Flame sheet starting estimates for counterflow diffusion flame problems

We develop a flame sheet starting procedure for the detailed numerical modeling of counterflow diffusion flames. These flames are characterized by the presence of a narrow reaction zone stabilized between counterflowing jets of fuel and oxidizer. Despite the outwardly simple form of the governing equations, the determination of a good initial solution estimate can be difficult. Failure to obtain such an approximation can cause the numerical solution procedure to converge slowly or to diverge. The flame sheet model we consider couples the conservation of mass and momentum with a Shvab-Zeldovich equation to provide starting estimates for the mass flux in the transverse direction, the similarity function, the temperature, and the stable major species in the flame. Application of the model to two methane-air flames reveals the effectiveness of the procedure in generating starting estimates for such problems.