Heat-loss effects on the chaotic behavior of cellular premixed flames generated by intrinsic instability were studied by two-dimensional unsteady calculations of reactive flows based on the compressible Navier-Stokes equation.The disturbance with the linearly most unstable wave number, i.e. the critical wave number, was superimposed on a planar flame. As the superimposed disturbance evolved, the cellular-flame front formed owing to intrinsic instability. The unstable behavior of cellular flames appeared at low Lewis numbers and became stronger as the heat-loss parameter increased. Owing to the unstable behavior, the burning velocity fluctuated with time. To study the characteristics of the unstable behavior, the power spectrum density of the fluctuation of the burning velocity was obtained. The power spectrum density had a sharp peak, whose frequency corresponded to the typical oscillation frequency of the unstable behavior, and the 1/f 2 spectrum was found in low frequency range. Moreover, we performed the time series analysis on the burning-velocity fluctuation. We obtained the attractor and correlation dimension to study the characteristics of the chaotic behavior of cellular premixed flames. The characteristics depended strongly on the heat-loss parameter and Lewis number, i.e. on intrinsic instability. The results suggest that the present analysis is applicable to the diagnostics of the flame instability.
The effects of the activation energy on the intrinsic instability of adiabatic and non-adiabatic premixed flames were studied by two-dimensional unsteady calculations of reactive flows based on the compressible Navier-Stokes equation. A sinusoidal disturbance was superimposed on a planar flame to obtain the relation between the growth rate and the wave number, i.e. the dispersion relation, and the burning velocity of a cellular flame generated by intrinsic instability. When the Lewis number Le = 1, the activation energy had no effects on the instability of adiabatic flames. In non-adiabatic flames, the growth rate and burning velocity decreased as the activation energy increased, because the reduction of temperature at the flame front had a great influence on the flame instability at large activation energies. When Le < 1, the activation energy had much effects on both adiabatic and non-adiabatic flames. As the activation energy increased, the growth rate and burning velocity increased drastically, because of the increase of the Zeldovich number. In addition, the unstable behavior of cellular-flame fronts was observed at large activation energies. When Le > 1, on the other hand, the growth rate and burning velocity decreased as the activation energy increased. This was because that the stabilizing influence of diffusive-thermal effects became larger. The obtained results showed that the activation energy played an important role in the intrinsic instability of adiabatic and non-adiabatic premixed flames.
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