Untitled - Aerobib - Universidad Politécnica de Madrid

11.5. FLAME STABILIZATION 275
Flame front
End of recirculation zone
Recirculation zone
Flame holder
Mixing zone
Propagating zone
Figure 11.2: Zones of a stabilized flame.
The theoretical study of this problem is very difficult. Several theories are
available whose development may be found in the works listed under Refs. [19]
through [21], but none of them has been experimentally confirmed. On the other
hand, the correlation between experimental results as presented by Longwell is very
difficult. At this stage it appears justified to perform the study by means of a dimensionless
analysis, searching for the significant variables and the relation existing
between them.
Inasmuch as we are far from the actual regime in which the compressibility
effect would appear, the dimensionless variable characteristic of the motion is the
Reynolds number referred to the velocity and state of the gases before the holder and
to a linear dimension of the same. The composition of the mixture is characterized by
the relationship between the fuel fraction and that corresponding to the stoichiometric
one. Finally, the variable we are trying to analyze is the blowing velocity or, if written
in dimensionless form although it is not generally necesary, this velocity referred to
the propagation velocity of the flame.
Zukoski and Marble [22] have performed a very interesting systematic analysis
on the experimental data available. A summary of this analysis appears in Figs. 11.3
and 11.4
Figure 11.3, corresponding to a circular flame holder as the one shown in
Fig. 11.2, gives the following: a) the influence of the Reynolds number on the maximum
blowing velocity of the flame, and b) the composition of the mixture for which
such velocity is reached, for a given Reynolds number.
Figure 11.4 shows the law of variation of the maximum blowing velocity as a
function of the Reynolds number for a set of experiments performed by other authors
with different types of flame holders.