INAUGURAL–DISSERTATION zur Erlangung der Doktorwürde der ...

4.1. One-dimensional Evaporating Water Spray in Nitrogen 57
Surface frequency [µm ­1 ]
0.12
1
0.1
0.08
0.06
0.04
0.02
0
0
10 1 10 2 10 3
Droplet diameter [µm]
0.8
0.6
0.4
0.2
Cumulative surface frequency [µm ­1 ]
Surface frequency [µm ­1 ]
0.12
1
0.1
0.08
0.06
0.04
0.02
0
0
10 1 10 2 10 3
Droplet diameter [µm]
0.8
0.6
0.4
0.2
Cumulative surface frequency [µm ­1 ]
Fig. 4.3: Experimental surface frequency distribution at cross section 0.14 m (left) and
0.54 m (right) away from the nozzle exit.
experiments, and they are calculated using the relation
√
ρ l − ρ g
v = 1.74 gd (4.1)
ρ g
given by Stieß [197], where d is droplet diameter, ρ l and ρ g are the liquid and gas
densities, respectively, and g is the acceleration due to gravity. This relation is the
estimate of the terminal velocity of the droplets [197], and it is proven to give accurate
value of the droplet velocity [191, 198].
The moment sets are calculated by means
of these droplet radius, velocity and surface frequency, which are used as initial data
for QMOM whereas for DQMOM these moments are in turn used to calculate the
weights (representing surface frequencies), radii and velocities through the Wheeler
algorithm [136] as explained in Chapter 3. These data (weights, radii and velocities)
are then used as initial data to start the computations.
Tab. 4.1 lists these initial
values with three-node approximation for 80 kg/h and 150 kg/h water inflow rate.
Tab. 4.1: Initial weights and abscissas
Liquid flow rate [kg/h] Weights [(µm) −1 ] Radii [µm] Velocities [m/s]
80 0.638 24.424 1.09
0.276 86.432 1.94
0.086 143.29 2.76
150 0.733 21.739 1.03
0.223 79.706 1.84
0.044 128.350 2.72