*2.3. Modeling Approach*

The adopted concept of the coupling among the nozzle flow, the Eulerian and the Lagrangian spray models is shown in Figure 4 (left). The first, independent, simulation step is the transient nozzle flow simulation, taking into account the three-dimensional needle movement and cavitation effects; for certain discrete time steps (360 in the current analysis), the flow data of the bulk liquid and the vapor phase at each orifice outlet are stored on a data file providing the boundary conditions for the dense spray simulation, in agreemen<sup>t</sup> with the conclusions reported in [29], where this approach is outlined as appropriate when evaluating the effects of asymmetries in multihole nozzles. The dense spray region is simulated with the Eulerian spray approach, whereas the dilute spray is based on the DDM (Discrete Droplet Method)–Lagrangian approach.

**Figure 4.** Simulation approach based on coupling among models (**left**); scheme of Control Volume intersection between elements belonging to the Near-Nozzle mesh and to the Spray Volume mesh (**right**).
