Effect of the reversibility of the chemical reaction on triple flames

We examine a new aspect of triple flames, namely the effect of the reversibility of the chemical reaction on flame propagation. The study is carried out in the configuration of the two-dimensional strained mixing layer formed between two opposing streams of fuel and oxidiser. The chemical reaction is modelled as a single reversible reaction following an Arrhenius law in the forward and backward directions. The problem is formulated within the constant-density (thermo-diffusive) approximation, the main non-dimensional parameters relevant to this study being a reversibility parameter R (equal to zero in the irreversible case), a non-dimensional measure of the strain rate ϵ and a stoichiometric parameter S. We provide analytical (asymptotic) expressions for the local burning speed of the triple flame in terms of ϵ, S, and R. In particular we describe how the propagation speed of the front is decreased by an increase in R and how the location of its leading edge is affected by reversibility. For example, it is found that the leading edge shifts towards the fuel stream for S > 1 and towards the oxidiser if S < 1, as R is increased. A detailed numerical study is conducted covering all propagation regimes ranging from weakly stretched positively propagating (ignition) fronts to thick negatively propagating (extinction) fronts. In the weakly stretched cases we show that the numerics are in good agreement with the asymptotic findings. Furthermore, the results allow the determination of the domains of the distinct propagation regimes, mainly in the terms of R and ϵ. In line with our physical intuition, it is found that reversibility reduces the domain of ignition fronts and promotes extinction. The results provide a systematic investigation which can be considered as a first step when considering a more realistic chemistry, or poorly explored aspects (such as the existence of a temperature gradient in the unburnt mixture), when analyzing triple flames.