Review of Theories Currently Being Used to Model Steady Plane Flames on Flame-Holders

摘要

The stability of burner flames for arbitrary Lewis number is considered on the basis of large activation energy modelling. Previous leading-order-only approaches are now extended to second order in theta (sub 1) (the inverse activation energy). The assumption that the unsteady perturbations are small (order epsilon) means that the distinguished limit implicit in the product must be discussed. Different governing equations (and in particular the inner zone equation) are obtained in the two cases, theta (sub 1) epsilon yields 0 and theta (sub 1) epsilon yields infinity. There are two important complex frequency relations governing the behavior of flames near burners and it is readily seen that the now classical free flame dispersion relation is derived as a special case for flames with infinite stand-off distance, and Lewis number close to unity.