Numerical and analytical models for prediction of the local scour under pipelines

This paper considers local scour around a pipeline under turbulent flow. The Navier-Stokes equations are solved with a shear stress turbulence model. The original bed deformation equation based on an analytical sediment transport model is used to describe the changes in the bottom surface. The proposed sediment transport equation is based on Coulomb’s friction law for granular flow, Prandtl’s friction law for turbulent flow, and agrees with a large number of phenomenological formulas by other authors. A numerical algorithm for solving the mathematical model of bed surface erosion is implemented in OpenFOAM. Numerical simulations of the problem show that under the influence of turbulent flow generated at the pipeline streamline, a characteristic bottom wave of low steepness appears, the parameters of which asymptotically agree with the experimental data. Based on the analysis of experimental and numerical studies of the considered case, an assumption about the self-similar behavior of the bed surface evolution is made. Based on this assumption, a new method of constructing the self-similar dependence of the bed surface on time and space coordinates is proposed. In the proposed approach, the average values of tangential bottom stresses are determined for a number of self-similar bottom surface shapes, and then the rates of change of bottom wave lengths and amplitudes are calculated using the proposed analytical model. A comparison with experimental data and numerical calculations shows that the solution error does not exceed a few percent and the computational time is reduced by up to 30 times.