## 5 Numerical Results and Experimental Validation  
As already stated in the previous section, the AdBlue injected at moderate pressure results in a weakly atomized spray that interacts with the SCR wall boundary especially the lower SCR wall. The spray dynamic is monitored in terms of the spray morphology, the droplet velocity and size, the spray-wall interaction and the liquid wall-film formation and subsequent evolution. The spray profile obtained is depicted in Figure 11, where it is superposed by the carrier gas velocity profile. Due to their lower momentum, the smaller droplets generally are carried away by the turbulent cross-flow while the larger droplets are responsible for the intense wall impingement events. These result in an AdBlue wall film whose formation and subsequent evolution are observed in Figure 12 in terms of film thickness. The film dynamic includes the accumulation of impinged droplets and the subsequent transport of formed wall film primarily due to impingement pressure unless there is a gravity force component tangent to a possibly inclined wall plane. The thickness of the wall film is higher towards the spray front due to continuous accumulation of impinged mass. To further quantify the spray-wall interaction, the impinging droplet size and corresponding velocity (normal to the wall) distribution are plotted in Figure 13, suggesting reasonably that larger-sized droplets (Sauter mean diameter-63 \(\upmu\)m) with lower normal velocity impinge on the wall. Furthermore, these droplets feature low We-number (Figure 14, left) and relatively small La-number (Figure 14, right), which are responsible for the deposition of the impinging droplets and formation of AdBlue wall film, as also reported in [34; 35].  
Figure 11: Injection and resulting spray dynamics in configuration C1: jet injection, evaporating spray convection by turbulent cross-flow, droplet–wall interaction, film formation and transport.  
Figure 10: The two instances of inlet boundary conditions based on the digital filtered method [46] at: (**a**) 1 sec; (**b**) 2 sec.  
In order to evaluate the predictability of the numerical methodology adopted, the evolution and buildup of the AdBlue wall film are compared against the experimental film thickness obtained for case 1 (C1) shown in Figure 15, especially during the early and late injection phase. The result shows reasonably good agreement with experiment for the measurement location. The continuous buildup of AdBlue wall film in the early film development phase is well captured by both experiment and numerical simulation but for only 21 injection events due to limited computational time. To gain more insight into the process evolution while further assessing the predictive capability of the suggested numerical model, a simulation is performed with an initial wall film thickness of 50 \(\upmu\)m corresponding to a late injection stage for configuration C1. The film is allowed to further build during the next series of injections. The resulting evolution of the AdBlue wall film is compared with the experiment for only 35 injection events. Considering the complex nature of spray-wall interaction and liquid film buildup, the simulated result exhibits a similar trend to the experiment for film thickness evolution. The good agreement observed clearly demonstrates not only the predictive capability of the present numerical method, but also confirms its potential to simulate complex spray-wall-interaction phenomena as encountered in a SCR-DeNOx system.  
Figure 14: Distribution of impinging droplets: (**a**) Weber number and (**b**) Laplace number.  
Figure 15: Comparison of AdBlue film thickness evolution during early and late injection stage for the configuration C1.