# Numerical Simulation of Cavitation Erosion Aggressiveness Induced by Unsteady Cloud Cavitation
## 3 Results
### Influence of Driving Pressure Definition  
The numerical results from two consecutive shedding cycles have been selected to calculate \(P_{load}\) on the hydrofoil surface with the different cavitation models and the obtained results have been plotted in Figure 5.  
The top graphs in Figure 5 have been obtained considering \(p_{d}\) as the flow field instantaneous pressure, \(p(t)\). Conversely, the bottom graphs have been obtained considering \(p_{d}\) as the averaged pressure over ten cycles, \(\overline{p}\). It can be observed that the space-time distributions of \(P_{load}\) on the suction side are different depending on which value has been used. For example, when taking the results obtained with the Sauer model, a region with high \(P_{load}\) has been predicted from 20% to 65% of the chord using \(\overline{p}\) in the initial time ranges of each cycle from 0.2 to 0.45 _T/T_ref_ and from 1.2 to 1.45 _T/T_ref_. It is observed that using \(p(t)\) the calculations can only capture a high \(P_{load}\) during a very short instant around 1.45 _T/T_ref_. Moreover, the amplitude of \(P_{load}\) is also different even though the attack occurs in a similar time-space region. Another large amplitude of \(P_{load}\) has been found with the use of both \(p(t)\) and \(\overline{p}\) on a location around 40% of the chord from 0.45 to 1.0 _T/T_ref_ for the first cycle and from 1.45 to 2.0 _T/T_ref_ for the second cycle. However, this amplitude was higher when taking \(\overline{p}\) as the driving pressure. To finish, similar differences have also been found when comparing the results of the other two cavitation models. Figure 4: Numerically predicted time evolution of the total vapor volume in the fluid domain with the different cavitation models. To understand such differences, the obtained _in_ from vapor to water has been presented in Figure 6 for the second cycle at various relative instants, _T/T_/_n_/, marked with dotted lines in Figure 5b. Three stages of the cavity shedding process can be roughly identified. Firstly, the formation of the sheet cavity and its detachment occurs from 1.0 to 1.2 at the initial stage of the shedding process. Figure 6a,b at instants 1.0 and 1.1, respectively, show how the main sheet cavity detaches due to the re-entrant jet and then how a cloud cavity forms and begins to be convected downstream. The second stage ranges from 1.2 to 1.45 and corresponds to the collapse of the cloud cavity. In Figure 6c,d, it can be seen at instant 1.3 how the cloud cavity flows downstream and starts to collapse. Afterwards, the final collapse occurs at instant 1.44. Finally, the stage from 1.45 to 2.0 corresponds to the new growth and formation of the attached sheet cavity. As shown in Figure 6e,f, the sheet cavity reaches its maximum length and then a stagnation point at its closure region forms because the flow over the cavity turns towards the surface. This stagnation point creates a high pressure region which drives the upstream re-entrant jet below the attached cavity and triggers the collapse of the small vapor structures detached at the rear part of the sheet. Figure 5: Comparison of calculated power load per unit area, \(P_{load}\), on the hydrofoil surface based on instantaneous pressure, \(p(t)\) (top) and on average pressure, \(\overline{p}\) (bottom). Figure 6: Contours of \(\dot{m}\) from vapor to water at different instants of the shedding cycle. Black isolines of \(\alpha_{v}\) = 0.1 show the locations of the main vapor cavities at each instant. The results obtained using both \(p(t)\) and \(\overline{p}\) have been plotted on the left- and right-hand sides of Figure 7 for comparison. In particular, the corresponding distributions of \(p(t)\) and \(\overline{p}\), the distribution of \(P_{den}\) as well as the evolution of \(P_{load}\) on the hydrofoil surface along chord (red line) have been plotted at different instants. Moreover, the isolines of \(\alpha_{v}=0.1\) (black lines) have been superimposed to those graphs to show the location of the main vapor cavities.