Premixed flames with a reversible reaction: propagation and stability

We consider the effect of the reversibility of the chemical reaction on the propagation and stability of laminar premixed flames, an important realistic aspect which has received little attention in the literature. For the sake of analytical tractability and clarity of the results, the thermodiffusive approximation of constant density is adopted, along with the simple framework of a single reversible reaction of the form F ⇀↽ P whose forward and backward rates follow an Arrhenius law. An asymptotic analysis is carried out for large values of an effective Zeldovich number β, and yields expressions for the flame speed U with arbitrary values of the Lewis numbers of the fuel, LeF , and the product, LeP . In particular, although U is found to decrease monotonically with the reversibility parameter r as expected, β turns out to be typically a non-monotonic function of r . The linear stability of the planar solution is then investigated, with particular emphasis on the influence of LeP , which did not appear in other studies. This is achieved by generalizing the so-called near-equidiffusional flame (NEF) approximation to the reversible case, which allows the stability problem to be reduced to that of the irreversible case, by an appropriate combination of variables. An effective reduced Lewis number is thus found to be the single control parameter in the resulting dispersion relation. The expression derived for the latter is used to delimit the stability and instability regions in the LeF -LeP -r space.