The role of pulsating instability and global Lewis number on the flammability limit of lean heptane/air flames

The unsteady propagation of lean heptane/air planar flames in the doubly infinite domain was computationally simulated with detailed chemistry and transport and with and without radiative heat loss. For the adiabatic situation, thermal-diffusive pulsating instability, promoted for large values of the Lewis and Zeldovich numbers, was observed to develop when the mixture became sufficiently lean. With subsequent progressive reduction in the equivalence ratio (φ), the mode of pulsation changes from that of monochromatic, to period doubling, and to hibernation characterized by bursts of high burning intensity separated by long periods of dormancy. The flame nevertheless does not extinguish. This behavior is similar to that of the rich hydrogen/air flame studied previously. However, when heat loss is considered, the onset of pulsation is facilitated, although the regime in φ for sustained pulsating propagation is extremely narrow, and extinction occurs readily when the amplitude of the flame temperature oscillation becomes large enough to extinguish the flame during the negative phase of the excursion. The abruptness of transition to extinction is quite different from that of the rich hydrogen/air flame. The pulsating extinction occurs at a large φ (= 0.5063) than steady extinction (φ = 0.4762), again implying that the flame extinguishes in the pulsating instead of the steadily propagating mode, and that the flammability limit is accordingly narrowed. It is further demonstrated that the states for the onset of adiabatic and non-adiabatic pulsation can be accurately estimated by using the criteria of Sivashinsky and of Joulin and Clavin, respectively, provided the Lewis number used is the global one, extracted from the response of stretched flames, demonstrating that it is a property of the flame instead of the unburned mixture alone. It is also suggested that the lean flammability limits of mixtures of large hydrocarbons and air can be estimated by using the criterion of Joulin and Clavin.