A collision model for grain-resolving simulations of flows over dense, mobile, polydisperse granular sediment beds

Abstract

We present a collision model for phase-resolved Direct Numerical Simulations of sediment transport that couple the fluid and particles by the Immersed Boundary Method. Typically, a contact model for these types of simulations comprises a lubrication force for particles in close proximity to another solid object, a normal contact force to prevent particles from overlapping, and a tangential contact force to account for friction. Our model extends the work of previous authors to improve upon the time integration scheme to obtain consistent results for particle-wall collisions. Furthermore, we account for polydisperse spherical particles and introduce new criteria to account for enduring contact, which occurs in many sediment transport situations. This is done without using arbitrary values for physically-defined parameters and by maintaining the full momentum balance of a particle in enduring contact. We validate our model against several test cases for binary particle-wall collisions as well as the collective motion of a sediment bed sheared by a viscous flow, yielding satisfactory agreement with experimental data by various authors.

A coupled lattice Boltzmann method and discrete element method for discrete particle simulations of particulate flows

“…Especially for dense particulate systems, where a large number of particle collision can be expected, a careful and accurate treatment of these particle interactions is necessary to obtain the correct system dynamics [9]. Therefore, detailed studies have been conducted to calibrate and validate the classical DNS approaches [10,11,12,13,14]. For that purpose, they commonly make use of experimental data featuring the collision dynamics of a single sphere with a wall [15].…”

High-resolution simulations of turbidity currents

“…A no-slip condition was applied at the top and bottom wall as well as at the particle surface. A detailed comparison validating the simulation results has been presented in great detail in Biegert et al (2017). Here, we extend this work to show data from the same physical setup, but with an increased flow rate, such that the gross of the particles are set into motion and interact in a complex network.…”

“…The lubrication force, F l , and contact force, F c , model close-range particle-particle interactions. With the exception of the tangential lubrication force, the methods used to evaluate these forces are described and validated in detail by Biegert et al (2017), but here, we present them briefly.…”

“…The particles have a density of ρ p /ρ f = 1.011, which is close to neutrally buoyant conditions. We assume material parameters corresponding to glass or silicate materials as thoroughly validated in Biegert et al (2017). In particular, we choose e dry = 0.97, μ k = 0.15, μ s = 0.8, and ν = 0.22, where e dry is the wall-normal restitution coefficient for dry collisions, μ k and μ s are the kinetic and static friction coefficients for oblique collisions, and ν is Poisson's ratio.…”

Transition of a Hyperpycnal Flow Into a Saline Turbidity Current Due to Differential Diffusivities

“…To calculate the evolution of the flow field, we employ our incompressible Navier‐Stokes solver P A R T I E S (Biegert, Vowinckel, & Meiburg, ; Biegert, Vowinckel, Ouillon, et al, ), which uses second order central finite differences to discretize the viscous terms, along with a second order upwind scheme for the advection terms. A third order low‐storage Runge‐Kutta method is used to advance the flow field in time.…”