Resolved simulations of submarine avalanches with a simple soft-sphere / immersed boundary method

Physical mechanisms at the origin of the transport of solid particles in a fluid are still a matter of debate in the physics community. Yet, it is well known that these processes play a fundamental role in many natural configurations, such submarines landslides and avalanches, which may have a significant environmental and economic impact. The goal here is to reproduce the local dynamics of such systems from the grain scale to that of thousands of grains approximately. To this end a simple soft-sphere collision / immersed-boundary method has been developed in order to accurately reproduce the dynamics of a dense granular media collapsing in a viscous fluid. The fluid solver is a finite-volume method solving the three-dimensional, time-dependent Navier-Stokes equations for a incompressible flow on a staggered. Here we use a simple immersed-boundary method consisting of a direct forcing without using any Lagrangian marking of the boundary, the immersed boundary being defined by the variation of a solid volume fraction from zero to one. The granular media is modeled with a discrete element method (DEM) based on a multi-contact soft-sphere approach. In this method, an overlap is allowed between spheres which mimics the elasto-plastic deformation of real grain, and is used to calculate the contact forces based on a linear spring model and a Coulomb criterion. Binary wall-particle collisions in a fluid are simulated for a wide range of Stokes number ranging from 10-¹ to 10⁴. It is shown that good agreement is observed with available experimental results for the whole range of investigated parameters, provided that a local lubrication model is used when the distance of the gap between the particles is below a fraction of the particle radius. A new model predicting the coefficient of restitution as a function of the Stokes number and the relative surface roughness of the particles is proposed. This model, which makes use of no adjustable constant, is shown to be in good agreement with available experimental data. Finally, simulations of dense granular flows in a viscous fluid are performed. The present results are encouraging and open the way for a parametric study in the parameter space initial aspect ratio - initial packing

Simulation of an avalanche in a fluid with a soft-sphere / immersed boundary method including a lubrication force.

The present work aims at reproducing the local dynamics of a dense granular media evolving in a viscous fluid from the grain scale to that of thousands of grains, encountered in environmental multiphase flows. To this end a soft-sphere collision / immersed-boundary method is developed. The methods are validated alone through various standard configurations including static and dynamical situations. Then, simulations of binary wall-particle collisions in a fluid are performed for a wide range of Stokes number ranging in [10-1, 104]. Good agreement with available experimental data is found provided that a local lubrication model is used. Finally, three-dimensional simulations of gravity/shear-driven dense granular flows in a viscous fluid are presented. The results open the way for a parametric study in the parameter space initial aspect ratio - initial packing

Modelling the normal bouncing dynamics of spheres in a viscous fluid

Bouncing motions of spheres in a viscous fluid are numerically investigated by an immersed boundary method to resolve the fluid flow around solids which is combined to a discrete element method for the particles motion and contact resolution. Two well-known configurations of bouncing are considered: the normal bouncing of a sphere on a wall in a viscous fluid and a normal particle-particle bouncing in a fluid. Previous experiments have shown the effective restitution coefficient to be a function of a single parameter, namely the Stokes number which compares the inertia of the solid particle with the fluid viscous dissipation. The present simulations show a good agreement with experimental observations for the whole range of investigated parameters. However, a new definition of the coefficient of restitution presented here shows a dependence on the Stokes number as in previous works but, in addition, on the fluid to particle density ratio. It allows to identify the viscous, inertial and dry regimes as found in experiments of immersed granular avalanches of Courrech du Pont et al. Phys. Rev. Lett. 90, 044301 (2003), e.g. in a multi-particle configuration

Modélisation numérique des écoulements granulaires denses immergés dans un fluide

