Numerical study on the formation of cellular premixed flames at high Lewis numbers

Abstract

Intrinsic instability and cell formation of premixed flames at high Lewis numbers (Le=1.0–3.0) are studied by two-dimensional, unsteady calculations of reactive flows. The relation between the growth rate and the wave number, i.e., the dispersion relation, is obtained to study intrinsic instability due to hydrodynamic and diffusive-thermal effects. The growth rate is positive at small wave numbers, and the marginal wave number separating stable and unstable ranges is found. The growth rate decreases and the unstable range narrows as the Lewis number becomes higher, since the diffusive-thermal effect has a stabilizing influence at Lewis numbers higher than unity. Positive growth rates caused by the hydrodynamic effect form a cellular flame. To study the formation of cellular flames, the disturbance with the linearly most unstable wave number is superimposed on a plane flame. The superimposed disturbance evolves, and eventually a cellular flame front is formed. The higher the Lewis number, the greater the cell size and cell depth. In addition, a stationary cellular flame is obtained when the inlet velocity of the unburned gas is set to the flame velocity, since cells on flame do not move laterally.