A modified kinetic theory for frictional-collisional bedload transport valid from dense to dilute regime

Abstract

Modelling sediment transport is still a challenging problem and is of major importance for the study of particulate geophysical flows. In this work, the modelling of sediment transport in the collisional regime is investigated with a focus on the continuum modelling of the granular flow. For this purpose, a frictional-collisional approach, combining a Coulomb model with the kinetic theory of granular gases, is developed. The methodology is based on a comparison with coupled fluid-discrete simulations, that classical kinetic theory model fails to reproduce. In order to improve the continuum model, the fluctuating energy balance is computed in the discrete simulations and systematically compared with the kinetic theory closure laws. Inter-particle friction is shown to affect the radial distribution function and to increase the energy dissipation, in agreement with previous observations in the literature. Due to saltating particles, whose motion can not be captured by the kinetic theory, departure from the viscosity and diffusivity laws are observed in the dilute part of the granular flow. Finally, the quadratic nature of the drag force is shown to increase the granular fluctuating energy dissipation. Based on these observations, modifications of the kinetic theory closure laws are proposed. The modified model reproduces perfectly the discrete simulations in the entire depth structure of the granular flow. These modifications are shown to impact the rheological properties of the flow and they make it possible to recover the µ(I) rheology in the dense regime.

Numerical investigation of unsteady effects in oscillatory sheet flows

“…is the radial distribution function adapted for sand particles. Compared with the definition proposed by Chassagne et al (2021), the radial distribution function does not diverge for φ = φ m but for a smaller value φ = φ b = 0.612, with φ b the effective maximum concentration in the bed. The fact that a radial distribution function diverging for a slightly smaller value of the volume fraction provides better results can be explained by the increased frictional contact for real sediment compared with the smooth spherical spheres used in the discrete element method simulations of Chassagne et al (2021).…”

“…with ν f and ν s the fluid and solid viscosities, respectively. The fluid is considered Newtonian with a constant viscosity but the solid-phase pressure and viscosity taking into account frictional, collisional and kinetic effects in the granular flow are modelled using the novel kinetic theory of granular flows proposed by Chassagne, Chauchat & Bonamy (2021).…”