Directional solidification has a wide interest due to its importance to the iron and steel industry. Examples of further application can be found in the aerospace industry regarding the manufacture of turbine blades and the semiconductor industry regarding single-crystal growth applications. Solute convection in the solidification process results in channel formation, which has a freckle-like appearance in cross-section and has a critical effect on the mechanical strength of a casting. For a solidification process that occurs via planar solidification from a solid boundary, one may consider the presence of three distinct regions often identified as horizontal layers, i.e. a fluid binary mixture (the melt), the solid layer and a two-phase (fluid-solid) mushy layer, separating the other two. The mushy layer is practically a porous medium consisting of an interconnected solid phase having its voids filled with the melt binary fluid. Channelling in the mushy layer and the creating of freckles are being considered the main reasons for non-homogeneous solidification and production of defects in the resulting solid product. The production of defects adversely affects the mechanical properties of the solid product leading to undesirable constraints on its industrial use. The purpose of this study is to evaluate the effect the vibrations have on the heat transfer during the solidification process as well as on the average density of the solid product and void formation. Experimental as well as theoretical investigations related to the solidification process were undertaken. Two effects that have been observed in previous experimental studies when metals and metal alloys are vibrated during solidification are a decrease in dendritic spacing, which directly affects density, and faster cooling rates and associated solidification times. Because these two effects happen simultaneously during solidification it is challenging to determine the one effect independently from the other. Most previous studies were on metals and metal alloys. In these studies, the one effect, i.e. the decrease in dendritic spacing, might influence the other, i.e. the faster cooling rates, and vice versa. The direct link between vibration and heat transfer has not yet been studied independently. The purpose of this study was to experimentally investigate the effect of vibration only on heat transfer and thus solidification rate. Experiments were conducted on paraffin wax, because it had a clearly defined macroscopic crystal structure consisting of mostly large straight-chain hydrocarbons. The advantage of the large straight-chain hydrocarbons was that the dendritic spacing was not affected by the cooling rate. Experiments were done with paraffin wax inside hollow plastic spheres of 40 mm diameter with 1 mm wall thickness. The paraffin wax was initially in a liquid state at a uniform temperature of 60°C and then submerged into a thermal bath at a uniform constant temperature of 15°C, which was approximately 20°C below the mean solidification temperature of the wax. Experiments were conducted in approximately 300 samples, with and without vibration at frequencies varying from 10 – 300 Hz. The first set of experiments were conducted to determine the solidification times. In the second set of experiments, the mass of wax solidified was determined at discrete time steps, with and without vibration. The results showed that paraffin wax had vibration independent of solid density contrary to other materials, eg. metals and metal alloys. Enhancement of heat transfer resulted in quicker solidification times and possible control over the heat transfer rate. The increase in heat transfer leading to faster solidifcation times was observed to first occur, as frequency increased and then to decrease. Experimental results showed that paraffin wax had vibration independent of solid density contrary to other materials, eg. metals and metal alloys. Enhancement of heat transfer resulted in quicker solidification times and possible control over the heat transfer rate. The increase in heat transfer leading to faster solidifcation times was observed to first occur, as frequency increased and then to decrease. Theoretical results of heat convection in a porous layer heated from below and subject to vibrations are presented by using a truncated spectral method in space. The partial differential equations governing the mass, momentum, heat, and solute transport were tranformed into a set of ordinary differential equations via a truncated modal expansion. Then the resutling equations were solved to identify the variety of regimes, and transitionbetween them, i.e. from steady convection, via periodic and quasi-periodic convection, towards chaotic or weak turbulent convection. The theoretcial results show that the heat convection subject to vibration is generally reduced when compared with the corresponding convection without vibrations. The exception for a certain frequency range shows about a 10% enhancement in the weak turbulent regime of convection, however, a 10% enhancement is still lower than the heat transfer prior to the transition to weak turbulence. Therefore, the heat transfer mechanism can be excluded as the main reason behind the improvement in solidification when vibrations are applied. Both experimental and theoretical results show an enhancement in heat transfer which correlate qualitativally. / Thesis (PhD)--University of Pretoria, 2014. / tm2015 / Mechanical and Aeronautical Engineering / PhD / Unrestricted

