## 1 Introduction  
China is rich in water resources; with the full use of water resources in China, a variety of hydraulic constructions are under-constructed. China is a country with many sediment-laden rivers, and the Yellow River basin is famous for its sediment. The erosion and wear of hydraulic structures caused by sand flow is a common disease of hydraulic structures [1, 2, 3]. According to the survey, 70% of hydraulic structures in sandy rivers suffer from wear and damage caused by high-speed sediment-laden flow. For example, since Yuzixi [4] Hydropower Station in Sichuan Province was put into operation in May 1986, the reinforced concrete and steel plate lining in the sand drainage tunnel cannot withstand the impact wear caused by flood discharge and sand discharge every year. Four years after the completion and operation of Ertan Hydropower Station [5], the local abrasion pit of the No.1 spillway tunnel was 20-30 mm deep. After working for 8666.34 h in total, serious abrasion pits appeared at the bottom of the curved gate of Xiaolangdi No.1 Sand Drain Tunnel, which seriously affected the safe operation of the gate. One year after the construction and operation of Daquke Hydropower Station, the erosion damage occurred in the sand scouring tunnel, the steel lining of the bottom plate of the working gate was seriously damaged, and the water sealing bolt on the bottom edge of the working gate was worn and fell off. At present, the erosion wear of hydraulic structures is mainly studied by scouring experiments with various scour experimental instruments. [PERSON] et al. [6] concluded through experimental studies that the erosion rate of concrete is basically linear with the increase in sediment concentration, and the change in velocity at a low angle scour has a great influence on the erosion rate. [PERSON] [7] and [PERSON] [8] improved the traditional erosion wear equipment, and conducted experiments with the improved equipment, and found that the erosion wear amount of concrete increased exponentially with the increase in jet velocity. [PERSON] [9] carried out the erosion wear experiment on Q345 steel and concluded that the erosion amount increased with the equivalent increase in particle size and concentration. With the change in impact angle, the wear quantity increases first and then decreases with the change in impact angle and reaches the maximum value at 30\({}^{\circ}\). [PERSON] et al. [10] carried out a preliminary experimental study on the three-phase flow (air-water-sand) in a horizontal pipe and introduced the application of the sand-liquid model in the literature. The results show that sand transport characteristics and critical deposition rate are closely related to gas-liquid two-phase flow state and sand concentration. With the development of computers, numerical simulation is widely used in erosion simulation [11; 12], such as black water pipelines, bifurcation pipelines of hydropower stations and oil-gas pipelines [13; 14]. [PERSON] [15] used the computational fluid dynamics method to numerically simulate the erosion wear behavior and mechanism of solid-liquid two-phase pipeline in coal gasification wastewater treatment system and optimized the bend of black water pipeline. [PERSON] et al. [16] simulated and analyzed the influence rules of fluid velocity, particle diameter and solid concentration on pipeline erosion and wear caused by multiphase flow mud. The simulation study by [PERSON] et al. [17] shows that there are two serious erosion positions in the oil delivery elbow, and the layout of the elbow and the particle size will significantly change the serious erosion positions of the elbow. [PERSON] etc.