Ce travail de thèse concerne la modélisation numérique fine des processus locaux dans le transport sédimentaire, à l'échelle d'un à plusieurs centaines de grains. Une méthode aux éléments discrets (DEM) basée sur la méthode dite des sphères molles et prenant en compte les contacts entre les grains a été développée et couplée à une méthode de frontière immergée (IBM) qui calcule l'écoulement autour d'objets solides mobiles dans un fluide Newtonien incompressible. Dans ce couplage, une force de lubrification est incluse pour représenter les interactions entre le fluide et les particules proches d'un contact. Il est montré que la méthode numérique reproduit de manière satisfaisante le coefficient de restitution effective mesuré dans des expériences de rebonds normal et oblique d'un grain sur un plan, ainsi que de rebond entre deux grains dans un fluide visqueux. Deux modèles analytiques associés au phénomène de rebond sont proposés et montrent l'importance de la rugosité de surface du grain et du nombre de Stokes sur le phénomène. La méthode numérique est ensuite utilisée pour simuler deux configurations tridimensionnelles d'écoulements granulaires pilotés par la gravité en milieu fluide : l'avalanche de grains sur un plan incliné rugueux et l'effondrement d'une colonne de grains. Dans le premier cas, les résultats permettent de caractériser les différents régimes d'écoulement granulaires (visqueux, inertiel et sec) observés dans les expériences en fonction du rapport de masse volumique grain-fluide et du nombre de Stokes. En particulier, les simulations apportent des informations originales quant aux profils de vitesse de grains et du fluide ainsi qu'aux forces prédominantes dans chacun des régimes. Dans le second cas, les résultats sont en bon accord avec les expériences et le mécanisme dit de « pore pressure feedback », qui dépend de la compacité initiale de la colonne, est pour la première fois observé dans des simulations numériques directes. ABSTRACT : This work deals with direct numerical simulations of sediment transport at the scale of O(103) grains. A soft-sphere discrete element method (DEM) taking into account grain contacts is developed and coupled to an immersed boundary method (IBM) which computes the flow around moving solid objects in an incompressible Newtonian fluid. A lubrication force is added for representing fluid-particles interaction near contact. The numerical method is shown to adequately reproduce the effective coefficient of restitution measured in experiments of the normal and oblique rebound of a grain on a plane and the rebound between two grains in a viscous fluid. Two analytical models are proposed and highlight the importance of the grain roughness and Stokes number on the rebound phenomenon. This numerical method is then used for simulating two three-dimensional configurations of gravity-driven dense granular flow in a fluid, namely the granular avalanche on a rough inclined plane and the collapse of a granular column. In the first case, results allow to characterize the granular flow regimes (viscous, inertial and dry) observed in experiments as a function of the grain-to-fluid density ratio and the Stokes number. In particular, the simulations provide insight on the grain and fluid velocity profiles and force balance in each regime. In the second case, results agree well with experiments and in particular the pore pressure feedback, which depends on the initial volume fraction of the column, is observed for the first time in direct numerical simulations

Modelling the dynamics of a sphere approaching and bouncing on a wall in a viscous fluid

The canonical configuration of a solid particle bouncing on a wall in a viscous fluid is considered here, focusing on rough particles as encountered in most of the laboratory experiments or applications. In that case, the particle deformation is not expected to be significant prior to solid contact. An immersed boundary method (IBM) allowing the fluid flow around the solid particle to be numerically described is combined with a discrete element method (DEM) in order to numerically investigate the dynamics of the system. Particular attention is paid to modelling the lubrication force added in the discrete element method, which is not captured by the fluid solver at very small scale. Specifically, the proposed numerical model accounts for the surface roughness of real particles through an effective roughness length in the contact model, and considers that the time scale of the contact is small compared to that of the fluid. The present coupled method is shown to quantitatively reproduce available experimental data and in particular is in very good agreement with recent measurement of the dynamics of a particle approaching very close to a wall in the viscous regime St <O(10), where St is the Stokes number which represents the balance between particle inertia and viscous dissipation. Finally, based on the reliability of the numerical results, two predictive models are proposed, namely for the dynamics of the particle close to the wall and the effective coefficient of restitution. Both models use the effective roughness height and assume the particle remains rigid prior to solid contact. They are shown to be pertinent to describe experimental and numerical data for the whole range of investigated parameters

Couplage IBM/DEM pour la modélisation des milieux granulaires dans un fluide

La physique des milieux granulaires denses immergés est à l'heure actuelle un domaine privilégié de la mécanique des fluides en raison des enjeux environnementaux et industriels importants associés. La dynamique d'un système dense d'objets solides en mouvement dans un fluide est particulièrement complexe car elle résulte d'interactions particule-fluide et particule-particule à petite échelle (fraction de la taille des particules), donnant lieu à des phénomènes de plus grande échelle (allant jusqu'au système complet). L'objectif ici est d'améliorer la compréhension de ces milieux via une modélisation à petite échelle, allant d'un grain à quelques milliers de grains, via le développement d'une méthode aux éléments discrets (DEM) couplée à une méthode de type frontières immergées (IBM), la première reproduisant les interactions solide-solide, la seconde les interactions solide-fluide. L'étude du rebond d'une particule sur une paroi montre que l'ajout d'une force de lubrification au voisinage du contact est nécessaire pour reproduire les cas réels. L'outil numérique ainsi validé est utilisé pour simuler un écoulement granulaire sur plan incliné dans un fluide

