## 1 Introduction  
Turbine and auxiliary machinery are key equipment in the hydropower industry, which is important to reduce environmental pollution by improving the efficiency of energy conservation and emissions reduction [1]. The reliability and advancement of hydraulic machinery such as propellers, turbines, pump, and valves as well as hydraulic discharge structures are largely dependent on the quality and performance of machinable metal materials [2]. Cavitation erosion is one of the main failure modes in hydraulic machinery, which is often caused by the action of stress pulses on the surface of metallic materials [3]. The main mechanisms of cavitation erosion on metal materials are shock wave and micro jet. [PERSON] [4] believed that the microjet penetrates the inside of the bubble and hits the solid wall, causing damage to the solid surface. [PERSON] [5] proposed that when the cavitation bubble collapses, the energy accumulated inside the bubble is released and a shock wave is formed, which erodes the solid surface. The pressure wave or high-speed jet is generated in the process of bubble collapse, which varies from several hundred MPa to one thousand MPa [6, 7]. Such high stress pulses could easily lead to deformation and the loss of metal materials in industry. Cavitation erosion is a microscopic, instantaneous and random complex phenomenon. A relatively complete theoretical analysis of cavitation erosion has not been established recently. The surface of hydraulic machinery is often affected by cavitation erosion, which will induce strong vibration, decreasing performance, and a reduced life and production efficiency. The loss caused by cavitation erosion is inestimable. Therefore, the research on the anti-cavitation erosion ability of metallic materials used for hydraulic machinery is not only of profound theoretical significance, but also of great practical engineering significance. Recently, while researchers have conducted much work on cavitation erosion, the technology of the anti-cavitation ability improvement of metallic materials needs more effort. [PERSON] [8] pointed out that only cavitation impacts with an energy larger than a certain threshold level affect the cavitation erosion of materials, and this fundamental threshold was obtained from the relationship between the erosion rate and the energy of the cavitation impacts. [PERSON] [9] found that the pitting damage on the surface of the material is mainly caused by the micro jet generated by the collapse of bubbles. The cavitation erosion phenomenon of a single hydrofoil was studied experimentally in the work of [PERSON] [10], and it was found that the degree of cavitation erosion was related to the cavitation structure. [PERSON] [11] studied the cavitation erosion in fluid jet machining, and pointed out that the cavitation intensity is related to the ultrasonic frequency. The lower the frequency, the more severe the cavitation erosion. [PERSON] [12] showed that the jet width and jet diffusion angle had a great influence on the strength of the cavitation. A larger jet velocity will lead to the larger area of erosion and deeper erosion depth. [PERSON] [13] investigated the erosion strength and efficiency of the cavitation jet. When the inlet pressure was 10 MPa and 15 MPa, the nozzle inner surface roughness value was 12.5 \(\upmu\)m, and the erosion efficiency was the best. When the inlet pressure was 20 MPa and 25 MPa, the surface roughness value of the nozzle was reduced to 6.3 \(\upmu\)m. [PERSON] [14] revealed that there were deep and rough spongy structural damages on the surface of the 316 LVM during the cavitation erosion stage. With the increase in time, small-sized cavitation pits first appeared on the surface of the material and then the surface plastic deformation increased. Four very similar Venturi shapes were used to observe the cavitation erosion test, and [PERSON] [15] pointed that despite the same convergence angle cavitation size, the appearance varied significantly when the divergence angle was changed.