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Updated: Jul 2, 2026
10:29
Experimental Methodology for Estimation of Local Heat Fluxes and Burning Rates in Steady Laminar Boundary Layer Diffusion Flames
Published on: June 1, 2016
Sivashinsky equation for corrugated flames in the large-wrinkle limit
1Laboratoire de Combustion et de Détonique, UPR 9028 du CNRS, ENSMA, 1 rue Clément Ader, B.P. 40109, 86961 Futuroscope Cedex, Poitiers, France. joulin@lcd.ensma.fr
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 4, 2008
Summary
This study analytically solves complex flame shape equations, revealing pole density patterns for various flame configurations. Findings offer insights into flame dynamics and validate numerical approaches.
Area of Science:
- Fluid Dynamics
- Combustion Theory
- Nonlinear Dynamics
Background:
- Sivashinsky's equation models corrugated flame shapes.
- Previous work by Thual et al. used integral equations for pole density in large-wrinkle limits.
Purpose of the Study:
- To analytically solve singular integral equations for flame pole density.
- To investigate flame shapes for isolated, monocoalesced, and bicoalesced periodic patterns.
- To compare analytical predictions with numerical results.
Main Methods:
- Analytical solution of singular linear integral equations.
- Pole-decomposition approach for flame dynamics.
- Comparison of analytical and numerical results.
Main Results:
- Exact analytical solutions for pole densities and flame shapes.
- Good agreement between analytical predictions and numerical data, even for moderate N.
- Insights into the dynamics of supplementary poles.
Conclusions:
- The analytical solutions provide accurate descriptions of flame patterns.
- The study validates the pole-decomposition approach for flame dynamics.
- Further research is suggested on open problems in flame dynamics.
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