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

4 Numerical Modeling and Simulation
1.4
s
Initial droplet diameter D 0
1.2
D 2 law
Simulation
Vaporization time τv
1.0
0.8
0.6
0.4
0.2
0.0
0 x 10 −6 50 x 10 −6 100 x 10 −6 150 x 10 −6 200 x 10 −6 m
Figure 4.8: Validation of Vaporization Time for Different Initial Droplet Diameters. The vaporization
time τ v is evaluated for water droplets as a function of the initial droplet
diameter D 0 .
stopped when the droplet diameter D drops below 0.1 % of D 0 . The D² law
and single droplet model show the same dependency on D 0 : The characteristic
time of vaporization τ v is proportional to D 2 0
, and the vaporization rate k is
approximately constant at a constant ambient temperature T ∞ . Generally, the
results are in good agreement. However, at large diameters, small differences
in k result in an increased absolute difference in τ v .
The droplet or, more precisely, the droplet surface temperature T S as a function
of the ambient temperature T ∞ is illustrated in Figure 4.9. The initial
droplet diameter D 0 is again kept constant at 100µm. As shown in Figure 4.9,
there is a roughly linear increase of T S with an increase of T ∞ , and both models
reproduce this behavior. The data points fit very well. The analytical
D² law predicts slightly higher droplet (surface) temperatures T S at high ambient
temperature T ∞ [298].
Generally, the analytical D² law is in good agreement with the numerical calculations
of the single droplet model. However, there are some discrepancies,
especially at high ambient temperature T ∞ : The vaporization time τ v is lower
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