Rate-ratio asymptotic analysis of nonpremixed n -heptane flames

Abstract

A rate-ratio asymptotic analysis of nonpremixed n -heptane (C 7 H 16 ) flames stabilized in the counterflow configuration is carried out. A reduced chemical-kinetic mechanism made up of three global reactions is employed in the analysis. In the first global step, fuel reacts with radicals to form the intermediate compounds hydrogen (H 2 ) and carbon monoxide (CO). The second and third global steps describe oxidation of these intermediate compounds to water vapor (H 2 O) and carbon dioxide (CO 2 ). The number of moles of radicals, α, that react with one mole of n -heptane in the first global step depends on the principal path of oxidation of the fuel in the detailed mechanism from which the reduced mechanism is deduced. The value of α obtained from different detailed chemical-kinetic mechanisms is not the same. In view of this uncertainty, the present study is focused on obtaining an improved understanding of the influence of α on the critical conditions of extinction. The asymptotic flame structure is presumed to comprise outer transport zones and a thin reaction zone. The outer transport zones are inert. Improvements in the present asymptotic analysis over previous asymptotic analyses are that in the transport zones the Lewis number of reactants and products is not presumed to be equal to unity, and heat losses by radiation are included. The Lewis number of any species i is defined as the ratio of thermal diffusivity to the coefficient of diffusion of species i . All chemical reactions are presumed to take place in the reaction zone. The reaction zone is presumed to be made up of an inner layer and an oxidation layer. The structure of the inner layer is obtained by introducing the approximation that only the first global reaction takes place in this layer. The second and third global reactions are presumed to take place in the oxidation layer. Analysis of the outer transport zones and the reaction zone gives the scalar dissipation rate at extinction χ f,q . For a given value of α, radiative extinction is observed when the scalar dissipation rate, χ f , is decreased below a critical value and diffusive extinction is observed when χ f is increased above a critical value. A flame cannot be stabilized for values of α larger than a critical value. The existence of flammable boundaries is a key finding of the present study.