & Kumar, R. N. 1969 Theory of laminar flame propagation with nonnormal diffusion. Combustion 6s Flame, 13, 285294.Google Scholar
Jain, V. K. & Ramani, N. 1969 Theory of burning of a monopropellant droplet-variable properties. Combustion Sci. Tech. 1, 112.Google Scholar
Korman, H. F. 1970 Theoretical modeling of cool flames. Combustion Sci. Tech. 2, 149159.Google Scholar
Lawver, B. R. 1966 Some observations on the combustion of N2H4 droplets. A.I.A.A.J. 4, 659662.Google Scholar
Lorell, J. & Wise, H. 1955 Steady-state burning of a liquid droplet. I. Monopropellant flame. J. Chem. Phys. 23, 19281932.Google Scholar
Pierce, B. O. & Foster, R. M. 1956 A Short Table of Integrals, 4th edn. Boston: Ginn.
Rosser, W. A. & Peskin, R. L. 1966 A study of decompositional burning. Combustion & Flame, 10, 152160.Google Scholar
Spalding, D. B. & Jain, V. K. 1959 Theory of the burning of monopropellant droplets. Aero. Res. Counc. Current Paper, no. 447.Google Scholar
Van Dyke, M. 1964 Perturbation Methods in Fluid Mechanics. Academic.
Wllliams, F. A. 1959 Theory of the burning of monopropellant droplets. Combustion & Flame, 3, 529544.Google Scholar
Williams, F. A. 1965 Combustion Theory, chaps. 1, 3, 5 and 10. Addison-Wesley.
Williams, F. A. 1971 Theory of combustion in laminar flows. In Annual Review of Fluid Mechanics, vol. 3 (ed. by M. Van Dyke, W. G. Vincenti & J. V. Wehausen), pp. 171188. Annual Reviews Inc.