The primary focus of the present work is to model the entire casting process from filling stage to complete solidification. The model takes into consideration any phase change taking place during the filling process. An implicit volume of fluid (VOF) based algorithm has been employed for simulating free surface flows during the filling process and the model for solidification is based on a fixed-grid enthalpy-based control volume approach. Solidification modelling is coupled with VOF through User Defined Functions (UDF) developed in commercial fluid dynamics (CFD) code FLUENT 6.3.26. The developed model is applied for the simultaneous filling and solidification of pure metals and binary alloy systems to study the effects of filling process on the solidification characteristics, evolution of mushy zone and the final macrosegregation pattern in the casting. The numerical results of the present analysis are compared with the conventional analysis assuming the initial conditions to be a completely filled mould cavity with uniform temperature, solute concentration and quiescent melt inside the cavity. The effects of process parameters, namely the degree of superheat, cooling temperature and filling velocity etc. are also investigated. Results show significant differences on the evolution of mushy zone and macrosegregation between the present analysis and the conventional analysis. The application of present model to simulate three dimensional sand casting is also demonstrated. The three dimensional competetive effect of filling generated residual flow and the buoyancy-induced convective flow pattern cause significant difference in macrosegregation pattern in casting.

L’interface noyau-graine (ICB) est instable et une zone dendritique se forme sous des conditions très particulières, c’est à dire que la cristallisation est très lente par rapport à la convection très vigoureuse du noyau liquide. Afin de reproduire expérimentalement des conditions semblables, nous avons étudié une zone dendritique sous hyper gravite, dans une centrifugeuse. La hauteur de cette zone diminue quand la gravite augmente alors que la fraction solide augmente fortement : similairement, les études sismologiques suggèrent que la fraction solide dans la graine est proche de l’unité a l’ICB. De plus, la sismologie montre une graine très hétérogène en termes d’anisotropie élastique, d’atténuation ou de vitesse des ondes et met en lumière une forte dichotomie Est-Ouest. Celle-ci pourrait être engendrée par une translation de la graine qui provoquerait de la cristallisation sur une face et de la fusion sur l’autre. Cette hypothèse est testée en conduisant des expériences de cristallisation et de fusion d’une zone dendritique. Nous avons utilisé des ultrasons comme analogues aux ondes sismiques pour quantifier les changements de structure dans la zone dendritique à partir des mesures de l’atténuation et la diffraction. Extrapoles a la graine, nos résultats montrent que l’ICB pourrait fondre sur l’hémisphère Ouest et cristalliser sur l’hémisphère Est. D’autre part, avec du gaz xénon en hyper-gravite, nous avons observé un gradient adiabatique, pour la première fois dans un dispositif expérimental. Cette thèse montre la faisabilité de ces expériences et la possibilité de vérifier expérimentalement les approximations utilisées pour la convection compressible. / The inner core boundary (ICB) is unstable, and a mushy layer forms under very particular conditions in which the crystallization is very slow compared to the very vigorous convection of the liquid core. To mimic these conditions, we have investigated a mushy layer under hyper-gravity in a centrifuge. The thickness of a mushy layer decreases with gravity and the solid fraction increases. This is coherent with seismological studies suggesting that the solid fraction at the ICB is close to unity. Moreover, seismology shows that the inner core is very heterogeneous in terms of elastic anisotropy, attenuation or wave velocity and that there exists a strong East-West dichotomy on the ICB. One hypothesis is that the latter is due to a translation of the inner core that would cause crystallization on one hemisphere and melting on the other one. We have tested that hypothesis with experiments of solidification and melting of a mush. We have used ultrasounds as an analogue to the seismic waves to quantify structural changes in the mush from measurements of attenuation and scattering. From our observations, it is plausible that the ICB on the Western hemisphere s melting while it is solidifying on the Eastern hemisphere. In other experiments, using xenon gas under hyper-gravity, we have observed an adiabatic gradient for the first time. This thesis shows the feasibility of these experiments and the possibility to check experimentally the approximations used for compressible convection.

