Stability of the homogeneous steady state for a model of a confined quasi-two-dimensional granular fluid

United States

A linear stability analysis of the hydrodynamic equations of a model for confined quasi-two-dimensional granular gases is carried out. The stability analysis is performed around the homogeneous steady state (HSS) reached eventually by the system after a transient regime. In contrast to previous studies (which considered dilute or quasielastic systems), our analysis is based on the results obtained from the inelastic Enskog kinetic equation, which takes into account the (nonlinear) dependence of the transport coefficients and the cooling rate on dissipation and applies to moderate densities. As in earlier studies, the analysis shows that the HSS is linearly stable with respect to long enough wavelength excitations.

Powders &amp; Grains 2021

[EPJ Web of Conferences, Volume 249 (2021)](https://www.epj-conferences.org/articles/epjconf/abs/2021/03/contents/contents.html)

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Powders & Grains 2021

Powders & Grains 2021 will be held in Buenos Aires (Argentina, VIRTUAL) July 5, 13, 21, 29 and Aug 6, 2021. The aim of the conference is to give an up-to-date picture of the broad research field of granular media, powders and grains. Contributions from experts around the world will focus on research topics that cover a wide range of open problems in the field.

technical paper

Flowing grains can clog an orifice by developing arches, an undesirable event in many cases. Several strategies have been put forward to avoid this. One of them is to vibrate the system in order to undo the clogging. Nevertheless, the time taken to break an arch under a constant vibration has a distribution displaying a heavy tail. This can lead to a situation where the average breaking time is not well defined. Moreover, it has been observed in some experiments that these tails tend to flatten for very long times, exacerbating the problem. Here we will review two conceptual frameworks that have been proposed to understand the phenomenon and discuss their physical implications.

On the broad tails in breaking time distributions of vibrated clogging arches

Mixing granular particles of different sizes is a common way of increasing the packing fraction. Recently, a model predicting the packing fraction, taking into account the inhomogeneity of the mixed small and large particles, has been proposed by S. Pillitteri et al. Under certain conditions, this model can be simplified and analytical solutions can be found. We present here these solutions, compared to experimental data, and the physical interpretation they can bring.

Forced segregation in binary granular mixtures

The aim of this work is to explore the capability of the μ(I)-rheology model and its numerical implementation in addressing a silo discharge problem by computational simulation. In order to do so, the model was implemented in the general structure of an Eulerian multiphase solver based on the Volume-Of-Fluid (VOF) method of the
OpenFOAM(R) suite. First, the implementation is validated against the results of another Lagrangian and Eulerian codes in a two-dimensional discharge problem. After that, the model is tested against the experimental results of a lab-scale and industrial-scale discharge problem. While the results of the first one were satisfactory in terms of discharge rate, for the latter one, the model exhibits disagreements in the flow patterns inside the silo. The study shows the limits of applicability of the standard formulation of the model for real scale silos and sets the ground for further discussion and improvements.

The performance of the μ(I)-rheology model on flat bottom silos discharge

Granular dilatancy has been previously characterised through a simple linear relationship between the packing fraction and dimensionless shear rate. However, this relationship was developed for granular flows in a simple shear cell geometry. Here we examine volume changes in a shear cell with gravity and a vertical chute. In so doing, we show that the packing fraction displays both a local and non-local response, analogous to what is typically observed for the stress ratio μ. We then extend this analysis, looking at the direct connection between the packing fraction and the stress ratio, as well as how these variables behave in a more complex system, specifically a pseudo 2D hopper.

Evidence of a non-local φ(I) response

Granular dampers are passive devices used to attenuate mechanical vibrations. The most common configuration consists in an enclosure, partially filled with particles, attached to the vibrating structure that needs to be damped. The energy is dissipated due to inelastic collisions and friction between the grains and between the grains and the inner walls of the container as the structure vibrates. As a result of the collisions, the mechanical response of the system often results in chaotic motion even if the driving is harmonic. Despite the vibration attenuation achieved, this chaotic response may render the granular damper unsuitable for a range of applications. In this work, we showcase two simple modifications of the enclosure design that are able to mitigate the chaotic response of the granular damper. To this end we use Discrete Element Method simulations of: (a) a granular damper with a conical base, and (b) a granular damper with obstacles fixed inside the enclosure. We compare results against a standard flat-base enclosure damper. The basic mechanical response of the dampers is characterized by measuring the apparent mass and the loss factor. The suppression of the chaotic response is assessed qualitatively via the phase space diagram.

