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

4.7 Scope and Limitations of Single Droplet Combustion
be practicable to employ a higher degree of abstraction within the modeling
process, for instance for the processes in the boundary layer near the droplet
surface or in the chemistry modeling itself. In the latter case, the utilization
of single-step mechanisms is most common, which is supplemented by NO
post-processing if NO x emissions are of interest. Furthermore, tabulation of
chemistry or intermediate results is also a very common option for reducing
the computational costs.
Apart from the numerical study presented in Chapter 3.3, which is precise regarding
geometry but simplified regarding the physico-chemical processes,
Kikuchi et al. [205, 206] have also conducted numerical studies on droplet
array combustion. These studies focus on the flame spread mechanisms in
different temperature environments and for different dimensionless droplet
spacing ratios S/D. Baessler [31] conducted numerical studies on single
droplets with the alkane n-heptane (C 7 H 16 ) against the background of NO x
formation, with which he laid the foundation for the numerical work at hand.
His single droplet studies also supported the interpretation of his experimental
results on spray combustion [32]. Beck [38] and Beck et al. [39, 40, 41]
report on an advanced axisymmetric droplet-gas phase model that is capable
of predicting NO production as a function of the slip velocity between
droplet and gas phase, ambient temperature and pressure, and droplet size.
This two-dimensional single droplet model can be embedded into a primary
CFD context to reproduce the environment of gas turbine combustion chambers.
Parametrization and tabulation of a reduced set of model variables account
for the detailed processes of NO formation around single droplets in
this overall complex technical configuration. Beck [38] further advances the
hypothesis that single droplet combustion can be used as the basis of modeling
partially pre-vaporized droplets in lean spray flames.
For the case of droplets being ignited and burning in a hot atmosphere of exhaust
gas, the following analytical derivation helps in assessing the impact of
droplet interaction [298]: A first attempt to model sprays from single droplets
might be to superpose emissions due to droplets and due to ambient conditions.
6 The interaction between droplets would be neglected within this first
6 Ambient NO x emissions are basically a function of residence time of the ambient gas atmosphere at a particular
temperature level (cf. Fig. 2.7). On the other hand, droplet-caused NO x emissions are a somewhat theoretical
value and due to the presence of the droplet only. This value needs to be calculated by the difference of a
droplet atmosphere with and without droplet, thus canceling the impact of the atmosphere itself.
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