Effects of the unburned-gas temperature and Lewis number on the intrinsic instability of high-temperature premixed flames

The effects of the unburned-gas temperature and Lewis number on the intrinsic instability of high-temperature premixed flames under the constant-enthalpy conditions were investigated by two-dimensional unsteady calculations of reactive flows. 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. This was due to the increase of the burning velocity of a planar flame. In addition, the obtained numerical results were consistent with the theoretical solutions in small wave-number region. As the Lewis number became smaller (larger), the growth rate increased (decreased) and the unstable range widened (narrowed), which was due to diffusive-thermal effects. The dispersion relation yielded the linearly most unstable wave number, i.e. the critical wave number. The critical wave number increased as the unburned-gas temperature became higher. Thus, the critical wavelength shrank, and then the cell size shrank. To clarify the characteristics of cellular flames induced by intrinsic instability, a finite disturbance with the critical wavelength was superimposed. The superimposed disturbance evolved, and a cellular-shaped front formed. In all Lewis numbers, the behavior of cellular flames became milder as the unburned-gas temperature became higher, even though the growth rate increased. The normalized burning velocities of cellular flames decreased monotonously. 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, which was generated by the conditions of constant enthalpy, i.e. constant burned-gas temperature.