A Two-Dimensional Model of Predicting Sand Erosion in Elbows for Liquid Flow

A two-dimensional theoretical procedure is proposed in this study to estimate sand particle erosion in 90-degree elbows for liquid flow. The two-dimensional model adequately describes the erosion occurring along the centerline of the elbow extrados and to an extent reflects the erosion level on the whole elbow. The sand erosion prediction procedure is divided into three steps: building a two-dimensional liquid flow model, tracking the particle trajectories and predicting the penetration depth. First, a motion expression of the fluid streamline in an elbow is deduced from the continuity equation and the Euler equations, supposing the incompressible flow in the elbow is steady and inviscid. The radial velocity is introduced into the present model to reflect the effect of secondary flow on the symmetry plane. Second, particle trajectories are computed using the Lagrange approach based on the obtained expression of flow field distributions. The effects of the fluid drag force and the virtual mass force are considered as the main factors, and the particle impact velocity and angle are predicted through this method. Third, the penetration depth can be calculated from erosion correlations and the erosion profile along the centerline of the 90-degree elbow can also be worked out. Several typical experiments are selected to verify the two-dimensional theoretical model by comparing the predicted erosion results with the measured data.