In the transportation process of oil and gas, solid particle erosion in pipelines is an inevitable problem. The erosion usually occurs in fittings with changing flow directions, such as elbows. A theoretical model based on mechanism analyses is developed for predicting the solid particle erosion on the symmetry plane of elbows for annular flow. This model is a sort of generalized erosion prediction procedure, which resolves the erosion process into the description of the flow field velocity profile, particle motion rules, and penetration calculation. The 1/7th power law is adopted to represent the velocity profile of gas core, and a linear velocity profile is assigned to the liquid film. The trajectories of particles in the gas core and the liquid film are discretized, and a mathematical model is developed by analyzing external forces acting on particles. The impact speeds and angles of particles can be obtained from the mathematical model, and the penetration ratios are then estimated by incorporating the impingement information of particles into the erosion formulas. By contrast with experimental data, the mechanistic model is validated and indicates advantages in both accuracy and efficiency. Furthermore, the effects of different parameters on penetration ratios are discussed in detail, including the superficial gas velocity, superficial liquid velocity, pipe diameter, particle diameter, curvature radius, and liquid viscosity.
The mathematical model of the process of the dissolution of the solid particle in the liquid metal under the conducting of the electric current