# Analysis of Vorticity and Velocity Fields of Jets from Gas Injector Using PIV
## 5 Jet Morphology  
Another aspect examined in this work is the morphology of the jet/s, thus its penetration and the plume angle. Both parameters were measured through the use of a code built on Matlab used to detect the edge of the jet. The working principle of the code is based on the velocity threshold defined by the user to return the coordinates of the borders all around the jet perimeter. More in detail, considering the generic operative condition, the threshold value was set equal to the 20% of the mean value of the peak velocities of all 20 frame pairs, thus using a less severe approach compared to that used for measuring the size of the jet core for recalculation. The jet penetration values were normalized with respect to the diameter of the nozzle orifices. In particular, considering the tendency of the individual jets to merge into a single structure from early stages after injection, an equivalent diameter was hypothesized based on the total orifice area. Accordingly, the measured penetration values were normalized using diameters of 3.00 mm, 2.35 mm and 2.25 mm for the first, second and third geometries, respectively. The resulting normalized values are shown in the histograms in Figure 12. The graphs below confirm that the first geometry exhibits the slowest jet penetration in the early stages, showing a significant gap compared to the other two configurations. This phenomenon can be attributed to the near-instantaneous collimation of the individual jets into a single coherent structure, which initially reduces the axial velocity. However, this structure becomes more effective in sustaining penetration in the mid-to-long term. In detail, the jet produced by the first accelerates faster than the other two configurations, with an increasing gap ranging from 15% to 30% with the other two geometries before achieving the edge ROI. The second and third nozzle tips are more directly comparable, having similar equivalent diameters but different nozzle layouts (see Figure 1, bottom). In particular, the reduced spacing between the inner and outer orifices in the second geometry promotes more effective jet penetration, especially under low pressure ratio (PR) conditions. The increased orifice size and reduced inclination in the second geometry offer an initial advantage in jet penetration, which reduces as PR increases. Ultimately, L/D values tend to converge across the two configurations examined, emphasizing the influence of orifice angle over shape, and suggesting that orifice spacing affects jet extension primarily during early injection stages. Noticeable is the variability that kept always showing in the reduced values, ranging from 1% to 5%, thus suggesting good repeatability for the measurement of the jet extension. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**8 Ms aSOE** & **PR2** & **PR2.9** & **PR4** & **PR5** & **PR10** & **PR20** \\ \hline
1 st [s\({}^{-1}\)] & 130,196.4 & 150,371.9 & 163,636.1 & 170,049.6 & 199,911.5 & 239,255.5 \\ \hline
2 nd [s\({}^{-1}\)] & 130,663.6 & 159,241.1 & 160,284.6 & 161,613.8 & 192,116.3 & 221,887.2 \\ \hline
3 rd [s\({}^{-1}\)] & 122,528.1 & 142,982.7 & 158,985.9 & 154,918.1 & 202,046.9 & 229,685.7 \\ \hline \end{tabular}
\end{table} 
Table 4: Average vorticity peaks recorded at 8.0 ms aSOE. Regarding the plume angle, it is more appropriate to refer to half of the plume angle for this study. In fact, considering the three nozzle tips analyzed, the second geometry is the only one that does not provide a symmetrical view of the jet structure. It was therefore decided to measure only half of the above parameter, \(\beta\). This parameter \(\beta\) was then normalized by the angle \(\alpha\), defined as the inclination of the external orifice channels relative to the injector axis (15\({}^{\circ}\), 18\({}^{\circ}\) and 20\({}^{\circ}\) for first, second and third nozzle). The resulting ratio, \(\beta/\alpha\), provides a measure of how effectively a given geometry preserves or modifies the original geometrical dispersion angle.