## 5 Conclusions  
In this study, a 0D model was developed to simulate fuel injection rates from experimental data using mathematical equations based on numerical statistical tools. The study of the experimental tests and the model validation results has allowed us to draw the following conclusions:  
* The division of the injection rate signal into three phases (needle lift, holding injection, and needle closure) has allowed the model to better adapt to each phase defined. * The representativeness study of all variables linked to the experimental trials showed the most important variables affecting the injection rate were fuel properties, nozzle diameter, injection pressure, and energizing time. In addition, it was observed that the most relevant variables varied according to the injection phase. In the first phase (needle lift), injection pressure and test time had a significant influence. In the holding injection phase (second phase), energizing time and hole diameter were the predominant factors. Energizing time and test time had more impact in the needle closure phase (third phase). * The linear models proposed show high coefficient of determination (R\({}^{2}\)) values for the needle lift, holding injection, and needle closure phases, 90.02, 97.24, and 90.45%, respectively. This accuracy analysis methodology provides a solid basis to support the validity and reliability of the results obtained in the study. * The model can correctly simulate, regardless of hole size. However, it has more difficulty reproducing rates as hole size decreases, an aspect that is probably due to a greater dependence on cavitation in the test. Figure 11: Comparison between both measured and calculated fuel injection rate with diesel fuel, with nozzle diameter 115 \(\upmu\)m, 50 MPa injection pressure, 40 \({}^{\circ}\)C fuel temperature, and ET of 2 ms (**a**), 1.5 ms (**b**), and 1.0 ms (**c**). * Regarding fuels, the model adapts quite well to the use of different fuels, and it has been shown that, even without having the correlations of density and viscosity variation with the exact fuel pressure and temperature (as in the case of HVO fuel), the model can reproduce the injection rate quite well. * At low pressures, the model starts to have difficulty following the experimental curve. In these situations, the injector needle lift shows more significant oscillation, the discharge process becomes more unstable, and the experimental injection rate curves have less uniformity and stability, which the model cannot reproduce. In summary, this model can predict rate behavior over different pressure ranges, fuel types, and variations in injection nozzle diameter. This model proposal can help solve some parts of more complex computational fluid-dynamic predictive models using simple input data from experimental results. Also, this model can be used as input data for thermodynamic predictive models. The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app14062446/s1](https://www.mdpi.com/article/10.3390/app14062446/s1)]([https://www.mdpi.com/article/10.3390/app14062446/s1](https://www.mdpi.com/article/10.3390/app14062446/s1)), Table S1: Fuel mass injected per stroke (mg/st) in every experimental tested; Table S2: Time values for each phase for nozzle with 115 um; Table S3: Time values for each phase for nozzle with 130 um; Table S4: Time values for each phase for nozzle with 150 um. Conceptualization, C.M. and J.A.S. ; methodology, V.R.-R.; software, V.R.-R.; validation, C.M. and J.A.S. ; formal analysis, V.R.-R.; investigation, V.R.-R.; resources, C.M. and J.A.S. ; data curation, V.R.-R.; writing--original draft preparation, V.R.-R.; writing--review and editing, C.M., J.A.S. and O.A. ; visualization, V.R.-R.; supervision, O.A. ; project administration, O.A. ; funding acquisition, O.A. All authors have read and agreed to the published version of the manuscript. This research was funded by (i) the government of Castilla-La Mancha community to the project ASUAV, Ref.