# Numerical Simulation of Cavitation Erosion Aggressiveness Induced by Unsteady Cloud Cavitation
## 2 Experiment Description and Numerical Model  
### Experiment Description  
The experimental conditions and results used to validate the numerical models are listed in Table 1, comprising the hydrofoil incidence angle, \(a\), the chord length, \(c\), the free stream velocity, \(U_{\mathit{inf}}\), the cavity length, \(l\), the cavitation number, \(\sigma\), the shedding frequency, \(f\), and the Strouhal number, St. \(\sigma\) and St have been calculated with Equations (1) and (2), respectively, where \(P_{in}\) and \(P_{v}\) are the inlet and the vapor saturation pressures, respectively. The computational fluid domain corresponding to the cavitation tunnel test section is shown in Figure 1 and a more detailed description of experiment can be found in [PERSON] et al. [29] and [PERSON] [30]. \[\sigma=\frac{P_{in}-P_{v}}{0.5\rho_{l}U_{\mathrm{inf}}l^{2}} \tag{1}\]  
\[St=\frac{fl}{U_{\mathrm{inf}}} \tag{2}\]  
In the experiment, material specimens 30 mm in width made of standard copper and stainless steel polished down to mirror were mounted along the hydrofoil suction side at different chord positions. The specimens were obtained by an accurate electroerosion machining, glued with cyanoacrylate adhesive and removed after the tests by heating to 400 \({}^{\circ}\)C. The erosion intensity was assessed with a statistical analysis of the pitting data measured on the specimens during the incubating period. The pitting results were quantified with the mean pitting rate at the specimen location \(k\), \(\tau_{n}\) (\(k\)), and the mean volume deformation rate at location \(k\), \(\tau_{v}\) (\(k\)), which were respectively defined as:  
\[\tau_{n}(k)=\frac{N_{k}}{T_{pil}\times L_{x}\times L_{y}} \tag{3}\]  
\[\tau_{v}(k)=\frac{\sum Vd(x_{i},y_{i})}{T_{pil}\times L_{x}\times L_{y}} \tag{4}\]  
where \(N_{k}\) is the number of cavitation impacts on location \(k\), \(L_{x}\) and \(L_{y}\) are the side lengths of the tested specimen and \(T_{pit}\) is the time duration of the pitting test. \(Vd\) (\(x_{i}\), \(y_{i}\)) represents the volume of the indentations on the surface at position (\(x_{i}\), \(y_{i}\)), which was measured with a 3D profilometer. Figure 2 presents the cavitation erosion results obtained for a \(U_{inf}\) of 20 m/s for two different materials: copper and stainless steel. Firstly, the influence of the material strength can be seen by comparing the amplitudes of the erosion indicators for copper in Figure 2a with those for stainless steel in Figure 2b. For copper, the maximum values of \(\tau_{n}(k)\) are of about 0.03 mm\({}^{-2}\)s\({}^{-1}\) at 40% of the chord and the maximum values of \(\tau_{v}(k)\) are of about 160 \(\upmu\)m\({}^{3}\)mm\({}^{-2}\)s\({}^{-1}\) at 50% of the chord. Meanwhile, the maximum \(\tau_{n}(k)\) and \(\tau_{v}(k)\) values are of about 0.0004 mm\({}^{-2}\)s\({}^{-1}\) and 1.9 \(\upmu\)m\({}^{3}\)mm\({}^{-2}\)s\({}^{-1}\), respectively, at 50% of the chord for stainless steel. Therefore, the pitting rate suffered by the copper is almost two orders of magnitude higher than that for stainless steel. Regarding the location of the damages, the most eroded areas for both materials are found approximately in the range from 40 to 50% of the chord, as expected, because they have been submitted to the same cavitation conditions and the cavity  
\begin{table}
\begin{tabular}{c c c c c c} \hline \(\alpha\) [\({}^{\circ}\)] & /closure region was located at 40% of the chord (\(|\!/\!\!\!c=0.4\)) as indicated in Table 1. For copper, \(\tau_{n}(k)\) shows the maximum at 40% of the chord but \(\tau_{v}(k)\) shows the maximum at 50% of the chord. This seems to indicate that the hydrofoil surface suffers a large amount of impacts with small intensity at 40% and a lower number of impacts with a stronger intensity at 50%. A slightly different erosion pattern is found for stainless steel since it presents the maximum \(\tau_{n}(k)\) in the range from 40% to 50% but the \(\tau_{v}(k)\) shows a minimum value at 40% and a maximum value only at 50%.