Nous avons étudié les phénomènes convectifs et leur interaction dynamique avec la formation des microstructures pendant la solidification dirigée d’alliages étalliquesbinaires.La méthode post-mortem a été utilisée d’abord pour étudier la Transition olonnaire-Equiaxe pendant la solidification dirigée d’échantillons cylindriques d’Al-3,5wt%Ni non affiné sous la Technique de Rotation Accélérée de Creuset. La simulation numérique a été éffectuée et acquérie les résultats en concordance avec les manipulations.La technique in-situ a été appliquée pour comprendre l’évolution en fonction de temps des grains pendant solidification d’Al-4wt%Cu. La caractéstiques tatistiques des grains ont été discutées.La convection d’instabilité déclenchée par la poussée ou la tension superfaciale sous les gradients thermiques verticale et horizontale dans un système de double couches liquide-zone poreuse ont réspectivement étudié par analysis d’instabilité linéaire.L’inhomogénéité de la perméabilité de zone pateuse dendritique a été tenue en compte afin de comprendre son influence sur le début de convection pendant la solidification dirigée d’Al-3,5wt%Li. / We studied the convective phenomena and their dynamical interaction with the formation of the microstructurs during directional solidification of binary metallic alloys.The post-mortem method was used first to study the Columnar-Equiaxed-Transition during the directional solidification of unrefined Al-3.5wt%Ni in cylindric samples under the Accelerated Crucible Rotation Technique. The numerical imulation was carried out and achieved the results in agreement with experiments.The in-situ technique was applied to understand the evolution of equiaxed grains during solidification of Al-4wt%Cu in function of time. The statistical characteristics of equiaxed grains were discussed.The buoyancy-driven and surface-tension-driven instability convection under vertical and horizontal thermal gradients in a liquid-porous double-layered system were respectively investigated through linear instability analysis.The inhomogeneity of the dendritic mush permeability was taken into account in order to understand its influence on the triggering of convection during the directional solidification of Al-3.5wt%Li.

<p>Severe accidents in a Light Water Reactor (LWR) have been a subject of the research for the last three decades. The research in this area aims to further understanding of the inherent physical phenomena and reduce the uncertainties surrounding their quantification, with the ultimate goal of developing models that can be applied to safety analysis of nuclear reactors. The research is also focusing on evaluation of the proposed accident management schemes for mitigating the consequences of such accidents.</p><p>During a hypothetical severe accident, whatever the scenario, there is likelihood that the core material will be relocated and accumulated in the lower plenum in the form of a debris bed or a melt pool. Physical phenomena involved in a severe accident progression are complex. The interactions of core debris or melt with the reactor structures depend very much on the debris bed or melt pool thermal hydraulics. That is why predictions of heat transfer during melt pool formation in the reactor lower head are important for the safety assessment.</p><p>The main purpose of the present study is to advance a method for describing turbulent natural convection heat transfer of a melt pool, and to develop a computational platform for cost-effective, sufficiently-accurate numerical simulations and analyses of Core Melt-Structure-Water Interactions in the LWR lower head during a postulated severe core-melting accident.</p><p>Given the insights gained from Computational Fluid Dynamics (CFD) simulations, a physics-based model and computationally-efficient tools are developed for multi-dimensional simulations of transient thermal-hydraulic phenomena in the lower plenum of a Boiling Water Reactor (BWR) during the late phase of an in-vessel core melt progression. A model is developed for the core debris bed heat up and formation of a melt pool in the lower head of the reactor vessel, and implemented in a commercial CFD code. To describe the natural convection heat transfer inside the volumetrically decay-heated melt pool, we advanced the Effective Convectivity Conductivity Model (ECCM), which was previously developed and implemented in the MVITA code. In the present study, natural convection heat transfer is accounted for by only the Effective Convectivity Model (ECM). The heat transport and interactions are represented through an energy-conservation formulation. The ECM then enables simulations of heat transfer of a high Rayleigh melt pool in 3D large dimension geometry.