Three-dimensional cellular premixed flames generated by hydrodynamic and diffusive-thermal instabilities (Effects of unburned-gas temperature and heat loss)

Abstract

We dealt with three-dimensional cellular premixed flames generated by hydrodynamic and diffusive-thermal instabilities to elucidate the effects of unburned-gas temperature and heat loss. To obtain the dispersion relation, a sinusoidal disturbance with sufficiently small amplitude was superimposed on a planar flame. As the unburned-gas temperature became lower and the heat loss became larger, the growth rate decreased and the unstable range narrowed, owing to the decrease of the burning velocity of a planar flame. Using the preheat zone thickness and burning velocity of a planar flame, the dispersion relation was normalized. With a decrease of unburned-gas temperature, the normalized growth rate increased and the normalized unstable range widened, which was because the temperature ratio of burned and unburned gases became larger. With an increase of heat loss, instability phenomena became noticeable, which was because diffusive-thermal instability became stronger. To investigate the characteristics of cellular flames generated by hydrodynamic and diffusive-thermal instabilities, we superimposed a disturbance with the critical wave number corresponding to the maximum growth rate. The superimposed disturbance evolved, and a hexagonal cellular flame formed. The obtained cellular fronts were qualitatively consistent with the experimental results. The cellular fronts became deeper as the unburned-gas temperature became lower, even though the growth rate decreased, which was due to the strength of thermal-expansion effects. As the heat loss became larger, the burning velocity of a cellular flame normalized by that of a planar flame increased. This was because diffusive-thermal effects became stronger owing to the increase of apparent Zeldovich number caused by the decrease of flame temperature.