Asymptotic analysis of outwardly propagating spherical flames

Asymptotic analysis is conducted for outwardly propagating spherical flames with large activation energy. The spherical flame structure consists of the preheat zone, reaction zone, and equilibrium zone. Analytical solutions are separately obtained in these three zones and then asymptotically matched. In the asymptotic analysis, we derive a correlation describing the spherical flame temperature and propagation speed changing with the flame radius. This correlation is compared with previous results derived in the limit of infinite value of activation energy. Based on this correlation, the properties of spherical flame propagation are investigated and the effects of Lewis number on spherical flame propagation speed and extinction stretch rate are assessed. Moreover, the accuracy and performance of different models used in the spherical flame method are examined. It is found that in order to get accurate laminar flame speed and Markstein length, non-linear models should be used.