Numerical and asymptotic studies of the structure of stoichiometric and lean premixed heptane flames

Abstract

Numerical calculations and rate-ratio asymptotic analysis are performed to obtain the structure and burning velocities of premixed heptane flames. The numerical calculations are performed using a detailed chemical-kinetic mechanism comprising 257 elementary reactions, a skeletal chemical-kinetic mechanism comprising 34 elementary reactions and a reduced chemical-kinetic mechanism made up of six overall steps. The reduced chemical-kinetic mechanism is deduced from the skeletal mechanism. The rates of the overall reactions in the reduced mechanism are related to the rates of elementary reactions appearing in the skeletal chemical-kinetic mechanism. The values of burning velocities calculated numerically using the reduced chemical-kinetic mechanism are found to agree well with those calculated using the skeletal chemical-kinetic mechanism and the detailed chemical-kinetic mechanism. The asymptotic structure of premixed heptane flames is analyzed using the reduced chemical-kinetic mechanism. The flame structure is presumed to consist of three zones—a preheat zone of thickness of order unity, a thin reaction zone, and a post-flame zone. In the preheat zone, the rates of chemical reactions are presumed to be negligibly small. In the post-flame zone, the products are in chemical equilibrium and the temperature is equal to the adiabatic flame temperature. In the reaction zone, the chemical reactions are presumed to take place in three layers—an inner layer, a C 2H 4CH 2O consumption layer, and a H 2CO oxidation layer. Within the inner layer, there is a fuel-consumption layer of thickness of order δ where the fuel n-C 7H 16 is consumed and the intermediate hydrocarbon species C 2H 4 and CH 2O are formed. These intermediate hydrocarbon species are consumed in the C 2H 4CH 2O consumption layer of thickness of order μ, and CO and H 2 are formed. Most of the final products, CO 2 and H 2O, are formed in the H 2CO oxidation layer, which has a thickness of order ν. In the H 2CO oxidation layer, H 2 is presumed to be in steady state everywhere except in a thin sublayer of thickness of order ϵ which is located within the H 2CO oxidation layer. It is presumed that δ ⪡ μ ⪡ ϵ ⪡ ν ⪡ 1. The burning velocities calculated using the results of the asymptotic analysis are found to agree reasonably well with those calculated numerically using the skeletal chemical-kinetic mechanism and the detailed chemical-kinetic mechanism.