# Modeling the Formation of Urea-Water Sprays from an Air-Assisted Nozzle
## 4 Conclusions  
In the present study, an air-assisted nozzle for the atomization of UWS has been modeled using a commercial CFD code. The model comprises the geometry of the hot gas test bench applied for the optical investigations that have provided the experimental droplet data to validate the model. The outflow channel of the atomizer is included in the computational mesh to correctly depict the boundary conditions of the emerging gas jet. A detailed modeling of the gas jet has been performed by an appropriate meshing strategy, with a cell size of 125 \(\upmu\)m in the near nozzle region and an adjustment of the turbulence model to correct the spreading rate of the gas jet. A suitable droplet spectrum is derived from experimental results 50 mm downstream of the atomizer and imprinted on the initial droplets directly downstream of the nozzle exit. The initial velocity of the droplets is estimated by means of an analytical investigation of the two-phase flow inside the nozzle. Moreover, the numerical simulation is complemented by the WAVE breakup model in order to control the largest droplet size of the spray in regions of strong aerodynamic forces. The experimental data is determined from microscopic shadowgraphs and provides correlations of the droplet size, velocity and radial position inside the spray plume. This data is used for a detailed validation of the CFD model. Thereby, the velocity profile of the droplets 50 mm downstream of the nozzle exit could be predicted quite accurately by the model for three different operating points with varying ambient conditions and compressed air mass flows. Thus, the model is able to capture the effects of the ambient density and initial momentum flux. The droplet sizes were also evaluated in the radial direction by the characteristic parameters D\({}_{10}\), D\({}_{32}\) and DV\({}_{90}\). The radial profile of the DV\({}_{90}\), which is quite sensitive to a small amount of large droplets, is predicted very well, indicating an appropriate selection of the initial conditions of the droplets and a good performance of the breakup model. Further on, this proves the suitability of the application of the modeling approach, which is also used in the case of cavitating diesel nozzles, in air-assisted atomizers. In contrast to the experimental results, a considerable amount of small droplets is missing in the outer area of the spray. A deeper analysis of the droplet distribution inside the spray suggests an underestimation of the turbulent transport phenomena. This is confirmed by an investigation of the radial fluctuations of the droplet velocity, which are much lower in the simulation than in the experiment. As a consequence, the turbulent dispersion may be underestimated. However, to finally assess this topic further investigations of the turbulent dispersion model and the influence of the initial conditions of the droplets on the turbulent dispersion are necessary. An analysis of the formation of the initial droplets by the process of a primary breakup would require a detailed simulation of the mixing chamber, which may be done by applying a large eddy simulation and a volume-of-fluid method. Further on, the LES is able to provide a deeper insight  
Figure 17: Droplet size at the limit of water evaporation as a function of the axial distance from the nozzle for the three investigated operating points. into the turbulent flow phenomena inside the spray. This could provide a more detailed basis for the evaluation and the adaption of the turbulent dispersion models to improve the RANS results. Further investigations will be carried out to verify the droplet evaporation calculated by the CFD model. The experimental data further downstream of the nozzle will serve as a good starting point for the evaluation of the evaporation model. The first steps have already been taken to investigate the transition from water evaporation to urea thermolysis, serving promising results.