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

5.2 Combustion of Partially Pre-Vaporized Droplets
Impact of Ignition Position on General Droplet Burning Behavior
The flame stand-off ratio, being a major characterization criterion of droplet
burning, by itself is a key indicator for the quality of droplet combustion. Thus,
it was also consulted in the verification of the present results. Cho and Dryer
[74], for instance, identified four different stages of droplet burning. In order
to compare the burning regimes of droplets of different sizes, the dimensionless
flame stand-off ratio ζ is employed (Eq. (5.5)). It correlates the actual
flame position r f with the respective droplet radius R. In this context, the
flame position r f is associated with the maximum specific heat release of the
reaction zone. The specific heat release, ∑ N
m=1 ˙ω mhm 0 , in turn, is part of the
energy conservation (Eq. (4.6) or (4.52)).
ζ= r f
R
(5.5)
Since the droplet combustion under consideration is initiated by forced ignition,
heat introduction and extraction play an essential role. However, as a
result of the verification process, both heat transfer processes only have a minor
impact on the overall droplet burning behavior. This is essential for the
general validity of the numerical results [297].
A representative evolution of the flame stand-off ratio ζ is plotted in
Figure 5.10 for both ignition approaches and a pre-vaporization rate of
Ψ= 0.3. It sheds light on the position of maximum specific heat release and
its dependency on the ignition position r m,in . The absolute times and, thus,
the progression of ζ are directly comparable in Figure 5.10. At the beginning,
the flame is located at the position of heat introduction with r m,in /R ≈ 18 for
“ignition fixed” and r m,in /R ≈ 14 for “ignition variable”. However, the flame ignited
closer to the droplet (“ignition variable”) stabilizes more rapidly (cf. also
Figs. 5.6 and 5.7). The accelerated ignition process in regions of increased
flammability allows a fast movement of the flame to a stable position ζ. This
faster flame stabilization, in turn, contributes to the radical difference in NO x
formation (cf. Figs. 5.8 and 5.9). After the two initial stages of vaporization and
unsteady burning, the flame stabilizes at a virtually constant position in either
case. Towards the end of droplet lifetime, the droplet shrinks more rapidly
than the flame position r f , which causes a rise of the flame stand-off ratio ζ.
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