The quality of parts fabricated using Laser Solid Freeform Fabrication (LSFF) is highly dependent on the physical phenomena and operating parameters which govern the process. For instance, the thermal stress patterns and intensity, induced throughout the process domain due to the layer-by-layer material deposition and the temperature distribution characteristics, contribute significantly to potential delamination and crack formation across the fabricated part. In this research, some of the main features as well as drawbacks of this technique are studied through a multi-physics analysis of the process. For this purpose, a coupled time-dependent 3D model is developed with which the geometry of the deposited material as well as temperature and thermal stress fields across the process domain can be predicted. In the proposed approach, coupled thermal and stress domains are numerically obtained assuming a decoupled interaction between the laser beam and powder stream. To predict the geometry of the deposited material, once the melt pool boundary is obtained, the process domain is discretized in a cross-sectional fashion based on the powder feed rate, elapsed time, and intersection of the melt pool and powder stream projected on the substrate. Layers of additive material are then added onto the non-planar domain. The main process parameters affected by a multilayer deposition due to the formation of non-planar surfaces, such as powder catchment, are incorporated into the modelling approach to enhance the accuracy of the results. To demonstrate the proposed algorithm and to study the main features of the process, a four-layer thin wall of AISI 304L steel on a substrate of the same material is numerically and experimentally fabricated. The numerical analyses along with the experimental results are then used to investigate the correlation between the temperature-thermal stress fields and crack formation across the fabricated parts. The trend of the results reveals that by preheating the substrate prior to the fabrication process, it is possible to substantially reduce the formed micro-cracks. To demonstrate the feasibility of preheating on the reduction of micro-cracks, several simulations and experiments are performed in which a crack-free result is obtained, with a 22 per cent reduction in thermal stresses when the substrate is preheated to 800 K. The numerical and experimental results are also used to study the circumstances of the microstructural formation during the fabrication process. To conclude this research, the developed modelling approach is further extended to briefly discuss the effects of the path patterns and the main operating parameters on the outcomes of the process. The effects of the material properties and their variations on the temperature distributions and thermal stress fields are studied by fabrication of a thin wall of two Stellite 6 layers and two Ti layers on a stainless steel substrate.

The quality of parts fabricated using Laser Solid Freeform Fabrication (LSFF) is highly dependent on the physical phenomena and operating parameters which govern the process. For instance, the thermal stress patterns and intensity, induced throughout the process domain due to the layer-by-layer material deposition and the temperature distribution characteristics, contribute significantly to potential delamination and crack formation across the fabricated part. In this research, some of the main features as well as drawbacks of this technique are studied through a multi-physics analysis of the process. For this purpose, a coupled time-dependent 3D model is developed with which the geometry of the deposited material as well as temperature and thermal stress fields across the process domain can be predicted. In the proposed approach, coupled thermal and stress domains are numerically obtained assuming a decoupled interaction between the laser beam and powder stream. To predict the geometry of the deposited material, once the melt pool boundary is obtained, the process domain is discretized in a cross-sectional fashion based on the powder feed rate, elapsed time, and intersection of the melt pool and powder stream projected on the substrate. Layers of additive material are then added onto the non-planar domain. The main process parameters affected by a multilayer deposition due to the formation of non-planar surfaces, such as powder catchment, are incorporated into the modelling approach to enhance the accuracy of the results. To demonstrate the proposed algorithm and to study the main features of the process, a four-layer thin wall of AISI 304L steel on a substrate of the same material is numerically and experimentally fabricated. The numerical analyses along with the experimental results are then used to investigate the correlation between the temperature-thermal stress fields and crack formation across the fabricated parts. The trend of the results reveals that by preheating the substrate prior to the fabrication process, it is possible to substantially reduce the formed micro-cracks. To demonstrate the feasibility of preheating on the reduction of micro-cracks, several simulations and experiments are performed in which a crack-free result is obtained, with a 22 per cent reduction in thermal stresses when the substrate is preheated to 800 K. The numerical and experimental results are also used to study the circumstances of the microstructural formation during the fabrication process. To conclude this research, the developed modelling approach is further extended to briefly discuss the effects of the path patterns and the main operating parameters on the outcomes of the process. The effects of the material properties and their variations on the temperature distributions and thermal stress fields are studied by fabrication of a thin wall of two Stellite 6 layers and two Ti layers on a stainless steel substrate.

