An implicit relation between temperature and reaction rate in the SLFM

Abstract

The Arrhenius law implies that reaction rate is a continuous function of temperature. However, the steady laminar flamelet model (SLFM) does not explicitly give this functional relationship. The present study addresses this relation in the SLFM. It is found that reaction rate is not continuous in the mixture-fraction space. As a result, the SLFM is unable to predict local extinction and reignition. Furthermore, we use the unstable branch of the "S-curve" to fill the gap between steady burning branch and extinction one, and find that this modification leads to a continuous dependent of reaction rate on temperature. Thus the modified SLFM can describe the local extinction and reignition.Keywords nonpremixed turbulent combustion, local extinction and reignition, steady laminar flamelet model, unstable branch Flamelet models are fundamentally important to turbulent combustion. The simplest and most frequently used flamelet model is the steady laminar flamelet model (SLFM). This model assumes that the reaction is quasisteady and consequently the transient effects can be neglected. [1] Recently, many works have focused on the validation and improvement of the SLFM. Cuenot and Poinsot [2] investigated the applicability of the SLFM to turbulent nonpremixed combustion through direct numerical simulation (DNS) of flame-vortex interactions. They found that the SLFM becomes invalid when curvature, unsteadiness and quenching become important. Pitsch et al. [3] used the unsteady flamelet model with Lagrangian time scale to discuss the transient effect in modeling diffusion flame. Claramunt et al. [4] and Cònsul et al. [5] analyzed the application of the SLFM in nonpremixed laminar flames and laminar partially premixed flames, and compared the SLFM with the unsteady laminar flamelet model. It was found that the SLFM is incapable of predicting unsteady reaction processes such as pollutant formation, local extinction and reignition, lift-off or blow-out. A widely accepted explanation is that unsteady processes can not be reasonably represented by the models which assume them to be steady. [6] The reaction rate provided by the SLFM controls the reaction process. According to the Arrhenius law the reaction rate has to be continuously dependent on temperature. However, the relation between temperature and reaction rate has not been explicitly stated in the SLFM. It remains unknown whether the Arrhenius law can be truely represented in the SLFM or not. In this study, this essential problem is addressed. We will give a new explanation on why the SLFM does not work in predicting local extinction and reignition. This explanation is helpful to further development of flamelet a)