Avoiding chaos in granular dampers

Rock particle shape plays a crucial role in influencing shear resistance and energy consumption during transient loads. The dynamics of such granular materials are complex and cannot be properly described using closed-form solutions when the problem involves more than a few particles. Thus, for the sake of computational efficiency, it is common practice to implement simplified numerical models that involve a limited number of particle interactions. In this study, a novel approach is used to capture realistic particle shapes while maintaining a relatively high simulation efficiency. The geometry of the particles is determined by a Delaunay triangulation which operates on a set of vertices and returns the corresponding network of facets and grid connections. Inertial and material properties are assigned to the rock prototype which are representative of realistic gravel particles. The algorithm is validated by performing a series of numerical simulations for various particle configurations, demonstrating that mass and momentum are conserved. A potential application of this work is related to rockfall barriers and their response to rigid boulder impacts. This innovative model, based on the discrete element method (DEM), is shown to be capable of simulating rock particles with realistic shapes and complex physical interactions.

DEM modelling of 3D polyhedra with applications to gabion rockfall barriers

This talk summarises the numerical and experimental studies of brittle, hollow, cylindrical particles, called shells. It addresses the influence of shell properties both at the particle and assembly scales. Extreme compressibility has been recorded in the oedometer tests. Due to the large internal porosity of the shell, the breakage phenomena lead to highly compressive deformations with a significant stress dissipation. Using the Discrete Element Method (DEM), we have investigated in depth the micro-mechanical phenomena governing this macroscopic response. By quantifying the breakage and separating the double-porosity of the material, the foundations of a future constitutive model have been established throughout a simple prediction model applicable to the engineering practice.

High compressibility caused by particle breakage: a DEM investigation

I am interested in the evaluation of debris flow impact on structures. I developed a discrete numerical model able to simulate such impacts at the scale of the close surrounding of the structure. The largest particles carried by the flow are modelled explicitly using Distinct Element Method and the finer solid particles are integrated in a fluid phase, which induces two interactions on the largest particles, i.e. buoyancy and drag. The fields of fluid velocity and of fluid free surface are obtained from Computational Fluid Dynamics code then imported in the DEM simulation in a one way coupling scheme. For the results, the influence of particle shape on the impact forces generated on the obstacle is investigated: spherical particles and polygonal rigid blocks (r-blocks) are considered. The shape of the particle influences the contact surface and therefore the impact pressure. With an angular shape and several facets like r-blocks, the impact pressure on an obstacle is more important for a flow with the same characteristics.

Influence of the particle shape on the impact force of lahar on an obstacle

In this work, we study bidispese mixtures of self-propelled magnetic particles of different shapes via discrete element method simulations. We show how this particles self-assemble into clusters and how these clusters depends on the ratio of the mixture, the magnetic interaction, and the shape of the grains. It is found that the mix ratio of the system controls the cluster size. Besides, the intensity of the magnetic dipoles and the shape of the grains in the mixture rule the average number of neighbors in contact and the shape of the clusters. By varying the intensity of the interactions, globular, linear and branched clusters were obtained.

Self-assembly of self-propelled magnetic grains

Size limitations of geotechnical testing equipment often require that samples of coarse granular materials have to be scaled in order to be tested in the laboratory. Scaling implies a convenient modification of the particle size distribution (PSD) to reduce particle sizes. However, it is well known that particle size and shape may be correlated in nature, due to geological factors (as an example). By means of two-dimensional contact dynamics simulations, we analyzed the e↵ect of altering the size span on the shear strength of granular materials when particle size and shape are correlated. Two di↵erent systems were considered: one made of only circular particles, and the second made of size-shape correlated particles. By varying systematically the size span we observed that the resulting alteration of material strength is not due to the change in particle sizes. It results instead from the variation of the particle shapes induced by the modification of the PSD, when particle size and particle shape are correlated. This finding suggests that particle shape distribution is a higher order factor than PSD for the shear strength of granular materials. It also highlights the importance of particle shape quantification in soil classification and the case for its consideration in activities such as sampling, sub- sampling, and scaling of coarse materials for geotechnical testing

Stability of the homogeneous steady state for a model of a confined quasi-two-dimensional granular fluid

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On the broad tails in breaking time distributions of vibrated clogging arches

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Stability of the homogeneous steady state for a model of a confined quasi-two-dimensional granular fluid

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Next from Powders & Grains 2021

On the broad tails in breaking time distributions of vibrated clogging arches

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Discrete modeling of waste rock dumps stability under seismic loading

Stay up to date with the latest Underline news!

PRESENTATIONS

CONFERENCES

COMPANY

RESOURCES

Downloads