The large activation energy analysis of extinction of counterflow diffusion flames with non-unity Lewis numbers of the fuel

Resumen

Large-activation-energy asymptotic techniques are used to describe the effects of non-unity Lewis numbers of the fuel on strain-induced extinction of axisymmetric counterflow diffusion flames. The present work extends and clarifies previous investigations by accounting also for variable density and variable transport properties of the gas. In our asymptotic analysis the flame structure near extinction is, at leading order, given by the Burke–Schumann limit of infinitely fast reaction; i.e. two outer regions of equilibrium flow, with the fuel and the oxygen separated by an infinitesimally thin reaction layer where they arrive by diffusion in stoichiometric proportions. The leading-order description provides the basic flow structure, including the flame-sheet location, the fuel-consumption rate, the temperature gradients on both sides of the flame, and the peak value of the temperature, which plays a dominant role in flame extinction and differs significantly from the adiabatic-flame value for non-unity Lewis numbers. In the near-extinction regime small departures, due to finite rates, from the fast-reaction limit are enough to dominate the structure of the reaction layer, and must be taken into account in this thin layer and in the outer chemically frozen regions, where the corrections are associated with the reactants leaking, with small mass fractions, through the flame. The main effect of the differential diffusion in the nearextinction regime is due to the strong modification of the reaction rates resulting from the changes in the Burke–Schumann peak temperature, with only moderate corrections due to leakage of the reactants through the flame. For large values of the overall stoichiometric ratio S of the diffusion flame, defined as the mass of the air stream needed to burn to completion the unit mass of the fuel stream, the extinction conditions occur in a premixed-flame regime, in which the reaction layer is displaced towards the fuel side with respect to the Burke–Schumann flame sheet position and a fraction of the arriving fuel mass flux leaks through the reaction layer, while the mass fraction of the leaking oxygen decreases to negligibly small values. The asymptotic predictions are tested by comparison with numerical integrations of extinction curves based on continuation methods.