Funded PhD on “The fluid and granular mechanics of magmatic sulphide ore formation” in collaboration with A. Slim from Monash University, funded by AUFRANDE (deadline:January 24th 2024).
Nonsteady discharge of granular media from a silo drivenby a pressurized gas
We studied experimentally and numerically the effect of an imposed gas pressure on the discharge flow of granular media from a cylindrical silo. This study is motivated by a nuclear safety related phenomenology of fuel fragments displaced from a fuel rod under several accidental conditions, the flow being potentially driven by pressurized fission gases within the rod. We imposed a moderate constant air pressure at the top of the granular column (≈3000 Pa) and we varied the size and type of the particles and the surrounding fluid where the discharge occurs, using air and water to test the role of the coolant fluid in the nuclear safety problem. The measured parameters are the particle mass flow rate, the volumetric flow rate of air, and the pressure along the silo. The particle and air flow rates are found to be nonsteady and to increase with time. To model these behaviors, we use a twophase
continuum model with a frictional rheology to describe particle-particle interactions, and we propose a simple quasisteady analytical model considering the air-pressure gradient at the orifice as an additional driving force to the gravity. We implemented numerically the two-phase continuum model in an axisymmetric configuration which reproduces the experimental results.
- Z. Zou, P. Ruyer, P.-Y. Lagrée and P. Aussillous 2022 Nonsteady discharge of granular media from a silo driven
by a pressurized gas Phys. Rev. Fluids 7, 064306.
Rheology of mobile sediment beds sheared by viscous, pressure-driven flows
We present a detailed comparison of the rheological behaviour of sheared sediment beds in a pressure-driven, straight channel configuration based on data that were generated by means of fully coupled, grain-resolved direct numerical simulations and experimental measurements previously published by Aussillous et al. (J. Fluid Mech., vol. 736, 2013, pp. 594–615). The highly resolved simulation data allow us to compute the stress balance of the suspension in the streamwise and vertical directions and the stress exchange between the fluid and particle phases, which is information needed to infer the rheology, but has so far been unreachable in experiments. Applying this knowledge to the experimental and numerical data, we obtain the statistically stationary, depth-resolved profiles of the relevant rheological quantities. The scaling behaviour of rheological quantities such as
the shear and normal viscosities and the effective friction coefficient are examined and compared to data coming from rheometry experiments and from widely used rheological correlations. We show that rheological properties that have previously been inferred for annular Couette-type shear flows with neutrally buoyant particles still hold for our set-up of sediment transport in a Poiseuille flow and in the dense regime we found good agreement with empirical relationships derived therefrom. Subdividing the total stress into parts from particle contact and hydrodynamics suggests a critical particle volume fraction of 0.3 to separate the dense from the dilute regime. In the dilute regime, i.e. the sediment transport layer, long-range hydrodynamic interactions are screened by the porous medium and the effective viscosity obeys the Einstein relation.
B. Vowinckel, E. Biegert, E. Meiburg, P. Aussillous and E. Guazzelli 2021 Rheology of mobile sediment beds sheared by viscous, pressure-driven flows J. of Fluid Mech. 921 A20
Discharge of a silo through a lateral orifice: role of the bottom inclination versus friction
In this work, we propose to identify the relative role of the inclination of gravitational acceleration and the friction on the discharge flow rate of a granular media from a rectangular silo, by varying the silo geometry thanks to an inclined bottom which ends up at a lateral outlet. The study is motivated by a nuclear safety problem: a fuel rod (modelled by an elongated silo) accidentally releases fuel fragments (modelled by grains). We performed experiments where we measured independently the mass flow rate and the velocity profiles, together with discrete particle simulations and continuum simulations with a frictional rheology described by a mu(I) constitutive law and taking into account the wall friction. We study mono-layer flows and 3D flows and we propose an analytical model that predicts the discharge flow rate of particles from a rectangular silo with an inclined bottom according to its outlet aspect ratio and the bottom inclination angle.
Z Zou, Pierre Ruyer, Pierre-Yves Lagrée and Pascale Aussillous 2020 Discharge of a silo through a lateral orifice: Role of the bottom inclination versus friction Physical Review E 102, 052902.
Discharge flow of granular media from rectangular silos: role of an obstacle and modelling by an orifice at the corner
We present an experimental study on the discharge flow of a granular media from a rectangular silo with a cylindrical obstacle placed above the outlet. As described in the literature, the presence of an obstacle decreases the flow rate, but the characteristic lengths to be chosen in the flow rate law are not known.
To predict the flow rate we vary the obstacle diameter and vertical position, the outlet size and the particle diameter. However due to the large number of parameters we find that the characteristic length which control the flow rate can not be thoroughly defined. To model the effect of an obstacle on the flow rate we design a new configuration with an orifice at the corner of the silo. We study the two extreme cases (a bottom orifice at the wall and a lateral orifice) and we show that for the corner all the data are in between these two cases.
S. Laidaoui, P. Aussillous, M. Djermane and B. Dalloz-Dubrujeaud 2020 Discharge flow of granular media from rectangular silos: role of an obstacle and modelling by an orifice at the corner Mechanics & Industry, EDP Sciences, 21 (5), pp.516
Gas-assisted discharge flow of granular media from silos
We 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.
