# Analysis of Vorticity and Velocity Fields of Jets from Gas Injector Using PIV
## 4 Results and Discussion
### Velocity Magnitude
However, it is worth noting that the values determined in Figure 7 refer to the velocity calculated in the jet core, rather than near the nozzle tip, since in this area a sufficient number of seed particles are not yet trapped to follow the jet flow. A further set of 20 pairs of frames was recorded at 8.0 ms aSOE for each ratio examined, when the jet was in steady state conditions. The recorded maximum speed values are presented in Table 2.  
The data listed in Table 2 have been used to calculate the Reynolds number (\(Re\)). The latter is a dimensionless quantity defined as the ratio between inertial and viscous forces. The Reynolds number is used to characterize flow regime, and it is calculated as follows:  
\[Re=\frac{\rho UD}{\mu} \tag{6}\]  
where \(\rho\) is the gas density, thus \(\approx\) 0.85, 1.71 and 3.43 kg/m\({}^{3}\) for helium at 5, 10 and 20 bar, respectively (at 300 K). \(U\) is the speed of the jet, \(D\) the characteristic length and \(\mu\) the dynamic viscosity (1.98 \(\times\) 10\({}^{-5}\) Pas at 300 K). As far as the speed and characteristic length, it was noted that under steady state conditions the areas characterized by the highest values of velocity (the same presented in Table 2) were always located downstream of the weak correlation area, 5-15 mm far from the injector, depending on the pressure ratio. At this distance, the jet width is rather narrow and by setting a threshold equal to 80% of the maximum recorded velocity, to assume the presence of only helium [33], the jet core size was measured. The calculated Re number values are listed in Table 3.  
All the operating conditions examined fall within the turbulent flow regime. The first geometry was the most stable, returning a jet diameter of approximately 3.5-3.8 mm at peak velocity. In contrast, the second and third geometries revealed a higher degree of variation in this parameter. More specifically, the second geometry returned to a diameter between 2.0 and 3.2 mm, with maximum value measured at intermediate PR conditions. The third geometry, on the other hand, showed the lowest diameter values, i.e., from 1.8 to 2.2 mm, except in the case of the most severe injection pressure. At PR 20 the three jets merged in a single structure, leading to an increase in the overall jet width to 5.4 mm near the peak velocity. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**8 Ms aSOE** & **PR2** & **PR2.9** & **PR4** & **PR5** & **PR10** & **PR20** \\ \hline V1 st [m/s] & 105.4 & 138.1 & 167.0 & 179.2 & 248.7 & 309.4 \\ \hline V2 nd [m/s] & 108.1 & 125.2 & 141.9 & 154.4 & 211.6 & 280.6 \\ \hline V3 rd [m/s] & 90.8 & 109.3 & 127.6 & 142.5 & 208.6 & 297.3 \\ \hline \end{tabular}
\end{table} 
Table 2: Average velocity peaks recorded at 8.0 ms aSOE. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**8 Ms aSOE** & **PR2** & **PR2.9** & **PR4** & **PR5** & **PR10** & **PR20** \\ \hline Re1 st [-] & 30,691 & 40,213 & 52,796 & 56,653 & 78,625 & 97,815 \\ \hline Re2 nd [-] & 17,987 & 33,332 & 35,416 & 33,398 & 38,729 & 58,362 \\ \hline Re3 rd [-] & 13,598 & 18,187 & 24,416 & 27,267 & 52,064 & 136,038 \\ \hline \end{tabular}
\end{table} 
Table 3: Reynolds number values at 8.0 ms aSOE.