In the past years, more concerns are focused on the nuclear waste management due to the very long half-lives of various actinides produced in Light Water Reactors (LWRs). Sodium Fast Reactors (SFRs) are thus becoming more attractive since they are known to be very efficient to transmute long-lived radionuclides present in spent fuel. However, the current simulation tools (thermal-hydraulics code with point kinetics) and safety assessment methods are not as mature as for LWR applications and need to be enhanced. This thesis aims at filling the gap in safety analysis of SFR cores to reach a standard similar to LWR applications by applying multi-physics modelling. In contrast to LWRs, the reactivity in SFRs is affected by three main feedback: the Doppler broadening reactivity effect, the sodium density change reactivity effect and the thermal expansion of several mechanical components of the reactor. In this thesis, the thermal-hydraulic system code ATHLET is coupled with the three-dimensional neutron-physics code PARCS for transient analysis. Developed at GRS, ATHLET was recently upgraded for sodium coolant properties. The nodal diffusion codes PARCS, developed at the University of Michigan, can solve the multi-group diffusion equation in hexagonal geometry. While both codes already have the main features to simulate SFRs, the development of models dedicated to the thermal expansion effect of reactivity is necessary. The latter has three main origins i.e. the core axial thermal expansion effect (caused by the fuel and the cladding axial thermal expansion), the core radial thermal expansion effect (caused by the diagrid thermal expansion), the control rod displacement due to the thermal expansion of the Control Rod Drive Lines (CRDLs), the strongback and the reactor vessel. Thus, the three main new developments achieved in the scope of this work are: - Development of a method to generate homogenized multi-energy-group neutron macroscopic cross sections (needed by PARCS) for SFR applications which consider not only the Doppler temperature and sodium density but also the core axial and radial thermal expansion. - Development of a three-dimensional core radial thermal expansion model and its implementation in PARCS. A core axial thermal expansion model has already been developed for PARCS prior to this work. - Development of a module in ATHLET for modelling the control rod displacement as a result of the influence of the reactor structures thermal expansion. The parametrized homogenized multi-energy-group neutron macroscopic cross section libraries for PARCS applications are generated with the Monte Carlo reactor-physics code Serpent. For all materials contained in fuel assemblies, a three-dimensional model is used while the SPH method is applied to materials contained in non-fuel assemblies (e.g. control rods, etc.). The cross section libraries are collapsed into a 12-energy-group structure. Furthermore, a dedicated module was successfully developed and implemented within the core simulator KMACS (developed at GRS). The core radial thermal expansion effect is implemented in PARCS using a coordinate transformation of the diffusion equation from the expanded state to the nominal geometry. The core radial thermal expansion depends on the diagrid temperature. It is calculated by ATHLET and transferred to PARCS by the extended interface between both codes. The modelling of the control rod displacement as a result of the reactor structures thermal expansion is performed by a module linked to ATHLET. The strongback, the reactor vessel and the CRDLs are modelled as heated structures in ATHLET, which calculates their respective temperature. The module can compute the thermal expansion of each structure as well as the total control rod banks displacement. The new techniques are verfied on a selected case study, the ASTRID core design. First, full core criticality simulations are performed with the Monte Carlo reactor-physics code Serpent (considered as reference calculations) and with PARCS. Good agreement between the two codes is achieved in terms of multiplication factors and power distribution. This allows to conclude that the developed method for neutron cross section libraries can be used for SFR applications. The newly implemented core radial expansion model in PARCS is successfully verified on the ASTRID core with the standalone version of PARCS. Then, various transient simulations are performed in order to separately analyse the different contributions to the reactivity by: the Doppler broadening effects, the sodium density change effect, the core radial and axial thermal expansion effect and the control rod displacement effect. It is demonstrated that the core power responses are plausible which allows the conclusion that all the different thermal