**2. Materials and Methods**

### *2.1. Reference Nozzle and Off-Axis Configuration of the Needle*

The reference VCO layout for the investigation has been identified among the real applications, ye<sup>t</sup> preserving the general validity of the study. The choice fell on a commercial six hole nozzle that equips the second generation electro-injectors (injection pressure up to 1600 bar) in the automotive field (cylinder displacement in the range of 500 cm3). Once defined, the real nozzle has been sectioned and optically investigated (Figure 1); thus, the internal geometry has been digitalized to allow the construction of the computational grids. The relevant nozzle features are reported in Table 1. The simulations have been extended to a half-sector of the whole geometry, decreasing the computational costs, thanks to the plane-symmetry of the implemented off-axis configuration (as described in the next paragraph).

**Figure 1.** Internal view of the investigated nozzle and computational nozzle grid.

**Table 1.** Specifications of nozzle layout.


<sup>1</sup> VCO: Valve Covered Orifice.

The nozzle flow simulation considers the operation of the needle under ballistic conditions; the adopted operating condition of the needle reflects the multiple-injection strategies, where low lifts and short injection shots are usual. The purely axial needle lift law is obtained by means of a lumped-parameter mechanical-hydraulic model of the complete electro-injector. The model has been built in the *LMS Amesim* environment [25] (by Siemens AG Digital Factory, Nurnberg, Germany), and it has been experimentally validated in terms of Rate of Injection (ROI), transient pressure signal at injector inlet and cumulative injected mass. ROI measure is based on the well-known Bosch Tube system [26], in which the pressure wave is measured by means of a piezo-resistive pressure sensor (*4067-type* by Kistler, Winterthur, Switzerland). The same sensor is used to measure the pressure signal at injector inlet, and the cumulative mass of 1000 injection shots has been measured by analytical balance. The complete information about the model and its validation is reported in [27]. The adopted needle lift curve and the related test conditions are reported in Figure 2.

**Figure 2.** Needle displacement time traces (**left**); test conditions (**right**).

The grid of the nozzle body is structured and made of hexahedral elements. The hole grids are structured as well, and they are connected to the nozzle body through arbitrary grid interfaces. Such a meshing approach allows for adopting identical grids for the holes. Different meshing approaches are possible, such as the Cartesian cut cell method [17], but the same mesh topology for each hole is not guaranteed. Therefore, the adopted meshing approach is viewed as a good practice in the attempt to avoid hole-to-hole grid dependencies. The modeling of needle displacement in the current CFD analysis is based on "mesh deformation", which consists of the use of a mesh-set to reproduce the needle displacement step-by-step. In such an approach, some cell layers undergo a deformation according to the needle displacement at each simulation time-step and never change in number. To prevent the adoption of extremely small cells at a near-zero needle lift, the approach proposed in [17] has been adopted, so that a minimal gap has been used (4 μm, which correspond to about 2.2% of the maximum lift). It has to be noted that the cell layers in the gap at minimum lift, made of hexahedral elements, have orthogonal faces; during the needle lift, the cells of the layer are deformed, with a well-tolerated skewness level at maximum lift. The nozzle computational grid and the relevant details are visible in Figure 1.

### *2.2. Off-Axis Displacement of the Needle*

As reported in [17], the off-axis displacement is due to needle oscillations during the injection; these have been identified as cantilever-type vibrations of the needle with respect to the needle guide, which is located upstream of the tip. Separate analysis of *x* and *y* motion components (assuming the needle is lifting along *z*) revealed that these lateral oscillations are quite often in-phase. Moreover, it has been evidenced that the oscillation occurs mainly on one side of the nozzle and the needle tip does not move back to the opposite side, crossing the centerline. In [17], the attention is focused on relatively long injections (2 ms), in which a specific needle wobble profile has been considered, with the needle performing three oscillation peaks in the *x*-plane. Since these lateral oscillations are purely mechanical in nature, the oscillation period is independent from injection duration [28]. In the current investigation, as the considered injection shot is shorter, the occurrence of just one oscillation peak is assumed. According to [17], it is assumed that the needle performs a pure two-dimensional translation, starting from the closing position; the radial component affecting the needle displacement has been set as a percent (8%) of the maximum vertical displacement (Figure 2, left).

As shown in the scheme of Figure 3, the needle displacement is along a straight direction, represented here by the A-B line. The A-B line and the axes of two opposite holes (*N*1 and *N*4) lie in the same plane. As visible, hole *N*1 is the most approached by the needle, whereas the other *N*4 is in the opposite condition. Thus, in the case of *N*1 and *N*4, the off-axis displacement allows for evaluating the influence of the needle proximity to the hole during the injection. In the case of *N*2 and *N*3, the off-axis displacement alters the proximity and also the symmetry of the needle towards the axes of the holes (*N*2 and *N*3). In summary, the current off-axis needle displacement has been chosen to realize a different configuration between the needle and each of the four holes, as evidenced by Figure 3 (right).

**Figure 3.** Off-axis needle displacement (cantilever-type) (**left**); adopted scheme for off-axis displacement (translation along A-B line) (**center**); displacement influence on the hole inlets (**right**).