</p><p>In order to describe the phase-change heat transfer associated with core debris, a temperature-based enthalpy formulation is employed in the ECM (the phase-change ECM or so called the PECM). The PECM is capable to represent possible convection heat transfer in a mushy zone. The simple approach of the PECM method allows implementing different models of the fluid velocity in a mushy zone for a non-eutectic mixture. The developed models are validated by a dual approach, i.e., against the existing experimental data and the CFD simulation results.</p><p>The ECM and PECM methods are applied to predict thermal loads to the vessel wall and Control Rod Guide Tubes (CRGTs) during core debris heat up and melting in the BWR lower plenum. Applying the ECM and PECM to simulations of reactor-scale melt pool heat transfer, the results of the ECM and PECM calculations show an apparent effectiveness of the developed methods that enables simulations of long term accident transients. It is also found that during severe accident progression, the cooling by water flowing inside the CRGTs plays a very important role in reducing the thermal load on the reactor vessel wall. The results of the CFD, ECM and PECM simulations suggest a potential of the CRGT cooling as an effective mitigative measure during a severe accident progression.</p>

Severe accidents in a Light Water Reactor (LWR) have been a subject of intense research for the last three decades. The research in this area aims to reach understanding of the inherent physical phenomena and reduce the uncertainties in their quantification, with the ultimate goal of developing models that can be applied to safety analysis of nuclear reactors, and to evaluation of the proposed accident management schemes for mitigating the consequences of severe accidents.  In a hypothetical severe accident there is likelihood that the core materials will be relocated to the lower plenum and form a decay-heated debris bed (debris cake) or a melt pool. Interactions of core debris or melt with the reactor structures depend to a large extent on the debris bed or melt pool thermal hydraulics. In case of inadequate cooling, the excessive heat would drive the structures' overheating and ablation, and hence govern the vessel failure mode and timing. In turn, threats to containment integrity associated with potential ex-vessel steam explosions and ex-vessel debris uncoolability depend on the composition, superheat, and amount of molten corium available for discharge upon the vessel failure. That is why predictions of transient melt pool heat transfer in the reactor lower head, subsequent vessel failure modes and melt characteristics upon the discharge are of paramount importance for plant safety assessment.  The main purpose of the present study is to develop a method for reliable prediction of melt pool thermal hydraulics, namely to establish a computational platform for cost-effective, sufficiently-accurate numerical simulations and analyses of core Melt-Structure-Water Interactions in the LWR lower head during a postulated severe core-melting accident. To achieve the goal, an approach to efficient use of Computational Fluid Dynamics (CFD) has been proposed to guide and support the development of models suitable for accident analysis.   The CFD method, on the one hand, is indispensable for scrutinizing flow physics, on the other hand, the validated CFD method can be used to generate necessary data for validation of the accident analysis models. Given the insights gained from the CFD study, physics-based models and computationally-efficient tools are developed for multi-dimensional simulations of transient thermal-hydraulic phenomena in the lower plenum of a LWR during the late phase of an in-vessel core melt progression. To describe natural convection heat transfer in an internally heated volume, and molten metal layer heated from below and cooled from the top (and side) walls, the Effective Convectivity Models (ECM) are developed and implemented in a commercial CFD code. The ECM uses directional heat transfer characteristic velocities to transport the heat to cooled boundaries. The heat transport and