The effects of unburned-gas temperature on intrinsic instability of premixed flames at high Lewis numbers under the adiabatic and non-adiabatic conditions

Abstract

We treated numerically premixed flames at high Lewis numbers under the adiabatic and non-adiabatic conditions to elucidate the effects of unburned-gas temperature on intrinsic instability. Numerical calculations of two-dimensional unsteady reactive flow were performed, based on the compressible Navier-Stokes equation including one-step chemical reaction. Lewis numbers higher than unity were adopted, and radiative heat loss was employed. Superimposing a sinusoidal disturbance with sufficiently small amplitude on a stationary planar flame, we obtained the relation between the growth rate and wave number, so-called dispersion relation. When the Lewis number was higher than unity, the growth rate was small and the unstable range was narrow, compared with premixed flames at Lewis number of unity, which was because of the weakness of intrinsic instability due to diffusive-thermal effects. As the unburned-gas temperature became higher, the growth rate increased and the unstable range widened. This was because of the increase of the burning velocity of a planar flame. Taking account of radiative heat loss, we obtained small growth rates and narrow unstable range. To study the characteristics of cellular flames generated by intrinsic instability, we superimposed a disturbance with the critical wave number corresponding to the maximum growth rate. The superimposed disturbance evolved, and a cellular flame formed. The burning velocity of a cellular flame normalized by that of a planar flame decreased as the unburned-gas temperature became higher. As the heat loss became larger, the normalized burning velocity of a cellular flame decreased. This indicated that the heat loss inhibited the instability of premixed flames at high Lewis numbers.