# Modeling the Formation of Urea-Water Sprays from an Air-Assisted Nozzle
## 2 Experimental and Numerical Methods
### Computational Method
#### 2.2.4 Initialization of the Liquid Phase  
As discussed in the previous subsections, the liquid urea-water droplets are modeled using a discrete droplet approach. The two-phase flow inside the mixing chamber of the atomizer and the subsequent primary breakup are not modeled in detail in the present numerical investigation. Instead, a suitable droplet diameter distribution, derived from experimental results 50 mm downstream of the atomizer, is imprinted on the initial parcels. These parcels are released into the computational domain 0.5 mm downstream of the nozzle exit over an area, which matches the cross section of the outflow channel of the atomizer with a diameter of 2 mm. This approach is chosen since the air-assisted atomizer is operated at high gas-to-liquid ratios greater than 0.4. Hence, it may be assumed that the two-phase flow inside of the discharge orifice is fully dispersed and leaves the atomizer in the form of droplets suspended in the atomizing gas [20]. The important conclusion is that a significant part of the primary atomization process may already be finished upstream of the nozzle exit. Furthermore, the gas temperature in the near nozzle region is dominated by the relatively cold gas jet of the atomizer. Therefore, the effect of evaporation on the droplet diameter distribution of the spray is assumed to be negligible up to the first measurement position downstream of the atomizer. For these reasons, the initialization of the experimentally determined droplet diameter distribution directly downstream of the nozzle exit is a promising strategy for modeling the spray formation and propagation of the air-assisted atomizer. Detailed experimental data is available 50 mm downstream of the atomizer. At this distance from the atomizer, spray characteristics were recorded at six equidistant positions in a radial direction within a range of 5 mm, which is schematically illustrated in Figure 4a. The corresponding droplet diameter distributions at different radial distances r from the center line of the spray cone are shown in Figure 4b. Obviously, the spray is characterized by a core region within a radial range of 2 mm from the center line featuring a narrow droplet size distribution. With increasing the radial distance from this core region, the size distribution is dominated by larger droplets. The modeling approach of the present study is to combine the experimental data into a spatially averaged droplet diameter distribution, which can be used to initialize parcels homogenously over the defined parcel release area 0.5 mm downstream of the nozzle exit. However, it is not straightforward to derive a spatially averaged droplet diameter distribution from the experimental results. First, it is important to consider that the representative area of the equidistant radial measurement positions increases with increasing radial distance from the center line of the spray cone (see Figure 4a). For this reason, the detected number of droplets at each measurement position is weighted with its representative area. Moreover, the difference between the experimentally determined volume distribution of droplets and the flux density distribution has to be taken into account, as described by [PERSON] [36]. This means that fast droplets are underrepresented in the droplet diameter distributions, which are shown in Figure 4b. Hence, the known correlation between droplet size and velocity is utilized to correct this biasing effect. The spray under investigation can generally be characterized by small droplets with high velocities in the core region and larger droplets with low velocities at the outer radial positions. Therefore, the two  
Figure 4: **(a)** Schematic of the experimental measurement positions and representative cross section areas of the spray cone. **(b)** Droplet diameter distributions measured at different radial distances from the center line of the spray, and **(c)** spatially averaged and corrected droplet diameter distributions.