Continued emission of green house gases has energized research activity worldwide to develop efficient ways to harness renewal energy. The availability of large scale energy storage technologies is essential to make renewal energy a reliable source of energy. Redox flow batteries show potential in this direction. These batteries typically need expensive membranes which need replacement be-cause of fouling. The recently proposed soluble lead redox flow battery (SLRFB), in which lead ions deposit on electrodes in charge cycle and dissolve back in discharge cycle, can potentially cut down the cost of energy storage by eliminating membrane. A number of challenges need to be overcome though. Low cycleability, residue formation, and low efficiencies are foremost among these, all of which require an understanding of the underlying mechanisms. A model of laminar flow-through SLRFB is first developed to understand buildup of residue on electrodes with continued cycling. The model accounts for spatially and temporally growing concentration boundary layers on electrodes in a self consistent manner by permitting local deposition/dissolution rates to be controlled by local ion transport and reaction conditions. The model suggests controlling role for charge transfer reaction on electrodes (anode in particular) and movement of ions in the bulk and concentration boundary layers. The non-uniform current density on electrodes emerges as key to formation of bare patches, steep decrease in voltage marking the end of discharge cycle, and residue buildup with continuing cycles. The model captures the experimental observations very well, and points to improved operational efficiency and decreased residue build up with cylindrical electrodes and alternating flow direction of recirculation. The underlying mechanism for more than an order of magnitude increase in cycle life of a beaker cell battery with increase in stirrer speed is unraveled next. Our experiments show that charging with and without stirring occurs identically, which brings up the hitherto unknown but quite strong role of natural convection in SLRFB. The role of stirring is determined to be dislodgement/disintegration of residue building up on electrodes. The depletion of active material from electrolyte due to residue formation is offset by “internal regeneration mechanism”, unraveled in the present work. When the rate of residue formation, rate of dislodging/disintegration from electrode, and rate of regeneration of active material in bulk of the electrolyte becomes equal, perpetual operation of SLRFB is expected. The identification of strong role of free convection in battery is put to use to demonstrate a battery that requires stirring/mixing only intermittently, during open circuit stages between charge and discharge cycles when no current is drawn. Inspired by our experimental finding that the measured currents for apparently diffusion limited situations (no external flow) are far larger than the maxi-mum possible theoretical value, the earlier model is modified to account for natural convection driven by concentration gradient of lead ions in electrolyte. The model reveals the presence of strong natural convection in battery. The induced flow in the vicinity of the electrodes enhances mass transport rates substantially, to the extent that even in the absence of external flow, normal charge/discharge of battery is predicted. The model predicted electrochemical characteristics are verified quantitatively through voltage-time measurements. The formation of flow circulation loops driven by electrode processes is validated qualitatively through PIV measurements. Natural convection is predicted to play a significant role in the presence of external flow as well. The hitherto unexplained finding in the literature on insensitivity of charge-discharge characteristics to electrolyte flow rate is captured by the model when mixed mode of convection is invoked. Flow reversal and wavy flow are predicted when natural convection and forced convection act in opposite directions in the battery. The effect of the presence of non-conducting material (PbO on anode) on the performance of SLRFB is studied using a simplified approach in the model. The study reveals the presence of charge coup de fouet phenomenon in charge cycle. The phenomenon as well as the predicted effect of depth of discharge on the magnitude of charge coup de fouet are confirmed experimentally.

