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Theory and modeling of accelerating flames in tubes
Vitaly Bychkov1, Arkady Petchenko, V'yacheslav Akkerman
1Institute of Physics, Umeå University, SE-901 87, Umeå, Sweden.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 31, 2005
Summary
An analytical theory explains how premixed laminar flames accelerate exponentially in tubes, potentially leading to detonation. This model accurately predicts flame acceleration and profiles, offering insights into turbulent flame behavior.
Area of Science:
- Combustion science
- Fluid dynamics
- Chemical kinetics
Background:
- Flame acceleration is crucial for understanding the transition to detonation.
- Previous models lacked comprehensive analytical descriptions for accelerating flames in confined geometries.
Purpose of the Study:
- To develop an analytical theory for premixed laminar flame acceleration in tubes.
- To provide formulas for acceleration rate, flame shape, and velocity profiles.
- To extend the theory's applicability to turbulent flame acceleration.
Main Methods:
- Development of an analytical theory based on hydrodynamic combustion equations.
- Validation through extensive numerical simulations incorporating thermal conduction, viscosity, diffusion, and chemical kinetics.
Main Results:
- The theory predicts exponential flame acceleration from a closed end with nonslip walls.
- Analytical formulas for acceleration rate, flame shape, and velocity profiles were derived.
- Theoretical predictions showed good agreement with numerical simulation results.
Conclusions:
- The developed analytical theory accurately describes premixed laminar flame acceleration in tubes.
- The theory provides a foundation for understanding flame transition to detonation.
- The model offers insights applicable to the acceleration of turbulent flames.