From one-step to chain-branching premixed flame asymptotics

Dold, J. W.; Thatcher, R. W.; Omon-Arancibia, A. A.; Redman, J.

doi:10.1016/s1540-7489(02)80186-9

Cited by 33 publications

(45 citation statements)

References 13 publications

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“…For the chain-branching model, this surface occurs at T = T c , and suitable jump conditions need to be applied across it [14,15]. An analysis of the inner branching reaction zone structure [1,14,15] determines the outer jump conditions to be applied at the reaction sheet:…”

Section: The Modelmentioning

confidence: 99%

“…Furthermore, any weak temperature dependence in the completion reaction rate will not qualitatively effect the leading order high-activation energy results (which are themselves approximate) studied here. Hence it is hence worth retaining the mathematical simplicity of the flame structure equations (by considering n = 2) which was one of the original motivations for the two-step model [14,15].…”

Section: The Modelmentioning

confidence: 99%

“…Transforming to Y 0 as the independent variable by employing equation (15), then in the region x < 0 equation (24) becomes…”

Section: Asymptotic Solution As X → −∞mentioning

confidence: 99%

“…For the purposes of the mathematical theory of flames, however, any improved model should still be sufficiently simple and generic such that transparent, fundamental insights can be obtained and that some analytical or asymptotic progress is still possible. In this spirit, Dold and co-workers [14][15][16] have suggested a two-step chemistry model, consisting of a single chain-branching step, F+Y→2Y, and a single completion reaction step, Y+M→P+M, where Y represents a lumped or 'pooled' amalgam of intermediate species, and M is any species required to trigger the completion reactions, but is unchanged in the process. In the simplest version of this model, the branching reaction is assumed to have a high activation temperature but is thermally neutral, while the completion reaction is assumed to be temperature insensitive but releases all the heat.…”

Section: Introductionmentioning

confidence: 99%

“…Dold and co-workers [14][15][16] have applied the high-activation energy asymptotic limit of the two-step chemistry model to a number of flame problems, in the context of the purely thermal-diffusive constant density model. These include studies of the structure and stability of flame balls [16] and of premixed flames [14].…”

Section: Introductionmentioning

confidence: 99%

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Effect of thermal expansion on the linear stability of planar premixed flames for a simple chain-branching model: The high activation energy asymptotic limit

Sharpe

2008

Combustion Theory and Modelling

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Published paperThe linear stability of freely propagating, adiabatic, planar premixed flames is investigated in the context of a simple chain-branching chemistry model consisting of a chain-branching reaction step and a completion reaction step. The role of chain-branching is governed by a crossover temperature. Hydrodynamic effects, induced by thermal expansion, are taken into account and the results compared and contrasted with those from a previous purely thermal-diffusive constant density linear stability study. It is shown that when thermal expansion is properly accounted for, a region of stable flames predicted by the constant density model disappears, and instead the flame is unstable to a long-wavelength cellular instability. For a pulsating mode, however, thermal expansion is shown to have only a weak effect on the critical fuel Lewis number required for instability. These effects of thermal expansion on the two-step chain-branching flame are shown to be qualitatively similar to those on the standard one-step reaction model. Indeed, as found by constant density studies, in the limit that the chain-branching crossover temperature tends to the adiabatic flame temperature, the two-step model can be described to leading order by the one-step model with a suitably defined effective activation energy.

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