京都大学 / 新制・課程博士 / 博士(エネルギー科学) / 甲第23395号 / エネ博第422号 / 新制||エネ||80(附属図書館) / 京都大学大学院エネルギー科学研究科エネルギー社会・環境科学専攻 / (主査)教授 河本 晴雄, 教授 亀田 貴之, 教授 杉山 淳司 / 学位規則第4条第1項該当 / Doctor of Energy Science / Kyoto University / DFAM

Cette thèse porte sur la force de résistance au mouvement à faible vitesse d'un objet (sphère, cylindre ou disque) dans un empilement de grains dense et sec. Des expériences ont été menées sur deux dispositifs permettant un mouvement à vitesse contrôlée, en s’intéressant à l’influence des tailles des objets et des grains, des conditions aux limites de l’empilement, de la gravité, et d’une éventuelle vibration de l’empilement. Dans un premier dispositif expérimental permettant un mouvement vertical, nous avons consacré une partie importante de ce travail à l'étude de la forte asymétrie de la force lors de cycles de pénétration/extraction d’un cylindre horizontal et d’une sphère. Pour tenter de comprendre l'origine de cette asymétrie, différentes conditions aux limites ont été considérées : parois rigides ou souples sur les côtés ou au fond de l’empilement, surface libre ou surmontée d’un couvercle plus ou moins chargé en haut de l’empilement. La longueur caractéristique issue du champ de vitesse des grains autour d'un cylindre a été montrée comme la longueur pertinente à considérer pour le confinement latéral, ainsi que pour les déformations de la surface libre telles que la formation d’un cratère consécutif à la pénétration ou d’une bosse lors de l’extraction. Ces déformations peuvent être retrouvées par intégration d’un modèle de champ de vitesse autour de l’objet. La présence d'un couvercle chargé a par ailleurs permis de mettre en évidence une riche et complexe variété de comportements, notamment en extraction où la force ne diminue plus avec la profondeur de l’objet. Dans un second dispositif permettant le mouvement horizontal d’un gros disque intrus à l’intérieur d’une couche de petits disques photoélastiques vibrés ou non, nous avons mesuré la force globale sur l’intrus et visualisé les distributions de contraintes au sein du milieu granulaire. Au-delà des importantes fluctuations spatio-temporelles, des valeurs moyennes de force sur l’intrus et des tenseurs locaux de contraintes et taux de déformations autour de l’intrus ont pu être obtenus, dans la perspective d’établir une loi de comportement locale pour le milieu. La vibration de la couche de grains a été montré pouvoir changer considérablement la dépendance de la force avec la vitesse de l’intrus, avec un effet de fluidification du milieu. / This thesis focuses on the force of resistance to the slow motion of an object (sphere, cylinder or disk) in a dense and dry granular medium. Experiments were conducted using two devices that permitted movement at constant velocity, with the aim of studying the influence of the object size, the grain size, the boundary conditions, and vibration of the grains. Using the first device in which the object moved vertically, we studied in detail the strong asymmetry of the resistance force during cycles of penetration/withdrawal of a horizontal cylinder and a sphere. In an attempt to understand the origin of this asymmetry, we implemented different boundary conditions: rigid and deformable walls on the sides and/or the bottom of the device, and free and quasi-rigid (loaded cover) conditions at the top. Previous work has shown that the characteristic length scale of the velocity field around a moving cylinder is the relevant length for both the lateral confinement and the deformation of the free surface, such as the formation of a crater during penetration or a mound during withdrawal. These deformation fields can be found by integrating a model of the velocity field around the object. Our use of a loaded-cover boundary condition has also revealed a variety of complex behaviors, including a force that no longer decreases with the depth of the object during the withdrawal phase. The second device allows the horizontal movement of a large hard intruder into a monolayer of small photoelastic disks which could be vibrated or not. Using this, we measured the overall force on the intruder and visualized the stress distribution in the granular medium. We were able to measure not only the large spatio-temporal velocity fluctuations, but also average values of the force on the intruder and the local stress and strain rate tensors around it, which allowed us to determine a local constitutive law for the medium. Finally, we have shown that vibration of the grains significantly changes the dependence of the force on the intruder speed, indicating a fluidization effect.

