## 2 Flow Inside the Nozzle
### Transparent Nozzles  
Optical accessible transparent nozzles are needed to investigate the cavitation phenomena inside the nozzle for the evaluation of the model capability [14]. For the approach taken, the tip of the original nozzle of the injector is removed with a fine milling process, Figure 7, left side. It is replaced by the transparent nozzle, being made from polymethyl methacrylate (PMMA), as this material has nearly the same refraction index as the fuel and allows the application of optical methods. Additionally, this material is sufficiently robust, if a suitable housing is constructed to absorb the forces of high-pressure fuel injection. With this setup, the nozzles were normally measured up to 100 MPa, and a maximum injection pressure of 180 MPa was feasible. The sac region and the injection holes are of original size. The outer body of the transparent part is much larger than the original, with plane surface area on the incoming and outgoing side of the optical path. In order to allow realistic injection hole sizes, bigger drilling holes are applied behind the exit of the nozzle (Figure 7, enlarged view on the right side, with the flow passages being indicated by a green color). With this arrangement the stability is given for the transparent nozzle, and the flow conditions inside the injector are realistic, while the spray breakup cannot be investigated here. The housing around the transparent nozzle is not shown in the figure. With such arrangements, it is possible to investigate transparent injectors with one, two or three nozzle holes. Because of the position of the cutting plane, the needle tip is visible through the transparent material. One basic geometry is a single hole nozzle, as is shown in Figure 8. The cylindrical orifice has a diameter of 200 \(\upmu\)m and a length of 850 \(\upmu\)m. The inlet of the orifice is slightly chamfered after drilling the orifice. Three transparent nozzles are manufactured with the same basic geometry (nozzle A). For two of them (nozzle B and C), a hydro-erosive rounding process is applied [15; 16] to create a smooth curvature on their inlet. After this process, the actual nozzle shapes are slightly different (Figure 9). Both nozzles have a slight step at the nozzle inlet, being located for nozzle B \"shortly\" behind the inlet and for nozzle C about 100 \(\upmu\)m downstream of the inlet (Figure 9). The detailed geometries of these cases are freely available on the [PERSON] data base [17]. Figure 7: Transparent nozzle and the nozzle holder. For the optical investigation of the cavitation region in the nozzle, a high speed camera with a long distance microscope was adapted to the injector setup. Additionally, the shapes of the transparent nozzles are traced from the images for generating the geometry for the comparable flow simulations. The transparent nozzles are slightly non-axisymmetric. In this study, the nozzle curvatures at the right and left side from the images were averaged and the axisymmetric geometries were used for the simulations. The experiments and simulations are performed under 60 MPa injection pressure. The phase interaction between two phases is defined by the mass transfer mechanism from the cavitation model of Schnerr-Sauer [18]. The Schnerr-Sauer model has been validated and discussed in earlier work [19; 20] and by other research groups (e.g., [21; 22]). There are tunable model constants, but in this study, the default constants are used, as the detailed modeling work is beyond the purpose of this publication. Preliminary and qualitative comparisons of the cavitation areas between experiment and simulation are presented in Figure 10. The left half of each image shows the high speed image of the cavitation at a quasi-steady state during the injection period. The right half side displays the calculated volume fraction of the liquid at the center cut plane of the nozzle. The red color indicates 100% diesel liquid, and the other colors indicate lower volume fraction regions with cavitation.