Extinction of Premixed Flames in a Stagnation Flow Considering General Lewis Number

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Abstract
The effects of the velocity gradient on the premixed flame in the stagnation flow field have been studied theoretically considering general Lewis number. The steady two-dimensional stagnation flow and the uni-molecular reaction were assumed, and the governing equations were solved numerically. The influence of the velocity gradient and the Lewis number on the flame temperature were discussed. There are two effects of the velocity gradient on the flame. One effect is that the velocity gradient causes the flame temperature to increase or to decrease due to the imbalance between the excess heat flow from the reaction zone to the unburned gas and the excess diffusion flow of the reactant from the unburned gas to the reaction zone, and this effect largely depends on the Lewis number. By the velocity gradient, the flame temperature increases when Le>1 and decreases when Le< 1. When Le= 1, the velocity gradient has no effect on the flame temperature. Another effect is tha velocity gradient causes the flame temperature to decrease due to the incomplete combustion; this effect occurs when the velocity gradient is large enough and the flame is in contact with the wall surface. By means of these two effects, the extinction process of the flame is classified into four patterns, corresponding to four ranges of the Lewis number, which are Le≫1, Le 1. When Lc> 1, the flame temperature increases with the velocity gradient and is larger than the one-dimensional adiabatic flame temperature until the effect of the incomplete combustion becomes so large. The flame is extinguished by the effect of the excess heat loss from the reaction zone and/or by the effect of the incomplete combustion. The flame extinction only by the excess heat loss from the reaction. zone occurs when the Lewis number is very small.