## 2 Materials and Methods
### Methodology  
To obtain the specific data for controlling the fuel injection in the vehicle, a straight, unsloping paved road with an extension of 4 kilometres was chosen, located at an approximate elevation of 2411 m above sea level (masl). A normal driving cycle was implemented, respecting the speed limit established by local traffic regulations. From these tests, specific values of injection pressure and injector activation time were obtained from idle (695 min\({}^{-1}\)) to maximum engine load, which was reached at an engine speed of 3000 min\({}^{-1}\). The values obtained in these different engine conditions are presented in Table 5. \begin{table}
\begin{tabular}{l c c c} \hline
**Denomination** & **Fuel 1** & **Fuel 2** & **Units** \\ \hline Commercial designation & Viscor 1487 AW-2 & Diesel & - \\ Density & 780 & 850 & [kg/m\({}^{3}\)] \\ Viscosity kinematics at 40 \({}^{\circ}\)C & 2.62 & 4.1 & [mm\({}^{2}\)/s] \\ Kinematic viscosity at 100 \({}^{\circ}\)C & 1.07 & 1.9 & [mm\({}^{2}\)/s] \\ Kinematic viscosity at 20 \({}^{\circ}\)C & 102 & 52 & [mm\({}^{2}\)/s] \\ \hline \end{tabular}
\end{table} 
Table 4: Characteristics of the fuels used. Figure 1: Work flowchart. A test plan based on the behaviour of the injection map of the electronic control system of the 4J1 engine was carried out to generate a more reliable data acquisition and to ensure that the data from the injection bench were within the ideal working range of the vehicle, which is detailed in Table 6. It should be noted that this plan was applied in each nozzle, and for each time of energization, seven different pressures were used, resulting in a total of 210 tests carried out in each nozzle. The modelling of the nozzle geometry was developed, defining the physical parameters, especially the number and dimensions of the hole diameters. This procedure was performed using a 20\(\times\) magnification microscope with TouyView software (version 4.11). In this context, 4 different nozzles designed for the Denso 8-98011604 injector were examined and analysed. The detailed characteristics of these nozzles are listed in Tables 7 and 8, so their visual representations can be found in Figures 2 and 3. This approach to nozzle identification allows for an accurate assessment of the impact on spray behaviour and provides the opportunity to continually improve associated processes. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Number Test** & **Pressure [MPa]** & **Energy Time [\(\upmu\)s]** \\ \hline
5 & 27–33 & 614 \\
5 & 44–50 & 855 \\
5 & 60–66 & 1200 \\
5 & 83–89 & 1470 \\
5 & 100–106 & 1665 \\
5 & 113–119 & 1800 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Test plan. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Denomination** & **Value** & **Units** \\ \hline Injector manufacturer & Denso & - \\ Model & 8-98011604 & - \\ Inductance & 100 \(<\) I \(<\) 1200 H & Henry \\ Nozzle & 8 & Holes \\ Hole diameter & 145.98 & \(\upmu\)m \\ Average injection flow & 300 & mm\({}^{3}\)/h \\ Return flow & 82.5 & mm\({}^{3}\)/h \\ Work pressure & 25 \(<\) P\({}_{\text{inj}}\) \(<\) 150 & MPa \\ Weight & 689 & \(\upbeta\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Injector characteristics. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Engine Speed** & **Injection Pressure** & **Injection Pulse** & **Injector Current** & **Injector Voltage** \\
**[min\({}^{-1}\)]** & **[Bar]** & **[\(\upmu\)s]** & **[A]** & **[V]** \\ \hline
695 & 300 & 614 & 9.94 & 14.3 \\
1000 & 470 & 855 & 12.93 & 14.2 \\
1500 & 630 & 1200 & 17.20 & 14.2 \\
2000 & 860 & 1470 & 21.47 & 14.2 \\
2500 & 1030 & 1665 & 25.74 & 14.2 \\In the development of the 0D models in this section, the model of Equation (1) was used. This model is based on the calculation of the injection rate of the mass injected each time to analyse the injection behaviour (mass flow).