Stability of Premixed Flames with Two Thin Reaction Layers

Source abstract

An asymptotic analysis is presented for the structure of premixed laminar flames and for their response to nonplanar perturbations when the reaction mechanism can be modeled by two sequential reactions with large activation energies. The reaction rates are such that the two reactions occur in separate thin reaction layers. The analysis is carried out within the framework of the thermal-diffusive approximation. The analysis leads to a simplified model which can be used for the description of the nonlinear response of the two reaction sheets to nonplanar perturbations. The model involves only three parameters, associated with the Lewis numbers of both reactants and the distance H between the reaction layers in the steady planar flame. A linear stability analysis of the planar flame shows a smooth transition in the stability properties toward those of the regime of merged reaction zones when the two reaction sheets tend to coalesce. The analysis suggests that close to the boundary of the domain of stability one can expect: chaotic response, cellular flames, traveling waves, pulsating flames and a Hopf bifurcation with frequencies that, when H is small, are of the order of the inverse of the residence time between the two reaction layers.