Toward CFD-DEM simulations of the blast furnace raceway

Gas injections at the bottom of the blast furnace create void regions in the coke matrix called the raceways which play a role in the gas distribution in the furnace and is directly linked to the iron production. In this region, complex physical phenomena occur, including particle-fluid with combustion, and, to our knowledge, there is no consensus on its shape and dynamics as well as its creation and stability. A better understanding of the raceway region could lead to a more efficient and stable blast furnace process. An unresolved CFD-DEM approach is used to study the gas-solid flows where coke particles are modelled as a discrete phase and the gas as continuous solving the RANS modelling of the turbulence. In order to clarify the main phenomena occurring in the raceway dynamics, we develop a CFD-DEM model of a 1/5 scale 2d slot pilot of the blast furnace for which alternative raceway collapses are monitored. First, DEM simulations are realized without the fluid contribution and shows that the pilot geometry influences the mechanical load applied on the raceway with a saturation of the granular stress inside the pilot. Also, dry raceway collapse shows a modification of this stress in a short characteristic time. Then, CFD-DEM model of the pilot permits to investigate the gas and granular flows when the raceway is imposed as in the experiment. The dynamics of the collapse with the coupling is solved and displays a complex particle-gas 3d flow. Further implementation in the model will allow coke particle combustion

Immersed granular collapse: from viscous to free-fall unsteady granular flows

The collapse of a granular column in a liquid is investigated using numerical simulations. From previous experimental studies, it has been established that the dynamics of the collapse is mostly influenced by the Stokes number St, comparing grain inertia and viscous fluid dissipation, and the initial volume fraction of the granular column φi. However, the full characterization of the collapse in the (St, φi) plane is still missing, restricting its modelling as a physical process for geophysical applications. Only numerical tools can allow the variation over the parameter space (St, φi) that is hardly reachable in experiments as well as a full description of the granular phase that plays a major role in dense granular flows. For this purpose, a dedicated numerical model is used including a discrete element method to resolve the granular phase. The specific objectives of the paper are then twofold: (i) the characterization of the dynamics of the collapse and its final deposit with respect to (St, φi) to complement available experimental data, and (ii) the description of the granular rheology according to these two dimensionless numbers including dilatancy effects. A simple predictive model stems from the obtained results, allowing one to explain the evolution of the final deposit with (St, φi)

Large-scale 3D printing with cable-driven parallel robots

Gantry robots and anthropomorphic arms of various sizes have already been studied and, while they are in use in some parts of the world for automated construction, a new kind of wide workspace machinery, cable-driven parallel robots (CDPR), has emerged. These robots are capable of automated movement in a very wide workspace, using cables reeled in and out by winches as actuation members, the other elements being easily stacked for easy relocation and reconfiguration, which is critical for on-site construction. The motivation of this paper is to showcase the potential of a CDPR operating solely on motor position sensors and showing limited collisions from the cables for large-scale applications in the building industry relevant for additive manufacturing, without risk of collisions between the cables and the building. The combination of the Cogiro CDPR (Tecnalia, LIRMM-CNRS 2010) with the extruder and material of the Pylos project (IAAC 2013) opens the opportunity to a 3D printing machine with a workspace of 13.6 × 9.4 × 3.3 m. The design patterns for printing on such a large scale are disclosed, as well as the modifications that were necessary for both the Cogiro robot and Pylos extruder and material. Two prints, with different patterns, have been achieved with the Pylos extruder mounted on Cogiro: the first spanning 3.5 m in length, the second, reaching a height of 0.86 m. Based on this initial experiment, plans for building larger parts and buildings are discussed, as well as other possible applications for CDPRs in construction, such as the manipulation of assembly processes (windows, lintels, beams, floor elements, curtain wall modules, etc.) or brick laying