INAUGURAL–DISSERTATION zur Erlangung der Doktorwürde der ...

4.1. One-dimensional Evaporating Water Spray in Nitrogen 61
Tab. 4.2: Droplet size distribution of water spray
d(t = 0 s) [µm] f [(µm) −1 ] d(t = 1 s) [µm] d(t = 50 s) [µm] ]
10.643 0.409 0.000 0.000
12.913 4.091 0.000 0.000
15.588 11.434 0.000 0.000
18.745 11.762 0.000 0.000
22.468 8.472 0.000 0.000
26.858 7.112 0.000 0.000
32.037 7.093 5.138 0.000
38.145 7.481 21.332 0.000
45.350 7.304 32.506 0.000
53.848 6.609 43.584 0.000
63.870 5.439 55.492 0.000
75.692 4.491 68.770 0.000
89.635 4.073 83.872 0.000
106.080 4.319 101.257 0.000
125.478 4.574 121.427 0.000
148.355 3.579 144.946 0.000
175.337 1.490 172.462 0.000
207.163 0.255 204.735 0.000
244.697 0.015 242.646 99.381
The k value is usually estimated from the material properties such as density, diffusivity,
etc., and in general, it has a value in the range of 10 −7 to 10 −11 . Just for the sake of
explanation, k is assumed to be 1.0E-09 m 2 /s. The change in the droplet diameter is
computed at t = 1 s using d 2 law is given in Tab. 4.2, see the third column. Comparing
the values of droplet diameter at t = 0 s and t = 1 s, it shows that the droplet diameter
decreases and lower size droplets vanish. Using these data, the computed d 32 at t =
1 s is 117.126 µm, which shows an increase from initial value. This increase continues
till certain evaporation time (see last column in Tab. 4.2), whereupon the Sauter mean
diameter starts to decrease because most of the smaller size droplets vanish and only
few droplets have finite size. The Sauter mean diameter of this distribution decreases
to 99.381 µm after 50 s of d 2 law evaporation rate (see the last column in Tab. 4.2).
Figure 4.8 shows the plots of droplet velocities subjected to only drag force (left),
and drag force with gravity (right) for three different sized droplets, respectively. In
case of only drag caused by the surrounding gas with initial velocity of 0.078 m/s (experimental
value), the velocity decreases at first due to drag force and later the droplets