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

4.3 Modeling of Ignition
In the end, the study of nitrogen oxide emissions is only one representative
example of how results can be sensitive against the ignition position [297].
Generally, the pre-vaporization of fuel droplets is carried out at temperatures
far below the auto-ignition temperature of the respective fuel. In such a low
temperature atmosphere, it is necessary to initiate combustion by some kind
of forced ignition. A plausible modeling of this ignition process is essential
in the case of spherically symmetric single droplet combustion. It has to be
correlated to the ignition and burning of fuel sprays. In the experiments of
Baessler [31], pre-vaporized fuel sprays were ignited while passing by a hot
wire. Here, the hot wire raises the local temperature and acts as an energy
source to the atmosphere of fuel droplets passing by. A different mechanism
of droplet ignition results from droplet interaction in fuel sprays. There, the
droplets are ignited by flame spread from close-by burning droplets. 1 The
heat release due to the combustion of a neighboring droplet can be considered
as an energy source for a particular single droplet. Roth et al. [366] experimentally
studied this type of flame spread in monosized droplet streams,
forming planar droplet arrays and igniting them by a hot wire. Experimental
and numerical studies of flame spread in one-dimensional droplet arrays under
microgravity conditions can also be found in Kikuchi et al. [205, 206] and
Mikami et al. [282, 283].
A method to model the ignition of single droplets with spherical symmetry
was presented by Moesl et al. [297, 298]. The model allows for heat introduction
and heat extraction by prescribing the distribution of a specific heat
source in the gas phase of the computational domain. Both experimental
cases of droplet ignition and flame spread can be approximated by this model.
When only introducing heat (no heat extraction), this model is related to the
experimental case of a droplet passing by an ignition source. If heat introduction
and extraction are applied, the modeling is rather correlated to the flame
spread in droplet arrays. In the latter case, the heat introduction corresponds
to the heat release of a burning neighboring droplet, whereas the heat extraction
models the heat flow to another close-by but non-burning droplet.
Similar to the work of Dietrich et al. [102], the heat source is modeled by a
source term in the energy equation. However, the energy profile is chosen
1 In general, diffusive transport maintains the flame propagation. It is responsible for the mixing of vaporized
fuel, air, and hot exhaust gas until the onset of ignition.
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