# Modeling the Formation of Urea-Water Sprays from an Air-Assisted Nozzle
## 3 Results and Discussion
### Evaluation of Droplet Velocities
The simulation results show a good correlation with the experimental data for all operating points, which suggests a predictivity of the model in the present range of the operating conditions. Droplets are also detected at a radial position of \(\pm\)4 mm in the simulation. Thus, those droplets are less-aligned to the center of the spray by the high gas velocity inside the gas jet. However, at a radial position of \(\pm\)5 mm, there are still no 8 \(\upmu\)m droplets detectable in the simulation. The velocity profiles of droplets with diameters greater than 15 \(\upmu\)m are illustrated in Figure 10. These droplets represent large droplets in the present spray. In this case, the comparability of the simulation with the experiment is dependent on the conformity of the droplet spectra, due to the dependence of the droplet velocity on the droplet size. The simulated velocity profile for OP 1 (Figure 10a) is in a good agreement with the experimentally observed velocities. The maximum velocity in the center of the spray is slightly underpredicted. For OP 2 (Figure 10b) and OP 3 (Figure 10c), the velocity profile is predicted significantly wider by the simulation than in the experiment. This is followed by an overestimation of the droplet velocity in the outer area of the jet. The lower density of the hot gas in OP 2 and OP 3 results in a reduction of the momentum transfer between the gas phase and the liquid phase. This results in an underestimation of the deacceleration of larger droplets in the outer area and of the acceleration of larger droplets in the center of the spray. Figure 8: Simulated and measured radial velocity profiles of droplets with a diameter of 5 \(\upmu\)m for OP 1 (**a**), OP 2 (**b**) and OP 3 (**c**). Figure 10: Simulated and measured radial profiles of the mean droplet velocity for all droplets with a diameter greater than 15 \(\upmu\)m for OP 1 (**a**), OP 2 (**b**) and OP 3 (**c**). Figure 9: Simulated and measured radial velocity profiles of droplets with a diameter of 8 \(\upmu\)m for OP 1 (**a**), OP 2 (**b**) and OP 3 (**c**). One must consider the initial velocity imprinted on the droplets in the simulation for a more detailed interpretation of these phenomena. All droplets are initialized with a constant velocity. Imprinting the corresponding velocity for each size class on the initial droplets according to Section 2.2.4 may improve the results. This way, small droplets will emerge from the nozzle with a higher velocity, while larger droplets will emerge with a lower velocity. This will enhance the momentum transfer between the gas phase and larger droplets due to a reduction of the momentum flux to smaller droplets due to smaller relative velocities. Nevertheless, the estimated droplet initial conditions, in combination with the tuning of the turbulence model, provide reasonable results for a wide range of droplet sizes that are in good agreement with the experimentally determined velocity profiles. In addition to the mean velocities, the turbulent fluctuations inside the spray are of interest, because they represent the basis for the turbulent dispersion of the droplets. Further on, the turbulence enhances the heat and mass transfers, which increase the evaporation rate of the spray. Therefore, the turbulence kinetic energy calculated by the turbulence model in the gas phase is compared with the experimentally estimated turbulence kinetic energy from the velocity fluctuations of the 5 \(\upmu\)m droplets. This droplet class can be used as an indicator for the turbulent fluctuations of the gas phase, as demonstrated in [17]. The radial profiles of the simulated and the experimentally evaluated turbulence kinetic energy at the first measurement position are depicted in Figure 11a. The shape of the two curves is qualitatively in a good agreement, while the absolute values in the center and the outer area of the spray are underestimated by the simulation.