The Unstable Motion of Cellular Premixed Flames Caused by Intrinsic Instability

Abstract

The unsteady calculations of two-dimensional (2-D) and three-dimensional (3-D) reactive flows are performed to study the unstable motion of cellular premixed flames caused by intrinsic instability. The compressible Navier-Stokes (N-S) equation including a one-step irreversible chemical reaction is employed. An infinitesimal disturbance is superimposed on a stationary planar flame to obtain the relation between the growth rate and the wave number, i.e., the dispersion relation. As the Lewis number becomes lower, the growth rate increases and the unstable range widens. For upward propagating flames, the growth rate increases and the unstable range widens as the acceleration increases. In addition, the dispersion relation of 2-D flames is nearly the same as that of 3-D flames. The disturbance with the peculiar wavelength corresponding to the maximum growth rate is superimposed to study the unstable motion of cellular flames. When the Lewis number is lower than unity, the lateral movement of cells is observed. The lateral velocity of cellular flames increases as the Lewis number becomes lower. In addition, the lateral velocity of 3-D flames is about twice that of 2-D flames. The body-force effect has an influence on the lateral velocity. For upward propagating flames, the lateral velocity decreases as the acceleration increases, even though intrinsic instability becomes stronger. The reason is that the high-temperature region behind a convex flame front with respect to the unburned gas becomes larger as the acceleration increases.