L'objectif général de la thèse est d'améliorer la modélisation numérique RANS des flux thermiques turbulents notamment en proposant un modèle fonctionnant dans les trois régimes de convection thermique (forcée, mixte et naturelle).Pour ce faire, un état des lieux, non exhaustif, des modèles des flux thermiques utilisant les approches algébriques et à équations de transport, est effectué. Puis, le modèle EB-RSM (Elliptic Blending-Reynolds Stress Model) étant utilisé pour modéliser la turbulence, le principe de la pondération elliptique est appliqué aux modèles des flux thermiques turbulents algébriques EB-GGDH (EB-General Gradient Diffusion Hypothesis), EB-AFM (EB-Algebraic Flux Model) et à équations de transport EB-DFM (EB-Differential Flux Model). Une attention particulière a été apportée aux échelles de temps et de longueur utilisées pour ces modèles. Il en résulte qu'utiliser une échelle de longueur thermique différente de l'échelle de longueur dynamique et une échelle de temps mixte dans le terme de flottabilité de l'équation de la dissipation turbulente est préférable.Pour valider les formulations retenues, nous avons effectué des tests pour des fluides usuels (nombre de Prandtl de l’ordre de 1) dans les trois régimes de convection à l'aide de l'outil de calcul Code_Saturne sur des configurations académiques, semi-académiques et industrielles.Des résultats satisfaisants ont été obtenus en associant l'EB-RSM et le GGDH en convection forcée ou mixte et l'EB-RSM aux modèles EB-DFM et AFM en convection naturelle. / The PhD main objective is to improve the turbulent heat flux RANS modelling especially by proposing a model working in the three thermal convection regime (forced, mixed and natural).In order to achieve this, a non-exhaustive state of art of heat flux model, using algebraic approach and transport equations, is done. Then, as EB-RSM model (Elliptic Blending-Reynolds Stress Model) is used to model turbulence, elliptic blending approach is apply to algebraic turbulent heat flux model EB-GGDH (EB-General Gradient Diffusion Hypothesis), EB-AFM (EB-Algebraic Flux Model) and transport equation model EB-DFM (EB-Differential Flux Model). Special attention was paid to time and length scales used with these models. It follows that using a thermal length scale different from dynamic length scale and a mixed time scale in the buoyant term of turbulent dissipation equation is better.To validate these models, some test were done for common fluids (Prandtl number in the order of 1) in the three convection regimes with the tool Code_Saturne on academic, mid-academic and industrial cases.Good results were obtained combining EB-RSM with GGDH in forced or mixed convection and EB-RSM with EB-DFM or AFM in natural convection.

The performance evaluation and parametric studies of an Inertance Tube Pulse Tube Refrigerator (IPTR) are performed for different length-to-diameter ratios, with the Computational Fluid Dynamics (CFD) package FLUENT. The integrated model consists of individual models of the components, namely, the compressor, compressor cooler, regenerator, cold heat exchanger, pulse tube, warm heat exchanger, inertance tube and the reservoir. The formulation consists of the governing equations expressing the conservation of mass, momentum and energy with axi-symmetry assumption and relations for the variable thermophysical properties of the working medium and the regenerator matrix, and friction factor and heat transfer coefficients in oscillatory flows. The local thermal non-equilibrium of the gas and the matrix is taken into account for the modeling of heat exchangers and the regenerator which are treated as porous zones. In addition, the wall thickness of the components is also accounted for. Dynamic meshing is used to model the compressor zone. The heat interaction between pulse tube wall and the oscillating gas, leading to surface heat pumping, is quantified. The axial heat conduction is found to reduce the overall performance. The thermal non-equilibrium results in a higher cold heat exchanger temperature due to inefficiencies. The dynamic characteristics of pulse tube are analyzed by introducing a time constant. The study is extended to other types of PTRs, namely, the Orifice type Pulse Tube Refrigerator (OPTR), Double Inlet type Pulse Tube Refrigerator (DIPTR) and a PTR with parallel combination of inertance tube and orifice (OIPTR). The focus of the second phase of analysis is the pulse tube region. The oscillatory flow and temperature fields in an open-ended pipe driven by a time-wise sinusoidally varying pressure at one end and subjected to an ambient-to-cryogenic temperature difference across the ends, is numerically studied both with and without the inclusion of buoyancy effects. Conjugate effects arising out of the interaction of oscillatory flow with heat conduction in the pipe wall are taken into account by considering a finite thickness wall with an insulated exterior surface. Parametric studies are conducted with frequencies in the range 5-15 Hz for an end-to-end temperature difference of 200 K. As the pressure amplitude increases, the temperature difference between the wall and the fluid decreases due to mixing at the cold end. The pressure amplitude and the frequency have negligible effect on the time averaged Nusselt number. The effect of buoyancy is studied for hot side up and cold side up configurations. It is found that the time averaged Nusselt number does not change significantly with orientation or Rayleigh number. Sharp changes in Nusselt number and velocity profiles and an increase in energy transfer through solid and gas were observed when natural convection comes into play with hot end placed down. Cooldown experiments are conducted on a preliminary experimental setup. Comparison of the numerical and experimental cooldown curves disclosed a number of areas where improvement is required, primarily the leakage past the piston and the design of the heat exchangers. The setup is being improved to bring out a second and improved version for attaining the lower cold heat exchanger temperature.

