*2.6. Cavitation Model Assessment*

The cavitation model adopted for the current investigation and the related settings have been assessed simulating two reference cases, i.e., the experiment proposed by Winklhofer et al. [46] and the more recent experiment proposed by Sou et al. [47]. As recently reported in [19], many other contributors [48,49] have considered the experiment of Winklhofer as a significant reference case. This experiment is based on the investigation of an optically accessible channel (inlet section 0.300 × 0.301 mm; outlet section 0.284 × 0.301 mm; 1 mm length, 0.02 mm inlet curvature radius). During the experimental research, the inlet pressure was fixed (10 MPa), at a uniform fuel temperature of 300 K, whereas the outlet pressure was adjusted in order to obtain the required flow rate. The same technique has been applied in the simulations. Figure 6 (left) shows the computational grid used in the cavitation model assessment; it represents 1/4th of the real channel geometry, thanks to symmetry of domain. The flow behavior of the throttle has been positively tested in several operating points. On one side, the hydraulic prediction has been found to be good agreemen<sup>t</sup> with experiments, as visible in Figure 6 (right) and in Table 2, which reports the details of mass flow rate in the conditions evidenced by [46] (cavitation incipience—Point A, critical cavitation—Point B and super cavitation—Point C). On the other side, the cavitation patterns related to the three fundamental conditions, as evidenced in [46], have been consistently reproduced, as reported in Figure 7; it has to be explicitly mentioned that the cavitation patterns observed by Winklhofer were fluctuating, due to the highly turbulent flow environment and they have been obtained by an ensemble averaging process of a set of twenty images taken under the same operating conditions.

**Figure 6.** Computational grid used to model the experiment of Winklhofer et al. [46] (**left**); mass flow within the throttle channel (**right**).

**Table 2.** Mass flow conditions in throttle channel.


**Figure 7.** Cavitation at throttle flow conditions (**A**, **B**, **C**); simulated cavitation regions (**left**); experiment of Winklhofer et al. [46] (**right**); CS: cavitation start; CC: critical cavitation.

Moving to the second assessment phase, the experiment of Sou [47] has been reproduced by simulation. The experiment consists of a flow through a transparent channel allowing the visualization

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(based on Laser Doppler Velocimetry) of cavitation incipience and development. In the experiments, a water flow is produced. The discharge ambient is kept at a constant pressure (ambient pressure) and the inflow condition is varied to realize different flow regimes, represented by the mean liquid velocity (*V*n) in the channel. The incipience and the development of cavitation is well reproduced by the simulation, as indicated by the contours of liquid mass fraction shown in Figure 8. The quantitative comparison between the experiment and the simulation is reported in Figure 9, where the available data on velocity profile provided by Sou [47] are compared with the simulations. The trends are referred to three different axial locations along the throttle axis, as evidenced by the sketch of throttle layout of Figure 9. Good agreemen<sup>t</sup> has been found in all of the cases.

**Figure 8.** Cavitation at throttle flow conditions; simulation LVF (-) (liquid volume fraction) (**right**); Experiment of Sou et al. [47] (**left**), cavitation inception at black circle.

**Figure 9.** Velocity profiles in the nozzles at *V*n = 12.8 m/s [47].

### *2.7. Grid Sensitivity Tests and Spray Model Assessment*

Once the cavitation model is validated, a thorough pre-computation procedure has been performed to find the best computation settings on the used grids; the effect of local refinements has been evaluated as well. The tested grid types and the adopted cell number are listed in Table 3. In the same table, the mass flow rate differences among the nozzle flow tests are reported. Figure 10 reports the graphical results in terms of the velocity profile and cavitation development, when adopted, and the most refined nozzle grids are compared.

**Table 3.** Grid properties and adopted refinements.

**Figure 10.** Velocity field contours and cavitation patterns in the case of the adopted and finest nozzle grid.

Since the spray model is used to chase the hole-to-hole spray differences, a crucial check in the current investigation is to assess the penetration dependence on computational grid refinement. Figure 11 (left) reports the trends obtained for the hole *N*1, depending on the refinement of spray domains.

**Figure 11.** Penetration dependence on spray-domain refinement (**left**); spray model assessment against "ECN Spray-A" reference case (**right**).

The spray model capability has also been assessed against experimental data; Figure 11 (right) reports the comparison between experimental and simulated penetration lengths, referring to "ECN Spray-A" case [50], Table 4.


**Table 4.** Spray-A conditions.