expansion models are properly implemented. Furthermore, the presented simulations show very different core power responses. It appears that the effect of the sodium density change on reactivity is a parameter that is strongly heterogeneous (depending on the core location). This shows the importance of using a three-dimensional neutron kinetics model rather than a point-kinetic model for transient simulations with thermal-hydraulic codes. Moreover, the time-scale of the various effects are ranging from few seconds to several hundred seconds. While the Doppler broadening, the sodium density change, as well as the core axial and radial thermal expansion effects on reactivity are fast, the thermal expansion of the strongback and the vessel only appears after several hundred seconds. This emphasizes the importance of considering all thermal expansion effects in addition to the usual thermal-hydraulic feedback parameters (e.g. fuel temperature, coolant density etc.) to be able to compute the core behavior realistically.:Contents Abstract II List of Figures VII List of Tables X List of Acronyms XI Acknowledgments XIII 1 Introduction 1.1 Sodium cooled fast reactors 1.1.1 Fast reactor development 1.1.2 Comparison of sodium fast reactor and pressurized water reactor designs 1.1.2.1 Neutron spectrum 1.1.2.2 Breeding 1.1.2.3 Partitioning and Transmutation 1.1.2.4 Control of the reactivity in the core 1.1.2.5 Coolant properties 1.1.2.6 Reactivity feedback 1.1.2.7 Comparison summary 1.2 Objectives and structure of the thesis 1.2.1 Objectives 1.2.2 Structure of the thesis 2 State of the art of Sodium Fast Reactor safety assessment 2.1 Relevant safety events to consider for Sodium Fast Reactors 2.2 Major reactivity feedback mechanisms 2.3 State of the art of safety analysis methods for Sodium Fast Reactor 3 Methods and codes for safety assessment of sodium cooled fast reactors 3.1 Neutronics core calculations 3.1.1 Core calculations with the diffusion code PARCS 3.1.2 Generation of nodal few-group cross sections with the Monte Carlo code Serpent 3.1.3 Core simulator KMACS 3.2 Thermal-hydraulics simulations with the system code ATHLET 3.3 Coupled three-dimensional thermal-hydraulics / neutronics calculations 4 Development of three-dimensional thermal expansion models 4.1 General calculation approach proposed for safety assessment 4.2 Thermal expansion in solids 4.3 Model for generating nodal few-energy-group cross sections for deterministic core analysis 4.3.1 Energy group structure 4.3.2 Full-scale three-dimensional fuel assembly models in Serpent 4.3.3 Two-dimensional non-fuel assembly models in Serpent 4.3.4 Super homogenization method for non-multiplying media 4.3.5 Automated creation of Serpent models for parametrized cross section generation with KMACS 4.4 Core radial thermal expansion effect 4.4.1 Description of the core radial thermal expansion phenomenon 4.4.2 Coordinate transformation of the diffusion equation 4.4.3 Implementation of the coordinates transformation in PARCS 4.4.4 Adapted cross section parametrization scheme for the core radial expansion model 4.4.5 Diagrid model in ATHLET and temperature transfer 4.5 Core axial thermal expansion effect 4.5.1 Description of the core axial thermal expansion phenomenon 4.5.2 Implementation of a core axial thermal expansion model in PARCS 4.5.3 Appropriate cross section parametrization scheme 4.6 Control rod displacement due to reactor structures thermal expansion effects 4.6.1 Modelling scheme 4.6.2 Strongback model in ATHLET 4.6.3 Vessel model in ATHLET 4.6.4 Control rods drive lines ATHLET model 5 Verification on a case study 5.1 Description of the ASTRID reactor 5.2 Full core models 5.2.1 Full core Serpent reference models of the ASTRID core 5.2.2 Three-dimensional neutron kinetics model of ASTRID core in PARCS 5.2.3 Generation of appropriate few-group cross sections 5.2.4 Thermal-hydraulic model in ATHLET and ATHLET-PARCS feedback mapping 5.3 Verfications of the radial core expansion model 5.4 Assessment of the Doppler and sodium density effects 5.4.1 Assessment of the Doppler effect 5.4.2 Assessment of the sodium density effect 6 Coupled three-dimensional thermal-hydraulics/neutron-physics transient simulations with ATHLET-PARCS 6.1 Description of the models and transient simulations 6.2 Simulation 1: Doppler effect 6.2.1 Description 6.2.2 Results 6.3 Simulation 2: Sodium density effect 6.3.1 Description 6.3.2 Results 6.4 Simulation 3: Doppler and sodium density effects 6.4.1 Description 6.4.2 Results 6.5 Simulation 4: Core radial thermal expansion effect 6.5.1 Description 6.5.2 Results 6.6 Simulation 5: Doppler, Sodium density and core radial thermal expansion effects 6.6.1 Description 6.6.2 Results 6.7 Simulation 6: Core axial thermal expansion effect 6.7.1 Description 6.7.2 Results 6.8 Simulation 7: