Numerical investigations of the force experienced by a wall subject to granular lid-driven flows: regimes and scaling of the mean force

Abstract

Discrete element simulations are used to model a two-dimensional gravity-free granular sample, which is trapped between two smooth sidewalls and one bottom rough wall while being subject to a constant shearing velocity at the top under a given confinement pressure. This system, inspired by conventional fluid mechanics, is called a granular liddriven cavity. Attention is firstly paid to the time-averaged dynamics of the grains once a steady-state is reached. Strong spatial heterogeneities associated with a large-scale vortex formed within the whole volume of the lid-driven cavity are observed. The mean steady force on the sidewall facing the shearing velocity is then investigated in detail for different cavity lengths, shearing velocities and confinement pressures at the top. The ratio of the force on the latter wall to the top confinement pressure force is not constant but depends on both the shearing velocity and the confinement pressure. Above a critical value of the cavity length relative to the wall height and over a wide range of both shearing velocity and top confinement pressure, all data merge into a one-to-one relation between the mean force scaled by the top pressure force and the macroscopic inertial number of the lid-driven cavity. This result reveals the key role played by the inertial rheology of the granular material in the granular force transmission.

Force fluctuations experienced by a boundary wall subjected to a granular flow in two distinct systems

“…By contrast, this effect was never detected for the immersed wall. This observation illustrates the fact that the cavity can produce high confinement pressure on the right top corner (see [5] for much more discussion).…”

“…where r = 0.53, Δr = 0.33 and I 0 M = 0.2 in this study (see detail in [5,6]). The values of r and Δr depend on the mechanical properties of the grains, for instance the interparticle friction, as reported in [6] where results from DEM simulations with μ = 0.27 are presented too.…”

“…We considered μ = 0.5 and e = 0.5. Full information on how the values of those parameters were implemented is given in our initial study of the lid-driven cavity system [5].…”

“…Because the two systems presented above are by construction different, they show two different time-averaged dynamics. First, a standing vortex-like structure is formed inside the cavity volume [5,6], while longitudinal streamlines with a curvature in the vicinity of the wall take place in the immersed wall system [7]. Second, the mean force scalings allowed us to identify different relevant spatial scales specific to each system.…”

“…(2)). Much more details about the specific features of the liddriven cavity and the immersed wall system can be found in [5,6] and [7], respectively. However, we show in the following how these two distinct systems exhibit very similar-not to say, for some aspects, identical-key features in terms of the force distributions and the force time-series autocorrelations on the boundary wall, and we will identify a robust signature of the transition from quasistatic to dense inertial granular flow regime.…”