The body-force efféct on the structure of cellular flames

Abstract

The two-dimensional (2-D) and three-dimensional (3-D) unsteady reactive flows are calculated to study the structure of downwards/upwards propagating cellular flames at the Lewis number unity. We superimpose an infinitesimal disturbance on the stationary plane flame to obtain the growth rate depending on the wave number, i. e., the dispersion relation. When premixed flames are propagated downwards/upwards, the growth rate decreases/increases and the unstable range becomes narrower/broader with an increase in acceleration. Since we have positive growth rates, the cellular shape of flame fronts appears owing to intrinsic instability. To study the formation of a cellular flame front, we superimpose the disturbance with the peculiar wave number which corresponds to the maximum growth rate. The disturbance on a flame is evolved, and eventually the cellular flame front is formed. When the flame is propagated downwards, the spacing between cells is almost constant and the depth of cells becomes smaller as the acceleration increases. When the flame is propagated upwards, on the other hand, the former becomes smaller and the latter becomes larger.