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

4 Numerical Modeling and Simulation
since not only vaporization but also burning rates are relevant. Besides, the
impact of chemistry can also be included in this step of the validation process.
In an early, still ground-based work, Hall and Diederichsen [164] experimentally
investigated the burning characteristics of free and suspended droplets
of alkanes and alcohols for a pressure range of 1 to 20 bar. Law and Williams
[237] derive a burning rate of k = 0.93 mm 2 s −1 from those experiments for a n-
decane droplet of D 0 = 1.10 mm (with T ∞ = 293 K and p g = 1bar). Their own
model predicts values of 0.79 and 0.66 mm 2 s −1 for the respective cases with
and without natural convection. The work of Shaw et al. [394] represents one
of the first investigations conducted under microgravity conditions that is relevant
to the present study. Shaw et al. measured the quasi-steady burning rate
k of n-decane droplets in air at room temperature and atmospheric pressure,
ignited by a spark-ignition system. The reported k-values spread over a wide
range, and results are shown as subdivided into minimum, maximum, and orthogonal
least-square values – probably due to scattering. In later work, Shaw
and Dee [392] measured k = 0.78mm 2 s −1 for a burning C 10 H 22 droplet with
D 0 = 1.12mm at T ∞ = 298K. They also report unsteady flame stand-off ratios
for an ambient oxygen mole fraction of 0.21 combined with different diluents.
In the experimental work of Nakaya et al. [307, 309], an averaged k-value of
k = 0.72mm 2 s −1 is obtained for similar conditions. The corresponding instantaneous
burning rate fluctuates between values of 0.5 and 1.0 mm 2 s −1 .
Dietrich et al. [102] also performed microgravity experiments plus numerical
modeling. However, most experimental results are retrieved from atmospheres
with reduced pressure. Jackson and Avedisian [192] report a decreasing
tendency of the k-value with an increase in the initial droplet diameter for
n-heptane and 1-chloro-octane, both for suspended as well as free-floating
droplets. Xu et al. [465] extend this observation for n-decane towards an inverse
influence of the initial droplet diameter on the vaporization and burning
rates in cold and hot ambiences. The effects of flame radiation and soot
formation as well as soot oxidation are discussed in detail, including their impact
on the burning rates of droplets of different diameter. On the one hand,
the work of Xu et al. [465] naturally covers a wide range of ambient temperatures
and is therefore considered for validating the single droplet model of
the present study (cf. Tab. 4.1). On the other hand, the mentioned effects of
radiation and soot formation are not captured with the present model. Consequently,
a certain deviation from the measurements has to be expected. Fur-
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