Untitled - Aerobib - Universidad Politécnica de Madrid

278 CHAPTER 11. SIMILARITY IN COMBUSTION. APPLICATIONS
11.1 in which the constancy of the ignition time may be clearly seen. Hence, the
characteristic dimensionless group determining the blowing velocity of the flame is
Damköhler’s first parameter
and blowing velocity is reached for Da 1 = 1.
Da 1 = L/V
τ i
, (11.57)
The advantage of this study lies on the fact that it separates two variables. One,
being mechanical, depends only on the conditions of motion, whereas the other, being
physico-chemical, depends exclusively on the composition and state of the mixture.
Fig. 11.5, from Ref. [17], shows the law of variation for τ i as a function of the mixture
composition for a typical case.
1.8
1.6
Characteristic ignition time (ms)
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
φ, Equivalence ratio
Figure 11.5: Ignition time as a function of the composition of the mixture (see [17] for more
details).
With reference to the mechanical time, the problem reduces to a study of the
relationship between the length L of the wake and the characteristics of the holder.
For a great number of holders it has been proved that, in the supercritical regime, this
relation is of the form
L ∼ D 1/2 , (11.58)
which explains the law of variation of V with D observed by experimentation.
There exist, however, other cases for which the following condition is satisfied
L ∼ D, (11.59)