Manufacturing of light-weight materials is associated with several types of casting defects during solidification. Porosity defects are common, especially in aluminum and its alloys, which initiate crack propagation and thereby cause drastic deterioration in the mechanical properties. These defects, classified as micro and macro defects (based on their sizes), are mainly governed by release of hydrogen into the liquid at the solid-liquid interface, which triggers the nucleation and growth of hydrogen bubbles in the melt. Subsequently, these bubbles interact with solidifying interfaces such as dendritic arms and eutectic fronts, leading to the formation of pores. Macroscopic defects in the form of voids are created due to solidification shrinkage. The primary focus of the present work is to develop phenomenological models for the evolution of microporosity and microstructures during solidification. The issues outlined above typically occur in multi-phase environments comprising of solid, liquid and gaseous phases, and over a range of length and time scales. Any phenomenological prediction would, therefore, require a multi-phase-scale approach. Principles of volume averaging are applied to equations of conservation to obtain single-field formulations. These are then solved with appropriate interface tracking techniques such as Enthalpy, Level-set, Volume-of-fluid and Immersed-boundary methods. The framework is built up on a standard pressure based incompressible fluid flow solver (SIMPLER algorithm) and coupled modeling strategies are proposed to address the interfacial dynamics. A two-dimensional framework is considered with a fixed-grid Cartesian co-ordinate system. Scaling analyses are performed to bring out the relative effects of various competing parameters in order to obtain further insights into this complex phenomenon. The numerical results and scaling predictions are validated against experimental observations published in literature. In literature, numerical predictions of microporosity mainly include criteria based models based on empirical relations and deterministic/stochastic models based on diffusion driven growth assuming spherical bubbles. The dynamic evolution of non-spherical bubble-metal interface in a three-phase system is yet to be captured. Moreover, several in-situ experiments have shown elongated bubble shapes during the engulfment phase, therefore a criterion to define the dependence on cooling rates and the resulting bubble morphology can possibly deliver further practical insights. We propose a numerical model for hydrogen bubble growth, its movement and subsequent engulfment by a solidifying front, combining the features of level-set and enthalpy methods for tracking bubble-metal and solid-liquid interfaces, respectively. The influx of hydrogen into heterogeneously nucleated bubbles results in growth of bubbles to sizes up to a few hundreds of microns. In the first part of this numerical study, a methodology based on the level-set approach is developed to simultaneously capture hydrogen bubble growth and movement in liquid aluminum. The solidification is first assumed to occur outside the micro-domain providing a specified hydrogen influx to the bubble-in-liquid system. The level-set equation is formulated in such a way as to account for simultaneous growth and movement of the bubble. The growth of a bubble with continuous and fixed hydrogen levels in the melt is studied. The rates of growth of bubble-liquid and solidifying interfaces are compared using an order of magnitude analysis. This scaling analysis explains the thought experiment proposed in the literature, where difference in bubble shapes was attributed to the cooling rate. Moreover, it shows explicit dependence on bubble radius and cooling rate leading to a new criterion for bubble elongation proposed in this thesis. This also highlights the comparison between solidification and hydrogen diffusion time-scales which primarily govern the competitive growth behavior. The bubble-in-liquid model is coupled with microscopic enthalpy method to incorporate effects of solidification and study the interaction of solid-liquid and bubble-liquid interfaces. The phenomena of bubble engulfment and elongation are successfully captured by the proposed model. A parametric study is carried out to estimate the bubble elongation based on different initial bubble sizes and varying cooling rates encountered in typical sand, permanent mold and die casting processes. Although simulation of microstructures has been extensively studied in the literature, very few models address the phenomena of simultaneous growth and movement of equiaxed dendrites. The presence of different flow environments and multiple dendrites are known to alter the position and shape of the dendrites. The proposed model combines the features of the following methods, namely, the Enthalpy method for modeling growth; the Immersed Boundary Method (IBM) for handling the rigid solid-liquid interfaces; and the Volume of Fluid (VOF) method for tracking the advection of the dendrite. The algorithm also performs explicit-implicit coupling between the techniques used. Validation with available literature is performed and dendrite growth in presence of rotational and buoyancy driven flow fields is studied. The expected transformation into globular microstructure in presence of stirring induced flows is successfully simulated. A simple order estimate for time required for stirring is performed which agrees with numerical predictions. In buoyancy driven environment of a settling dendrite, the arm tip speeds show expected higher velocity of the upstream tip compared to its counterpart. The model is extended to study thermal and hydrodynamic interactions between multiple dendrites with appropriate considerations for different orientations and velocities of the dendritic solid entities. The present model can be used for the prediction of grain sizes and shapes and to simulate morphological transformations due to different melt flow scenarios. In the final part, the methodology presented for growth and engulfment of hydrogen bubbles is extended to study the phenomenon of diffusion driven bubble growth occurring in direct foaming of metals. The source of hydrogen is determined by the rate of decomposition of the blowing agent. This is accounted for by a source term in the hydrogen species conservation equation, and growth rate of hydrogen bubbles is calculated on the basis of diffusive flux at the interface. The level-set method is used for tracking the bubble-liquid interface growth, and the macroscopic enthalpy model is used for obtaining heat transfer and solid front position. The model is validated with analytical solution by comparing the front position and the solidification time. The variation of foam density with a transient hydrogen generation source is studied and qualitatively compared with results reported in literature. The modeling strategies proposed in this work are generic and therefore have potential in simulating a variety of complex multi-phase problems.

