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

5.4 Influence of Droplet Size
The influence of droplet size on the emission index EI NOx can also be estimated
analytically, based on the definition of EI NOx . Here, the mass of nitrogen
oxides is given by
(
m NOx ∝ τ v V f exp − E )
a
, (5.9)
R T
and the mass of fuel by
m C10 H 22
∝ D 3 0 . (5.10)
As stated in the D² law, the vaporization time τ v is proportional to D 2 0 , where
D 0 is taken as characteristic length (Eq. (4.68)). The volume of the flame V f depends
on the area of a spherical shell (∝ D 2 0 ) and the thickness of the flame δ f .
The exponential factor results from the Arrhenius law (Eq. (4.18)). Assuming
a constant thickness δ f and neglecting differences in the temperature profile
yields
EI NOx ∝ D 2 0 D 2 0
D 3 0
= D 0 . (5.11)
Hence, the estimated emission index goes linear with the initial droplet diameter
D 0 , which is consistent with the numerical results of Figure 5.21 [298].
These numerical and analytical findings are supported by the experimental
results on droplet arrays (Fig. 5.22). The TEXNOX drop tower campaign allowed
for a systematic variation of the initial droplet diameter D 0 in combination
with the inter-droplet distance S, while keeping the total length of the
droplet array fixed to L = 72 mm (cf. Tabs. 3.1 and B.1). Here, the linear trend
of the NO x emissions becomes apparent by varying the initial droplet diameter
D 0 . In addition to the relatively large database for S = 4.5mm, the other
data fit in well, also indicating a linear trend. Furthermore, there is a consistent
decrease in NO x formation due to an increase in inter-droplet distance S.
These different levels of NO x formation are a result of a varying interaction of
the sphere of influence of every droplet with its neighbors. If the parameter
S is small, the specific energy density increases and the specific heat losses to
the environment decrease. Thus, there will be a rise in temperature as well as
in NO x production. The absolute NO x values are comparable for Figures 5.21
and 5.22, but the zero-intercept is different, which is due mainly to the significant
heat losses of the combustion chamber during the experiment runs.
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