Statistics of flame displacement speeds from computations of 2-D unsteady methane-air flames

Results of two-dimensional numerical computations of turbulent methane flames using detailed and reduced chemistry are analyzed in the context of a new theory for premixed turbulent combustion. This theory defines the thin reaction zones regine, where the Kolmogorov scale is smaller than the preheat zone thickness but larger than the reaction zone thickness. The two numerical computations considered in this paper fall clearly within this regime. A lean and a stoichiometric flame are considered. The former is characterized by a large ratio of the turbulence intensity to the laminar burning velocity and the latter by a smaller value of that ratio.

The displacement speed of the reaction zone relative to the flow is defined as the displacement speed of the isoscalar line at a fuel mass fraction corresponding to 10% of the upstream value. The three different mechanisms that are contributing to the displacement of the reaction zone, namely, normal and tangential diffusion and reaction, are analyzed and their probability density functions are evaluated. Although these contributions fluctuate considerably, the mean value of the overall displacement speed is found to be only around 40% different from the burning velocity of a plane premixed flame at the same equivalence ratio. Furthermore, the contribution of tangential diffusion, which can be expressed as a curvature term, cancels as far as the mean overall displacement speed is concerned, while the contributions of normal diffusion and reaction are large but have opposite signs. These contributions depend implicitly on curvature. This dependence is small for the lean flame but considerable for the stoichiometric flame where it leads to an enhanced diffusivity. This diffusivity is compared to the Markstein diffusivity that describes the equivalent curvanture effect in the corrugated flamelet regime.