This thesis deals with fibre orientation in wall-bounded shear flows. The primary application in mind is papermaking. The study is mainly experimental,but is complemented with theoretical considerations.The main part of the thesis concerns the orientation of slowly settlingfibres in a wall-bounded viscous shear flow. This is a flow case not dealt withpreviously even at small Reynolds numbers. Experiments were conducted usingdilute suspensions with fibres having aspect ratios of rp ≈ 7 and 30. It is foundthat the wall effect on the orientation is small for distances from the wall wherethe fibre centre is located farther than half a fibre length from the wall. Farfrom the wall most fibres were oriented close to the flow direction. Closer tothe wall than half a fibre length the orientation distribution first shifted to bemore isotropic and in the very proximity of the wall the fibres were orientedclose to perpendicular to the flow direction, nearly aligned with the vorticityaxis. This was most evident for the shorter fibres with rp ≈ 7.Due to the density difference between the fibres and the fluid there is anincreased concentration near the wall. Still, a physical mechanism is requiredin order for a fibre initially oriented close to the flow direction at about half afibre length from the wall to change its orientation to aligned with the vorticityaxis once it has settled down to the wall. A slender body approach is usedin order to estimate the effect of wall reflection and repeated wall contacts onthe fibre rotation. It is found that the both a wall reflection, due to settlingtowards the wall, and contact between the fibre end and the wall are expectedto rotate the fibre closer to the vorticity axis. A qualitative agreement withthe experimental results is found in a numerical study based on the theoreticalestimation.In addition an experimental study on fibre orientation in the boundarylayers of a headbox is reported. The orientation distribution in planes parallelto the wall is studied. The distribution is found to be more anisotropic closerto the wall, i.e. the fibres tend to be oriented closer to the flow direction nearthe wall. This trend is observed sufficiently far upstream in the headbox.Farther downstream no significant change in the orientation distribution couldbe detected for different distances from the wall. / QC 20100706

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The wall effect is known to present difficulties when attempting to predict the pressure drop over randomly packed beds. The Nuclear Safety Standard Commission, “Kerntechnischer Auss-chuss" (KTA), made considerable efforts to develop an equation which predicts the pressure drop over cylindrical randomly packed beds consisting of mono-sized spheres. The KTA was able to estimate a limiting line, which defines the region for which the wall effect is negligible, however the theoretical basis for this line is unclear. The goal of this investigation was to determine the validity of the KTA limiting line, using an explicit approach. Packed beds were generated using Discrete Element Modelling (DEM), and the flow through the beds simulated using Computational Fluid Dynamics (CFD). STAR-CCM+R was used for both DEM and CFD operations, and the methods developed for this explicit approach were validated with empirical data. The KTA correlation predictions for friction factors were com- pared with the CFD results, as well as the predictions from a few other correlations. The KTA correlation predictions for friction factors did not correspond well with the CFD results at low aspect ratios and low modified Reynolds numbers, due to the influence of the wall effect. The KTA limiting line was found to be valid, but not exact. A new limiting line for the KTA correlation was suggested, however the new limiting line improved little on the existing line and was the result of some major assumptions. In order to improve the determination of the position of the KTA limiting line further, criteria need to be established which determine how small the error in predicted friction factor must be before the KTA correlation can be accepted as accurate. / MIng (Nuclear Engineering), North-West University, Potchefstroom Campus, 2014

The wall effect is known to present difficulties when attempting to predict the pressure drop over randomly packed beds. The Nuclear Safety Standard Commission, “Kerntechnischer Auss-chuss" (KTA), made considerable efforts to develop an equation which predicts the pressure drop over cylindrical randomly packed beds consisting of mono-sized spheres. The KTA was able to estimate a limiting line, which defines the region for which the wall effect is negligible, however the theoretical basis for this line is unclear. The goal of this investigation was to determine the validity of the KTA limiting line, using an explicit approach. Packed beds were generated using Discrete Element Modelling (DEM), and the flow through the beds simulated using Computational Fluid Dynamics (CFD). STAR-CCM+R was used for both DEM and CFD operations, and the methods developed for this explicit approach were validated with empirical data. The KTA correlation predictions for friction factors were com- pared with the CFD results, as well as the predictions from a few other correlations. The KTA correlation predictions for friction factors did not correspond well with the CFD results at low aspect ratios and low modified Reynolds numbers, due to the influence of the wall effect. The KTA limiting line was found to be valid, but not exact. A new limiting line for the KTA correlation was suggested, however the new limiting line improved little on the existing line and was the result of some major assumptions. In order to improve the determination of the position of the KTA limiting line further, criteria need to be established which determine how small the error in predicted friction factor must be before the KTA correlation can be accepted as accurate. / MIng (Nuclear Engineering), North-West University, Potchefstroom Campus, 2014

