Unstable behavior of hydrogen-air lean premixed flames (Effects of unburned-gas temperature, heat loss and scale)

Unstable behavior of hydrogen-air lean premixed flames was studied by numerical calculations of two-dimensional unsteady reactive flow to clarify the effects of unburned-gas temperature, heat loss and scale. We adopted the numerical model containing the detailed hydrogen-oxygen combustion with 17 elementary reactions of 8 reactive species and a nitrogen diluent, compressibility, viscosity, heat conduction, molecular diffusion, and heat loss of Newtonian type. A disturbance with sufficiently small amplitude was superimposed on a planar flame to obtain the relation between the growth rate and wave number, i.e. dispersion relation, and the linearly most unstable wave number, i.e. critical wave number. As the unburned-gas temperature became lower and the heat loss increased, the growth rate decreased and the unstable range narrowed. These were due mainly to the decrease of flame temperature and burning velocity. To study the characteristics of cellular flames, the disturbance with the critical wave number was superimposed. The disturbance developed owing to intrinsic instability, and then the cellular shape of flame fronts appeared. The burning velocity of a cellular flame normalized by that of a planar flame became larger as the unburned-gas temperature became lower and the heat loss increased. The burning velocity of a cellular flame became monotonically larger with an increase in scale. This was because that the long-wavelength components of disturbances affected the unstable behavior of cellular flames.