# On the Link between Diesel Spray Asymmetry and Off-Axis Needle Displacement
## 3 Results
### Flow Features at the Outlet of the Holes  
In the interpretation of the spray behavior seen previously, the trends of discharge-coefficient \(C_{D}\), velocity-coefficient \(C_{V}\) and area-coefficient \(C_{A}\) have been obtained for each hole, based on the 3D-CFD nozzle flow modeling. Maximum value of \(C_{D}\) 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 \(N2\) 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 \(N2\) 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 agreement 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 \(N2\) changes. The trend of discharge coefficient \(C_{D}\) is modified and from 0.4 ms ASOI becomes similar to that of \(N1\) and \(N4\) 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 14: SMD (Sauter Mean Diameter) of the spray versus time (**left**); % difference on SMD among the sprays (**right**).  
The discharge coefficient \(C_{\text{D}}\) of hole \(N3\) is relatively high during the initial stage of the injection, in contrast to what was seen in the \(N2\) case. The velocity coefficient \(C_{\text{V}}\) is aligned to the values of the other cases and the area coefficient \(C_{\text{A}}\) 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 \(C_{\text{D}}\) starts decreasing significantly (Figure 15), due to the drop of \(C_{\text{V}}\) and \(C_{\text{A}}\) (Figure 16).  
The \(N1\) and \(N4\) holes show slight differences in mass flow rate (Figure 15) and the needle off-axis effects are better highlighted by the trends of coefficients \(C_{\text{A}}\) and \(C_{\text{V}}\) (Figure 16). The coefficients indicate that the outlet velocity at hole \(N4\) is higher; this factor does not significantly increase the mass  
Figure 16: Nozzle hole velocity coefficient \(C_{\text{V}}\) (**left**), nozzle hole Area coefficient \(C_{\text{A}}\) (**right**).  
Figure 17: Liquid volume fraction at nozzle hole outlet section (-) (**left**); turbulent kinetic energy at nozzle hole outlet section (\(\text{m}^{2}/\text{s}^{2}\)) (**right**).  
Figure 15: Nozzle hole discharge coefficient Cd and mass flow of injected liquid phase.  
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 \(N4\), compared to the case \(N1\).