Flames with Chain-Branching/Chain-Breaking Kinetics

Abstract

Abstract.A steady plane flame subject to the chain-branching/chain-breaking kineticsis considered for a certain distinguished limit of parameter values corresponding to fast recombination.Here A is the reactant, X the radical, P the product, and M a third body. The activation energy of the production step is very large, while that of the recombination step is small and taken to be zero. These kinetics are the most attractive of the two-step schemes that have been proposed for explaining interesting phenomena not covered by one-step kinetics, and the purpose is to provide a firm foundation for exploitation of the scheme. The object is to find the "laminar-flame eigenvalue" A, representing the burning rate, as a function of r, which is essentially the ratio of the two reaction rates. The response function A(r) is described by numerical integration and by asymptotic analysis for r-»0, oo.

Combustion waves in a model with chain branching reaction and their stability

“…In the first group of models three types of reactions are considered: (i) simple competing scheme C 1 : A → P 1 , A → P 2 ; (ii) competing chain reaction scheme C 2 : A → B, A + B → P ; (iii) competing chain branching scheme C 3 : A + B → 2B, A + B → P , where A is the reactant, B the radical, P the product. The second group of the reactions includes several schemes: [3,13,14,15,18] A + B → 2B, nB + M → nP + M , where n = 1 in [14,15] and n = 2 in [3,13] and M is a third body. These schemes were investigated either analytically by using high activation energy asymptotic or numerically.…”

“…As noted in [14] the chain branching reaction is more realistic in describing real flames such as hydrocarbon flames in comparison to other two-step reaction models. This model was initially considered in [3] and then generalized in [13]. It is usually referred to as Zeldovich-Liñán model.…”

“…It is usually referred to as Zeldovich-Liñán model. In [13] the model is considered in a limiting case when the recombination step is fast in comparison to heat conduction time. Firstly,the resulting problem is investigated semi-analytically by using activation energy asymptotic first which provides a set of equations for the inner problem.…”

“…In [11] a reduced two-step chain branching reaction for oxidation of hydrogen was studied. The methodology used in this paper is similar to [13] (i.e. semi-analytical investigation using activation energy asymptotics and numerical integration of the resulting equations).…”

Flame balls with thermally sensitive intermediate kinetics

“…With only a few exceptions (as found in [14][15][16][17][18][19]), analytical solutions describing laminar flames have been founded on the one-step model; flames have also been described using a variety of reduced-kinetic models for the chemistry [20][21][22], the rates of which are combinations of the rates of elementary hydrocarbon oxidation reactions, but these models are much more problematic to analyse in any general way. References for all the achievements of the one-step model are far too numerous to cite here; the reader can find many suitable citations in texts and review articles on combustion theory and in recent articles on the subject, e.g.…”