Dans ce travail de thèse, une méthode de pénalisation en volume pour la simulation d'écoulements magnétohydrodynamiques (MHD) en domaines confinés est présentée. Les équations incompressibles de la MHD résistives sont résolues par le truchement d'un solveur pseudo-spectral parallèlisé. La pénalisation en volume est une méthode de frontières immergées, caractérisée par une grande flexibilité dans le choix de la géométrie de l'écoulement. Dans le cas présent, elle permet d'utiliser des conditions aux limites non-périodiques dans un schéma pseudo-spectral Fourier. La méthode numérique est validée et sa convergence est quantifiée pour des écoulements hydrodynamiques et MHD, en deux et trois dimensions, en comparant les résultats numériques à ceux de la littérature et à des solutions analytiques. Dans un second temps, la génération spontanée de moment cinétique et magnétique est étudiée pour des écoulements MHD confinés 2D et 3D. L'influence du nombre de Reynolds et du rapport des énergies cinétique/magnétique est explorée, ainsi que les différences induites par les conditions aux limites. Le fait que l'axisymétrie des frontières résulte en un terme de pression non-nul est primordial pour engendrer de grandes valeurs du moment cinétique. L'exclusivité de cette auto-organisation aux écoulements 2D est étudiée en considérant la MHD 3D en présence d'un fort champ magnétique axial. La suite est consacrée à la simulation d'un fluide conducteur dans un cylindre avec un forçage magnétique axial et poloidal. En faisant varier l'amplitude du forçage poloidal, différents états dynamiques sont atteints. Enfin, l'effet du nombre de Prandtl sur le seuil des instabilitées est étudié. / A volume penalization method for the simulation of magnetohydrodynamic (MHD) flows in confined domains is presented. Incompressible resistive MHD equations are solved in 3D by means of a parallelized pseudo-spectral solver. The volume penalization technique is an immersed boundary method, characterized by a high flexibility in the choice of the geometry of the considered flow. In the present case, it allows the use of conditions different from periodic boundaries in a Fourier pseudo-spectral scheme. The numerical method is validated and its convergence is assessed for two- and three-dimensional hydrodynamical and MHD flows by comparing the numerical results with those of the literature or analytical solutions. Then, the spontaneous generation of kinetic and magnetic angular momentum is studied for confined 2D and 3D MHD flows. The influence of the Reynolds number and of the ratio of kinetic/magnetic energies is explored, as well as the differences induced by the boundary conditions. The fact that axisymmetric borders introduce a non-zero pressure term in the evolution equation of the angular momentum is essential to generate large values of the angular momentum. It is investigated whether this self-organization is exclusively observed in 2D flows by considering 3D MHD in the presence of a strong axial magnetic field. The last part is devoted to the simulation of a conducting fluid in a periodic cylinder with imposed axial and poloidal magnetic forcing, implying a resulting magnetic field. By varying the amplitude of the poloidal forcing, different dynamical states can be achieved. The effect of the Prandtl number on the threshold of the instabilities is then studied.

Mines have an inherent risk of geotechnical failure in both rock excavations and tailings storage facilities. Geotechnical failure occurs when there is a combination of exceptionally large forces acting on a structure and/or low material strength resulting in the structure not withstanding a designed service load. The excavation of rocks can cause unintended rock mass movements. If the movement is monitored promptly, accidents, loss of ore reserves and equipment, loss of lives, and closure of the mine can be prevented. Mining companies routinely use deformation monitoring to manage the geotechnical risk associated with the mining process. The aim of this dissertation is to review the geotechnical risk management process to optimize the geotechnical risk management analysis. In order to perform a proper analysis of slope instability, understanding the importance as well as the limitations of any monitoring system is crucial. Due to the potential threat associated with slope stability, it has become the top priority in all risk management programs to predict the time of slope failure. Datasets from monitoring systems are used to perform slope failure analysis. Innovations in slope monitoring equipment in the recent years have made it possible to scan a broad rock face in a short period with sub-millimetric accuracy. Instruments like Slope Stability Radars (SSR) provide the quantitative data that is commonly used to perform risk management analysis. However, it is challenging to find a method that can provide an accurate time of failure predictions. Many studies in the recent past have attempted to predict the time of slope failure using the Inverse Velocity (IV) method, and to analyze the probability of a failure with the fuzzy neural networks. Various method investigated in this dissertation include: Minimum Inverse Velocity (MIV), Maximum Velocity (MV), Log Velocity (LV), Log Inverse Velocity (LIV), Spline Regression (SR) and Machine Learning (ML). Based on the results of these studies, the ML method has the highest rate of success in predicting the time of slope failures. The predictions provided by the ML showed ~86% improvement in the results in comparison to the traditional IV method and ~72% improvement when compared with the MIV method. The MIV method also performed well with ~75% improvement in the results in comparison to the traditional IV method. Overall, both the new proposed methods, ML and MIV, outperformed the traditional inverse velocity technique used for predicting slope failure.

