# Modeling the Formation of Urea-Water Sprays from an Air-Assisted Nozzle
## 3 Results and Discussion
### Characteristics of the Gas Jet  
The simulations of the gas jet were carried out on the computational mesh shown in Figure 3. Before the gas jet is initialized, the hot gas flow in the test bench was calculated to provide a well-converged flow field. During these flow simulations, the time step is increased from 1 us to 10 us in order to speed up the calculation time. A resulting flow field is shown exemplarily for OP 2 in Figure 6a, whereby the gas velocity is illustrated on a plane cut through the center axis of the test bench. Downstream of the inlet of the computational domain, the gas is accelerated in the tapered cross section to velocities over 100 m/s. Passing the injector shaft mounted in the center of the pipe, the flow detaches from the injector cone and starts to recombine downstream of the nozzle exit. At the first measurement position, at a distance of 50 mm downstream, the nozzle the flow is still not completely recombined, resulting in the radial profiles of the gas velocity shown in Figure 6b. For OP 2, the velocity decreases from 100 m/s in the outer area to 60 m/s in the center of the pipe, which has to be considered for the evaluation of the gas jet and the spray characteristics. The velocity reduction is, for all operating points, in the range of 40%. Obviously, this velocity gradient is followed by the formation of a shear layer, which locally increases the turbulence. This behavior is clarified by the radial profiles of the turbulence kinetic energy depicted in Figure 6c. Thereby, two peaks are detectable \(\pm\)3 mm away from the center axis, indicating the position of the shear layer. An unchanged position of these peaks can be found in all three operating points, even if the flow velocity and the turbulence level are completely different. The reason for these phenomena is the preservation of the Reynolds number by means of choosing the conditions for the hot gas flow by [PERSON] et al. [17]. Starting from the simulations of the hot gas flow, the gas jet is initialized in the outflow channel of the nozzle. The gas flow inside the channel is in a subsonic state and accelerates to supersonic speed downstream of the nozzle exit, which is characteristic for under-expanded nozzles. Thereby, flow velocities over 400 m/s are present in the vicinity of the nozzle exit. The flow velocity on a plane cut through the center axis of the test bench and an isoline representing a Mach number (Ma) of one  
Figure 6: (**a**) Velocity of the bulk gas flow for OP 2 shown on a plane cut through the center line of the test rig. (**b**) Gas velocity and (**c**) turbulence kinetic energy over the radial position for the three selected operating points at the first measurement position downstream of the atomizer. are depicted in Figure 7a. The expanding gas jet preserves a supersonic core up to 25 mm downstream the nozzle. Further downstream of the nozzle, the jet is rapidly decelerated on its center axis by radial momentum flux, leading to the widening of the radial velocity profile. The spreading rate determines the resulting velocity profile at the first measurement position and is strongly influenced by the choice of the turbulence model and the discretization. For the investigation of the impact of the used k-\(\varepsilon\) turbulence model on the spreading rate, the model parameter \(C_{\varepsilon 1}\), which controls the influence of the production term P in the transport equation of the dissipation rate, is adjusted, as already discussed in Section 2.2.2. In Figure 7b, the velocity profiles for three different values of the \(C_{\varepsilon 1}\) parameter are plotted for OP 2. Obviously, the spreading rate of the jet is very sensitive to this parameter. Higher \(C_{\varepsilon 1}\) values lead to a smaller spreading rate and a narrower profile. Lower values result in a wider velocity profile.