Heat-loss effects on the chaotic behavior of cellular premixed flames generated by intrinsic instability

Abstract

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/f2 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.