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Les instabilités hydrodynamiques en cavité chauffée latéralement jouent un rôle important dans certains processus de fabrication de matériaux tels que le procédé de Bridgman horizontal. En effet, le fluide (métal liquide qui va se solidifier) est le siège d’une circulation thermoconvective due à l’existence d’un gradient de température horizontal qui est susceptible de devenir instationnaire via des instabilités oscillatoires. La connaissance et la maîtrise de ces instabilités sont donc primordiales afin de pouvoir améliorer la qualité des cristaux obtenus par cette technique. Dans cette thèse, nous nous sommes intéressés en premier aux instabilités affectant la circulation convective dans une cavité tridimensionnelle de dimensions 4×2×1. (longueur × largeur × hauteur). Grâce aux techniques numériques de continuation, nous avons pu obtenir les solutions stationnaires et oscillatoires, ainsi que leur stabilité, jusqu’à l’apparition de la quasi-périodicité en fonction du nombre de Grashof Gr et pour un nombre de Prandtl allant de 0 à 0,025. Ensuite, pour un éventuel contrôle des instabilités, nous nous sommes intéressés aux effets induits par la rotation de la cavité. Nous avons tout d’abord considéré un modèle monodimensionnel que nous avons développé durant cette thèse. Ce modèle analytique, bien que simplifié, est en très bon accord avec les observations en dynamique des écoulements atmosphériques (déviation des masses fluides vers la droite de la composante de vitesse dominante et vents thermiques). La stabilité linéaire de cet écoulement est ensuite effectuée en fonction du taux de rotation donné par le nombre de Taylor et du nombre de Grashof pour un nombre de Prandtl allant de 0 à 10. Nous avons pu montrer à travers ce modèle que la rotation possède un caractère stabilisant vis-à-vis de ce type d’écoulement. Enfin, nous nous sommes focalisés sur les effets de la rotation sur l’écoulement pleinement tridimensionnel dans la cavité de dimensions 4×2×1. Nous avons mis en évidence deux régimes d’écoulements : un régime dominé par la convection, où la circulation du fluide est déviée par la rotation dans la diagonale de la cavité, et un deuxième régime dominé par la rotation où la circulation du fluide est concentrée dans les couches limites dites d’Ekman et de Stewartson. Un très bon accord est observé entre le modèle analytique simplifié et la simulation numérique tridimensionnelle. / Hydrodynamic instabilities in laterally heated cavities play an important role in some material processing techniques such as the horizontal Bridgman process. Indeed, the fluid (liquid metal to be solidified) is the seat of a thermoconvective circulation due to the existence of a horizontal temperature gradient which is likely to become unsteady via oscillatory instabilities. The knowledge and the control of these instabilities are thus essential in order to be able to improve the quality of the crystals obtained by this technique. In this thesis, we are first interested in the instabilities of the convective circulation in a three-dimensional cavity of dimensions 4×2×1 (length × width × height). Thanks to the numerical continuation techniques, we were able to obtain the stationary and oscillatory solutions, as well as their stability, until the appearance of the quasi-periodicity according to the Grashof number Gr and for a Prandtl number Pr ranging from 0 to 0.025.Then, the effects induced by a rotation of the cavity around the vertical axis parallel to gravity (for a possible control of the instabilities) are studied and a one-dimensional model developed during this thesis was first considered. This analytical model, although simplified, is in very good agreement with the observations of the atmospheric flows (deviation of the fluid masses towards the right of the component of the dominant velocity and thermal winds). The linear stability of this flow as well as an energy analysis at the thresholds are then performed as a function of the rotation rate given by the Taylor number Ta and the Grashof number Gr for a Prandtl number Pr ranging from 0 to 10. Through this model, we have been able to show that the rotation has a stabilizing effect on this type of flow.We finally focused on the effects of this type of rotation on the steady fully threedimensional flow observed in the cavity 4×2×1 at low Grashof numbers.We have highlighted two flow regimes: a regime dominated by convection where the fluid circulation, deviated by the rotation, occurs in the diagonal of the cavity, and a second regime dominated by rotation where the fluid circulation is concentrated in the so-called Ekman and Stewartson boundary layers. A very good agreement is observed between the simplified analytical model and the three-dimensional numerical simulation.

