## 5 Results and Discussion  
### Streamer Variability  
Figure 11 Shows, at a glance, the cycle-by-cycle streamer dispersion in motored conditions. It contains the points of maximum penetration for all the recorded engine cycles, all in the same picture for the sake of comprehensibility. The corresponding quantitative results can be found in Table 5. In Figure 12, the sequence of all P\({}_{\text{max}}\) values can be found, together with a visualization of average and standard deviation for each quadrant. From this figure, it can be stated that there is not a time-dependent trend; thus, the previous cycle seems not to affect the max penetration of the following one. In the tested operating condition, streamers coming from the fourth quadrant tip were, on average, the longest (about 7 mm), while those from the second and third quadrants were the shortest (about 4 mm). It is worth noting that the corresponding penetration standard deviation was not so different among the tips, ranging from 0.9 to 1.0 mm. This resulted in a coefficient of variation of such penetration that, for the fourth tip, was the lowest, while that for the second and third ones was the highest. Figure 10: Binarized area during the discharge/combustion event, first quadrant. Black dotted lines refer to each discharge event in motored conditions (no combustion), and the black solid line is their average. Red and blue dashed curves with markers are, respectively, the curves corresponding to the \(\lambda\) = 1.0 second event and the \(\lambda\) = 1.4 sixth event, as examples. Finally, red and blue solid lines are the corresponding smoothed curves (five-point moving average). For both combustion cases, we would expect a visible flame kernel in the narrow range between the 13 th and the 16 th frame after the start of discharge (aSOD; green ellipse). In future work, further analysis will be carried out to determine if such a distribution was due to the features of the igniter or to the conditions in the combustion chamber, i.e., if a change in the igniter orientation would affect such variability. For example, it can be noted that the first and the fourth tips, which featured the highest \(\mathrm{P_{max}}\) on average, were the closest to the engine intake valves, while the second and third tips were the closest to the exhaust side. This observation will be evaluated in future work. Figure 11: Max penetration distribution of streamers in the four quadrants. The white cross in the middle is the igniter center. The discharge in the background is only for the sake of comprehensibility. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Feature** & **Unit** & **1 st quadrant** & **2 nd quadrant** & **3 rd quadrant** & **4 th quadrant** \\ \hline Series average & mm & 5.87 & 4.15 & 4.11 & 7.27 \\ Series standard deviation & mm & 1.02 & 0.947 & 0.911 & 0.994 \\ Series CoV & \% & 17.4 & 22.8 & 22.1 & 13.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: \(\mathrm{P_{max}}\) statistic results: series average, series standard deviation, and series coefficient of variation for the four quadrants. Figure 12: Details of max penetration distribution for the four quadrants over the 63 consecutive discharges. White-filled circles represent the single events, while dashed lines represent the series average value (avg) for each quadrant. Dotted lines represent the series standard deviation (\(\pm\mathrm{dev_{std}}\)) from the corresponding average value. experimental campaigns, in order to investigate whether in-cylinder flow motion is responsible for this asymmetry. Sensitivity to \(\rm V_{d}\) and \(\rm T_{d}\) will be analyzed as well, with the methodology here presented. Finally, this method did not take into account the angular position of the maximum penetration; two streamers which penetrated up to the same distance from the same tip, but with a different orientation, were equivalent in this code. In future developments, we will also evaluate such parameters.