[EN] The aim of this work is to demonstrate theoretically and experimentally how acoustic wave propagation can be controlled by temperature gradients. Starting with the simplest case of two hot wires in air the study extends over periodic structures known as Sonic Crystals (SCs). The Finite Elements Method (FEM) has been employed to perform numerical simulations in order to demonstrate collimation and focusing effect of acoustic waves in two-dimensional (2D) SC whose filling fraction is adjusted by temperature gradients. As a part of the research, Bragg reflection and Fabry-Perot type of acoustic effects are investigated for the proposed type of SC. As example, a SC with desired transmittance can be tailored. Also, gradient index (GRIN) 2D sonic lenses are studied. Using parallel rows of heated wires whose temperatures vary according to a prefixed gradient index law a GRIN lens can be designed with a given performance. Moreover, by changing the temperature of the wires a change in the filling fraction inside the GRIN SC can be achieved. Thus, the local refraction index, which is directly related to the filling fraction, is changed too and an index gradient variation inside the GRIN SC is obtained. This GRIN SC is a direct analogy of gradient media observed in nature. Like their optical counterparts, the investigated 2D GRIN SC lenses have flat surfaces and are easier for fabrication than curved SC lenses. The bending of sound waves obtained by GRIN acoustics structures can be used to focusing and collimating acoustic waves. Another aspect of this work is about tuning some SC properties as effective refractive index, effective mass density, etc. in order to obtain a SC with prefixed properties. Since active tuning of the phononic band gaps is certainly desirable for future applications with enhanced functionalities, few attempts have been made to develop tunable SCs thus far. By controlling the incident angle or operating frequency, a GRIN SC can dynamically adjust the curved trajectory of acoustic wave propagation inside the SC structure. Among the last studies of tunable SCs, the filling fractions were tuned either by direct physical deformation of the structure or external stimuli. The former is impractical for most applications and the latter often requires very strong stimuli to produce only modest adjustment. In this work another way to tune the SC properties is proposed. Hot and cold media have different density, speed of sound, refractive index, etc. in comparison with the same properties at normal conditions, so inserting temperature gradients inside the medium can be used to tune the SC properties in certain limits. The proposed way to obtain temperature gradients inside SC is by wires made of Nicrom which are heated by electrical currents. There are some important advantages of this method. First, changing the electrical current intensity through the wires the SC properties can be changed dynamically. Second, it is relatively easier to change the filling fraction simply by adjusting the current intensity than physically changing the structure or applying strong electric or magnetic fields. In conclusion, the method proposed in this thesis allows us, in principle, to get materials and structures with dynamically adjustable acoustic properties using the temperature control through electric current in the wires, within certain limits. Thus, it is easy to carry out experiments of wave propagation phenomena in a macroscopic scale similar to those that occur in microscopic structures for the propagation of electromagnetic waves of high frequency (microwaves and light). / [ES] El objetivo de este trabajo es demostrar teoréticamente y experimentalmente como la propagación de ondas acústicas puede ser controlada por gradientes de temperatura. Empezando con el caso más simple de dos hilos calientes en aire, el estudio se extiende sobre estructuras periódicas conocidas como cristales sónicos (CS). Se ha utilizado el Método de Elementos Finitos (FEM) para realizar simulaciones numéricas con el objetivo de demonstrar la colimación y focalización de ondas acústicas en CS bidimensionales (2D) cuya fracción de llenado es ajustable mediante gradientes de temperatura. Como parte de la investigación se ha analizado la reflexión de Bragg y el efecto de tipo Fabry-Perot asociados con los CSs estudiados. Entre los ejemplos tratados figuran un CS con una transmitancia ajustable a voluntad, dentro de ciertos límites. También se han estudiado lentes acústicas bidimensionales de gradiente de índice, basadas en gradiente de temperatura. Utilizando cortinas paralelas de hilos calientes cuya temperatura varía según una ley dada se puede diseñar una lente GRIN con propiedades determinadas. Por otra parte, cambiando la temperatura de los hilos se puede lograr un cambio en la fracción de llenado dentro del GRIN CS. Así, el índice de refracción local, que está directamente relacionado con la fracción de llenado, se cambia también y se obtiene una variación de gradiente de índice dentro del GRIN CS. Este GRIN CS es una analogía directa de medios con gradiente, observados en la naturaleza. Otro aspecto de este trabajo trata sobre el ajuste de algunas propiedades de un SC como el índice de refracción efectivo o la densidad efectiva con