interactions are represented through an energy-conservation formulation. The ECM then enables 3D heat transfer simulations of a homogeneous (and stratified) melt pool formed in the LWR lower head. In order to describe phase-change heat transfer associated with core debris or binary mixture (e.g. in a molten metal layer), a temperature-based enthalpy formulation is employed in the Phase-change ECM (so called the PECM). The PECM is capable to represent natural convection heat transfer in a mushy zone. Simple formulation of the PECM method allows implementing different models of mushy zone heat transfer for non-eutectic mixtures. For a non-eutectic binary mixture, compositional convection associated with concentration gradients can be taken into account. The developed models are validated against both existing experimental data and the CFD-generated data. ECM and PECM simulations show a superior computational efficiency compared to the CFD simulation method. The ECM and PECM methods are applied to predict thermal loads imposed on the vessel wall and Control Rod Guide Tubes (CRGTs) during core debris heatup and melting in a Boiling Water Reactor (BWR) lower plenum. It is found that during the accident progression, the CRGT cooling plays a very important role in reducing the thermal loads on the reactor vessel wall. Results of the ECM and PECM simulations suggest a high potential of the CRGT cooling to be an effective measure for severe accident management in BWRs. / <p>QC 20100812</p>

La radiographie X synchrotron ou avec une source microfocus a été appliquée pour étudier différents phénomènes dépendants du temps en relation avec la solidification directionnelle d'alliages Al-Cu. Les effets de la gravité ont été étudiés par comparaison d'expériences sur Terre et en microgravité dans le cadre du projet ESA-MAP XRMON. Les mouvements des fragments sont le sujet majeur de notre étude. Sur Terre, le mouvement des fragments est imposé par la poussée d'Archimède, avec une forte influence des effets de paroi et de la morphologie du fragment, alors qu'en microgravité, la force motrice pour le mouvement des fragments est l'écoulement du fluide interdendritique induit par la contraction du solide. L'effet d'un champ magnétique permanent sur la solidification des grains équiaxes dans un gradient de température a été également étudié. Nous avons montré qu'un couplage entre le gradient de température et le champ magnétique donne naissance à une force Thermo-électromagnétique qui agit sur les grains solides. Une bonne description a été obtenue en utilisant un modèle analytique pour une particule sphérique. Enfin, nous avons étudié l'évolution d'une zone pâteuse dans un gradient de température fixe. Trois régimes successifs ont été identifiés, suivant l'intensité de la diffusion du soluté dans la zone pâteuse et dans le bain fondu. L'analyse quantitative des radiographies par traitement d'image a clarifié le rôle de chaque phénomène de diffusion (TGZM, fermeture des canaux, murissement et diffusion du soluté dans le bain fondu). / X-ray radiography with synchrotron and microfocus sources was applied to investigate various time-dependent phenomena related to directional solidification of Al-Cu alloys. Gravity effects were investigated by a comparative study of ground and microgravity experiments in the framework of ESA-MAP XRMON project. Fragment motion was the major subject of our investigation. On Earth, fragmentation motion was imposed by buoyancy, with a strong dependency on wall influence and fragment morphology, whereas in microgravity conditions, the driving force for fragment motion is the interdendritic fluid flow induced by the solid shrinkage. The effect of a permanent magnetic field on the solidification of equiaxed grains in a temperature gradient was also studied. We have shown that a coupling between the temperature gradient and the magnetic field gives birth to a Thermo-Electro-Magnetic force that acts on the solid grains. A good description was obtained by using an analytical model for a spherical particle. Finally we studied the evolution of the mushy zone in a fixed temperature gradient. Three successive regimes were identified, depending on the relative magnitude of solute diffusion in the mushy zone and in the bulk liquid. Quantitative analysis of radiographs by image processing enlightened the role of each diffusion phenomena (TGZM, channel closure, coarsening and solute diffusion in the bulk liquid).

