## 4 Results
### A Comparison of Different Turbulence Closures  
A peculiar modelling issue regarding the cavitation dynamics was observed during the simulations. The case with \(\sigma=1.27\) was initially begun with the SST model, but the predicted suction side sheet cavitation remained stable throughout the simulations. We observed no natural shedding of the sheet cavitation, and the time histories of the global forces were flat. We carried out the simulations with the SST model until \(t\approx 0.155\) s, after which the DDES approach was activated. The outcome is illustrated in Figure 19 in terms of the time histories of the lift and drag coefficients. It was observed that almost immediately after the DDES approach was activated, the suction side sheet cavitation began its shedding behavior, leading to high-frequency oscillations also in the global force coefficients.  
A comparison of the DDES and the SST simulation is shown in Figure 20, made from visualizations of the eddy-viscosity levels near the LE of the foil on a cut plane at mid-span, cavitation extents and vortical flow structures. We observe a significant difference in the eddy-viscosity distributions. The SST simulation predicts several orders of magnitude larger eddy-viscosity levels on the suction side of the foil. This not only suppresses any vortical structures around the foil, but also prevents the natural shedding mechanisms of the sheet cavitation to take place. Instead, the predicted suction side cavitation remained stable as consequently did the lift and drag forces as well, as we noted in Figure 19. By contrast, when using DDES, similar levels of eddy-viscosity are not predicted by the model at the closure of the sheet cavity. We also note considerably more unsteady vortical flow structures with DDES, shed in the wake of the foil. Due to these reasons, the natural shedding of the sheet cavity did occur as was demonstrated in Sections 4.2 and 4.3.  
Figure 19: Illustration of an effect of DDES. Simulations were carried out using SST \(k-\omega\) until \(t\approx 0.155\) s, after which the DDES approach was activated. Medium grid, \(U_{\infty}=8\) m/s, \(\sigma=1.27\).  
Figure 18: A sequence of snapshots depicting the formation of a partial cavitating ring vortex in the wake of the foil. DDES with medium grid, \(\sigma=0.53\). On the left in each frame: left foil with iso-surface of void fraction \(\alpha=0.1\) colored as orange, together with an iso-surface of \(Q=40,000\), which is colored by the helicity H. On the right in each frame: three cut planes at \(y/s=[0.25,0.50,0.75]\) which are colored by the rate of evaporation R, with iso-surface of void fraction \(\alpha=0.1\) colored as orange.  
We note here the natural shedding behavior of the case with lower cavitation number was reasonably captured also with the used URANS approach, as discussed in Section 4.2 and seen in Figures 10 and 11. 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 medium grid.