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

Table D.3: Progression of Droplet Vaporization (t Ψ = 18s) [208, 317–319].
Pre-vaporization Droplet diameter D(t Ψ ) in mm Pre-vaporization rate Ψ (Eq. (1.1))
time t Ψ in s Method No. 1 Method No. 2 Method No. 1 Method No. 2
0 1.5500 1.6084 0.0000 0.0000
1 1.5633 1.6225 −0.0260 −0.0266
2 1.5510 1.6268 −0.0020 −0.0347
3 1.5642 1.6288 −0.0277 −0.0386
4 1.5557 1.6227 −0.0110 −0.0270
5 1.5484 1.6164 0.0030 −0.0150
6 1.5371 1.5981 0.0248 0.0191
7 1.5362 1.5864 0.0265 0.0404
8 1.5065 1.5710 0.0819 0.0681
9 1.4938 1.5528 0.1048 0.1001
10 1.4792 1.5359 0.1308 0.1292
11 1.4437 1.5128 0.1920 0.1679
12 1.4267 1.4892 0.2202 0.2063
13 1.4072 1.4653 0.2517 0.2439
14 1.3780 1.4343 0.2974 0.2908
15 1.3500 1.4076 0.3393 0.3297
16 1.3346 1.3773 0.3616 0.3720
17 1.3173 1.3502 0.3862 0.4084
18 1.2983 1.3190 0.4124 0.4485
alent droplet diameter, defined by (a 2 b)/3, where a and b are the minor and
major axis of the droplet, respectively. The major difference between “Method
No. 1” and “Method No. 2” is the filter that distinguishes between droplet and
background. The droplet diameter D(t Ψ ) increases during the first 2 to 3s, and
the associated Ψ-value appears to be negative for up to 5s due to the thermal
expansion of the droplet. 1 This is a well-documented behavior for the initial
period of droplet heating [210, 307, 309, 312, 465]. The droplet diameter
squared increases accordingly, as illustrated in Figure D.5. Considering data
fluctuation and reproducibility as well as the deviation from pre-estimated
figures, Method No. 2 shows a higher consistency than Method No. 1. Hence,
it is chosen for data analysis throughout this work. The vaporization rate
for steady-state conditions (t Ψ ≥ 7s) calculates to k = 0.075±0.025 mm 2 s −1 .
Figure D.6 shows corresponding results from the drop tower campaign.
1 The experimental results discussed in Chapter 5 are compensated for this effect according to Equation (5.4).
In this context, Chin and Lefebvre [70] studied the role of the heat-up period in droplet evaporation in an
analytical way.
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