# Numerical Simulation of Cavitation Erosion Aggressiveness Induced by Unsteady Cloud Cavitation
## 3 Results
### The Mechanism of Cavitation Erosion  
In this section, the numerical results obtained with the Sauer model have been used to discuss the mechanisms of cavitation erosion based on the comparison with the experimental observations. For that, the second cycle results from instants 1 to 2 have been considered without any loss of generality because the Sauer model has shown a good repeatability for all the simulated shedding cycles. Figure 12b shows that the maximum \(P_{tot\_load}\) is found both at the closure region of the attached sheet cavity and at the location where the main cloud cavity collapses. Nevertheless, the calculation of \(P_{tot\_load}\) without taking into account the fact that a \(P_{threshold}\) level exists is not an accurate method to estimate the actual erosion risk. Therefore, a \(P_{threshold}\) has been set to eliminate the contribution of low intensity collapses not being sufficiently high to cause material damage. For that, the number of effective time steps at which \(P_{load}\) is higher than \(P_{threshold}\) at any chord location, \(N_{eff}\), has been considered to estimate the average erosive power load, \(P_{ave\_load}\), at each effective time step and hydrofoil position with the following expression:  
\[P_{ave\_load}=\frac{P_{tot\_load}}{N_{eff}} \tag{24}\]  
If \(N_{ref}\) is the number of time steps in one cycle of duration \(T_{ref}\), then the ratio \(N_{eff}N_{ref}\) accounts for the percent time duration during one shedding cycle with \(P_{load}\) values higher than \(P_{threshold}\). In the present study, two \(P_{threshold}\) levels with values of 30 kW m\({}^{-2}\) and 90 kW m\({}^{-2}\) have been considered to investigate the influence of the particular material resistance to cavitation erosion and the corresponding distributions of \(P_{tot\_load}\), \(N_{eff}N_{ref}\) and \(P_{ave\_load}\) along the chord have been plotted in Figure 13. Note here that it can be assumed that the lower level of 30 kW m\({}^{-2}\) represents copper and that the level of 90 kW m\({}^{-2}\) represents stainless steel since there is no doubt that copper has a lower yield strength than stainless steel. For \(P_{threshold}\) of 30 kW m\({}^{-2}\), the maximum values of \(P_{tot\_load}\) and \(N_{eff}N_{ref}\) are found at 40% of the chord but at this location \(P_{ave\_load}\) is relatively small compared to the rest of values farther downstream. This is because small vapor structures are collapsing at the cavity closure region for a long time duration (0.7 \(T_{ref}\)) but they are individually inducing relatively small \(P_{load}\). This prediction is in agreement with the experimental results that show a high pitting rate at this location but with a relatively small deformation volume rate. The second peak value of \(P_{tot\_load}\) is located at 53% of the chord. In this case, \(N_{eff}N_{ref}\) is around 0.2 while \(P_{ave\_load}\) shows its maximum value. This indicates that, at the region of the cloud collapses, the erosion intensity is very high but its time duration during one cycle is relatively short. This is again in agreement with the experiment that shows a relatively smaller pitting rate but with the highest deformation volume rate in the same position. When \(P_{threshold}\) increases to 90 kW m\({}^{-2}\), the strongest erosions are also predicted at the sheet cavity closure and at the location where the main clouds collapse. However, it can be seen in Figure 13a,b that \(P_{tot\_load}\) and \(N_{off}N_{nf}\) decrease significantly in the sheet cavity closure region but only slightly in the cloud collapse region when compared with the results obtained with 30 kW m\({}^{-2}\). Now the maximum \(P_{tot\_load}\) is located at around 53% of the chord instead of 40%, which is also in accordance with the experimental results for the stainless steel specimen that showed the highest pitting rate at around the 50%.