## 3 Results  
### Flow Test Results  
In Figure 2, the results obtained in terms of the mean injected quantity, parametrically varying both the injection pressure level from 5 to 15 bar,g and the water temperature at the injector inlet from 20 \({}^{\circ}\)C to 110 \({}^{\circ}\)C, are reported. On the left in the same figure, the results are reported for when Pinj 7 = bar,g was assumed as the reference injection pressure level.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & & \multicolumn{3}{c}{**Water Temperature (\({}^{\circ}\)C)**} \\ \cline{3-6}  & & **20** & **55** & **90** & **110** \\ \hline \multirow{4}{*}{\(\mathrm{P}\  
From the obtained results, the effect of the water temperature increasing on the injected mass is evident. For a given injection pressure level, the higher the fluid temperature, the lower the injected quantity. With the ET at 5 ms and the water temperature changing from 20 \({}^{\circ}\)C to 110 \({}^{\circ}\)C, the mass percentage difference ranged from 5.7 % at P\({}_{\rm inj}\) = 7 bar,g to 11.5% at P\({}_{\rm inj}\) = 15 bar,g. This is likely to be ascribed mainly to the reduced magnetic force exerted by the solenoid on the injector needle, caused by the increased coil resistance. As is reported in Figure 3, for the reference injection pressure level, the injector current was significantly reduced in high water temperature conditions. Furthermore, the current time history slope--and presumably the needle rise--was slowed at high water temperatures, as is suggested by the delayed occurrence of the needle's fully raised position, evidenced by the sudden slope change in the current profile around 1.5 ms after the ET started.  
The effect of the fluid's temperature on the injector dynamics was particularly evident for short injection events, during which the injector operated in the so-called \"ballistic regime\". In ballistic operation, the needle did not attain the fully raised position, and consequently, the flow could not reach a static rate condition. As is reported in Figure 4a, where the flow results are plotted against the injection pressure level (with ET = 2 ms and P\({}_{\rm inj}\) = 15 bar,g), the injector's opening phase was drastically altered by high water temperature levels. In these conditions, the progressively reduced available magnetic force caused the mean injected mass to be lower at P\({}_{\rm inj}\) = 11 bar,g (and equal for T\({}_{\rm w}\) = 20 \({}^{\circ}\)C). Only for ET values longer than 3 ms was the expected rising dependence of the injected mass on P\({}_{\rm inj}\) obtained, given the presumable attained steady flow conditions and the reduced significance of the needle's opening phase with respect to the entire injection process.  
Figure 3: Injector current as a function of the water temperature. P\({}_{\rm inj}\) = 7 bar,g, and ET = 8.0 ms.  
Figure 2: Mean injected quantity for T\({}_{\rm w}\) range 20–110 \({}^{\circ}\)C and P\({}_{\rm inj}\) = 7 bar,g (**a**) and from 5 to 15 bar,g (**b**).  
The obtained flow results seem to suggest that P\({}_{\rm injj}\) = 15 bar,g is not a feasible operating condition for this injector with a high water temperature and will no longer be investigated in terms of the spray evolution and drop size.