• Transactions of the Korean Society of Mechanical Engineers B
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• v.38 no.6
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• pp.493-500
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• 2014

Nonlinear characteristics of cellular counterflow diffusion flame near the radiative extinction limit at large Damk$\ddot{o}$hler number are numerically investigated. Lewis number is assumed to be 0.5 and flame evolution is calculated by imposing an infinitesimal disturbance to a one-dimensional(1-D) steady state flame. The early stage of nonlinear development is very similar to that predicted in a linear stability analysis. The disturbance with the wavenumber of the fastest growing mode emerges and grows gradually. Eventual, an alternating pattern of reacting and quenching stripes is developed. The cellular flame temperature is higher than that of 1-D flame because of the gain of the total enthalpy. As the Damk$\ddot{o}$hler number is further increased, the shape of the cell becomes circular to increase the surface area per unit reacting volume. The cellular flames do not extinguish but survive even above the 1-D steady state extinction condition.

• Journal of the Korean Society of Combustion
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• v.18 no.2
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• pp.42-50
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• 2013

Linear stability analysis of radiating counterflow diffusion flames is numerically conducted to examine the instability characteristics of cellular patterns. Lewis number is assumed to be 0.5 to consider diffusional-thermal instability. Near kinetic limit extinction regime, growth rates of disturbances always have real eigen-values and neutral stability condition of planar disturbances perfectly falls into quasi-steady extinction. Cellular instability of disturbance with transverse direction occurs just before steady extinction. However, near radiative limit extinction regime, the eigenvalues are complex and pulsating instability of planar disturbances appears prior to steady extinction. Cellular instability occurs before the onset of planar pulsating instability, which means the extension of flammability.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.21 no.9
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• pp.1218-1229
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• 1997

The diffusional-thermal instability of diffusion flames in the premixed-flame regime is studied in a constant-density two-dimensional counterflow diffusion-flame configuration, to investigate the instability mechanism by which periodic wrinkling, travelling or pulsating of the reaction sheet can occur. Attention is focused on flames with small departures of the Lewis number from unity and with small values of the stoichiometric mixture fraction, so that the premixed-flame regime can be employed for activation-energy asymptotics. Cellular patterns will occur near quasisteady extinction when the Lewis number of the more completely consumed reactant is less than a critical value( ~ =0.7). Parametric studies for the instability onset conditions show that flames with smaller values of the Lewis number and stoichiometric mixture fraction and with larger values of the Zel'dovich number tend to be more unstable. For Lewis number greater than unity, near-extinction flame are found to exhibit either travelling instability or pulsating instability.