## 5 Conclusions  
We studied the ITTC Standard Cavitator numerically in a cavitation tunnel at different cavitation numbers. To our knowledge, our numerical analyses are the first reported ones for the ITTC standard cavitator. Emphasis was put upon the assessment of sheet-cavitation dynamics. A compressible two-phase flow model was used for the flow solution, and two turbulence closures are employed: a two-equation RANS model, SST \(k-\omega\), and a hybrid RANS/LES model, called the delayed-detached eddy simulation (DDES). A homogeneous mixture model was used for the two phases. We compared the simulations with observations made in the cavitation tunnel experiments. Good agreement was achieved with the mean cavitation extent, in terms of the sheet cavitation on the foils, and the hub vortex cavitation which formed behind the cavitator body. The numerically predicted sheet-cavitation shedding frequencies can also be observed with some hydrophones in the acoustic measurements, which were carried out in the cavitation tunnel. Streak cavitation at the hemispherical head of the cavitator body was predicted as an attached sheet cavitation in the simulations. The numerical grid resolution did not permit the capturing of the very fine tip vortex cavitation that was observed in the experiments. Also, the prediction of flows with bubble cavitation is difficult with a homogeneous two-phase mixture model. Detailed analysis of the cavitation shedding mechanism confirmed that the dynamics of the sheet cavitation are dictated by the re-entrant jet. Once the jet impinges the sheet cavitation, a detachment takes place together with complex interaction between the re-entrant jet, vortical flow structures and mass transfer near the phase boundary. We observed that the break-off cycle was relatively periodic in both investigated cases with an approximately constant shedding frequency. The Strouhal numbers lay within the usual ranges reported in the literature for sheet-cavitation shedding. Furthermore, we noted that a strong vortical flow formed around the detached cavity. In the case of the lower cavitation number, we demonstrated that the vortical flow structures convected to the slipstream of the foils, where they developed striking cavitating toroidal vortices. An intricate interplay with the shed vapor clouds and the liquid-phase flow introduced vast vortical flow structures when the sheet cavity detachment took place. We showed that once the toroidal vortex ring was formed, the vorticity was in  
Figure 20: Snapshots of simulations with DDES and SST. Medium grid, \(\sigma=1.27\). Left frame depicts a cut plane of the left foil at mid-span with the contour of void fraction \(\alpha=0.1\) denoted by the grey curves, and the plane is colored by the eddy-viscosity ratio. The right frame shows the cavity extent near the left foil by an iso-surface of the void fraction \(\alpha=0.1\), colored by light blue, and vortical flow structures by an iso-surface of \(|\Omega_{i}|=300\,1/\mathrm{s}\) as the transparent grey color. most parts strong enough for the flow inside the vortex rings to cavitate. Furthermore, a collapse event of a cavity cloud in the slipstream of the foils gave rise to a considerable pressure peak and subsequent wave-like fronts. DDES and simulations with the URANS model revealed a difference of approximately 5 Hz in the sheet-cavitation shedding for the case with the lower cavitation number. The shedding behavior was reasonably captured also with a two-equation turbulence model. This observation might be because the foil was, in an average sense, at a super-cavitating state where the attached sheet cavitation momentarily covered the entire suction side of the foil. It appears that in this case the shedding mechanism is strong enough to overcome the, perhaps excess, diffusion originating from the eddy-viscosity modelling even on the rather coarse grids.