Abstract: Abstract: Most of the existing erosional prediction is based on the premise of constant flow boundary conditions. However, when the flow surfaces are corroded, the hydrodynamic parameters changed with the change of the flow boundary. Thus, the existing erosional prediction approach is difficult to be consistent with the reality. The practice shows that the end clearance surface and the shaft of the turbine guide vane are corroded by sand-laden water, which is a development process of non-homogeneous and backward. The generation of erosional damage has a negative impact on the normal operation of the unit and the safety of production. In order to accurately describe the physical reality of the erosional shape evolution of the end clearance surface，in this article, we proposed erosional differential quadrature concept. The approximate expression of the geometric shape in the main erosional surface was constructed by creating as much surfaces. The numerical simulation methods combined RNG k-ε (Re- normalization group k-ε) turbulence model with DPM (discrete phase model) was applied. According to the test and numerical results of the full flow field for San-yuan hydropower company, the calculated boundary conditions and initial conditions were set. The model inflow boundary could be assumed to be velocity inlet and outflow. The inlet speed was 10 m/s, and the pressure of inlet was 1.9 MPa. The model of the end clearance flow of turbine guide vane under sand-laden water was simplified as the flow around a circular cylinder and a step, and then the three-dimensional unsteady numerical calculation was carried out. The average erosional rate distributions were obtained on the main erosional surface at different stage. The main erosional surfaces include the back of shaft as well as the step surface of the guide vane and the head cover. The mathematical model and approximate solution method of average erosional rate and erosional time related to erosional depth variation on flow surface were established. The surface morphology of the clearance flow model was changed according to the amount of erosional depth variation. When the geometrical form of the clearance flow surface was approximately the same as the degree of erosion in the actual operation, the geometrical form of model was no longer changed. Thereby, the gradual erosional shape of the flow surface was predicted. The temporal and spatial evolution of the erosional morphology on the flow wall during the period of erosion was analyzed, and then the flow evolution mechanism of the backflow on the end surface and the step surface of the turbine guide vane was analyzed. As the particles at the outer edge of the vortex in the step surface of the guide vane continually to erode the surfaces, where the deep erosional pits appeared, the vortex developed backwards, the reattachment position on the guide vane surface was also migrated upstream, and then the erosional area had a significant increase and also migrated upstream. In addition, the main reason for the erosion behind the shaft was the generation of the Karman Vortex Street. Due to the airfoil of guide vane was the asymmetric reduction, the erosion on the right side (observing from the entrance direction) was more serious. When the period was from 0.2 T to 0.4 T, the change degree of erosional morphology on turbine guide vanes were the most intense. The numerical results were approximately similar to the erosional depth on the erosional surface under the actual running time of the unit, which verified the validity of the method. This paper provides a reference for effective prediction of the erosional condition of fluid machinery. In addition, it also provides a theoretical reference for structural design, erosional protection and material selection in the end clearance surface of turbine guide vane.