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Intrinsic Instability of Three-Dimensional Premixed Flames Under Low- and High-Temperature Conditions: Effects of Unburned-Gas Temperature on Hydrodynamic and Diffusive-Thermal Instabilities

The intrinsic instability of three-dimensional (3D) premixed flames under low- and high-temperature conditions was numerically treated to study the effects of unburned-gas temperature on hydrodynamic and diffusive-thermal instabilities. Superimposing a sinusoidal disturbance with sufficiently small amplitude on a planar flame, we obtained the relation between the growth rate and wave number, i.e., the dispersion relation. As the unburned-gas temperature became lower, the growth rate decreased and the unstable range narrowed due to the decrease of the burning velocity of a planar flame. At sufficiently small wave numbers, the obtained numerical results were consistent with the theoretical solutions. When the Lewis number was small, we obtained a large growth rate and wide unstable range due to diffusive-thermal effects. The growth rate and wave number were normalized by the burning velocity of a planar flame and preheat zone thickness. The normalized growth rate increased and the normalized unstable range widened with a decrease of unburned-gas temperature. This was because thermal-expansion effects became stronger owing to the increase of the temperature ratio of burned and unburned gases. To elucidate the characteristics of cellular flames generated by intrinsic instability, we superimposed a disturbance with the critical wave number corresponding to the maximum growth rate, i.e., the linearly most unstable wave number. The superimposed disturbance evolved, and a hexagonal cellular flame formed. The behavior of cellular flames became stronger as the unburned-gas temperature became lower, even though the growth rate decreased. The burning velocity of a cellular flame normalized by that of a planar flame increased due to the strength of thermal-expansion effects.