## 3 Results and Discussion
### Discussion of Velocity Fluctuations  
Since the temporal average of the gas velocity can be derived with sufficient accuracy, the discussion is extended to the statistical analysis of velocity fluctuations. This requires the post-processing, as presented in Section 2.3, to be extended in order to exclude spurious vector assignments, which may compromise the statistical analysis. The universal outlier detection of Westerweel and Scarano [45] is widely used for Particle Image Velocimetry (PIV) data. This technique is based on a normalised median filter, which considers the neighbour velocity vectors of the vector under concern. Furthermore, this filter was verified for a wide range of Reynolds numbers ranging from \(10^{-1}\) to \(10^{7}\). In contrast to PIV data, Particle Tracking Velocimetry (PTV) yields non-equidistant neighbour vectors. Hence, a weighting of neighbour vectors based on the distance from the droplet velocity vector concerned is used as proposed by [PERSON] et al. [46]. Finally, this filter is applied using a conservative threshold of 2 to ensure that spurious vectors are effectively removed. The droplet data at specific spatial positions are split into droplet diameter classes with a constant width of \(0.5\,\upmu\)m in order to evaluate the effect of droplet size on velocity fluctuations. The probability distribution of the radial velocity is illustrated exemplarily for two droplet diameter classes at a distance of \(x=50\,\mathrm{mm}\) downstream of the atomiser in Figure 13a. Obviously, this velocity component is normally distributed and the mean value is approximately \(0\,\mathrm{m}\,\mathrm{s}^{-1}\). Furthermore, the radial velocity of the smaller droplets has a higher standard deviation, which may indicate that those droplets follow the velocity fluctuations of the gas phase considerably better compared to larger ones. For a more detailed analysis, the standard deviation of the radial velocity is calculated for each droplet diameter class in the range between \(4\,\upmu\)m and \(20\,\upmu\)m. The result reveals a decreasing standard deviation with increasing droplet diameter at all positions downstream of the atomiser as shown in Figure 13b. The most interesting observation is that, at the position closest to the atomiser nozzle (\(x=50\,\mathrm{mm}\)), the standard deviation of the radial velocity is found to be proportional to \(D_{\mathrm{d}}^{-2}\). Considering the timescale of droplet relaxation, as indicated by Equation (3), there is strong evidence that the standard deviation of the droplet velocity is due to the fluctuations of the gas velocity. Hence, the generally high standard deviation at position 0 obviously results from strong turbulent fluctuations of the gas phase. At this measurement position, a strong shear layer turbulence is generated by the interaction of the rapid cold gas injected by the atomiser with the substantially slower hot gas flow. This result is supported by the strong gradient of the axial droplet velocity as shown in Figure 10b. The positions further downstream of the atomiser are characterised by a generally lower level of the standard deviation and a considerably weaker dependency on droplet size. This result is sensible, since the influence of the atomiser air flow and the resulting shear layer turbulence decays with increasing distance downstream of the atomiser. The standard deviation of the radial velocity, as shown in Figure 13b, represents a valuable result, since it can be directly applied for predicting the turbulent dispersion. Consequently, the droplet trajectories in the test section can be computed dependent on the droplet size. In addition, the standard deviation of the velocity may contain vital information about the turbulent fluctuations of the gas phase. These velocity fluctuations impose an additional relative velocity between droplets and gas, which may affect evaporation or atomisation considerably.