La compacité des matériaux granulaires est une grandeur qui intéresse un grand nombre de secteurs, notamment les bétons hydrauliques. Lorsque les fractions granulaires ne possèdent pas des rapports de tailles infinis, deux interactions géométriques se développent : l’effet de paroi et l’effet de desserrement. La première peut se décrire ainsi : une grosse particule isolée constitue un « intrus » contre lequel viennent se ranger les petites particules, créant un supplément de vides à l’interface. La seconde se produit lorsque les petits grains sont insuffisamment fins pour se glisser entre les gros. Nous analysons comment elles sont prises en compte dans un certain nombre de modèles d’empilement en nous fixant finalement sur celui de de Larrard et al. : le modèle d’empilement compressible (MEC), l’un des plus efficaces. Dans celui-ci, les effets de paroi et de desserrement sont quantifiés par l’intermédiaire de deux coefficients dont les expressions sont obtenues par lissage de données expérimentales en fonction du rapport des diamètres fins/gros. Cependant, il n’existe aucune théorie pleinement satisfaisante permettant de les obtenir. Cette thèse vise à combler ce chaînon manquant. Nous avons conduit notre étude dans le cadre des empilements ordonnés et compacts de particules afin d’être en adéquation avec les hypothèses de constitution du MEC qui propose, comme préalable à l’obtention de la compacité réelle, la détermination d’une compacité virtuelle définie comme la compacité maximale susceptible d’être atteinte si l’on pouvait déposer, un à un, chaque grain à son emplacement idéal. Cette façon de procéder permet la création de cellules élémentaires juxtaposées. Dans ce cadre, l’interaction exercée par une espèce granulaire sur une autre de taille différente est menée à partir d’une étude localisée autour d’une particule « intruse » de la classe dominée, entourée de particules de la classe dominante. La simulation numérique apporte une confirmation de la validité du modèle. En plus de fournir des coefficients d’effets de paroi et de desserrement très proches de ceux prédits théoriquement, elle a permis l’étude d’empilements désordonnés de compacité maximale pour des billes bidispersées sans frottement dont les rapports de tailles valent 0,2 et 0,4. Le concept de « pressions partielles », qui tient compte à la fois des aspects géométrique et mécanique, a permis d’affiner la notion de classe dominante et de mieux appréhender la constitution du squelette porteur de l’édifice granulaire. En plus des zones constituées par les « fins dominants » et par les « gros dominants », il existe une zone mixte que nous avons dénommée « zone de synergie du squelette porteur » où les « pressions partielles » fines-grosses sont les plus importantes. En tenant compte de la nouvelle théorie développée pour les interactions géométriques, le modèle d’empilement compressible (MEC) subit une évolution et devient le MEC 4-paramètres, qui sont : les coefficients d’effet de paroi et d’effet de desserrement, le rapport de tailles de caverne critique et l’indice de compaction du mélange. Ce dernier ayant subi un nouvel étalonnage, le MEC 4-paramètres montre son efficacité quant à la prédiction de compacités sur mélanges binaires à partir de l’analyse de 780 résultats obtenus sur différents types de matériaux. Enfin, un modèle visant à prédire la viscosité d’une suspension concentrée de particules sphériques multidimensionnelles suspendues dans un fluide visqueux est présenté. Compatible avec la relation d’Einstein, il fait appel au concept de changement d’échelle de Farris et à une loi de viscosité de type Krieger-Dougherty. Lorsque la fraction volumique de solide atteint sa valeur critique, la suspension devient empilement et le mélange atteint la compacité du squelette solide déterminée par le MEC 4-paramètres / Packing density of granular materials is a quantity which interests many sectors, in particular hydraulic concrete. When two monodimensional grain classes have no very different sizes, two geometrical interactions develop : the wall effect and the loosening effect. The first one express the perturbation of the packing of the small grains at the interface between large and small grains. The second one occurs when small grains are not enough fine to insert into small cavities created by the touching larger grains. We analyze how they are taken into account in existing packing models. We select finally the compressible packing model (CPM) of de Larrard et al., one of the most effective. In this one, wall effect and loosening effect are quantified by two coefficients. They can, of course, be calculated from experimental results on binary mixtures, as a function of fine/coarse diameter ratios. However, there is no satisfactory theory allowing to calculate them. This doctoral thesis is done to fill this missing link. Ordered and very packed piles of particles are used as a reference frame to be in adequation with the CPM assumptions which require, before the calculation