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

4 Numerical Modeling and Simulation
Numerical simulations of single droplets were conducted in order to complement
the experimental findings of this study (cf. Figs. 1.1 and 1.2). Particularly,
the physical and chemical mechanisms promoting NO x emissions were
systematically investigated including a configuration to elucidate the effect of
partial droplet pre-vaporization. Therefore, an approach for modeling and
simulation of NO x generation in the gas phase surrounding single burning
droplets is presented.
Presuming spherical symmetry, with no gravity and no forced convection, the
governing equations are derived first. Then, the essentials of forced droplet ignition
by an external energy source are introduced. Special attention is given
to the modeling of NO x formation, as the numerical work focuses on the adequate
combination of detailed chemistry and the pre-vaporization process as
well as droplet combustion in hot exhaust gas. Both are technically relevant
in liquid fuel combustion. Simplifications are introduced and shown to be appropriate.
The model is validated, and finally the portability of the results from
the one-dimensional, spherically symmetric model to more complex droplet
arrays and cluster regimes is evaluated (Fig. 1.1).
4.1 Description of Involved Processes
The main phenomena characterizing droplet combustion are transport of
heat and mass as well as chemical reaction [443, 461]. A description of the
combustion in flows is, therefore, based upon fluid mechanics coupled with
the conservation laws of thermodynamics, including particular transport phenomena
of heat and mass transfer. Typical ways to describe droplets in a continuous
phase are the Euler-Lagrange and Euler-Euler methods. However, as
the droplets given are presumed to be at rest, both approaches are identical,
and it is not necessary to differentiate here. Still, the liquid phase of the droplet
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