Simulations of Granular Bed Erosion Due to Laminar Shear Flow

Simulations of granular bed erosion due to laminar shear flow

Sediment transport and erosion of granular beds occurs in natural (river beds, dune formation) as well as in engineered (dredging, sand issues in oil production) systems. The incipient erosion, i.e. the minimal flow conditions that bring about motion of solids in the upper layer of the granular bed is characterized by a critical value of the Shields number (the dimensionless Shields number is the ratio of viscous forces at the bed surface and net gravity on the grains forming the bed). The critical shields number depends on the granular bed characteristics (topology, particle size (distribution) etc.) and on the flow above the bed. We report direct simulations on the initial stages of granular bed erosion where the bed is made of uniformly sized spherical particles, and the flow above the bed is a laminar simple shear flow. The simulations make use of the lattice-Boltzmann method (LBM) for simulating the flow above the bed and in between the solid particles. We largely resolve the solid-liquid interfaces and the solid-liquid interaction by means of an immersed boundary method. The spheres undergo hard collisions with one another. Lubrication forces are explicitly added when solid surfaces are in such close proximity that the LBM cannot resolve hydrodynamic interactions anymore. The results provide detailed insight into the granular bed erosion process, including information regarding hydrodynamic forces acting on the particles (their averages and fluctuation levels), and solid and liquid velocity profiles in and closely above the bed. The figure shows sample results for three values of the Shields number (0.1, 0.2, 0.4 from left to right) that are around the critical value. In the figure the spheres are coloured by their absolute velocity.