## 1 Introduction  
As an important control element in digital hydraulic systems, high-speed on/off valves are widely used in the energy, chemical, aerospace, and automotive fields due to their simple structure, fast response, and low cost. However, in practice, contaminated particles, such as metal filings and dust in the oil fluid, will hit the wall with high kinetic energy driven by the fluid medium, resulting in erosion at the valve port of the high-speed on/off valve, which severely affects the control accuracy and service life of the high-speed on/off valve.  
Numerous studies have been carried out to address the problem of valve orifice erosion caused by contaminated particles. [PERSON] et al. [1] found that with increases in the particle diameter of 25%, 50%, and 75% in the open state of the ball valve, the rate of erosion is increased. On the contrary, the opposite rule governs in a completely open state of the ball valve. [PERSON], [PERSON] et al. [2] used a developed empirical equation for mass removal to examine erosion in choke valve components for aqueous slurry flows. While flow characteristics and erosion locations were identified satisfactorily, erosion rates were seriously underestimated. [PERSON] et al. [3] established a two-dimensional slide valve model and solved the trajectory of particles based on a stochastic separated flow model, and then obtained the wear profile using the time-discrete and spatial-discrete update methods. [PERSON] et al. [4] analyzed the erosion wear of electro-hydraulic servo valves under different contaminated fluid conditions and explored the variation law of servo valve pressure gain and zero leakage with the erosion wear of the valve port. Basedon the erosion theory, a mathematical model and a simulation model of the erosion wear of the servo valve of the jet pipe were established [5; 6], obtaining the simulated predicted life and the theoretically calculated life of the jet pipe servo valve. [PERSON] et al. [7] established a two-dimensional cone valve model, then performed the numerical calculation of solid-liquid two-phase flow using the DPM model, and analyzed the causes of erosion at the valve port.  
Some scholars have used the two-dimensional model to simulate valve orifice erosion and have obtained good simulation results, which proved the feasibility and accuracy of numerical simulation in erosion prediction. However, due to the characteristics of the high-speed jet and the special orifice structure of the high-speed on/off valve, large-scale fluid vortices are easily generated at the valve orifice. The fluid vortices not only affect the flow state of the fluid near the vortices but also cause changes in the flow of the fluid at other locations of the valve orifice due to the vortex effect, which aggravates the erosion at the valve orifice. The two-dimensional model is not applicable, and a three-dimensional model was employed to simulate the effect of fluid vortices on the orifice erosion of high-speed on/off valves in this study.  
In addition, at this stage, there have been few studies on the effects of changes in the internal flow field and particle motion caused by changes in different factors on valve port erosion. Therefore, the orifice erosion locations and erosion rates were obtained for different orifice erosion-influencing factors in this topic to reveal the relationship between particle collision behavior and orifice erosion morphology and provide a reference for the optimization design of high-speed on/off valves against erosion by investigating the changes in orifice erosion under different factors.