Fractal flame structure due to the hydrodynamic Darrieus-Landau instability

Area of Science:

• Fluid dynamics
• Combustion science
• Complex systems

Background:

• Hydrodynamic instabilities, specifically the Darrieus-Landau (DL) instability, cause initially planar flame fronts to develop complex, fractal structures.
• The fractal nature of these DL fractal flames and their propagation characteristics have been subjects of long-standing debate in combustion research.

Purpose of the Study:

• To investigate the development of fractal structures in flame fronts using large-scale numerical simulations.
• To clarify debated issues concerning Darrieus-Landau fractal flames.
• To analyze the relationship between flame propagation speed, fractal properties, and flame characteristics like density drop.

Main Methods:

• Large-scale numerical simulations were employed to model flame front dynamics.
• The study analyzed the development of fractal structures from initially planar fronts under DL instability.
• Box counting methods were used to determine the fractal dimension of simulated flame front shapes.

Main Results:

• Simulations confirmed the development of fractal structures in flame fronts due to DL instability.
• Flame propagation speed was observed to increase with a hypothetical channel width, which influences the instability's length scale.
• This speed increase follows a power law, indicating mean fractal properties, with the exponent depending on the flame's density drop, not being a universal constant.
• The fractal flame dimension, determined by box counting, was found to be smaller than predicted by the power law at intermediate scales but showed a similar dependence on density drop.
• Formation of pockets, previously associated with turbulent burning, was observed in DL fractal flame fronts.

Conclusions:

• The study clarifies key aspects of DL fractal flames, demonstrating their fractal nature and dependence on flame properties.
• The findings suggest that flame propagation speed and fractal dimension are linked to the density drop across the flame front.
• The observation of pocket formation challenges previous associations and broadens the understanding of flame front dynamics.