Theory of multi-diffusion flames

Authors:
T. M. Liu and H. H. Chiu

Journal:
Quart. Appl. Math. **34** (1977), 373-383

DOI:
https://doi.org/10.1090/qam/99650

MathSciNet review:
QAM99650

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Abstract | References | Additional Information

Abstract: A theory which provides categorical classification and prediction of flame configurations for multi-component mixtures consisting of species has been developed. The application of the theory of irreducible operators decouples the species equations; and the fundamental solutions, if they exist, satisfy the same equations as that of a binary mixture. The theory is applied to two flow configurations: first, the flame at the mouth of a tube in a duct, and second, the flame in an unconfined jet. The single mode flame structure is essentially the same as that of binary diffusion approximation with proper modification of the effective diffusivity. The double mode structure consists of two diffusion modes. The individual mode satisfies the diffusion equation with characteristic effective diffusivity. The theory could be easily used by experiments and designers for practical purposes such as correlating experimental data or estimating burner size.

**[1]**S. S. Penner,*Chemistry problems in jet propulsion*, Pergamon Press, New York, 1957**[2]**F. A. Williams,*Combustion theory*, Addison-Wesley Inc., Palo Alto, 1965**[3]**S. P. Burke, and T. E. W. Schumann, Ind. Eng. Chem.**20**992-1004 (1928)**[4]**P. A. Libby and M. Pierucci,*Laminar boundary layer with hydrogen injection including multicomponent diffusion*, AIAA J.**2**, 2118-2126 (1964)**[5]**P. R. Nachtscheim,*Multicomponent diffusion in chemically reacting laminar boundary layers*, in*Proceedings of the***1967***Heat Transfer and Fluid Mechanics Institute*, Stanford University Press, pp. 78-87**[6]**W. C. Davy, R. A. Craig and G. C. Lyle,*An evolution of approximations used in the analysis of chemically reacting stagnation-point boundary layers with wall injection*, in*Proceedings of 1970 Heat Transfer and Fluid Mechanics Institute*, Stanford University Press**[7]**T. M. Liu and P. A. Libby,*Flame sheet model for stagnation point flows*, Combustion Sci. Tech.**2**, 377-388 (1971)**[8]**H. H. Chiu,*Theory of irreducible operators of linear systems*, Quart. Appl. Math.**27**(1969), 87–104. MR**0244596**, https://doi.org/10.1090/S0033-569X-1969-0244596-6**[9]**H. H., Chiu,*Unsteady vaporization of liquid droplet*, Quart. Appl. Math.**29**, 421-437 (1971)**[10]**M. Petrizzelli and H. H. Chiu,*Transient vaporization of fuel liquid droplet with thermal diffusion characteristics*, AIAA Preprint No. 71-126, 1971**[11]**J. A. Fay,*The distribution of concentration and temperature in a laminar jet diffusion flames*, J. Aeronaut. Sci., 681-689 (1954)**[12]**A. Goldburg and S. I. Cheng,*A review of the fluid dynamic problem posed by the laminar jet diffusion flame*, Combustion and Flame,**9**, pp. 259-272, 1965**[13]**Hermann Schlichting,*Boundary layer theory*, Translated by J. Kestin. 4th ed. McGraw-Hill Series in Mechanical Engineering, McGraw-Hill Book Co., Inc., New York-Toronto-London; Verlag G. Braun, Karlsruhe, 1960. MR**0122222**

Additional Information

DOI:
https://doi.org/10.1090/qam/99650

Article copyright:
© Copyright 1977
American Mathematical Society