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

4.7 Scope and Limitations of Single Droplet Combustion
In order to compare the amount of fuel spread homogeneously in the gas atmosphere
to the fuel given in the liquid droplets, each droplet is packed into a
cubical imaginary atmosphere of the side length 2L. Thus, the amount of fuel
in the droplet is calculated from
m l,fuel = ρ l π D 3 0
6 = D 3 0· 319.7 kg m−3 ,
and the mass of gaseous fuel in the surrounding atmosphere (φ=0.8) is
m g ,fuel = ρ g Y fuel (2L) 3 = D 3 0· 1038.3 kg m−3 .
The mass fraction Y fuel is an input value here and corresponds to the selected
equivalence ratio of φ=0.8 for the gas phase. Finally, the fraction of the above
amounts of fuel is calculated for the present case to
m g ,fuel
m l,fuel + m g ,fuel
= 0.7646.
Almost 80% of the fuel 7 have to be spread homogeneously in the gaseous state
in the imaginary atmosphere discussed to fulfill the condition presented in
Equation (4.69). Hence, one cannot speak of a “classical” spray anymore. For
droplets burning in a hot exhaust gas atmosphere, a superposition of ambient
NO x and droplet-caused NO x emissions is not directly justified. Heat transfer
from one droplet to another and competition for oxygen have to be considered,
as well [298]. Generally, the validity of the approach of superposing NO x
emissions depends on the prevailing group combustion and flame propagation
modes, as illustrated in Figures 2.4 and 2.5, respectively.
7 This value does not automatically correspond to droplet pre-vaporization with Ψ= 0.7646, as commonly understood,
because a homogeneous gas phase is presumed here. Furthermore, this estimation is derived for
droplets burning in an atmosphere of hot exhaust gas.
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