Flame stability under flow-induced anisotropic diffusion and heat loss

Abstract

A two-dimensional model for premixed flames accounting for flow-enhanced diffusion or Taylor dispersion and heat loss is investigated. This is the first analytical study addressing the effect of Taylor dispersion on the thermo-diffusive instabilities of non-adiabatic flames. It is also the first numerical study coupling flame instability with Taylor dispersion. A linear stability analysis is carried out in the limit of infinite Zeldovich number β. This leads to a dispersion relation, generalising classical relations in the literature, and involving three parameters, l (the reduced Lewis number), p (the Taylor-dispersion coefficient which is proportional to the Peclet number), and κ (the heat loss coefficient). Stability diagrams are determined and their implications on the cellular and oscillatory instabilities are discussed. A Kuramoto–Sivashinsky type equation incorporating the parameters l, p and κ and characterising the flame dynamics in the weakly non-linear regime near the onset of the cellular instability is derived. The theoretical results demonstrate the ability of Taylor dispersion and heat loss to significantly affect the flame stability. In particular, the oscillatory instability is found to be promoted by an increase in κ and hampered by an increase in p. On the other hand, both p and κ have a destabilising effect in connection with the cellular instability. Also, the theory provides a formula predicting the typical size of cells first emerging from the cellular instability which is found to be a decreasing function of p.Numerical simulations are carried out illustrating and significantly extending the analytical findings. Particular attention is devoted to the influence of β. In particular, we reconcile apparent quantitative and sometimes qualitative discrepancies between the numerical and theoretical predictions, which are found to be more pronounced for larger values of p. Luckily, the asymptotic theory is found to be robust in the sense that its predictions are recovered numerically if β is taken large enough, although such predictions may be questionable for realistic values of β. In general, the effect of β on flame stability is found to be opposite to that of p: an increase in p or a decrease in β have a destabilising effect in connection with the cellular instability, and a stabilizing effect in connection with the oscillatory instability; both instabilities are promoted by an increase in κ.