## 1 Introduction  
The wear due to particles on materials is extremely complicated as it is affected by the particle size, density, concentration, and impact angle and different operating conditions. The different particle parameters and operating conditions can lead to different degrees of wear [1, 2, 3]. Similarly, particles will also cause different degrees of wear in a pump, which wear is mainly manifested on the surface and inside of the flow passage components. In practical engineering applications, the wear characteristics of particles on a pump under different operating conditions cannot be ignored as they are directly related to the service life and reliability of the pump [4, 5, 6]. There are many influencing factors involved in the wear of particles on pump materials. To optimize a centrifugal slurry pump impeller, [PERSON] et al. [7] analyzed the wear characteristics of the solid-liquid two-phase flow in the pump based on a Euler-Euler mixture model and compared the performance of the original pump and the optimized pump. The results showed that the optimized pump had a lower wear rate and a smaller loss of mass than the original pump. [PERSON] et al. [8] analyzed the wear of the double-suction centrifugal pump by particles, which provided a reference for predicting the wear of the centrifugal pump. [PERSON] et al. [9] studied the wear due to particles of different sizes on the material of a pump, analyzed the wear mechanism, established a relationship between the wear rate and particle shape, and carried out an experimental verification. [PERSON] et al. [10] also studied the wear mechanism of particles colliding with pump materials at multiple angles. [PERSON] et al. [11] used a Monte Carlo simulation of the physical process to study the wear of solid particles on turbomachinery. [PERSON] et al. [12] proposed a semi-mechanistic model for the erosion of different target materials due to solid particles and tested it using 150-\(\upmu\)m sand particles to verify its effectiveness. Their results showed that the particles caused cutting and deformation wear on the tested material. [PERSON] et al. [13] analyzed the wear of the impeller caused by various sediment types and particle trajectories at the entrance, and they found that the wear of the impeller was mainly concentrated on the back cover and working surface. [PERSON] et al. [14] studied the wear of materials using sand particles of different sizes and flow rate conditions. Their test results showed that as the size of the sand particles increases, the wear profile changes from a \"W\"-shape to a \"U\"-shape. [PERSON] et al. [15] also studied the wear of solid particles on the elbow of a pump. Solid particles that are being conveyed will inflict wear on the flow passage components in pumps [16]. [PERSON] et al. [17] studied the wear associated with sludge concentration and particle size on a double-suction centrifugal pump. Their results showed that, compared with pure water, the pump head and shaft power were lower due to the presence of sludge. Moreover, the pump head and shaft power decreased as the sludge concentration and particle size increased. [PERSON] et al. [18] analyzed the wear due to sand particles of various sizes on the surface of pump blades based on a two-phase flow model. [PERSON] et al. [19] studied the wear of the impeller of a double-suction centrifugal pump as a result of the particle size, particle shape, and concentration of sediment from the Jingtai Yellow River Irrigation Project. Their results showed that the erosion and wear were mainly distributed near the leading and trailing edges of the impeller. [PERSON] et al. [20] analyzed the wear of the impeller of a pump as a result of the particle concentration of the sediment in the Ake River, Brazil, and conducted an experimental study. They demonstrated that the wear of the impeller increased linearly as the sediment concentration increased.