Effects of stoichiometry on premixed flames propagating in narrow channels: symmetry-breaking bifurcations

Abstract

Recent studies within the diffusive-thermal (constant-density) approximation have shown that, for premixed flames freely propagating in narrow adiabatic channels, the instabilities induced by differential diffusion may result in non-symmetric solutions and/or oscillating and rotating propagation modes. This has been shown in the context of lean mixtures, for which a single species transport equation with a single Lewis number (corresponding to the ratio of thermal to molecular diffusivity of the deficient reactant) can be used to describe the flame propagation problem. In the present work we extend the analysis to mixtures of any equivalence ratio. To this end, we consider a two-reactant model, where the different diffusivities of the two reactants introduce two different Lewis numbers. Steady-state computations and linear stability analysis are carried out for mixtures with large disparity between the Lewis number of the fuel (Le_F) and the oxidizer (Le_O), such as hydrogen-oxygen systems. It is shown that both differential diffusion and preferential diffusion have influence on the stability of the symmetric flame shape. For sufficiently lean and rich mixtures, the flame behaves as dictated by the Lewis number of the deficient reactant, i.e., the flame destabilizes toward non-symmetric solutions for large mass flow rates when the mentioned Lewis number is less than one. In near-stoichiometric mixtures the stability of the symmetric flame depends on a weighted average value of Le_F and Le_O. In particular, the symmetric solution is stable for large mass flow rates because of the difficulties found by the less diffusive reactant to reach the reactive zone of the flame.