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 (LeF ) and the oxidizer (LeO), 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 LeF and LeO. 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.

The role of conductive heat losses on the formation of isolated flame cells in Hele-Shaw chambers

“…with the Zel'dovich number defined as β = E(T a −T u )/(RT 2 a ). The factor s L = (S L )/(S L ) asp = 1.05 is the eigenvalue of the planar adiabatic problem [5], where the propagation velocity S L for finite β is compared with the propagation velocity for infinitely-large activation energy (S L ) asp .…”

“…The study of the propagation of premixed-gas flames in narrow chambers is key to understand most of these phenomena, which are typically enhanced by the geometrical restraint of the flow. Experimental, theoretical and numerical efforts have been instrumental in providing insight on the flame shape [5,6], the propagation rate [7][8][9] and the flame stability under various conditions and regimes [5,[10][11][12][13][14].…”

Superadiabatic small-scale combustor with counter-flow heat exchange: Flame structure and limits to narrow-channel approximation

“…1 with a dash-dot line. The possible impact of non-symmetric flames similar to those reported in [20][21][22][23] is out of the scope of the present study and will be reported elsewhere.…”

Taylor dispersion in premixed combustion: Questions from turbulent combustion answered for laminar flames

“…In this expression, which implies that u 0 = − 1 3 dp 0 /dx, the function dp 0 /dx is as yet unknown but can be determined by using (17) after averaging it, as is classically done in lubrication theory; hence…”

“…Since its introduction, the thick flame asymptotic limit has been adopted in studies by various workers and has gained some popularity partially due to an emerging interest in micropower generation using combustion [12]. Several aspects of thick flames have thus been investigated to date including the effect of heat loss and preferential diffusion [7,11,13], the effect of gas expansion [2,14,15], and flame stability [16,17]. The reader is referred to these publications and references therein for a proper account regarding these aspects.…”