Une rivière alluviale s'écoule sur une épaisse couche de sédiments. Lorsqu'elle construit son lit, elle entraîne, transporte et dépose des sédiments, façonnant ainsi sa propre forme. Ainsi, le couplage entre l'écoulement et le transport sédimentaire régit la taille et la forme de la rivière. Dans cette thèse, nous étudions l'influence du transport sédimentaire sur la forme et la stabilité d'une rivière alluviale. Pour ce faire, nous reproduisons des rivières en laboratoire en laissant s'écouler un liquide visqueux sur un lit granulaire. L'aspect du chenal ainsi formé dépend des débits de liquide et de sédiment injectés en entrée. A l'aide de ces expériences, nous mettons en évidence les deux mécanismes qui contrôlent l'équilibre d'une rivière. D'abord, la gravité entraîne les grains vers le centre du chenal. Ce mécanisme érode continuellement les berges de la rivière, et tend donc à l'élargir. Cependant, les collisions d'un grain avec le lit dévient sa trajectoire dans la direction transverse à l'écoulement. Les grains se comportent ainsi comme des marcheurs aléatoires, qui, collectivement, diffusent vers les berges de la rivière. A l'équilibre, cette diffusion compense la gravité, et fixe ainsi la forme de la rivière. Lorsque la diffusion prend le dessus sur la gravité, elle peut induire une instabilité. En effet, si on perturbe un lit sédimentaire avec des stries longitudinales, le cisaillement fluide est plus faible là où l'écoulement est moins profond. Par conséquent, les grains diffusent depuis les creux de la perturbation vers ses crêtes. Cette rétroaction déstabilisante pourrait générer de nouveaux chenaux, et expliquer la formation des rivières en tresses. / An alluvial river builds its own bed with the sediment it transports. The channel bounds the flow, which in turns deforms the channel through erosion and deposition. This coupling between flow and sediment transport selects the shape and the size of the river. In this manuscript, we investigate it using laboratory experiments. The first ingredient of this coupling is gravity, which pulls the moving grains towards the center of the channel, thus continually eroding the banks. However, due to the roughness of the bed, the trajectory of a moving grain fluctuates across the stream. The bedload layer is therefore a collection of random walkers which diffuse towards the less active areas of the bed. In a river at equilibrium, this diffusion counteracts gravity to maintain the banks. When gravity and diffusion are out of balance, their interaction causes an instability. Indeed, if an initially flat bed of sediment is perturbed with longitudinal streaks, the flow-induced shear stress is weaker where the flow is shallower. Therefore, bedload diffusion induces a sediment flux towards the crests of the perturbation. This positive feedback induces an instability which can generate new channels. We suggest that this mechanism could initiate the braiding of alluvial rivers.

