# Numerical Simulation of Cavitation Erosion Aggressiveness Induced by Unsteady Cloud Cavitation
## 1 Introduction
Nonetheless, its practical application to predict the erosion in hydraulic machinery is still limited since cavitation can take different patterns and the erosion is mainly caused by large-scale unsteady cavitation forms. A second approach consists of using the Eulerian-Lagrangian method, which treats the macroscopic flow field using Eulerian mechanics and the individual microscopic bubbles using Lagrangian mechanics. [PERSON] et al. [9] obtained the macroscopic flow field by solving the continuity, momentum and energy equations of a compressible two-phase flow. For the simulation of the microscopic bubbles, they considered that they follow the equation of motion driven by the pressure gradient, the drag and the virtual mass force, and they used the equation of bubble oscillation to evaluate the evolution of bubble radius. Finally, the cavitation erosion characteristics were predicted using the impact pressures on the wall surface induced by the propagating pressure waves induced by the bubble collapses. Similarly, [PERSON] and [PERSON] [10] applied Large Eddy Simulation (LES) to obtain the unsteady ambient pressures and velocity profiles around the bubbles and employed the Rayleigh-Plesset equation to determine the bubble radius. They predicted the cavitation erosion following the evolution of several representative bubbles in the averaged unsteady flow with cavitation. Although this method has the best theoretical background as it considers the bubble rebounds during the collapse and the macroscopic flow, it is uninfluenced by the bubble dynamics. Another problem lies in the choice of the bubbles' injection points because they play a major role in the predicted erosion intensity [11]. The third approach, developed by [PERSON] et al., [12; 13], consists of predicting the impact load spectra of a cavitating flow. This method, considers the two-phase flow as homogeneous, compressible and inviscid, and it resolves the collapse-induced pressure waves to determine the spectrum of collapse events in the fluid domain. [PERSON] and [PERSON] [14] used this method to assess the erosive cavitation flow around a hydrofoil with circular leading edge and obtained a good agreement with the experimental results. However, they indicated that this approach requires a very fine computational mesh in order to capture all scales of cavitation events. Moreover, a very short time step was required because shock waves, which propagate at the speed of sound in water, needed to be resolved near the solid wall. Consequently, the practical implementation of this method is very limited. For instance, this would require a very high computational cost and take too much time to simulate any full scale components, e.g., marine propellers. The last approach, which is the most widely applied one, only resolves the macroscopic cavitating flow field and predicts the cavitation aggressiveness by using different erosion models based on the flow properties. For example, [PERSON] et al., [15] developed four erosion indices which were based on pressure and volume fraction time derivatives as well as on absolute pressure differences. [PERSON] et al., [16] stated a numerical erosion model where the rapid increase of the local static pressure needed to exceed a certain threshold level for erosion to occur. [PERSON] et al., [17; 18] suggested an energy balance approach where the potential energy of the macroscopic cavitation structures was regarded as the main factor that generates erosion. Thus, the potential energy of a cavitation cloud is supposed to be converted into acoustic energy in the form of pressure waves. These pressure waves travel through the fluid and are able to damage the solid wall. [PERSON] et al., [19] defined a Cavitation Aggressiveness Index (CAI) based on the total derivative of pressure on the surface with values from zero that indicates the level of the hydrodynamic cavitation aggressiveness.