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

5 Results
atmosphere of Figure 5.1 is based on an equivalence ratio of φ= 0.8, providing
well-burned intermediate combustion products with sufficient oxygen remaining
for the ensuing droplet combustion. In the present case, the boundary
conditions at r = R ∞ are set to zero gradients (see Chap. 4.2.4). Otherwise
it would be difficult to account for any exhaust gas formation due to possible
concentration gradients at the outer boundary. The initial conditions of
T 0 and Y m,0 are set uniformly in the gas phase, and thus yield block profiles.
After droplet ignition and flame stabilization, the flame diameter slowly increases
in size, before it drastically decreases in response to the approaching
droplet burnout. Nitric oxide (NO) peaks in a narrow region in the proximity
of the flame front and diffuses into the regions on either side of the flame
front. Moreover, the high ambient temperature of T ∞ = 2080 K is responsible
for the non-zero NO mole fraction throughout the computational domain at
t = 0s as well as for a significant positive offset during the succeeding time
steps [298].
The exhaust gas atmosphere for itself has a high temperature and noticeable
concentrations of N 2 , O 2 , and atomic oxygen (O), which already leads to a considerable
formation of thermal NO. For studying the contribution of the burning
droplet to the total NO x formation, the effects resulting exclusively from
droplet combustion need to be isolated. Hence, the difference in production
of NO x is evaluated between exhaust gas atmospheres with and without a
droplet (cf. Fig. 5.1 and Eq. (5.1)). The latter setup acts as the reference for this
purpose. By subtracting the spatially integrated NO x production rates of this
reference from the results of the regular simulation, the actual NO x emissions
can be disclosed as they are generated by the presence of the droplet in the
hot exhaust gas atmosphere,
m NOx ,droplet= m NOx ,tot− m NOx ,atm. (5.1)
The total mass produced, m NOx ,tot, is obtained by integration in line with
Equation (4.45):
∫ tend
∫ R∞
m NOx ,tot=
t 0 R
˙ω NOx ,tot 4πr 2 dr dt. (5.2)
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