Crashback operation of a propeller is a common emergency slowing maneuver for ships and submarines. The reversing of the propeller while the vessel is moving forward results in large loads on the propeller blades and highly detached flow, which presents both practical concerns and fundamental fluid physics inquiries. This thesis contains a comprehensive numerical analysis of two propellers in crashback operation. Available numerical and experimental data for David Taylor Model Basin (DTMB) 4381 propeller are used for validation of the computational fluid dynamics solver used, REX. A second propeller, Maritime Research Institute Netherlands (MARIN) 7371R is used to classify the common crashback flow behavior into regimes. Four regimes were identified, each existing for a range of operating conditions. The most prominent and deciding feature of the flow regimes is the presence of a ring vortex, resulting from the opposing action of the free-stream flow and the propeller induced flow. The position, shape and strength changes between regimes, dominating the dynamics of the flow by altering the induced flow into the propeller disk. Flow conditions resulting from regime transitions are described. Changes in the ring vortex structure lead to two stable flow conditions of interest. One condition produces a reduction of thrust despite the increase in flow speed into the propeller and negligible side-forces. The other condition creates large side-forces capable of rotating a vessel, resulting from an asymmetry forming in the ring vortex. Additionally, massive flow separation occurs at high free-stream speeds that cause extreme blade loading. An extensive description of each flow regime is provided, with further investigation and discussion of the flow regimes that present more practical concerns and novel characteristics of the crashback flow.

I study dusty plasma produced by electrostatically confining melamine formaldehyde microparticles in a radio-frequency glow discharge plasma. Dusty plasma is a mixture of particles of solid matter (dust), electrons, ions, and neutral gas atoms. The dust particles have a very high charge and a mass compared to the electrons and ions in the ambient plasma. As a consequence, a dusty plasma exhibits collective phenomena such as dust acoustic waves, crystallization, and melting. The discrete nature of dust particles gives rise to compressibility. In this thesis I report findings of four tasks that were performed to investigate dust acoustic waves, compressibility, and melting. First, the nonlinear phenomenon of synchronization was characterized experimentally for the dust acoustic wave propagating in a dust cloud with many layers. I find four synchronized states, with frequencies that are multiples of 1, 2, 3, and 1/2 of the driving frequency. Comparing to phenomena that are typical of the van der Pol paradigm, I find that synchronization of the dust acoustic wave exhibits the signature of the suppression mechanism but not that of the phaselocking mechanism. Additionally, I find that the synchronization of the dust acoustic wave exhibits three characteristics that differ from the van der Pol paradigm: a threshold amplitude that can be seen in the Arnold tongue diagram, a branching of the 1:1 harmonic tongue at its lower extremity, and a nonharmonic state. Second, to assess which physical processes are important for a dust acoustic instability, I derived dispersion relations that encompass more physical processes than commonly done. I investigated how various physical processes affect a dust acoustic wave by solving these dispersion relations using parameters from a typical dust acoustic wave experiment. I find that the growth rate diminishes for large ion currents. I also find that the compressibility, a measure of the coupling between the dust particles, have a strong effect on the wave propagation. Comparing the kinetic vs. hydrodynamic descriptions for ions, I find that under typical laboratory conditions the inverse Landau damping and the ion-neutral collisions contribute about equally to the dust acoustic instability. Third, I performed dust acoustic wave experiments to resolve a previously unremarked discrepancy in the literature regarding the sign of the compressibility of a strongly-coupled dust component in a dusty plasma. According to theories compressibility is negative, whereas experiments suggest that it is positive. I find that the compressibility is positive. This conclusion was reached after allowing for a wide range of experimental uncertainties and model dependent systematic errors. Finally, the polygon construction method of Glaser and Clark was used to characterize crystallization and melting in a single-layer dusty plasma. Using particle positions measured in a previous dusty plasma experiment, I identified geometrical defects, which are polygons with four or more sides. These geometrical defects are found to proliferate during melting. I also identify a possibility of latent heat involvement in melting and crystallization processes of a dusty plasma.

