Quasi-periodic pulsating behavior of weakly stratified laminar premixed flames with Lewis numbers greater than unity

This study focuses on dynamic behavior of weakly stratified laminar premixed flames under the thermo-diffusive framework for Lewis numbers greater than unity. The extent of stratification is controlled by means of a premixedness parameter, which is defined based on the concentration gradient of the reactants upstream of the flame. The value of this premixedness parameter ranges from zero (unmixed reactants) to unity (fully premixed). This paper explores the region of Lewis number between 1.5-1.6 weakly stratified flames (premixedness near unity), where a transition from steady state to oscillatory regime was reported earlier. Different regimes of oscillations such as single frequency and multiple frequencies are identified in the Lewis number-Damköhler number parameter space. The flame behavior is further studied by varying the premixedness parameter in the vicinity of unity. The flame dynamics shows interference of waves generated from the triple point of the premixed flame branches with a short diffusion flame branch and the thermal-diffusive instability waves along the premixed flame branches. Quasi-periodic behavior is observed in this regime as a result of this process. This behavior is represented in the Fourier transform of the total heat release in the domain, where the two fundamental frequencies are observed to be in irrational ratio. Further the system is represented on a phase portrait, where a torus shaped dense portrait is seen confirming the quasi-periodic behavior of the oscillations.