  The general relation between ignition and deflagration analyses was studied
theoretically and computationally. Simple analysis showed that the temporal
evolutions of normalized fuel mass fraction and the normalized temperature in a
0D homogeneous ignition are equivalent to the spatial evolutions of those in a
1D laminar premixed flame at Lewis number of unity if a spatio-temporal
transformation of the flame is applied. Furthermore, computations showed that
the degree of reduction in normalized fuel mass fraction in the preheat zone
was found to be in the following order: when the Lewis number is less than
unity, when the Lewis number is unity (= ignition), and when the Lewis number
is greater than unity. This suggested that ignition in the preheat zone near
the explosive transition can only occur for 1D laminar premixed flames with
Lewis number greater than unity. In summary, the characteristic times of
ignition and flame propagation can be of the same order of magnitude in
premixed gases compressed by piston in engines or shock waves, and thus the
Lewis number determines the existence of premixed flame structure under such
conditions.
