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

5.1 Droplets in Exhaust Gas Atmosphere
Assuming homogeneous conditions within the reference domain, the NO x
production of the mere exhaust gas atmosphere calculates to
m NOx ,atm=
∫ tend
t 0
˙ω NOx ,atm
4
3 πR 3 ∞ dt. (5.3)
There are no partial derivatives in space in Equation (5.3), and the NO x production
rate ˙ω NOx ,atm can be taken directly from the outer gas phase boundary
if it remains unimpaired by droplet combustion. Besides, the droplet volume
does not need to be subtracted from the volume of the atmosphere in
Equation (5.3) because, by definition, the impact of the presence of the droplet
is investigated. This convention even includes small savings in NO x production
for the volume occupied by the liquid phase of the droplet and its boundary
layer (see also Fig. 5.1).
This whole approach and the associated data processing are indicated by the
term “Droplet NO x ” in the legend of Figure 5.2 below. The term “ref. droplet
mass” implies that the initial mass of the fuel droplet is taken as a reference
when calculating the emission index of NO x , EI NOx , but not the reacting fuel
mass (cf. Fig. 5.3).
The temperature and, in particular, the amount of the remaining oxygen in a
laminar premixed flame are a function of the equivalence ratio φ. While the
temperature of the exhaust gas increases with an increase in φ (see Fig. 5.2),
a continuously decreasing amount of oxygen remains available in the exhaust
gas atmosphere. Consequently, only lean combustion can be considered here,
which is φ ∈ [0,1]. Still, both parameters have a significant influence on
droplet combustion. On the one hand, a high ambient temperature leads to
an even higher flame temperature, and thus promotes NO production (see
also Fig. 2.7). On the other hand, there is a decreasing amount of oxygen and
an increasing fraction of thermal ballast stemming from the initial premixed
flame with an increase in φ. These reduce the adiabatic flame temperature,
thereby retarding the NO x formation process. These two effects are conflicting
here, and the result becomes apparent in Figure 5.2 with the maximum
temperature during droplet combustion approaching the initial temperature
before droplet combustion: For exhaust gas under stoichiometric conditions
(φ= 1.0), no droplet combustion could even occur in the second, main step
because there is no oxidizer left. In a first estimate, all NO x is formed in the
exhaust gas atmosphere and none due to the presence of the droplet. In the
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