## 3 Results and Discussion
### Evaporation Characteristics of Urea-Water Solution
For a further in depth analysis of the evaporation process, the difference between pure water and UWS will be briefly described. First, it is assumed that the Biot number  
\[Bi=\frac{\alpha\,D_{d}}{2\,\lambda_{d}}\ll 1, \tag{17}\]  
resulting in uniform temperature within the droplet. According to a Rapid Mixing evaporation model, uniform urea concentration inside the droplet is additionally assumed. With this assumption, the evaporation of an UWS droplet can be subdivided into two stages: The first stage is characterised by an almost exclusive evaporation of water. This means that there will be no evident difference between the evaporation of pure water and UWS. Once the water of the UWS droplet is consumed by evaporation, the evaporation and thermolysis of urea starts. This is the second stage, which can be described as an evaporation process with a considerably lower evaporation rate in comparison to water. Details of modelling the evaporation of UWS are discussed in the work of [PERSON] et al. [49]. The evaporation process of UWS and water droplets is illustrated in Figure 17 by means of model results for the present hot gas operating condition. Comparing two droplets after an exemplary residence time (dashed line) in the hot gas environment, the 10 \(\upmu\)m droplet still behaves like a regular water droplet, whereas the 8 \(\upmu\)m features a considerably lower evaporation rate in comparison to water. The important conclusion from the discussion of the evaporation characteristics is that a designated droplet size exists during the lifetime of each UWS droplet, at which the water is completely consumed, and the evaporation rate is drastically reduced. Figure 16: Normalised number PDF for urea–water solution (UWS) and water at (**a**) \(x=225\,\)mm; (**b**) \(x=270\,\)mm; and (**c**) \(x=495\,\)mm (The droplet data resulted at \(x=225\,\)mm, \(x=270\,\)mm from 3000 double images and at \(x=495\,\)mm from 5000 double images). This knowledge can be transferred to the discussion of the PDFs in Figure 16a-c. The difference in the PDFs between UWS and water is caused by the sudden change of the evaporation rate. In other words, all droplets smaller than a certain size undergo urea evaporation and the thermolysis process, which explains the higher number of UWS droplets in the small diameter classes in comparison to water. The higher probability of all larger diameter classes for the water spray is a consequence of the normalization of the PDF by the total number of droplets. The discussed difference of the PDFs grows stronger with increasing distance from the atomiser, since the residence time of the droplets in the hot gas increases. This results in a progress of spray evaporation and consequently larger droplets will undergo urea evaporation and thermolysis. In summary, the analysis of the evaporation characteristics reveals promising results, which can be used to study evaporating urea-water sprays. Therefore, the diagnostics may be used to provide validation data for numerical predictions that focus on the evaporation behaviour of UWS. Most importantly, the reasonable and very detailed differences in the droplet diameter distribution emphasize the accuracy of the present spray diagnostics.