Structure and extinction of diffusion flames with flame radiation

Using droplet combustion as a model problem, and capitalizing on the temperature-sensitive nature of radiative heat transfer, the structure and extinction of diffusion flames with flame radiation is studied via multi-scale activation energy asymptotics. The flame structure analyzed consists of an O(∈) reaction zone embedded within an O(δ) radiation zone which in turn is situated in the O(1) diffusive-convective flow field, where ∈≪δ≪1. The analysis yields the structure equation for the reaction zone, which can be cast in the same form as that of Liñán's adiabatic diffusion flame problem such that his extinction results can be readily used. Present results show that radiative heat loss promotes flame extinction in general, as expected. Furthermore, it can also lead to the phenomenon of dual extinction turning points in which flame extinction due to reactant leakage and thereby kinetic limitation occurs not only for sufficiently small droplets, as is well established, but also for sufficiently large droplets as a result of excessive heat loss from the correspondingly large flame. Consequently there exist diffusive-reactive-radiative systems for which steady combustion is not possible for all droplet sizes. An estimation of the dimensional radiative extinction droplet size is also given for the sample system studied.