**3. Results**

### *3.1. Hole-to-Hole Difference on Spray Penetration*

As a first step in analyzing the results, it has been checked whether the off-axis of the needle is tied to significant differences on the spray; accordingly, the penetration trends over time for each nozzle hole have been observed. The penetration distance is defined as the distance along the spray axis to the boundary of the spray, according to [51]. The curves of Figure 6 originate at time zero ASOI (After Start Of Injection) and reach the penetration of 0.01 m at different times. Incidentally, up to 0.01 m, the spray is in the Eulerian–Eulerian domain; when droplets exceed this limit, they are taken over by the Eulerian–Lagrangian simulation. The spray emerging from the hole *N*2 is the slowest, both in the Eulerian tract for the half part of the Lagrangian tract. Referring to the off-axis configuration of Figure 3, the comparisons were made in couples, first *N*4 and *N*1, then *N*2 and *N*3 and finally the pair *N*1– *N*3; the related trends, in terms of percentage differences, are shown in Figure 12 (right).

**Figure 12.** Spray penetration of simulated sprays (**left**); % penetration difference among the sprays (**right**).

Since the opening of the nozzle up to 0.1 ms ASOI, spray *N*4 prevails over spray N1; this difference decreases rapidly, vanishes in 0.11 ms ASOI and reverses back, up to more than half of the injection process. In the closing phase, the spray N4 returns to prevail on the spray N1 but with a more limited deviation to what occurs at the opening (3% versus 18%).

During the opening, the pair *N*3– *N*2 behaves likewise to the pair *N*4– *N*1, with the prevalence of *N*3 on *N*2, but, thereafter, the difference, while decreasing, does not fade and 0 is not reversed.

The trend of the pair *N*1– *N*3 shows the spray *N*1 below *N*3, but not in the period between 0.11 and 0.2 ms ASOI.

A graphical evolution of the spray shape, accompanied by the cut view of the nozzle flow, is reported in Figure 13; even if the thorough analysis of the flow structures within the nozzle is beyond the aim of the current contribution, it is desirable to focus on how the penetration dispersion among the holes is reflected by the shape of the spray plumes; the asymmetry of velocity and cavitation patterns is clearly evident.

**Figure 13.** Shape of the four sprays (numbered according to Figure 3) and cut views of the internal nozzle flow.

### *3.2. Hole-to-Hole Differences for Spray Sauter Mean Diameter (SMD)*

Time trends of the global SMD (Sauter Mean Diameter) for different sprays are shown in Figure 14, while maintaining the same comparison method based on couples seen in the previous paragraph.

**Figure 14.** SMD (Sauter Mean Diameter) of the spray versus time (**left**); % difference on SMD among the sprays (**right**).

With reference to the pair *N*4–*N*1, from the opening up to 0.21 ms ASOI, spray *N*1 shows significantly higher SMD values. The behavior is reversed for a short period, up to 0.42 ms ASOI, after which the spray *N*4 returns to exhibit lower SMD, with percentage differences within 5%.

The trend of the pair *N*3–*N*2 sees much lower initial values for the spray *N*3, but the behavior is reversed in 0.24 ms ASOI. The SMD of spray *N*2 assumes the values of the other cases throughout the rest of the injection, about 15% below *N*3.

The pair *N*1–*N*3 still highlights the high SMD value of *N*3, which exceeds *N*1 as low as 0.21 ms ASOI with differences very close to 20%.

### *3.3. Flow Features at the Outlet of the Holes*

In the interpretation of the spray behavior seen previously, the trends of discharge-coefficient CD, velocity-coefficient CV and area-coefficient CA have been obtained for each hole, based on the 3D-CFD nozzle flow modeling. Maximum value of CD is encountered when the needle is at maximum lift, and it is limited slightly below 0.3. According to [6], such a value could be expected for the same conditions in terms of pressure but at lower needle lift. Here, the obtained value reflects the geometrical features of the considered nozzle; indeed, the configuration of the needle closing passage in the modeled nozzle is able to influence the flow even at relatively high lift values, affecting the flow rate significantly.

Up to 0.2 ms ASOI, the hole *N*2 is characterized by the lesser fuel delivery, Figure 15. In this time interval, the flow rate is penalized by both coefficients *C*V and *C*A, shown in the graphs in Figure 16. This indicates that, in the initial stages of injection, the fluid reaches the output section of hole *N*2 with relatively low velocity and that the section of the hole is moderately active. The trends of Figure 13 reflect this scenario; the intensity of cavitation at the outlet section is relatively moderate (the liquid volume fraction is relatively high) in addition to the turbulence kinetic energy. In this initial period of the injection process, the mass flow rate is affected by an evident irregularity, which is slightly reproduced in the closing phase of injection. Such a behavior is in agreemen<sup>t</sup> with what was found in [17], and it is typically due to the flow perturbations induced by the needle eccentricity.

After 0.2 ms ASOI, the behavior of hole *N*2 changes. The trend of discharge coefficient *C*D is modified and from 0.4 ms ASOI becomes similar to that of *N*1 and *N*4 cases. The trend of the liquid fraction is similar to those of the other holes, except in the closing phase, where an increase is visible, accompanied by similar deviations of turbulence kinetic energy and *C*A coefficient.

**Figure 15.** Nozzle hole discharge coefficient Cd and mass flow of injected liquid phase.

**Figure 16.** Nozzle hole velocity coefficient *C*V (**left**), nozzle hole Area coefficient *C*A (**right**).

The discharge coefficient *C*D of hole *N*3 is relatively high during the initial stage of the injection, in contrast to what was seen in the *N*2 case. The velocity coefficient *C*V is aligned to the values of the other cases and the area coefficient *C*A indicates a relatively good utilization of the hole area. The liquid fraction reaches the lowest value at about 0.1 ms ASOI (Figure 17), and the trend of turbulence kinetic energy is relatively high with downward concavity. This scenario changes at 0.3 ms ASOI. The discharge coefficient *C*D starts decreasing significantly (Figure 15), due to the drop of *C*V and *C*A (Figure 16).

**Figure 17.** Liquid volume fraction at nozzle hole outlet section (-) (**left**); turbulent kinetic energy at nozzle hole outlet section (m2/s2) (**right**).

The *N*1 and *N*4 holes show slight differences in mass flow rate (Figure 15) and the needle off-axis effects are better highlighted by the trends of coefficients *C*A and *C*V (Figure 16). The coefficients indicate that the outlet velocity at hole *N*4 is higher; this factor does not significantly increase the mass flow since it is balanced by the reduced utilization of the geometric section of the hole, due to stronger cavitation. Indeed, the trends of Figure 17 show the lower liquid fraction at the exit section of hole *N*4, compared to the case *N*1.
