On the Formation of Nitrogen Oxides During the Combustion of ...

2 Combustion Theory
combustion, external group combustion, internal group combustion, and single
droplet combustion. 9 The abscissa S denotes the non-dimensional separation
between the droplets and ordinate N the total number of droplets
in the cloud. In addition to the classification given in Figure 2.4, Chiu et
al. [72, 73] found that the so-called internal group combustion mode occured
in the range of 1×10 −2 < G < 1, depending on fuel properties, stoichiometry,
and conditions of the environment. The group behavior of the droplet
cloud produces a rich, non-flammable mixture, and thus inhibits ignition in
the vicinity of an individual droplet. In general, an increase in G results in an
increase of flame size and characteristic burning time. According to Suzuki
and Chiu [427], the increase in burning time due to group combustion is also
conjectured to be a possible mechanism for incomplete combustion.
As far as droplet setups investigated within the present study are concerned,
the group combustion number calculates to G ≈ 0.05 for single droplets and
0.6< G < 7.3 for droplet arrays. This includes an estimate of Gogos et al. [153]
on the initial droplet Reynolds number due to the movement of the droplet
setup into the preheated combustion chamber. The scope of G covered by the
present study can be allocated at the lower left corner of Figure 2.4 but does
not fully fit into the area predefined by Chiu et al. [72, 73] as a result of an
overall small number of droplets and a quiescent ambient environment.
A different classification was proposed by Umemura and coworkers [446, 447]
with respect to droplet behavior during flame spread over a linear droplet array.
Five different flame propagation modes were theoretically predicted, as
shown in Figure 2.5. The appearance of these modes depends on two characteristic
parameters: the non-dimensional gas temperature R s T ∞ /∆h v and the
non-dimensional inter-droplet distance S/D 0 . Most essential to flame propagation
are Mode I, II, and III. In the case of Mode I, a partially premixed
flame propagates through a flammable fuel-air mixture, rapidly enclosing
non-burning droplets that start to vaporize abruptly due to the sudden heat
transfer. In the case of Mode II, the flame front at the “leading” droplet accelerates
vaporization of a close-by droplet until ignition and flame spread. The
ignited droplet is immediately enclosed in an envelope flame and burns as a
diffusion flame in the group combustion mode. In the case of Mode III, the
sequence is identical to Mode II until ignition. However, the droplet ignited
9 Annamalai et al. [19, 20] use a breakdown into six categories and a slightly different terminology.
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