el objetivo de obtener unas propiedades deseadas del cristal. Como el ajuste activo de los bandgaps fonónicos es ciertamente deseado para futuras aplicaciones con funcionalidades mejoradas, hasta ahora se han hecho varios intentos de desarrollar CSs de características ajustables. Controlando el ángulo de incidencia o la frecuencia de funcionamiento, un GRIN CS puede ajustar dinámicamente la curvatura de la trayectoria de propagación dentro de la estructura CS. Entre los últimos estudios de CSs las fracciones de llenado se ajustaron mediante una deformación física directa de la estructura o mediante estímulos externos (por ejemplo campos eléctricos o magnéticos). El primero es poco práctico para una gran parte de las aplicaciones y el segundo a menudo requiere estímulos muy fuertes para ajustes modestos. En este trabajo se propone otra forma de ajustar las propiedades de un CS. Las propiedades acústicas del medio de propagación (densidad, índice de refracción) dependen de la temperatura, por tanto, introduciendo gradientes de temperatura dentro de dicho medio pueden ajustarse a voluntad las propiedades del CS dentro de ciertos límites. La manera de obtener gradientes de temperatura dentro del CS, propuesta en este estudio, es mediante hilos de nicrom calentados con corrientes eléctricas. Hay algunas ventajas importantes de este método. En primer lugar, cambiando la intensidad de corriente eléctrica que circula por los hilos se puede conseguir cambiar dinámicamente las propiedades del CS. En segundo lugar, es relativamente más fácil de cambiar la fracción de llenado simplemente ajustando la intensidad de la corriente eléctrica que modificar físicamente la estructura o aplicar fuertes campos eléctricos o magnéticos. En conclusión, el método propuesto en esta tesis permite, en principio, conseguir materiales y estructuras con propiedades acústicas ajustables dinámicamente mediante el control de la temperatura a través de la corriente eléctrica en los hilos, dentro de ciertos límites. De esta forma se puede experimentar fácilmente a escala macroscópica fenómenos de propagación de ondas análogos a los que ocurren en estructuras microscópicas para la propagación de ondas electromagnéticas de alta frecuencia (microondas y l / [CAT] L'objectiu d'este treball és demostrar teorèticament i experimentalment com la propagació d'ones acústiques pot ser controlada per gradients de temperatura. Començant amb el cas més simple de dos fils calents en aire, l'estudi s'estén sobre estructures periòdiques conegudes com a cristalls sónics (CS) . S'ha utilitzat el Mètode d'Elements Finits (FEM) per a realitzar simulacions numèriques amb l'objectiu de demonstrar la col¿limació i focalització d'ones acústiques en CS bidimensionals (2D) la fracció de omplit de la qual és ajustable per mitjà de gradients de temperatura. Com a part de la investigació s'ha analitzat la reflexió de Bragg i l'efecte de tipus Fabry-Perot associats amb els CSs estudiats. Entre els exemples tractats figuren un CS amb una transmitancia ajustable a voluntat, dins de certs límits. També s'han estudiat lents acústiques bidimensionals de gradient d'índex, basades en gradient de temperatura. Utilitzant cortines paral¿leles de fils calents la temperatura de la qual varia segons una llei donada es pot dissenyar una lent GRIN amb propietats determinades. D'altra banda, canviant la temperatura dels fils es pot aconseguir un canvi en la fracció d'ompliment dins del GRIN CS. Així, l'índex de refracció local, que està directament relacionat amb la fracció d'ompliment, es canvia també i s'obté una variació de gradient d'índex dins del GRIN CS. Este GRIN CS és una analogia directa de mitjans amb gradient, observats en la naturalesa. Com les seues analogies òptiques, les lents, estudiades en este treball, tenen les superfícies planes i són més fàcils de fabricar que les lents corbades. La deflexión de les ones acústiques obtinguda per mitjà d'una lent de gradient GRIN es pot utilitzar per a focalitzar o colimar feixos de so. Un altre aspecte d'este treball tracta sobre l'ajust d'algunes propietats d'un SC com l'índex de refracció efectiu o la densitat efectiva amb l'objectiu d'obtindre unes propietats desitjades del cristall. Com l'ajust actiu dels bandgaps fonónicos és certament desitjat per a futures aplicacions amb funcionalitats millorades, fins ara s'han fet diversos intents de desenrotllar CSs de característiques ajustables. Controlant l'angle d'incidència o la freqüència de funcionament, un GRIN CS pot ajustar dinàmicament la curvatura de la trajectòria de propagació dins de l'estructura CS. Entre els últims estudis de CSs les fraccions d'ompliment es van ajustar per mitjà d'una deformació física directa de l'estructura o per mitjà d'estímuls externs. El primer és poc pràctic per a una gran part de les aplicacions i el segon sovint requerix estímuls molt forts per a ajustos modestos. En este treball es proposa una altra forma d'ajustar les propietats d'un CS. Les propietats acústiques del mig de propagació (densitat, índex de refracció) depenen de la temperatura, per tant, introduint gradients de temperatura dins del dit mitjà poden ajustar-se a voluntat les propietats del CS dins de certs límits. La manera d'obtindre gradients de temperatura dins del CS, proposta en