# Numerical Simulation of Cavitation Erosion Aggressiveness Induced by Unsteady Cloud Cavitation
## 1 Introduction  
Cavitation is an unique phenomenon in the field of hydrodynamics that occurs when the local pressure in a liquid drops below a critical value, usually close to the vapor pressure, and results in the development of various types of vapor structures such as attached cavities, travelling bubbles, vortical cavities and bubble clouds [1]. Cavitation can typically take place in some widely-used hydraulic machines like pumps, turbines and naval propellers. As a matter of fact, cavitation is often associated with some unwanted consequences like machine performance deterioration, cavitation noise, cavitation-induced vibration and cavitation erosion of solid surfaces [2]. Among the problems caused by cavitation, erosion is the one of the most complex ones since it involves the interaction between fluids and structures. Actually, cavitation erosion is caused by the collapse of the cavities. It has been observed that the collapse of a bubble is a condensation process that ends with the compression of the vapor and the subsequent emission of a shock wave creating a pressure pulse with a very strong amplitude. If the collapse takes place close to a solid wall, a high-speed liquid microjet forms, crosses the bubble and impacts the wall resulting in a very high impulsive pressure. If the impulsive forces resulting either from the impact of the microjet or theshockwave exceed the material threshold, such as its yield stress or its ultimate strength, local damage will be induced [1]. Advanced cavitation erosion may cause severe damage to components of hydraulic machines causing higher maintenance costs and deterioration of machine performance together with aggravated vibrations and noise. For example, turbine runners, fluid bearings and pump impellers among others may need replacement after several weeks/months of operation or require regular repair [2]. Therefore, from an industrial point of view concerning both design and maintenance, the evaluation of the erosive power of cavitating flows and the prediction of the material damage remains a major concern to manufacturers and operators. In this sense, several methodologies have been developed to predict cavitation erosion using Computational Fluid Dynamics (CFD) and Structural Mechanics. A first approach focuses on the Fluid-Structure Interaction (FSI) between the cavitation phenomenon and the response of the solid boundary. [PERSON] et al., [3] developed an in-house code based on FSI to study the material deformation due to the impact pressure caused by the collapse of a single bubble under different configurations, which provides a good resolution between flow field and material surface. [PERSON] et al., [4; 5; 6] proposed a one-way simulation method to compute the cavitation erosion based on the histogram of repetitive impact loads obtained experimentally from pitting tests and the analysis of the response of the material to them. However, the authors acknowledged that this approach to predict cavitation erosion needed further development. In addition, [PERSON] et al., [7; 8] investigated the effect of some bubble and material properties (e.g., stand-off ratio, bubble size, driving pressure, strain rate, etc.) on the induced cavitation erosion by employing a meshless Smooth Particle Hydrodynamic (SPH) solver. More specifically, they found that the stand-off ratio has a significant effect on the erosion that permits to explain that an attached cavity has more potential to accelerate the initial damage, i.e., it requires a smaller incubation time, whereas a detached cavity leads to a higher erosion rate. Moreover, they pointed out that the strain rate effect should not be neglected in the constitutive model of the solid and that the peak pressure on the solid does not coincide with the region of maximum erosion. In summary, the SPH modelling approach represents an accurate theoretical background and, therefore, it allows exploring the FSI mechanism of cavitation erosion and stablishing the relationship between the erosion intensity and the material properties.