L'explosion en supernova gravitationnelle représente le stade ultime de l'évolution des étoiles massives.La contraction du cœur de fer peut être suivie d'une gigantesque explosion qui donne naissance à une étoile à neutrons.La dynamique multi-dimensionnelle de la région interne, pendant les premières centaines de millisecondes, joue un rôle crucial sur le succès de l'explosion car des instabilités hydrodynamiques sont capables de briser la symétrie sphérique de l'effondrement.Les mouvements transverses et à grande échelle générés par deux instabilités, la convection induite par les neutrinos et l'instabilité du choc d'accrétion stationnaire (SASI),augmentent l'efficacité du chauffage de la matière par les neutrinos au point de déclencher une explosion asymétrique et d'impacter les conditions de naissance de l'étoile à neutrons. Dans cette thèse, les instabilités sont étudiées au moyen de simulations numériques de modèles simplifiés.Ces modèles permettent une vaste exploration de l'espace des paramètres et une meilleure compréhension physique des instabilités, généralement inaccessibles aux modèles réalistes.L'analyse du régime non-linéaire de SASI établit les conditions de formation d'un mode spiral et évalue sa capacité à redistribuer radialement le moment cinétique.L'effet de la rotation sur la dynamique du choc d'accrétion est également pris en compte.Si la rotation est suffisamment rapide, une instabilité de corotation se superpose à SASI et impacte grandement la dynamique.Les simulations permettent de mieux contraindre l'importance des modes non-axisymétriques dans le bilan de moment cinétique de l'effondrement du cœur de fer en étoile à neutrons.SASI pourrait sous certaines conditions accélérer ou ralentir la rotation du pulsar formé dans l'explosion.Enfin, une étude d'un modèle idéalisé de la région de chauffage est menée pour caractériser le déclenchement non-linéaire de la convection par des perturbations telles que celles produites par SASI ou les inhomogénéités de combustion pré-effondrement.L'analyse de la dimensionnalité sur le développement de la convection permet de discuter l'interprétation des modèles globaux et met en évidence les effets bénéfiques de la dynamique tridimensionnelle sur le déclenchement de l'explosion. / A core-collapse supernova represents the ultimate stage of the evolution of massive stars.The iron core contraction may be followed by a gigantic explosion which gives birth to a neutron star.The multidimensional dynamics of the innermost region, during the first hundreds milliseconds, plays a decisive role on the explosion success because hydrodynamical instabilities are able to break the spherical symmetry of the collapse.Large scale transverse motions generated by two instabilities, the neutrino-driven convection and the Standing Accretion Shock Instability (SASI),increase the heating efficiency up to the point of launching an asymmetric explosion and influencing the birth properties of the neutron star.In this thesis, hydrodynamical instabilities are studied using numerical simulations of simplified models.These models enable a wide exploration of the parameter space and a better physical understanding of the instabilities, generally inaccessible to realistic models.The non-linear regime of SASI is analysed to characterize the conditions under which a spiral mode prevails and to assess its ability to redistribute angular momentum radially.The influence of rotation on the shock dynamics is also addressed.For fast enough rotation rates, a corotation instability overlaps with SASI and greatly impacts the dynamics.The simulations enable to better constrain the effect of non-axisymmetric modes on the angular momentum budget of the iron core collapsing into a neutron star.SASI may under specific conditions spin up or down the pulsar born during the explosion.Finally, an idealised model of the heating region is studied to characterize the non-linear onsetof convection by perturbations such as those produced by SASI or pre-collapse combustion inhomogeneities. The dimensionality issue is examined to stress the beneficial consequences of the three-dimensional dynamics on the onset of the explosion.

