Nonlinear equation for curved nonstationary flames and flame stability

Area of Science:

• Combustion science
• Nonlinear dynamics
• Fluid mechanics

Background:

• Understanding flame propagation dynamics is crucial for combustion efficiency and safety.
• Curved flame fronts exhibit complex behaviors influenced by various physical parameters.
• Previous models often simplified flame thickness and nonlinearity.

Purpose of the Study:

• To derive a time-dependent nonlinear equation for nonstationary curved flame fronts.
• To analyze the stability of two-dimensional curved stationary flames in tubes.
• To investigate the outcomes of flame instability, including self-turbulization and fractal structures.

Main Methods:

• Derivation of a nonlinear equation for curved flame fronts.
• Stability analysis of stationary flames using the derived equation.
• Comparison with numerical simulations and semiqualitative analyses.
• Evaluation of fractal dimension and self-turbulized flame velocity.

Main Results:

• A nonlinear equation for curved flame fronts was successfully derived.
• Curved stationary flames were found to become unstable in sufficiently wide tubes.
• Instability outcomes include flame wrinkling and self-turbulization, leading to fractal flame fronts.
• Stability limits showed good agreement with numerical and semiqualitative results.

Conclusions:

• The derived nonlinear equation provides a robust framework for studying curved flame dynamics.
• Flame instability in wider tubes is a significant factor affecting flame propagation.
• The study quantifies flame self-turbulization as a fractal phenomenon with implications for turbulent combustion modeling.