Algebraic Models for Turbulent Transports in Premixed Flames

Abstract

The thermal expansion induced by the chemical reactions taking place in a turbulent reactive flow of premixed reactants affects the velocity field so strongly that turbulent transports can be controlled by reaction rather than by turbulence. Moreover, thermal expansion is well-known to cause countergradient turbulent diffusion as well as flame-generated turbulence phenomena. In the present article, a splitting procedure of the velocity field is used that allows the identification of two different effects of the thermal expansion in the specific flamelets regime of turbulent premixed combustion: (i) the thermal expansion occurring through the local flames (direct effect) and (ii) the effect of thermal expansion on the velocity field associated to the growth of the flame surface (indirect effect). Algebraic closures for the turbulent transport terms of mass and momentum are proposed where the effect of the turbulent mixing (nonreactive effect) is modeled by classical closures, i.e., gradient law, while the contributions associated with thermal expansion are closed by taking advantage of flamelet relationships. Finally, this simple model is applied to the numerical simulation of a turbulent flame stabilized by the sudden expansion of a 2D channel. Corresponding results are satisfactorily compared with experimental data and confirm the ability of the model to represent the behavior of turbulent transports in premixed flames.

Keywords:

• Countergradient diffusion
• Flame-generated turbulence
• Numerical simulation
• Turbulent combustion
• Turbulent scalar flux

ACKNOWLEDGMENTS

The present manuscript has benefited from the valuable suggestions made by two reviewers. We also wish to thank Emeritus Professors K. N. C. Bray (Cambridge University, United Kingdom) and R. Borghi (University of Marseille, France), who provided encouraging comments concerning this work.

Notes

Published as part of the 23rd International Colloquium on the Dynamics of Explosions and Reactive Systems (ICDERS) Special Issue with Guest Editor Derek Dunn-Rankin.