Combustion theory

The development of combustion theory has led to the appearance of several specialized asymptotic concepts and mathematical methods. An extremely strong temperature dependence for the reaction rate is typical of the theory. This makes direct numerical solution of the equations difficult but at the same time accurate. The basic concept of combustion theory, the idea of a flame moving at a constant velocity independent of the ignition conditions and determined solely by the properties and state of the fuel mixture, is the product of the asymptotic approach (18,19). Theoretical understanding of turbulent combustion involves combining the theory of turbulence and the kinetics of chemical reactions (19—23). 

F. A. WiUiams, Combustion Theory, The Benjamin/Cummings, Publishing Co. Inc., Menlo Park, Calif., 1985. 

Williams, F. A. (1985). Combustion Theory, 2nd ed. Menlo Park, CA Benjamm/Cummmgs. 

Various nonpremixed edge structures for symmetric cases (From Daou, R., Daou, ]., and Dold, J., Combust. Theory Model., 8,683,2004. With permission) (a) trihrachial, (b) cotton-bud shape, and (c) monobrachial structures and for asymmetric cases [19] (d) tribrachial and (e) bibrachial structures. 

S-shaped flame temperature response with Damkohler number exhibiting edge propagation characteristics. (From Kim, J. and Kim, J.S., Combust. Theory Model, 10, 21,2006.)... 

R. Daou, J. Daou, and J. Dold, The effect of heat loss on flame edges in a no-premixed counterflow within a thermo-diffusive model, Combust. Theory Model. 8(4) 683-699, 2004. 

J. Kim and J. S. Kim, Modelling of lifted turbulent diffusion flames in a channel mixing layer by the flame hole dynamics. Combust. Theory Model. 10 21-37, 2006. 

J. Daou and A. Linan, The role of unequal diffusivities in ignition and extinction fronts in strained mixing layers. Combust. Theory Model. 2 449-477,1998. 

R. W. Thatcher and J. W. Dold, Edges of flames that do not exit Flame-edge dynamics in a non-premixed counterflow, Combust. Theory Model. 4 435-457, 2000. 

S. R. Lee and J. S. Kim, On the sublimit solution branches of the stripe patterns formed in counterflow diffusion flames by diffusional-thermal instability. Combust. Theory Model. 6(2) 263-278,2002. 

P. Clavin and G. Searby. Unsteady response of chainbranching premixed-flames to pressure waves. Combustion Theory and Modelling, 12(3) 545-567, 2008. 

Buckmaster, J., The effects of radiation on stretched flames. Combust. Theory Model., 1, 1,1997. 

Pope, S. B., Computationally efficient implementation of combustion chemistry using in situ adaptive tabulation. Combust. Theory Model. 1 (1997)... 

Dally, B. B., D. F. Fletcher, and A. R. Masri (1998). Measurements and modeling of a bluff-body stabilized flame. Combustion Theory and Modelling 2, 193-219. 

Hewson, J. and A. R. Kerstein (2001). Stochastic simulation of transport and chemical kinetics in turbulent CO/H2/N2 flames. Combustion Theory and Modelling 5, 669-697. 

Masri, A. R., R. Cao, S. B. Pope, and G. M. Goldin (2003). PDF calculations of turbulent lifted flames of H2/N2 issuing into a vitiated co-flow. Combustion Theory and Modelling (in press). 

Williams, F. A., Combustion Theory, Chap. 6., Benjamin-Cummins, Menlo Park, California, 1985, See also Linan, A., and Williams, F. A., Fundamental Aspects of Combustion, Oxford University Press, Oxford, England, 1994. 

King, A. C. Billingham, J. Cooper, R. J. Combust Theory Model... 

Sirignano, W. A. 1983. Fuel droplet vaporization and spray combustion theory. Progress Energy Combustion Science 9 291-322. 

Pope, S.B. 1997. Computationally efficient impfementation of combustion chemistry using in situ adaptive tabufation. Combustion Theory Modeling 1 41. 

Thus, theoretical modeling of bluff-body flame stabilization cannot yet compete with the experimental approaches. Partially, it is due to the fundamental problems relevant to the turbulent combustion theory. The underestimation of the role of theory is also due to the lack of systematic studies based on existing models. 

Bai, X. S., and K. Seshadri. 1997. Rate-ratio asymptotic analysis of nonpremixed methane flames. Combustion Theory Modeling 3 51-75. 

Aghalayam, P., P.-A. Bui, and D. G. Vlachos. 1998. The role of radical wall quenching in flame stability and wall heat flux Hydrogen/air mixtures. Combustion Theory Modeling 2 515-30. 

Combustion Theories as Applied to Solid Propellants. See Vol 3 of Encycl, p C430-L... 

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