Premixed burning in diffusion flames—the flame zone model of libby and economos

Abstract

The flame zone model proposed by Libby and Economos is shown to be based upon the assumption of a one-step reversible chemical reaction with a large activation energy. The limit of large activation energies is exploited by the method of matched asymptotic expansions and the originally missing relation for the critical freezing temperature—essential for the flame zone model—is derived. It is found that the process of freezing is closely related to the flame propagation in an inhomogeneous mixture. The derivation is general but, following the original paper, the numerical results are presented for a locally similar partly premixed boundary layer diffusion flame. The flame zone is constructed as a two-dimensional region of chemical equilibrium bounded by two infinitely thin non-equilibrium layers that assure the transition to the surrounding frozen flow.