Molecular Diffusion Time and Mass Consumption Rate in Flames

Abstract

The recent interest in laminar flamelet concept in turbulent combustion modeling makes it necessary to understand correctly the behavior of laminar premixed and diffusion flames in nonuniform flows. It is well known that nonuniform flow affects flames through stretch and flame curvatures. However, it has not been made clear yet how the nonuniform flow can affect the combustion rate in flames. In order to understand the mechanism, we have to elucidate the roles played by convective flow, molecular transport processes and chemical reactions in flames. In this paper we develop a very simple dimensional analysis argument to identify these roles. The argument is restricted to steady laminar flames, which are stable and far from the extinction condition. The chemical reaction is characterized by high activation energy, and hence the reaction time scale is much shorter than those of the flow and molecular transport processes, leading to a laminar flame structure composed of a thin reaction zone and thick molecular diffusion layers. On the basis of this asymptotic flame structure, we make a dimensional analysis to elucidate the respective roles to derive a universal relation between the molecular diffusion time and the mass consumption rate of both premixed and nonpremixed laminar flames in general flow fields. It is shown that an increase in chemical reaction rate alone cannot increase the local combustion rate. In the case of a diffusion flame an increase in the local flow velocity is an effective way to increase the local combustion rate.