The Effect of Finite Front Thickness on the Enhanced Speed of Propagation

Abstract

Recently, Majda and Souganidis have presented a rigorous asymptotic theory governing the large-scale renormalized flame front dynamics for a reaction-diffusion-advection system involving KPP type chemistries and small scale turbulence. This theory is valid in the context of an infinitely thin reaction layer. Embid, Majda and Souganidis have explored this rigorous theory within the context of a shear layer flow geometry, and demonstrate that the enhanced burning speed is sensitively dependent upon the presence of a mean wind transverse to the direction of the flame propagation. Here, we address the effect that a thin reaction layer may have on the enhanced flame propagation for the case of a small scale shear layer with and without a transverse mean wind. We show through high resolution numerical simulations that the enhanced burning speed is sensitively dependent on the presence of a transverse mean wind in a qualitatively similar fashion to the asymptotic theory; but further, we exhibit that a finite reaction zone yields effective burning speeds which are smaller than the theoretical predictions for infinitely thin flame fronts and that the decay of these corrections depends upon the relative scale separation between the reaction layer scale, the turbulence scale, and the integral scale.

Keywords:

• Flame propagation
• K.PP chemistry

Notes

∗ Corresponding author. E-mail: [email protected]