Scalar dissipation rate at the extinction of turbulent counterflow nonpremixed flames

Abstract

An analysis based on the modeled governing equations for an axisymmetric turbulent isothermal opposed jet flow has been made with the purpose of facilitating estimates of the scalar dissipation rate in turbulent counterflow nonpremixed flames. The equation for the mean mixture fraction defined as unity in one stream and zero in the other has a solution identical to that for laminar opposed jet flow but with a turbulent diffusion coefficient instead of a laminar one and the only parameter that appears in the modeled equation for the rms mixture fraction fluctuations is the ratio of the turbulent to the bulk flow strain rate. Numerical solutions showed that the mixture fraction fluctuations increase as the bulk strain rate decreases and as the turbulent strain rate increases and these solutions, together with experimentally obtained values for the turbulent intensity at the extinction of counterflow nonpremixed flames with and without partial premixing, resulted in estimates of the mean scalar dissipation rates. The estimated scalar dissipation rate at extinction of flames at different bulk and turbulent strain rates had a constant value that increased with the volume fraction of air in the fuel stream. The present results provide support to the flamelet extinction theory of Peters and Williams [ AIAA J. 21:423 (1983)].