# Modeling the Formation of Urea-Water Sprays from an Air-Assisted Nozzle
## 2 Experimental and Numerical Methods
### Experimental Setup  
A picture of the test rig and the measurement technique is shown in Figure 1a in order to illustrate the experimental setup. The test rig was designed for experimental studies at elevated temperature and pressure conditions covering pre- and post-turbo injection scenarios of the urea-water solution. The atomizer is arranged on the center axis of a pipe flow, which is schematically illustrated in Figure 1b. This generic design was chosen in order to avoid droplet-wall interaction over a long distance downstream of the atomizer. Furthermore, the generic setup provides well-defined boundary conditions, which ensures the applicability of the experimental data for the validation of numerical simulations. The size and velocity of individual droplets were obtained using microscopic imaging diagnostics, which have been developed to handle the challenging thermodynamic conditions of the hot gas flow around the atomizer [17]. Moreover, a suitable calibration procedure was developed in order to  
Figure 1: (**a**) Picture of the experimental setup for investigation of urea-water sprays under high temperature and pressure conditions and (**b**) the schematic of the test section and the utilized diagnostics adapted from [17]. determine the droplet size, with an uncertainty in the range of the pixel resolution of 0.75 \(\upmu\)m [18]. This provides the basis for deriving the uncertainty of the velocity determination from the shift of one pixel within the time between two images of 0.5 \(\upmu\)s. Hence, the experimental uncertainty of determining the droplet velocity is estimated to be 1.5 m/s. One merit of this measurement technique is the ability to change the measurement position by simply moving the camera in the direction of its optical axis, while the illumination can stay in a fixed position, as illustrated in Figure 1b. By doing so, detailed correlations of the droplet diameter and velocity were recorded in the proximity of the atomizer [17; 18]. These spray characteristics were used to derive the droplet starting conditions for the numerical simulations and to validate the numerical methodology for predicting the spray formation process. The air-assisted atomizer used in the experiments was manufactured by CALDYN Apparatebau GmbH (Ettlingen, Germany). This atomizer employs the effervescent atomization principle, which involves a two-phase flow upstream of the discharge orifice [20]. In Figure 2, a simplified geometry of the nozzle illustrates the working principle. According to the review on effervescent atomization by [PERSON] et al. [20], the two main functions of the two-phase flow inside of the atomizer are the lower effective discharge orifice cross section for the liquid phase and the rapidly expanding gas phase as soon as the bubbly flow leaves the nozzle exit. In particular, the rapidly expanding gas enables a fine atomization at relatively low injection pressures in comparison to other methods of atomization. In the context of exhaust gas aftertreatment systems using SCR technology, a fine atomization is indispensable to ensure a fast and homogeneous conversion of the urea-water solution to ammonia and to avoid the formation of deposits. In addition, the relatively large orifice diameter may be helpful to prevent clogging problems of the atomizer. The decisive advantage of the effervescent atomizer for the experimental setup is a narrow spray angle and, at the same time, a very fine atomization. In combination with the geometry of the configuration, a significant amount of the injected urea-water solution will evaporate before the wall contact of the spray droplets becomes relevant. Hence, it is possible to extract detailed evaporation characteristics of the urea-water spray at different distances downstream of the atomizer, which is discussed in detail in a previous study of [PERSON] et al. [17]. This experimental data has been employed to evaluate the numerical predictions of the evaporation characteristics in the present study.