Influence of the Darrieus-Landau instability on the propagation of planar turbulent flames

The propagation of premixed flames in weak two-dimensional homogeneous turbulent flows is studied numerically via a hybrid Navier-Stokes/front capturing methodology within the context of a hydrodynamic model, which treats the flame as a surface of density discontinuity separating the burnt and unburnt gases. The focus is the influence of the Darrieus-Landau instability on the turbulent flame, which has been recognized recently to have a dramatic effect on its structure and the turbulent flame speed. Such instability, controlled by a parameter inversely proportional to the Markstein length, can be triggered in a laboratory setting by variations in system pressure or in fuel type and composition. Particular attention in this study is devoted to the influence of the Darrieus-Landau instability on a turbulent, statistically planar flame. Results are therefore limited to positive Markstein length corresponding to lean hydrocarbon-air or rich hydrogen-air mixtures. We show that, although the planar flame under similar but laminar conditions is stable, it is nonetheless affected by the instability in the presence of a turbulent incident flowfield. The turbulent flame speed is observed to exhibit, in addition to the effect of thermal expansion, a nontrivial dependence on the instability parameter and on the turbulence integral scale both effects modulating, in the weak turbulence regime, the well established quadratic dependence of turbulent flame speed on turbulence intensity.