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 becomes sufficiently lean. The mode of pulsation changed from that of monochromatic, to period doubling, and to hibernation characterized by burst of high burning intensity separated by long periods of dormancy with subsequent progressive reduction in the equivalence ration (φ). The flame nevertheless did not extinguish, which was similar to that of the rich hydrogen/air flame studied previously. However, the onset of pulsation was facilitated when heat loss was considered, although the regime in φ for sustained pulsating propagation was extremely narrow, and extinction occurred readily when the amplitude of the flame temperature oscillation became large enough to extinguish the flame during the negative phase of the excursion. The states for the onset of adiabatic and non-adiabatic pulsation can be accurately estimated by respectively using the criterion of Sivashinsky and of Joulin and Clavin, provided the Lewis number used was the global one, extracted from the response of stretched flames, demonstrating that it was a property of the flame instead of the unburned mixture alone. It was 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. Original is an abstract.