**4. Conclusions**

The current study showed that the lack of homogeneity in the mass-flow distribution is certainly a key factor behind the spray irregularities, but also that it is not the only one. In fact, even when the same discharge coefficient is found among the holes, irregularities are observed among the far sprays. The irregularities have been evidenced by the dispersion of penetration among the different orifices, and they have been addressed to the nozzle configuration by analyzing the flow features in terms of non-dimensional parameters. The velocity-coefficient *C*V and the area-coefficient *C*A have been found to provide valuable information to completely represent the flow conditions at nozzle outlets when needle off-axis is encountered.

The 3D-CFD modeling retains major relevance in the determination of these coefficients, due to the difficulties that would arise by the experimental techniques. In this scenario, the coupling with the spray models is the crucial step to quantify the differences that cannot be assessed only through the analysis of mass flow rate distribution.

From the industrial viewpoint, the current study made it possible to identify the range of variability that can be expected from the VCO nozzles, in the typical operating conditions of common rail systems (ballistic needle displacement and reduced lift), and the range of variability within the spray characteristics, expected to vary, has been defined. In the current case, these ranges have been found on the order of 15% for penetration and in the order of 20% for global SMD; following the same approach, these ranges can be identified for other specific injectors and operating conditions.

The values of *C*V and *C*A coefficients can be taken as a reference in further investigations (three-dimensional, multi-zone, or lumped-parameter based), in order to explore the effects of spray non-idealities on the engine performance, on the combustion behavior and, more generally, on those cases affected by sensitivity to the spray characteristics.

**Acknowledgments:** The authors acknowledge the fundamental contribution of AVL List–Graz providing the *FIRE™* code and giving the necessary support during the research activities.

**Author Contributions:** Giancarlo Chiatti conceived and organized the work; Ornella Chiavola and Fulvio Palmieri designed the investigations, analyzed the data and wrote the article; Pierluigi Frezzolini performed numerical simulations.

**Conflicts of Interest:** The authors declare no conflict of interest.
