Shear localization and effective wall friction in a wall bounded granular flow

EPJ Web of Conferences 140 , 03042 (2017 ) DOI: 10.1051/epjconf/201714003042 Powders & Grains 2017 Shear localization and effective wall friction in a wall bounded granular flow Riccardo Artoni1 , and Patrick Richard1 , 1 LUNAM Université, IFSTTAR, MAST, GPEM, F-44340 Bouguenais, France Abstract. In this work, granular flow rheology is investigated by means of discrete numerical simulations of a torsional, cylindrical shear cell. Firstly, we focus on azimuthal velocity profiles and study the effect of (i) the confining pressure, (ii) the particle-wall friction coefficient, (iii) the rotating velocity of the bottom wall and (iv) the cell diameter. For small cell diameters, azimuthal velocity profiles are nearly auto-similar, i.e. they are almost linear with the radial coordinate. Different strain localization regimes are observed : shear can be localized at the bottom, at the top of the shear cell, or it can be even quite distributed. This behavior originates from the competition between dissipation at the sidewalls and dissipation in the bulk of the system. Then we study the effective friction at the cylindrical wall, and point out the strong link between wall friction, slip and fluctuations of forces and velocities. Even if the system is globally below the sliding threshold, force fluctuations trigger slip events, leading to a nonzero wall slip velocity and an effective wall friction coefficient different from the particle-wall one. A scaling law was found linking slip velocity, granular temperature in the main flow direction and effective friction. Our results suggest that fluctuations are an important ingredient for theories aiming to capture the interface rheology of granular materials. 1 Introduction The rheology of granular materials is relevant to many industrials applications (grain transport and storage) and to natural events (avalanches, mud-slides. . . ). Several geometries have been used to probe the rheology of granular systems (inclined plane, shear cell, confined gravitydriven flows. . . ); however, a satisfying modeling of 3D flows is still lacking. This is particularly true for wallbounded configurations, in which the nonlocality of the rheology near a boundary and the non trivial boundary conditions increase the complexity of the physics. In this work we present discrete element simulations of a wallbounded three dimensional dense granular flow. The flow configuration studied in this paper, which can be referred as torsional shear flow, consists in a cylindrical geometry filled by the studied system, where the bottom wall rotates and the upper and cylindrical wall are fixed. In this work the flow is at fixed normal stress, i.e. the upper wall is free to move vertically under the action of the imposed normal force and the reaction of the particles contained in the cylinder. This configuration is interesting because simple velocity profiles were obtained for viscous and viscoelastic fluids, and therefore it is tempting to consider it as a granular rheometer. On the other hand, secondary flows were already observed for newtonian fluids in this geometry. The main objective of this work is therefore to characterize the granular flow in such a configuration. A particular focus will be given on the kinematics of the flow  e-mail:  e-mail: Fz H 2R Figure 1. Sketch of the torsional flow configuration. Fz is the imposed normal force, and Ω the angular velocity of the bottom bumpy wall. and on the flow regimes as a function of the main system parameters, and on the effective wall friction, and related scalings, at the cylindrical wall. 2 Simulation method Numerical simulations are performed using the non smooth contact dynamics method [1], as implemented in the LMGC90 open source framework [2]. The flow configuration studied in this paper, which can be referred as © The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0/). EPJ Web of Conferences 140 , 03042 (2017 ) DOI: 10.1051/epjconf/201714003042 Powders & Grains 2017 torsional shear flow, consists in a cylindrical geometry where the bottom wall rotates and the upper and cylindrical wall are fixed. In this work the flow is at fixed normal stress, i.e. the upper wall is free to move vertically under the action of the imposed normal force and the reaction of the particles contained in the cylinder. The top and bottom walls are bumpy, while the cylindrical wall is smooth but frictional. Gravity acts on the system along z. The top wall cannot move on the x- and y- directions but is free to move in the z-direction, simply according to the balance between its weight, the externally applied force and the force exerted by the grains. Simulations were performed with N slightly polydisperse spheres (uniform number distribution in the range 0.9d − 1.1d) interacting through perfectly inelastic collisions and Coulomb friction (μ p = 0.5). Each bumpy wall was composed of spheres with the same properties of the particles (positioned randomly with a surface density of approximately 0.2 spheres / d2 ). We chose perfectly inelastic grains to maximize dissipation and thus save computation time. Interactions of particles with the flat walls were also perfectly inelastic and frictional (with a coefficient of friction μ pw ). We performed several simulations varying the angular velocity of the bottom bumpy wall Ω, the force applied to the upper bumpy wall Fz , the particle wall friction coefficient μ pw , and the radius of the cylinder R (while maintaining approximately the same system height H ∼ 20d). The first two parameters can be made dimensionless for example  by considering a particle Froude number Ω̃ = ΩR/ gd and the ratio between the total force mass exerted by the top wall and the weight of the grains, z F̃ = Mg+F Nmg where m is the average particle mass, and M = 100m is the mass of the top wall. In particular, the investigated ranges correspond to μ pw = 0 − 0.3, Ω̃ = 0.12 − 2.4, F̃ = 0.2 − 100, R = 12 − 36d (corresponding to N = 10000 − 90000). Our simulations lie in a range of inertial number [3, 4] from 0 (for r = 0) to 10−1 , which corresponds to the quasistatic and dense regimes of flow. It is important to stress that, due to the cylindrical geometry, the inertial number is an increasing function of the radial coordinate. 20 012 0 03 1 012 0 23 3 012 0 23 4 0011 67 60 7 0 010 012 013 00 1021 014 02 015 610 Figure 2. Azimuthal velocity profiles along z, rescaled by the velocity of the bottom wall, for Ω̃ = 1.2, F̃ = 0.2, μ = 0.3, three different values of the cell radius, and two radial positions, 1d from the cylindrical wall (dashed lines), and 10d far from the wall (solid lines). rescaled by the velocity of the bottom plate, for Ω̃ = 1.2, F̃ = 0.2, μ = 0.3, three values of cell aspect ratio (at constant system height H). At first, the figure highlights the dependence of the velocity profile on the rad (...truncated)