Asymptotic Analysis of the Structure and Extinction of Spherically Symmetrical n-Heptane Diffusion Flames

Abstract

A minimal chemical-kinetic mechanism for the oxidation of n-heptane is reduced to a global two-step mechanism by the systematic application of partial-equilibrium and steady-state assumptions, with the global reaction rates related to the elementary rates. From this mechanism, the structure of spherically symmetrical diffusion flames around n-heptane droplets is analyzed using rate-ratio asymptotics. The outer transport zones are described by the classical flame-sheet analysis with Lewis numbers of unity. The inner structure consists of a thin fuel-consumption zone on the rich side of the flame and a broader but still thin layer on the lean side where H ₂ and CO are oxidized. The theory identifies a scalar dissipation rate, related to the droplet diameter, appropriate for droplet burning. From the analysis, the variations in flame temperature and in species concentrations with the stoichiometric scalar dissipation rate X ₁₁ were obtained. Since extinction occurs where x ₅₁ reaches a maximum, the extinction diameters for n-heptane droplets can be estimated from the results and are given for different pressures and ambient oxygen concentrations.