of the real packing density, the determination of a virtual packing density. The latter is defined as the maximum packing density attainable if each particle could be positioned in its ideal location. This approach allows the creation of elementary juxtaposed cells. In that context, the effect of a smaller grain (loosening effect) or a larger grain (wall effect) on the packed class is based on the study of a foreign sphere surrounded by dominant class neighbours. The numerical simulation confirms the validity of the model. In addition to predict wall effect and loosening effect coefficients close to those determined theoretically, numerical simulation was used to predict the solid fraction of maximally dense disordered packings of bidisperse spherical frictionless particles with 0,2 and 0,4 size ratios. The « partial pressures » concept, that includes both geometrical and mechanical aspects, allows to complete and improve the notion of dominant class and to better understand the build-up of the granular skeleton. In addition with « small grains packed » and « large grains packed » zones, the numerical simulation has highlighted a joint zone, called « synergism zone of the granular skeleton » where « partial pressures » fine-large particles are the most important. With this new theory developed for geometrical interactions, the compressible packing model (CPM) is evolving to the new 4-parameter CPM which are : the wall effect coefficient, the loosening effect coefficient, the critical cavity size ratio and the compaction index of the mixing, which requires a new recalibration. The 4-parameter CPM demonstrates its efficiency to predict the packing density of binary mixtures from the analysis of 780 results obtained on different types of materials. Finally, a model intended to predict the viscosity of a multimodal concentrated suspension with spherical particles suspended in a viscous fluid is presented. We resort to the iterative approach advocated by Farris and to a power-law relation (Krieger-Dougherty type) for the relative viscosity, compatible with the Einstein relation appropriate for a dilute suspension. When the solid volume fraction reaches its critical value, the suspension is jammed and the mixture reaches the packing density of the solid skeleton calculated with the 4-parameter CPM

Determining the hydrodynamic force acting on bubbles and particles moving parallel to a wall in a shear flow is a problem of fundamental importance, as this configuration is involved in a variety of technical and natural systems. The presence of the wall tends to increase the drag force, and more importantly causes a transverse lift force acting on the body. This thesis focuses on extending the current capability in predicting drag and lift forces on spherical bubbles and particles translating in a linear shear flow, primarily in the vicinity of a wall, and obtaining quantitative insight into the interaction mechanisms at work in the context of finite sphere Reynolds number. The investigations are performed through direct numerical simulation (DNS) using an accurate finite volume method. The first part of the thesis summarizes all expressions for the drag and lift forces available in the literature. A comprehensive review of existing results from analytical, experimental, and direct numerical simulation studies is given. The available correlations are critically assessed by comparison to data from these studies. Based on the comparison, recommendations are given which correlations to use including some new proposals, and gaps in the data are identified. The second part aims to fill the gaps mentioned above by means of DNS. Specifically, the three-dimensional flow around a non-rotating sphere translating steadily in a wall-bounded linear shear flow is investigated by solving the full Navier-Stokes equations. Numerical results and analytical expressions are combined to provide accurate semi-empirical expressions for the drag and lift forces at arbitrary Reynolds number and separation distance. Present numerical results help to rationalize and quantify the various mechanisms at work and the ways they interact. From a practical point of view, they also result in several closure models for the drag correction and transverse force, which are necessary inputs in the point-particle based Eulerian-Lagrangian simulations or in Eulerian-Eulerian simulations based on the interpenetrating continua concept.:1 INTRODUCTION 1.1 Background 1.2 Underlining mechanisms 1.3 State of the art 1.4 Motivation, goal and outline of the thesis 2 STATE OF THE ART 2.1 Statement of the problem 2.2 Overview of literatures 2.3 Unbounded linear shear flow 2.4 Linear shear flow with the wall lying in the inner region 2.5 Stagnant flow with the wall lying in the outer region 2.6 Linear shear flow with the wall lying in the outer region 2.7 Conclusions 3 NUMERICAL APPROACH AND PRELIMINARY TESTS 3.1 Numerical approach 3.2 Preliminary tests 4 CLEAN SPHERICAL BUBBLE IN WALL-BOUNDED FLOW 4.1 Characteristics of the flow field and fundamental mechanisms 4.2 Hydrodynamic forces on the bubble: fluid at rest at infinity 4.3 Hydrodynamic forces on the bubble: linear shear flow 4.4 Conclusions 5 RIGID SPHERE IN WALL-BOUNDED FLOW 5.1 Characteristics of the flow field and fundamental mechanisms 5.2 Hydrodynamic forces on the sphere: fluid at rest at infinity 5.3 Hydrodynamic forces on the sphere: Linear shear flow 5.4 Conclusions 6 CONCLUSIONS AND FUTURE WORK 6.1 Summary and conclusions 6.2 Future work 7 REFERENCE