Doppler, Sodium density and core axial thermal expansion effects 6.8.1 Description 6.8.2 Results 6.9 Simulation 8: Doppler effect, Sodium density effect, core radial thermal expansion effect and core axial thermal expansion effect 6.9.1 Description 6.9.2 Results 6.10 Simulation 9: Doppler effect, Sodium density effect, core radial thermal expansion effect, core axial thermal expansion effect and control rod displacement due to reactor structures thermal expansion effect 6.10.1 Description 6.10.2 Results 6.11 Preliminary conclusions of the test calculations 7 Conclusion and outlook for future developments 7.1 Summary and conclusions 7.2 Suggestions for future work Appendices A The Boltzmann equation B Macro-group structure Bibliography

L’utilisation des matériaux composites devient de plus en plus importante dans les structures aéronautiques de nouvelle génération. Le gain de masse engendré, et donc de carburant, pousse les constructeurs aéronautiques à les employer de façon optimale. Néanmoins, ces matériaux se dégradent rapidement lorsqu’ils sont soumis à des flux de chaleur importants, entraînant une perte de leur résistance mécanique. Ce problème peut être dramatique pour la sécurité des passagers car la tenue de ces nouvelles structures peut ne plus être assurée dans le cas d’un incendie. Les méthodes actuelles de certification de la tenue au feu des matériaux composites aéronautiques reposent principalement sur l’utilisation de moyens expérimentaux, dont les résultats ne sont représentatifs que des conditions particulières dans lesquelles les essais ont été réalisés. La compréhension des différents phénomènes thermiques, chimiques et mécaniques intervenant lors de la dégradation de ces matériaux, avec l’appui de simulations numériques et d’expériences, peut permettre d’améliorer les méthodes existantes et donc d’optimiser les futures structures aéronautiques dès la phase de conception.Cette étude s’est attachée à développer et valider un modèle thermo-chimique de dégradation des matériaux composites multi-dimensionnel et multi-constituants. Ce modèle permet de traiter des cinétiques de dégradation complexes suivant plusieurs réactions de décompositions et de prendre en compte le transport des gaz produits depuis leur formation jusqu’à leur évacuation hors du matériau. L’utilisation de lois d’homogénéisation avancées est proposée afin de rendre compte des effets des transformations sur les transferts de chaleur et de masse se produisant au sein du matériau. L’application du modèle thermo-chimique à un cas de dégradation sous flux thermique connu mais non-uniforme dans un environnement contrôlé permet de confronter les résultats de simulation aux mesures expérimentales et ainsi de valider l’approche multi-constituants adoptée. Enfin, l’étude numérique de la dégradation d’un composite soumis à une flamme met en avant l’effet des gaz de décomposition éjectés à l’interface sur le flux thermique pariétal échangé. / Composite materials are increasingly used in new generation aircraft structures. Mass and as a consequence fuel savingsencourage aircraft manufacturers to use them optimally. However, these materials can degrade quickly when exposed tosignificant heat fluxes, resulting in a loss of mechanical strength. This problem can be dramatic for passenger safety asmechanical resistance of such innovative structures can not be ensured in case of fire events. Current certification methodsof fire resistance of aeronautical composite materials are mainly based on experiments, that are only representative of thespecific conditions under which they were carried out. The understanding of thermal, chemical and mechanical phenomenaoccurring during the decomposition of these materials, with the support of numerical simulations and experiments, can helpimproving existing methods and optimizing the future aeronautical structures from the design chain. This study deals withthe development and validation of a multi-components and multi-dimensional thermo-chemical model of decomposing compositematerials. It can deal with complex degradations following several decomposition reactions as well as transport ofpyrolysis gases from their formation up to their ejection out of the material. The use of advanced homogenization laws isproposed to account for the chemical transformations on heat and mass transfers occurring in the material. The applicationof the thermo-chemical model to a laser degradation study under known but non-uniform heat flux in a controlled environmentallows to confront the simulation results with experimental measurements and thus validate the multi-componentsapproach. Finally, the numerical analysis of a decomposing composite material submitted to a flame highlights the effectof emitted decomposition gases on the exchanged parietal heat flux.

