Two-Dimensional Numerical Simulation of Saltating Particles Using Granular Kinetic Theory

Abstract

Most granular flows at environmental conditions are unsteady and exhibit a complex physical behavior. Dune formation and migration in the desert are controlled not only by the flow of saltating particles over the sand bed, but also by turbulent atmospheric airflow. In fact, sediments are transported by the atmospheric airflow within a thin layer only a few centimeters above the sandy surface. These jumping particles reach a maximum sediment mass flux level at a certain delay time (known as the "saturation time") after the initial movement by sliding and rolling begins. Unlike sediment transport in water where the particles are lifted by the turbulent suspension, the saltating particles are kept alive in the layer mainly due to particle-particle and particle-bed collisions. In order to model this Aeolian transport of sand, Jenkins and Pasini [1] proposed a two-fluid model (one-dimensional and steady state) using Granular Kinetic Theory (GKT) to describe the solid-phase stress. The present work extends the original idea of Jenkins and Pasini [1] by using a more robust model of GKT for the kinetic/collisional contributions to the solid-phase stress tensor, together with a friction model activated for sustained contacts between particles. In addition, a standard k-ε turbulence model for the air and a drag model for the interaction between the phases are employed. A rectangular 2D geometry was chosen with a logarithmic profile for the inlet air velocity, along with an initial amount of sand at rest in the lower part of the simulation domain, resembling the particle saltating flow commonly seen in the vertical middle plane within saltation wind tunnels. This model is validated with experimental data from Liu and Dong [2] and the results given by Pasini and Jenkins [1]. A good estimation for the particle erosion and mass flux in the saltation layer is predicted, even though the profiles of mass flux and concentration within the transport layer are very thin and lower.