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

4.6 Model Validation
Figure 4.7 depicts the vaporization rate k as a function of the ambient temperature
T ∞ . Crosses show the analytical solutions, and diamonds mark the values
calculated with the single droplet model that is implemented in the software
package Cosilab ® . The initial droplet diameter D 0 is set to 100µm for all
cases here. Furthermore, the initial droplet temperature T l,0 is set close to the
expected value for the numerical calculations to reduce effects of heat transfer
into and in the droplet. Analytical and numerical solutions correspond
very well. Both data sets show a similar tendency. The difference is small, especially
at a low ambient temperature T ∞ . With increasing temperature, the
discrepancy in the results increases as well.
The characteristic time of vaporization
τ v = D 2 0
k
(4.68)
is the time until all liquid is vaporized. It is presented in Figure 4.8 as a function
of the initial droplet diameter D 0 for the range of 25 to 150µm. The ambient
temperature is set to T ∞ = 473.15 K here. The numerical calculations are
8 x 10 −8
m 2 s −1
D 2 law
Simulation
Vaporization rate k
6 x 10 −8
4 x 10 −8
2 x 10 −8
0 x 10 −8
300 400 500 600 700 800 K
Ambient temperature T ∞
Figure 4.7: Validation of Vaporization Rate for Different Ambient Temperature Levels. The
vaporization rate k is evaluated for water droplets at a varying ambient temperature
T ∞ [298].
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