2013 年 8 巻 3 号 p. 233-246
We studied numerically the intrinsic instability of high-temperature premixed flames, where the burned-gas temperature was constant, under the conditions of constant density and constant pressure in the unburned gas. A sinusoidal disturbance with sufficiently small amplitude was superimposed on a planar flame to obtain the relation between the growth rate and wave number, i.e. the dispersion relation. As the unburned-gas temperature became higher, the growth rate increased and the unstable range widened, which was due to the increase of the burning velocity of a planar flame. In sufficiently small wave-number range, the obtained numerical results were consistent with the theoretical solutions. When the growth rate and wave number were normalized, the same dispersion relations were found under the conditions both of constant density and constant pressure in the unburned gas. The normalized growth rate decreased with an increase of the unburned-gas temperature, and the normalized unstable range narrowed. This was because that the thermal-expansion effects became weaker owing to the decrease of the difference in temperature between the burned and unburned gases. To clarify the characteristics of cellular flames induced by intrinsic instability, we superimposed a disturbance with the critical wavelength. The superimposed disturbance evolved, and a cellular-shaped flame front formed. The behavior of cellular flames became milder as the unburned-gas temperature became higher, even though the growth rate increased. The burning velocity of a cellular flame normalized by that of a planar flame decreased, which was due to the weakness of the thermal-expansion effects and diffusive-thermal effects. Moreover, the burning velocity of a cellular flame increased monotonously as the length of computational domain became larger, and the dependence of burning velocity on domain length became weaker with an increase of the unburned-gas temperature.
