The Effect of Particle Concentration on Bed Particle Diffusion in Dilute Flows

In this paper, we present the simulation results of a Lagrangian particle tracking model that computes the motion of saltating sediment particles, which is considered the most important mode of bedload transport in rivers and channels. The model is one-way coupled to a validated turbulent LES-WALE (Large Eddy Simulation – Wall-Adapting Local Eddy-viscosity) channel flow, i.e., the particles do not affect the computation of the flow velocities and pressures, as suggested for dilute flows. The model addresses the particle trajectories, the collision of the particles with the bottom wall, and collision among particles. The focus of this work is placed on the effect of different particle concentrations and flow intensities (different flow shear stresses) on jump statistics and particle diffusion. Numerical results are validated with experimental laboratory data obtained from the literature for particle diameters in the range of sands. The present results indicate that, at particle concentrations up to 2%, the diffusion coefficients in the streamwise and spanwise directions, (Formula presented.) and (Formula presented.), for the local range are nearly constants with a value close to one, corresponding to the ballistic regime. At a concentration of 4%, the largest concentration studied herein, values of (Formula presented.) and (Formula presented.) for the local range are slightly smaller, with a representative value of 0.9 regardless of flow intensities. For the intermediate regime, it was found that, on average, (Formula presented.) with (Formula presented.) ranging from 0.6 to 0.85 and (Formula presented.) within the range 0.45–0.70. For a fixed flow intensity, both diffusion coefficients increase with the particle concentration, which is an indication of the contribution of the collision among particles to particle diffusion. For highly controlled simulation conditions, the differences in particle velocity at a given concentration may change drastically, which should translate to important fluctuations in the computation of sediment transport rates. Finally, the employed computational resources are described as a function of particle concentration. Although the number of total collisions increases linearly with the number of particles, the number of collisions per particle reaches a plateau, thus indicating that there exists an upper limiting value for the number of collisions per particle.