On the Formation of Cellular Flames at High Lewis Numbers.

Abstract

Two-dimensional unsteady reactive flows are calculated to investigate the instability of premixed flames at high Lewis numbers and the formation of cellular flames due to inherent instability. We superimpose an infinitesimal disturbance on a stationary plane flame to obtain the relation between the growth rate and the wave number, i.e., the dispersion relation. We have positive growth rates at small wave numbers and the marginal wave number separating the stable/unstable range. As Lewis number increases, the growth rate decreases and the unstable range becomes narrower. Since there are positive growth rates, cellular flames appear at high Lewis numbers owing to inherent instability. To simulate the process of cellular-flame formation, we superimpose the disturbance with the peculiar wave number corresponding to the maximum growth rate. The disturbance on the flame is evolved, and eventually the cellular flame front is formed. With an increase in Lewis number, the spacing between cells becomes larger and the cell becomes deeper. In addition, the stationary cellular flame is obtained when the inlet-flow velocity is set to the flame velocity of the cellular flame because cells on the flame do not move laterally.