Due to the high sediment content in the Yellow River, the pump units in the pumping stations along the line are often eroded by sediment, causing the reduction of pump efficiency and structural damage. The purpose of this paper is to study the influence of particle diameter on the particle track, erosion distribution and erosion rate in a double-suction centrifugal pump in a pumping station of the Yellow River with a Lagrangian particle-tracking approach and a Tabakoff erosion model. The results show that the surface erosion of the impeller on both sides in the double-suction centrifugal pump has an asymmetric distribution, and the erosion rate on both sides is different. The particle diameter affects the moving trajectory of particles and has a significant effect on the erosion morphology and position in the impeller. With the increase of particle diameter, the velocity of the particles moving towards the pressure side of the blade inlet increases, resulting in punctate impact erosion. When the particle diameter decreases, sliding abrasion gradually forms on the pressure side of the blade outlet. The change rule of the solid particle volume fraction on the impeller wall is consistent with that of erosion distribution on the impeller wall. The larger the solid volume fraction is, the higher the wall erosion rate is.

The Yellow River has a high sand content, and sand deposition in the pipelines behind the pumping station occurs from time to time. It is of great significance to reasonably predict the critical velocity of the small-angled V-inclined water transportation pipes. In this study, a Eulerian multiphase model was employed to simulate the solid–liquid two-phase flow. Based on the conservation of the sand transport rate, the critical velocity of the V-inclined pipe was predicted. The effects of simulated pipeline length, pipe inclination and particle size were investigated. The results show that when the simulated pipeline length reached a certain value, it did not affect the prediction of the critical velocity of the overall pipeline. The $\pm 2{}^{\circ }$ pipe inclination had a negligible effect on the critical velocity for transporting small-sized particles, but it led to the nonuniform and asymmetrical distribution of liquid velocity and sand deposition at the different cross-sections. As the particle size increased, the critical velocity also increased. However, the influence of particle size on the critical velocity is currently complicated, resulting in a large difference between numerical simulation and empirical formulas when transporting large-sized particles. Accurate prediction of critical velocity is important for long-distance water transportation pipelines to prevent sand deposition and reduce costs.

During the operation of the water transportation pipelines in the upstream of the Yellow River, varying degrees of sand deposition often occur under a low flow rate. Taking into account the effect of different pipe inclinations, pipe diameters, and inlet sand content, the Eulerian–Eulerian two-phase model was applied in the numerical simulation of sediment-laden flow in a V-inclined pipe. The results indicate that there is a significant difference between a V-inclined pipe and horizontal pipe affected by gravity. Compared with the downward inclined pipe, sand deposition is evident in the upward inclined pipe. The high-velocity region moves upward and the asymmetry of the cross-sectional velocity increases. As the pipe diameter increases, the interaction between sand and the wall as well as the degree of turbulence decrease, so that the distribution of sand volume concentration across the cross section will be more uniform. Under different inlet sand content, the lowest point of the pipe experiences the most sand deposition, with sand volume concentration and velocity distribution across the cross-sections becoming uneven as inlet sand content increases. The location of the maximum liquid velocity varies from section to section. When the inlet sand content increases from 0.42% to 5%, the liquid velocity of the pipe cross-section no longer satisfies the rule of high velocity for middle and low velocity near the wall.