Figure: flow rate versus the particle diameter for severals air flow rate. Dashed-lines: analytical model.
Y. Zhou, P.-Y. Lagrée, S. Popinet, P. Ruyer and P. Aussillous, Phys. Rev. Fluids 4, 124305 (2019) (pdf)
Granular surface avalanching induced by drainage from a narrow silo
Using theory and experiments, we investigate granular surface avalanching due to material outflow from a narrow silo. The assumed silo geometry is a deep rectangular box, of moderate spanwise width and small gap thickness between smooth front and back walls. A small orifice deep below the free surface lets grains drain out at a constant rate. The resulting granular flows can therefore be assumed quasi-two-dimensional and quasi-steady over most of the surface descent history. To model these flows, we couple a kinematic model of deep granular flow with a dynamic model of shallow surface avalanching. We then compare the calculated flow fields with detailed particle tracking measurements, letting the silo ascend relative to the high-speed camera to increase spatial resolution. The results show that the avalanching surface shape and near-surface flow are controlled by the spanwise gradient in subsidence velocity, and how this gradient is in turn controlled by the height above orifice and the gap thickness. Whereas the deep flow pattern is rate independent, shallow avalanching is paced by the granular rheology.
Figure : Qualitatively different avalanching flow pattern observed in silo of large gap thickness (a) long exposure image; (b) colour map of velocity magnitude.
C.-Y. Hung et al., J. Fluid Mech. (2018), vol. 856, pp. 444-469 (pdf)
Experiments on, and discrete and continuum simulations of, the discharge of granular media from silos with a lateral orifice
We compare laboratory experiments, contact dynamics simulations, and continuum Navier–Stokes simulations with a mu(I) visco-plastic rheology, of the discharge of granular media from a silo with a lateral orifice. We consider a rectangular silo with an orifice of height D which spans the silo width W, and we observe two regimes. For small-enough aperture aspect ratio A=D/W$ the Hagen–Beverloo relation is obtained. For thin-enough silos, we observe a second regime where the outlet velocity varies with W. This new regime is also obtained in the continuum simulations when the friction on side walls is taken into account in a thickness-averaged version of mu(I) + Navier–Stokes (in the spirit of Hele–Shaw flows.
Moreover most of the internal details of the flow field observed experimentally are reproduced when considering this lateral friction. These two regimes are recovered experimentally for a cylindrical silo with a lateral rectangular orifice of height D and arc length W. The dependency of the flow rate on the particle diameter is found to be reasonably described experimentally using two geometrical functions that depend respectively on the number of beads through the two aperture dimensions. This is consistent with 2D discrete simulation results: at the outlet, the volume fraction and the velocities depend on the particle diameter and this behaviour is correctly described by those geometrical functions. A similar dependency is observed in the 2D continuum simulations (pdf).
figure : Dimensionless mass flow rate as a function of D/W for particles of diameter d=190 mum.
Y. Zhou et al., J. of Fluid Mech. (2017) 829, 459-485 (pdf)
Actualités scientifiques – En direct des laboratoires
L’actualité scientifique « Une formation de rivières fractales lors de l’érosion d’un lit granulaire », relative à l’article Scale-free channeling patterns near the onset of erosion of sheared granular beds publié dans la revue PNAS, a été mise en ligne à la Une du site de l’INSIS à la rubrique « Actualités scientifiques – En direct des laboratoires ».
Scale-free channeling patterns near the onset of erosion of sheared granular beds
When fluid flows across a granular substrate, shearing forces detach material from the interface and transport it downstream. Although erosion-deposition constitutes a central geomorphological process that shapes Earth’s landforms, decades of research has failed to yield a complete description of these systems at the microscopic level. A central aspect is the existence of a threshold stress below which erosion stops, whose microscopic underpinning is debated.
We study experimentally the collective dynamics of the moving particles, using a flume apparatus to simulate river flow over a gravel bed, where the system spontaneously evolves toward the erosion onset. We characterize the spatial organization of the erosion flux.
Figure: Typical channeling patterns
We show that near the origin of erosion the flow of particles is spatially heterogeneous, carried by only a few concentrated channels in the bed (see figure) whose distribution is extremely broad, with strongly anisotropic spatial correlations. The distribution of the local flux σ displays scaling near threshold and follows P(σ)≈J/σ, where J is the mean erosion flux. Channels are strongly correlated in the direction of forcing but not in the transverse direction.
Furthermore, we demonstrate that these results support a model in which erosion is ultimately governed by a give and take between channelization, which accelerates erosion, and interactions among particles which tend to interfere with channeling. This model incorporating both the disorder of the static bed and the interactions between mobile particles support that, for laminar flows, erosion is a dynamical phase transition that shares similarity with the plastic depinning transition occurring in dirty superconductors. The methodology we introduce here could be applied to probe these systems as well.
P. Aussillous et al. PNAS (2016) 113: 11788-11793. (pdf)
Pascale Aussillous 