When entering a planet’s atmosphere, spacecraft induce a strong compression shock and must be protected from the resulting extreme heat flux by a thermal protection system made of either reusable or ablative materials. To characterise these materials, the harsh flow conditions of atmospheric entry are reproduced in plasma wind tunnels, where a jet of gas heated up to ionisation is directed at material samples for prolonged testing. Unfortunately, heated jets exhibit complex dynamic behaviours, resulting in oscillations that increase the uncertainties in the experiments.At sufficient Reynolds numbers, the dynamic behaviour of heated jets shifts from an amplifier to a self-sustained oscillator type via a Hopf bifurcation, if the centreline-to-ambient density ratio falls below a given threshold. This change is known in the literature to be related to the onset of absolute instabilities in the flow. However, this type of instability is usually studied for a simplified description of the gas, which is not suitable for the case of a plasma wind tunnel.This doctoral work investigates the nature of the instabilities responsible for the oscillations observed in a plasma jet, similar to the one in the VKI Plasmatron facility. The analysis is carried out by comparing results from different numerical methods, including linear stability analyses (both local and global) and direct numerical simulations. The thesis first describes the effect of high-temperature gas models on the stability of synthetic jets found in the literature, before analysing the case of Plasmatron.The analysis of synthetic jets with real-gas effects shows that the onset of the first dissociation reactions in the flow has a strong influence on the prevailing type of instability. Furthermore, if a sufficiently long region of absolute instability is present in the jet, the flow bifurcates to a periodic limit cycle, and steady state solutions become inadequate to describe the flow and its dynamic behaviour. In this case, a stability analysis of the time-averaged state can accurately reproduce the results of direct numerical simulations. In the case of Plasmatron, a large region of absolute instability is revealed in the plasma jet, suggesting that the observed oscillations are caused (in part) by a global non-linear mode and that the flow has entered a limit cycle. Trends of the absolute instability frequency with respect to the driving parameters of Plasmatron are in agreement with experimental observations.The present work confirms that global stability features of heated jet flows are very sensitive to subtle changes of the undisturbed or time-averaged state, which results from technological constraints in the case of Plasmatron. Furthermore, this thesis has shown the relevance of including high-temperature gas effects in the stability analysis of high-enthalpy jets. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished

Dans la configuration de Rayleigh-Bénard, on considère une fine couche de fluide placée entre deux parois horizontales, chauffée par le bas et refroidie par le haut. Cette couche peut être le siège d'une instabilité si le gradient thermique est suffisamment important : on passe alors de l'état conductif à l'état convectif et on parle de bifurcation primaire pour qualifier cette première transition. Cette mise en mouvement du fluide se fait de manière ordonnée : on constate ainsi l'émergence de différents motifs de convection comme des rouleaux, des carrés ou encore des hexagones. Ces structures vont à leur tour subir des instabilités qualifiées de secondaires qui vont limiter la gamme de nombres d'onde stables. On étudie ici théoriquement ces instabilités d'une part à proximité du seuil de la convection grâce à une approche faiblement non linéaire, d'autre part loin des conditions critiques grâce à une approche fortement non linéaire. Le fluide est rhéofluidifiant, ce qui correspond au comportement rhéologique le plus fréquemment rencontré, et est décrit par le modèle de Carreau. À proximité du seuil, on considère deux situations : la première correspond au cas où les plaques ont une conductivité finie, la seconde à celui d'un fluide thermodépendant. Dans chaque cas, l'influence du caractère rhéofluidifiant sur la nature du motif émergeant à la bifurcation primaire et sur les instabilités secondaires est mise en évidence. Pour étudier les motifs de convection loin des conditions critiques, on a recours à une procédure de continuation permettant de déterminer de proche en proche les caractéristiques de l'écoulement comme les champs de vitesse ou de température ainsi que le nombre de Nusselt. / In the Rayleigh-Bénard configuration, we consider a thin layer of fluid confined between two horizontal slabs which is heated from below and cooled from above. This layer undergoes an instability if the thermal gradient is strong enough: a transition from the conductive state to the convective state and called _ primary bifurcation _occurs. Moreover, it happens in an ordered way: we can notice the emergence of various convection patterns such as rolls, squares or hexagons. In their turn, these patterns undergo _ secondary instabilities _ that limit the range of stable wavenumbers. These instabilities are studied theoretically _firstly near the threshold thanks to a weakly nonlinear approach, and secondly far from critical conditions thanks to a strongly nonlinear approach. We consider a shear thinning fluid, the most common rheological behavior, which is described by the Carreau model. Near the threshold, two situations are considered: the first corresponds to finite conductivity plates, the second corresponds to a thermodependent fluid. In each case, the influence of the shear thinning effect on the nature of the pattern emerging at the primary bifurcation and on secondary instabilities is highlighted. To study the convection patterns far from the critical conditions, a continuation procedure is used to determine, step-by-step, the characteristics of the flow, such as the velocity or temperature fields and the Nusselt number.