Beaucoup de procédés utilisés dans l'industrie sidérurgique (coulée de lingots,coulée continue, …) peuvent générer des défauts : macro-ségrégation, mauvaises propriétés de la microstructure, défauts surfaciques. Ces problèmes peuvent être résolus par un contrôle de la température et de l’écoulement d'acier liquide. Le brassage électromagnétique (EMS) est une technique largement utilisée pour contrôler l’écoulement d'acier liquide par l’imposition d'un champ électromagnétique. Cette technique est complexe car elle couple plusieurs types de problèmes physiques:écoulement multiphasique, solidification,transfert de chaleur et induction électromagnétique à basse fréquence.En outre, l’approche expérimentale est difficile de par la dimension,l'environnement et le coût des procédés considérés. Pour ces raisons, des simulations numériques efficaces sont nécessaires pour comprendre les applications EMS et améliorer les procédés évoqués. L'objectif de cette thèse est de développer une méthodologie numérique robuste,efficace et précise pour la simulation multi-physique de l'EMS, en particulier pour le brassage dans le moule dans le cadre de la coulée continue d'acier. Cette méthodologie a été mise en oeuvre dans le code commercial THERCAST® pour être utilisé dans le cadre d’applications industrielles / Many of the processes used in thesteelmaking industry (e.g. ingot casting,continuous casting, …) can lead todefects: macro-segregation, poormicrostructure properties, surfacedefects. These issues can be solved bycontrolling the temperature and the flowof molten steel. Electromagnetic stirring(EMS) is a widely used technique to steerthe flow of liquid steel by thesuperimposition of an electro-magneticfield. This application is complex becauseit couples several physical problems:multi-phase flow, solidification, heattransfer and low frequency electromagneticinduction. In addition,experimental work is difficult because ofthe size, environment and cost of theconsidered processes. For thesereasons, efficient and effective numericalsimulations are needed to understandEMS applications and improve theaforementioned processes.The objective of this thesis is to developa robust, efficient and accurate numericalprocedure for the multi-physicssimulation of EMS, especially for in-moldstirring in the framework of continuouscasting of steel. This procedure has beenimplemented in the commercial codeTHERCAST® in order to be used forindustrial applications.

Les procédés de gazéification de bois à lits fixes étagés sont adaptés à la production d'électricité de petites puissances. Dans ces procédés, la pyrolyse est opérée dans un réacteur continu à lit fixe descendant. La particularité de ce type de réacteur est son fonctionnement autothermique. L'énergie nécessaire au chauffage, au séchage et à la pyrolyse est apportée par la combustion partielle du bois : on parle de “pyrolyse oxydante”. L'injection d'air par le haut du réacteur provoque la propagation d'une zone d'oxydation dans le milieu poreux à contre-courant des écoulements des solides et des gaz. Les travaux présentés dans ce manuscrit visent une meilleure description de cette étape du procédé. Le problème posé est de type multi-échelles. Ainsi, nous avons préalablement mené une étude à l'échelle de la particule isolée avant de s'intéresser au comportement global du lit fixe. A l'échelle de la particule, nous avons quantifié l'effet de l'oxygène et de la taille des particules sur la cinétique de la pyrolyse oxydante. Cette étude nous a guidés pour la mise en place d'un modèle cinétique de cette transformation. A l'échelle du lit fixe, la propagation de la zone d'oxydation a été caractérisée par des approches expérimentale et numérique, offrant ainsi une meilleure connaissance de cette étape du procédé étagé. / Wood Multi-staged gasification in a fixed bed reactor is suitable for small-scale electricity generation. In these processes, the pyrolysis is performed in a continuous downward fixed bed reactor. The main feature of this reactor is the autothermal operation. Energy for heating, drying and pyrolysis is supplied by partial combustion of wood, known as “oxidative pyrolysis”. The air introduced from the top of the reactor induces a combustion front that propagates countercurrent with the solids and gazes flows. The work presented in this document aimed to achieve a better description of this process. A multi-scale approach was considered. Therefore, we have firstly studied the behavior of an isolated particle before focusing on the overall fixed bed. At the particle scale, we have quantified the effect of oxygen and of particle size on the oxidative pyrolysis kinetics. This led us to the setup of a kinetic model for this transformation.At the fixed bed scale, the propagation of the combustion front was studied considering the experimental and numerical approaches, which provides a better understanding of this step of the wood staged gasifiers.