Flame balls with thermally sensitive intermediate kinetics

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

“…These studies address the fundamental (generic) properties of flames with multi-step reaction mechanisms rather than consider some specific combustion reaction. The two-step reactions can be split into two groups: reactions with competing steps [3,12] and sequential steps [3,13,14,15,16,17,18]. 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.…”

“…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.…”

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

“…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.…”

“…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].…”

“…These include studies of the structure and stability of flame balls [16] and of premixed flames [14]. In this paper, we extend the asymptotic linear stability analysis of the two-step chain-branching premixed flames to include hydrodynamic effects induced by thermal expansion, by considering the Re-active Navier-Stokes equations.…”