Continuum simulation of the discharge of the granular silo: a validation test for the mu(I)-visco-plastic flow law

Using both a continuum Navier-Stokes solver, with the mu(I)-flow-law implemented to model the viscous behavior, and the discrete Contact Dynamics algorithm, the discharge of granular silos is simulated in two dimensions from the early stages of the discharge until complete release of the material. In both cases, the Beverloo scaling is recovered. We first do not attempt quantitative comparison, but focus on the qualitative behavior of velocity and pressure at different locations in the flow. A good agreement is obtained in the regions of rapid flows, while areas of slow creep are not entirely captured by the continuum model. The pressure field shows a general good agreement. The evolution of the free surface implies differences, however, the bulk deformation is essentially identical in both approaches. The influence of the parameters of the mu(I)-flow-law is systematically investigated, showing the importance of the dependence on the inertial number I to achieve quantitative agreement between continuum and discrete discharge. The general ability of the continuum model to reproduce qualitatively the granular behavior is found to be very encouraging.Comment: 12 pages, 15 figure

Effect of Changing the Vocal Tract Shape on the Sound Production of the Recorder: An Experimental and Theoretical Study

Changing the vocal tract shape is one of the techniques which can be used by the players of wind instruments to modify the quality of the sound. It has been intensely studied in the case of reed instruments but has received only little attention in the case of air-jet instruments. This paper presents a first study focused on changes in the vocal tract shape in recorder playing techniques. Measurements carried out with recorder players allow to identify techniques involving changes of the mouth shape as well as consequences on the sound. A second experiment performed in laboratory mimics the coupling with the vocal tract on an artificial mouth. The phase of the transfer function between the instrument and the mouth of the player is identified to be the relevant parameter of the coupling. It is shown to have consequences on the spectral content in terms of energy distribution among the even and odd harmonics, as well as on the stability of the first two oscillating regimes. The results gathered from the two experiments allow to develop a simplified model of sound production including the effect of changing the vocal tract shape. It is based on the modification of the jet instabilities due to the pulsating emerging jet. Two kinds of instabilities, symmetric and anti-symmetric, with respect to the stream axis, are controlled by the coupling with the vocal tract and the acoustic oscillation within the pipe, respectively. The symmetry properties of the flow are mapped on the temporal formulation of the source term, predicting a change in the even / odd harmonics energy distribution. The predictions are in qualitative agreement with the experimental observations

The granular silo as a continuum plastic flow: the hour-glass vs the clepsydra

The granular silo is one of the many interesting illustrations of the thixotropic property of granular matter: a rapid flow develops at the outlet, propagating upwards through a dense shear flow while material at the bottom corners of the container remains static. For large enough outlets, the discharge flow is continuous; however, by contrast with the clepsydra for which the flow velocity depends on the height of fluid left in the container, the discharge rate of granular silos is constant. Implementing a plastic rheology in a 2D Navier-Stokes solver (following the mu(I)-rheology or a constant friction), we simulate the continuum counterpart of the granular silo. Doing so, we obtain a constant flow rate during the discharge and recover the Beverloo scaling independently of the initial filling height of the silo. We show that lowering the value of the coefficient of friction leads to a transition toward a different behavior, similar to that of a viscous fluid, and where the filling height becomes active in the discharge process. The pressure field shows that large enough values of the coefficient of friction ($\simeq$ 0.3) allow for a low-pressure cavity to form above the outlet, and can thus explain the Beverloo scaling. In conclusion, the difference between the discharge of a hourglass and a clepsydra seems to reside in the existence or not of a plastic yield stress.Comment: 6 pages, 6 figure

Gas-assisted discharge flow of granular media from silos

International audienceWe studied experimentally the discharge of a vertical silo filled by spherical glass beads and assisted by injection of air from the top at a constant flow rate, a situation which has practical interest for nuclear safety or air-assisted discharge of hoppers. The measured parameters are the mass flow rate and the pressure along the silo, while the controlled parameters are the size of particles and the flow rate of air. Increasing the air flow rate induces an increase in the granular media flow rate. Using a two-phase continuum model with a frictional rheology to describe particle-particle interactions, we reveal the role played by the air pressure gradient at the orifice. Based on this observation we propose a simple analytical model which predicts the mass flow rate of a granular media discharged from a silo with injection of gas. This model takes into account the coupling with the gas flow as well as the silo geometry, position and size of the orifice

The Cohesive Granular Collapse as a Continuum : Parametrization Study

Although intensive research on the flow of dry granular materials has allowed for the proposition of continuum rheology and modelling, the behaviour of flowing cohesive material has attracted less attention so far. To start modelling such cohesive flows, we first focus on the configuration of a granular collapse, which is a simple benchmark test. Specifically, we compare granular-collapse experiments of cohesive grains with numerical simulations, where we test a simple rheology for the material : the so-called µ(I)-rheology, supplmented by a yield stress for cohesion. This document reports the sensitivity of our numerical simulations on the parameters of the rheology, often challenging to measure in experiments

Stationary shear flows of dense granular materials : a tentative continuum modelling

We propose a simple continuum model to interpret the shearing motion of dense, dry and cohesion-less granular media. Compressibility, dilatancy and Coulomb-like friction are the three basic ingredients. The granular stress is split into a rate-dependent part representing the rebound-less impacts between grains and a rate-independent part associated with long-lived contacts. Because we consider stationary flows only, the grain compaction and the grain velocity are the two main variables. The predicted velocity and compaction profiles are in apparent agreement with the experimental or numerical results concerning free-surface shear flows as well as confined shear flow

Granular Pressure and the Thickness of a Layer Jamming on a Rough Incline

Dense granular media have a compaction between the random loose and random close packings. For these dense media the concept of a granular pressure depending on compaction is not unanimously accepted because they are often in a "frozen" state which prevents them to explore all their possible microstates, a necessary condition for defining a pressure and a compressibility unambiguously. While periodic tapping or cyclic fluidization have already being used for that exploration, we here suggest that a succession of flowing states with velocities slowly decreasing down to zero can also be used for that purpose. And we propose to deduce the pressure in \emph{dense and flowing} granular media from experiments measuring the thickness of the granular layer that remains on a rough incline just after the flow has stopped.Comment: 10 pages, 2 figure