Asymptotic theory of flame extinction with surface radiation

In order to further understand the general structure and extinction characteristics of diffusion and premixed flames in the presence of heat loss, and their dependence on the relative rates of reaction, transport, and loss, the heterogeneous combustion with surface radiative heat loss from either a bipropellant in an oxidizing counterflow or a monopropellant in an inert counterflow have been studied via activation energy asymptotics. The analysis yields solutions for the flame temperature, mass burning rate, and flamefront standoff distance. The structure equations for the reaction zone of both the diffusion flame and the premixed flame with subadiabatic downstream boundary are, respectively, found to be canonically identical to the near-equilibrium and premixed flame regimes of Liñán's generalized analysis of the diffusion flame structure. The actual flame response to stretch rate variations, however, exhibits a dual extinction turning point behavior in that flame extinction occurs not only for sufficiently large stretch rates and minimal radiative heat loss, but also for sufficiently small stretch rates and extensive heat loss. Consequently, there exist systems for which steady combustion is not possible for all stretch rates. For the premixed flame with adiabatic downstream boundary, extinction occurs only for situations with small stretch rates and extensive heat loss.