# A Study of Cavitation Erosion in Artificial Submerged Water Jets
## 1 Introduction  
When the local pressure falls below the saturated vapor pressure, vapor bubbles form in water, a phenomenon known as the cavitation effect [1]. Cavitation water jets offer numerous advantages, including cost-effectiveness, cleanliness, environmental friendliness, efficiency, and safety, and have found wide-ranging applications in various industrial fields such as mechanical treatment, oil drilling, and microbial degradation [2]. Traditional submerged cavitation water jets typically involve a continuous jet, wherein a high-velocity water stream is injected into a stationary body of water, resulting in intense shear cavitation and the generation of a significant number of vapor bubbles. However, in non-submerged conditions, when the cavitation water jet is exposed directly to the atmospheric environment, the cavitation effect diminishes rapidly at the nozzle outlet, making it difficult for cavitation vapor bubbles to reach the surface of the target object. To enhance the cavitation effect in non-submerged conditions, most studies employ an artificially created underwater environment by injecting a low-pressure water jet in the same direction around the periphery of the cavitation water jet, thus forming a water-loop-type submerged environment [3]. The exploration and examination of the cavitation water jet effect can be traced back to the late nineteenth century. [PERSON] [4] published a renowned paper titled \"On the pressure developed in a liquid during the collapse of a spherical cavity\". In this work, he systematically proposed the theory of cavitation jets and derived the well-known equation for the radial motion of vapor bubbles in the early twentieth century. The equation of motion for an ideal spherical cavity was established by solving the collapse of a single cavity in an infinite domain of a homogeneous, viscosity-free, incompressible liquid using the energy balance principle. [PERSON] and [PERSON] [5] derived the kinetic equation for acavity containing a compressible gas. They extended the understanding of cavitation by considering gas compressibility within the cavity. [PERSON] [6] investigated the collapse of spherical bubbles in compressible liquids through numerical solutions of the hydrodynamic equations. Their findings indicated that higher values of shear viscosity result in slower bubble collapse. When the vacuole reaches a critical scale, its wall velocity exceeds the speed of sound, the pressure within surpasses 1000 MPa, and the temperature exceeds 1000 K. This implies that at a certain scale, the vacuole harbors substantial potential energy. Upon collapse, this energy is rapidly released with high intensity, leading to material damage due to concentrated impacts on the workpiece surface, resulting in cavitation [7]. However, despite these advancements, the mechanism of cavitation erosion remains incompletely understood due to the complexity of turbulent structures and cavitation phenomena, and a universally accepted theory is yet to be established. Numerous experimental studies have been conducted on cavitation water jets, with erosion tests and high-speed visualization being commonly used methods. Erosion tests provide an intuitive and reliable means to examine the impact effect of the jet and study its cavitation performance. In a study by [PERSON] [8], cavitation erosion tests were performed on different materials, employing optical microscopy to identify wear mechanisms and observe damage characteristics under cavitation water jet and abrasive water jet erosion. [PERSON] [9] investigated the effect of various nozzle geometries on the erosion rate and determined the relationship between mass loss and erosion time at optimum target distances by varying the nozzle throat diameter as well as the diameter of the expansion section. The findings revealed that the erosion rate is dependent on the nozzle geometry, with the maximum erosion rates varying by over 600% across different nozzles.