Cette thèse s’inscrit dans le contexte de la durabilité des structures en acier au carbone envisagées pour le stockage des déchets radioactifs à haute activité et à vie longue. Ce travail porte plus particulièrement sur la simulation numérique de la corrosion généralisée (et de son évolution), principale forme de corrosion susceptible d’affecter ces aciers en phase aqueuse et en condition désaérée.Le processus de corrosion des aciers au carbone est grandement influencé par la formation de couches de produits de corrosion (CPC) dont le rôle sur l’évolution de la vitesse de corrosion a été mis en évidence dans de nombreuses études. Le caractère plus ou moins protecteur d’une CPC dépend de plusieurs paramètres physiques (porosité, épaisseur et propriétés électriques de CPC) et chimiques (pH, PCO2, formations de complexes,…). Le principal objectif de ce travail de thèse est l’étude du rôle d’une CPC de sidérite sur la vitesse de corrosion des aciers au carbone en condition désaérée. Le régime de corrosion est ainsi simulé sur la base de modèles mécanistes en faisant appel à une résolution par la méthode des éléments finis de l’équation de transport réactif en milieu poreux et en potentiel libre.Dans un premier temps, l’étude de la stabilité d’une CPC par expérience numérique est présentée et constitue une étape importante dans la mesure où elle permet de sélectionner les paramètres influençant cette stabilité et par conséquent le processus de corrosion. Cette expérience numérique confirme des résultats expérimentaux obtenus sur des coupons dans un environnement représentatif des conditions de stockage mais sur des durées beaucoup plus courtes (de l’ordre de quelques années). Ces calculs montrent qu’en fonction des conditions chimiques (pH, complexants,…), morphologiques (épaisseur, distribution de porosité dans la CPC, …) et des propriétés électriques de la couche, on obtient soit un dépôt stable pouvant potentiellement entraîner une diminution de la vitesse de corrosion, ou soit un dépôt instable mettant à nu la surface du métal et qui se traduit par une vitesse de corrosion élevée.De manière complémentaire, le transitoire de croissance d’une CPC est également étudié en prenant en compte numériquement le déplacement de l’interface métal – CPC correspondant à la création de vide par la dissolution du métal. Deux approches, la première dite « implicite » et la seconde dite « explicite », de mouvement de cette interface sont présentées. Tous ces modèles numériques sont comparés à différents retours d’expérience. A cet égard, une loi de précipitation de la sidérite, discutée et confrontée aux différentes lois de la littérature, est proposée. Les résultats de simulation d’un transitoire de croissance d’une CPC conductrice sont conformes à certains retours d’expériences, montrant d’abord une phase active de corrosion suivie d’une phase pseudo-passive où la vitesse de corrosion est ralentie par le recouvrement de la surface métallique par la CPC. / This thesis is related to the issue of the sustainability of carbon steel structures intended for the storage of high-level long-lived radioactive waste. This work focuses on the numerical simulation of the uniform corrosion (and on its evolution), representing the main form of corrosion likely to affect these steel components in aqueous and deaerated conditions.The corrosion process of carbon steels is greatly influenced by the formation of corrosion product layers (CPL) whose role on the evolution of the corrosion rate has been demonstrated in numerous studies. The more or less protective nature of a CPL depends on several physical (porosity, thickness and electrical properties of CPL) and chemical parameters (pH, PCO2, complex formations, ...). The main objective of this thesis is the study of the role of a siderite CPL on the corrosion rate of carbon steels in deaerated conditions. The corrosion regime is simulated on the basis of mechanistic models using a finite element method to resolve the reactive transport equation in porous media and in free potential conditions.Firstly, the stability of a CPL is studied by numerical experiment and constitutes an important step that permits to select the key parameters influencing this stability and consequently the corrosion process. This numerical experiment confirms experimental results obtained on coupons in an environment representative of the storage conditions but on much shorter durations (few years). These calculations show that depending on the chemical conditions (pH, complexing medium, ...), morphological (thickness, distribution of porosity in the CPC, ...) and the electrical properties of the layer, we obtain either a stable deposit that could potentially lead to a decrease of the corrosion rate, or an unstable deposit exposing the metal surface and resulting in a high corrosion rate.In a second time, the transient step i.e. the formation and growth process of a CPL, is also studied numerically considering the displacement of the metal-CPC interface corresponding to the creation of voids caused by the dissolution of the metal. Two approaches, the first one called "implicit" and the second "explicit", of the movement of this interface are presented. All these numerical models are compared with different experimental feedbacks. Thus, a kinetics law of precipitation of siderite, discussed and compared with different laws proposed in the literature, is implemented in these models. The results obtained by simulating the growth of a conductive CPL are consistent with some experimental feedbacks, showing firstly a period of active corrosion followed by a pseudo-passive period during which the corrosion rate is significantly decreased resulting from the coverage of the metal surface by the CPL.