Heat transfer and solidification models were developed for use in a numerical model of a continuous caster to provide a means of predicting how the developing shell would react under variable operating conditions. Measurement data of the operating conditions leading up to a breakout occurrence were provided by an industrial collaborator and were used to define the model boundary conditions. Steady-state and transient simulations were conducted, using boundary conditions defined from time-averaged measurement data. The predicted shell profiles demonstrated good agreement with thickness measurements of a breakout shell segment – recovered from the quarter-width location. Further examination of the results with measurement data suggests pseudo-steady assumption may be inadequate for modeling shell and flow field transition period following sudden changes in casting speed. An adaptive mesh refinement procedure was established to increase refinement in areas of predicted shell growth and to remove excess refinement from regions containing only liquid. A control algorithm was developed and employed to automate the refinement procedure in a proof-of-concept simulation. The use of adaptive mesh refinement was found to decrease the total simulation time by approximately 11% from the control simulation – using a static mesh.

Severe accidents in a Light Water Reactor (LWR) have been a subject of the research for the last three decades. The research in this area aims to further understanding of the inherent physical phenomena and reduce the uncertainties surrounding their quantification, with the ultimate goal of developing models that can be applied to safety analysis of nuclear reactors. The research is also focusing on evaluation of the proposed accident management schemes for mitigating the consequences of such accidents. During a hypothetical severe accident, whatever the scenario, there is likelihood that the core material will be relocated and accumulated in the lower plenum in the form of a debris bed or a melt pool. Physical phenomena involved in a severe accident progression are complex. The interactions of core debris or melt with the reactor structures depend very much on the debris bed or melt pool thermal hydraulics. That is why predictions of heat transfer during melt pool formation in the reactor lower head are important for the safety assessment. The main purpose of the present study is to advance a method for describing turbulent natural convection heat transfer of a melt pool, and to develop a computational platform for cost-effective, sufficiently-accurate numerical simulations and analyses of Core Melt-Structure-Water Interactions in the LWR lower head during a postulated severe core-melting accident. Given the insights gained from Computational Fluid Dynamics (CFD) simulations, a physics-based model and computationally-efficient tools are developed for multi-dimensional simulations of transient thermal-hydraulic phenomena in the lower plenum of a Boiling Water Reactor (BWR) during the late phase of an in-vessel core melt progression. A model is developed for the core debris bed heat up and formation of a melt pool in the lower head of the reactor vessel, and implemented in a commercial CFD code. To describe the natural convection heat transfer inside the volumetrically decay-heated melt pool, we advanced the Effective Convectivity Conductivity Model (ECCM), which was previously developed and implemented in the MVITA code. In the present study, natural convection heat transfer is accounted for by only the Effective Convectivity Model (ECM). The heat transport and interactions are represented through an energy-conservation formulation. The ECM then enables simulations of heat transfer of a high Rayleigh melt pool in 3D large dimension geometry. In order to describe the phase-change heat transfer associated with core debris, a temperature-based enthalpy formulation is employed in the ECM (the phase-change ECM or so called the PECM). The PECM is capable to represent possible convection heat transfer in a mushy zone. The simple approach of the PECM method allows implementing different models of the fluid velocity in a mushy zone for a non-eutectic mixture. The developed models are validated by a dual approach, i.e., against the existing experimental data and the CFD simulation results. The ECM and PECM methods are applied to predict thermal loads to the vessel wall and Control Rod Guide Tubes (CRGTs) during core debris heat up and melting in the BWR lower plenum. Applying the ECM and PECM to simulations of reactor-scale melt pool heat transfer, the results of the ECM and PECM calculations show an apparent effectiveness of the developed methods that enables simulations of long term accident transients. It is also found that during severe accident progression, the cooling by water flowing inside the CRGTs plays a very important role in reducing the thermal load on the reactor vessel wall. The results of the CFD, ECM and PECM simulations suggest a potential of the CRGT cooling as an effective mitigative measure during a severe accident progression. / QC 20101119