Nonlinear evolution of diffusion flame oscillations triggered by radiativeheat loss

Nonlinear dynamics of radiation-induced oscillatory instability in diffusio n flames is numerically investigated by employing a diffusion flame establi shed in stagnant mixing layer with optically thin gas-phase radiation and u nity Lewis numbers for all species as a model. Particular attention is focu sed on the radiation-induced extinction regime that occurs when the Damkohl er number is sufficiently large. Transient evolution of the flame, initiate d by imposing a Damkohler number perturbation on the steady solution, exhib its three types of flame-evolution behaviors, namely decaying oscillatory s olution, diverging solution to extinction, and stable limit-cycle solution. The locus of the critically perturbed Damkohler number, across which diver ging solutions are separated from decaying solutions or limit-cycle solutio ns, is obtained, and it can be used as a dynamic extinction boundary for la minar flamelet library. The bifurcation structure is found to be a double H opf bifurcation, involving a supercritical Hopf bifurcation and a subcritic al Hopf bifurcation. The stable limit-cycle solutions, which occur only in the radiation-induced extinction regime while not observed in the transport -induced extinction regime, are found in a small island-shaped parametric r egion of Damkohler number and flame temperature, in which the double Hopf b ifurcation exists, with perturbation amplitudes smaller than the amplitude of the unstable limit cycle of the subcritical Hopf bifurcation. The stable limit-cycle behavior is implied to be relevant to the remarkably sustainab le droplet-flame oscillations observed in the space shuttle experiment. (C) 2000 by The Combustion Institute.