INAUGURAL–DISSERTATION zur Erlangung der Doktorwürde der ...

4.1. One-dimensional Evaporating Water Spray in Nitrogen 59
3E+08
Number density [m ­3 ]
2.8E+08
2.6E+08
2.4E+08
2.2E+08
2E+08
1.8E+08
1.6E+08
1.4E+08
1.2E+08
Inhomogeneous
Homogeneous
Experiment
1E+08
8E+07
6E+07
0.14 0.28 0.42 0.56 0.7 0.84
Position [m]
0 1 2 3 4 5
Time [s]
Fig. 4.5: Homogeneous and inhomogeneous calculations of DQMOM.
Before carrying out simulations with an inhomogeneous system of DQMOM transport
Eq. (3.19), homogenous formulations of these equations, given by Eq. (3.20), are
simulated and the results are compared with inhomogeneous computations. Fig. 4.5
shows the computed and experimental profiles of number density at different cross sections
of the spray chamber with homogeneous and inhomogeneous system of DQMOM
equations (see Eq. (3.19)) for 80 kg/h water spray in nitrogen flowing with 0.078 m/s
velocity at 293 K. In the homogeneous results, the time axis of the model is matched
to experimental position through the droplet velocity. The number density decreases
along the spray axis due to droplet evaporation, and the predictions with inhomogeneous
formulation captures the physics of the spray more accurately [198, 200]. Thus,
the present work includes the numerical solutions of the inhomogeneous linear system,
which are formed through application of DQMOM in one physical dimension (axial
direction).
Figure 4.6 displays the results of Sauter mean diameter showing the comparison of
QMOM and DQMOM, where DQMOM results are shown for both lower and higher
Reynolds number. Here, the liquid flow rate is 80 kg/h. It can be seen that the
QMOM results strongly deviate from the experiment whereas DQMOM improves the
results of QMOM significantly even for lower droplet Reynolds numbers, and with
higher Reynolds number, which is the case in this simulations, the agreement between
DQMOM and experiment is very good [191]. A general intuitive question could be
”why the Sauter mean diameter increases in spite of evaporation in simulations as well
as the experiment?”. The answer is elaborated with an example by considering the
droplet size distribution of a water spray shown in Fig. 4.7, which displays the droplet