Fractal flame structure due to the hydrodynamic Darrieus-Landau instability

Abstract

By using large scale numerical simulations, we obtain fractal structure, which develops at originally planar flame fronts due to the hydrodynamic Darrieus-Landau (DL) instability bending the fronts. We clarify some important issues regarding the DL fractal flames, which have been debated for a long time. We demonstrate an increase of the flame propagation speed with the hypothetic channel width, which controls the length scale of the instability development. We show that this increase may be fitted by a power law indicating the mean fractal properties of the flame front structure. The power exponent in this law is found to be not a universal constant, rather it depends on the flame properties-on the density drop at the front. Using box counting on the simulated flame front shapes we show the fractal flame dimension at the intermediate scale is smaller than the one given by the power law, but it has a similar dependency on the density drop. We also obtain a formation of pockets at the DL fractal flame fronts, which previously has been associated only with turbulent burning.