# Analysis of Vorticity and Velocity Fields of Jets from Gas Injector Using PIV
## 4 Results and Discussion
### Velocity Magnitude  
The results described and discussed in this section are based on an analysis performed on 20 pairs of frames recorded at different time-instants after the start of energizing (aSOE). It was experimentally observed that the first frame at which it was possible to see the jet coming out from the nozzle tip corresponded to the time instant at 2.7 ms aSOE. Specifically, the jet becomes appreciable at 3.0 ms aSOE, thus all the data discussed in this work range from this time instant onwards. Figure 3 compares the velocity distributions generated by a single pair of frames and that obtained by an ensemble of 20 pair of frames. As expected, the averaged image looks much more homogeneous and the velocity distribution well defined, highlighting the regions featuring different levels of velocity magnitude. Differently, the information coming from the single pair of frames appears fragmented with a more chaotic distribution of the sub-structures. For this reason, most of the data discussed in this and following section refer to the post-processed frames obtained by the average data. The drawback of using such type of data is related to the loss of part of the details in local vortex structures, as well as an overall reduction in the velocity magnitude (and vorticity intensity) caused by the random position of the peaks in the individual frame pairs, thus resulting in a lower value when \"spatially\" averaged. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Geometry Nozzle**} & \multirow{2}{*}{**CVC Pressure [Bar]**} & \multicolumn{2}{c}{**Pressure of**} \\  & & **Injection [Bar]** & **Pressure Ratio [-]** \\ \hline \multirow{6}{*}{All geometries} & \multirow{2}{*}{1} & 20 & 20.0 \\ \cline{3-4}  & & 10 & 10.0 \\ \cline{3-4}  & & 5 & 5.0 \\ \cline{2-4}  & & 20 & 4.0 \\ \cline{2-4}  & & 10 & 2.0 \\ \cline{2-4}  & & 7 & 20 & 2.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experimental operating points. For the sake of brevity, the next graphs will show the solely data recorded with PR 4 and 20, representative of the low- and high-pressure ratio conditions. Figure 4 illustrates the velocity distribution generated by the first geometry at high and low PR conditions, highlighting the differences in terms of jet extension, as well as the phenomena addressed to the formation of vortex structures. Specifically, two lateral vortices (recognizable by the presence of a quasi-static area surrounded by non-zero velocity regions) were noticeable since the very early stage of the jet development for both ratios. At PR4, as the jet extends these structures start stretching trying to keep pace with the jet head region, thus contributing to the entrainment of air from the rear area. In the advanced stages, these structures were noted to become unable to match the jet extension, losing their capacity to further penetrate along the jet axis, thus collapsing. These large vortexes improve their capacity to keep up with the jet as the pressure ratio increases. In this condition, the jet rapidly reaches the border of the ROI, i.e., \(\approx\)3.6 ms at PR20. In a 3D perspective, these rings can be assumed to generate a toroidal corona surrounding the jet, the main contributor to the air dragging from the rear area of the jet. However, the mixing efficiency was noted to be mainly demanded by these structures since the achievement of the steady state conditions; then they were replaced by many small eddies positioned downstream the nozzle tip. Figure 5 shows the velocity distribution of the jet generated by the second geometry. At PR4 condition, both jets remain recognizable for the entire duration of the sequence recorded. The interaction with surrounding air leads to the formation of two vortexes. The one on the inner side appeared more stable, with a well-defined center, contributing to the air dragging from the rear area. Differently, the one on the outer side the vortex lasted for a short period before collapsing, i.e., \(\approx\)3.4-3.8 ms.