# Modeling the Formation of Urea-Water Sprays from an Air-Assisted Nozzle
## 3 Results and Discussion
### Evaluation of Droplet Velocities  
The following section covers the investigation of the droplet velocities derived from the experiment and the simulation. Thereby, the quality and the predictivity of the computational method will be discussed. Starting from the simulation of the gas jet, the droplets are released into the computational domain according to the initial conditions derived in Section 2.2.4. The droplet velocities were evaluated at the first measurement position 50 mm downstream of the nozzle exit in the radial direction. A traverse system was applied in the experiment to shift the measurement volume, starting from -5 mm to 5 mm, in 1 mm steps through the spray (see Section 2.1). Due to the higher signal-to-noise ratio, less droplets are detectable in the range of 0 mm to 5 mm, leading to less statistical significance and an asymmetric velocity profile. To overcome this, and to improve the comparability with the almost symmetric simulation data, the average of both sides is calculated and mirrored at the center axis [17]. The spray data derived from the simulations is processed using a MATLAB(r) (R2019b, The MathWorks, Inc., Natick, MA, USA) routine. Thereby, the data comprises the properties of every parcel in the simulation domain exported at different time steps. At first, the data is filtered to extract the parcels in the experimental measurement volume at the corresponding measurement positions. Subsequently, the temporal averages of the properties of different droplet size classes are calculated. This procedure is similar to the evaluation of the experimental data, where the derived values represent the temporal average of the detected droplets from the recorded images. The evaluated velocities of the droplets with a diameter of 5 \(\upmu\)m for the three investigated operating points are illustrated in Figure 8. This size class is slightly above the smallest detectable droplet size of the experimental methodology and gives an insight into the gas velocity due to a small Stokes number. Overall, the simulation results are in a good agreement with the experiment for all three operating points. The best fit could be achieved for OP 2 (Figure 8b), which served as a reference point for the model calibration. Thus, the \(C_{e1}\) parameter of the turbulence model seems to be chosen appropriately. Starting from a maximum value at the center axis, the velocity decreases with the radial distance until it reaches the range of the gas velocity at \(\pm\)5 mm. For OP 1 (Figure 8a), the simulated curve is a little wider than experimentally observed, resulting in a reduced maximum in the center. This may result from an overestimation of the spreading rate of the gas jet due to a higher gas mass flow and an increase of the ambient density from 0.54 kg/m\({}^{3}\) (OP 2) to 1.08 kg/m\({}^{3}\) (OP 1). Further on, there are no 5 \(\upmu\)m droplets detected at the radial positions \(\pm\)4 mm and \(\pm\)5 mm in the simulation. This behavior is suspected to be a result of underestimated turbulent transport phenomena inside the spray, since the turbulent fluctuations are not resolved. Small droplets will follow the turbulent motion inside the spray plume, which distributes the droplets inside the spray. By means of RANS simulations, the turbulent dispersion is modeled as described in Section 2.2.3. due to the fact that RANS solutions provide an averaged flow field that contains no detailed information about the turbulent fluctuations. A deeper insight into the turbulent transport phenomena could be achieved using a large eddy simulation that resolves the largescale turbulence structures. A further validation of the simulation is performed using the measured droplets with a diameter of 8 \(\upmu\)m. These droplets possess a higher inertia and respond to an acceleration or a deacceleration of the gas flow with some delay. The radial velocity profiles of the droplets with a diameter of 8 \(\upmu\)m are illustrated in Figure 9 for the three investigated operating points.