este estudi, és per mitjà de fils de Nicrom calfats amb corrents elèctrics. Hi ha alguns avantatges importants d'este mètode. En primer lloc, canviant la intensitat de corrent elèctric que circula pels fils es pot aconseguir canviar dinàmicament les propietats del CS. En segon lloc, és relativament més fàcil de canviar la fracció d'ompliment simplement ajustant la intensitat del corrent elèctric que modificar físicament l'estructura o aplicar forts camps elèctrics o magnètics. En conclusió, el mètode proposat en esta tesi permet, en principi, aconseguir materials i estructures amb propietats acústiques ajustables dinàmicament per mitjà del control de la temperatura a través del corrent elèctric en els fils, dins de certs límits. D'esta manera es pot experimentar fàcilment a escala macroscòpica fenòmens de propagació d'ones anàlegs a què ocorren e / Ivanov Angelov, M. (2016). Sound Scattering by Lattices of Heated Wires [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/63275 / TESIS

In dieser Arbeit werden neuartige Flachrohre für die Verwendung als Rückwandverflüssiger in der Haushaltskältetechnik mit numerischen und dynamischen Simulationen sowie Experimenten untersucht. Dabei kommen unterschiedliche überströmte Längen sowie der Einfluss horizontaler Abstände auf den Wärmeübergang durch freie Konvektion zur Betrachtung. Realisiert wird die numerische Strömungssimulation mit der Software Fluent 3.6.26, wobei das RNG-k-epsilon- als Turbulenzmodell und diskrete Ordinaten zur zusätzlichen Modellierung des Strahlungswärmeübergangs verwendet werden. Zur Verifizierung werden experimentelle Untersuchungen mit natürlicher Konvektion durchgeführt. Ebenso kommt ein kompakter Verflüssiger bei erzwungener Konvektion zur experimentellen Analyse. Mit einem neuen Verflüssigermodell wird außerdem ein Haushaltskühlschrank in Modelica 2.2.1 dynamisch simuliert. Diese Arbeit zeigt, dass die Verwendung eines Flachrohrverflüssigers großes Potenzial einer konkurrenzfähigen Alternative zu konventionellen Verflüssigern besitzt. / In this work novel flat tubes used as rear panel condensers in the household refrigeration technology are examined with numerical and dynamic simulations as well as experiments. Therefore different overflowed lengths and the influence of horizontal spacing on the heat transfer by free convection are taken into consideration. The CFD calculations are realized with the software Fluent 3.6.26, where the RNG-k-epsilon turbulence model and discrete ordinates for an additional modelling of radiation heat transfer are applied. For the verification, experimental studies with natural convection are carried out. Likewise, a compact condenser is experimentally analysed in forced convection. With a new model for the liquefier a domestic refrigerator is also dynamically simulated in Modelica 2.2.1. This work shows that the use of a flat tube condenser has a great potential of a competitive alternative to conventional liquefiers.

No description available.

No description available.

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

The semiconducting compounds CdTe and CdZnTe have important applications in high-energy radiation detectors and as substrates for infrared devices. The materials offer large band gaps, high resistivity, and excellent charge transport properties; however all of these properties rely on very precise control of the material composition. Growing bulk crystals by the travelling heater method (THM) offers excellent compositional control and fewer defects compared to gradient freezing, but it is also much slower and more expensive. A particular challenge is the current need to grow new crystals onto existing seeds of similar size and quality. Simulations and experiments are used in this work to investigate the feasibility of growing these materials by THM without the use of large seed crystals. A new fixed-grid, multiphase finite element model was developed based on the level set method and used to calculate the mass transport regime and interface shapes inside the growth ampoule. The diffusivity of CdTe in liquid tellurium was measured through dissolution experiments, which also served to validate the model. Simulations of tapered THM growth find conditions similar to untapered growth with interface shapes that are sensitive to strong thermosolutal convection. Favourable growth conditions are achievable only if convection can be controlled. In preliminary experiments, tapered GaSb crystals were successfully grown by THM and large CdTe grains were produced by gradient freezing. Beginning with this seed material, 25 mm diameter CdTe and CdZnTe crystals were grown on 10 mm diameter seeds, and 65 mm diameter CdTe on 25 mm seeds. Unseeded THM growth was also investigated, as well as ampoule rotation and a range of thermal conditions and ampoule surface coatings. Outward growth beyond one or two centimeters was achieved only at small diameters and included secondary grains and twin defects; however, limited outward growth of larger seeds and agreement between experimental and numerical results suggest that tapered growth may be achievable in the future. This would require active temperature control at the base of the crystal and reduction of convection through thermal design or by rotation of the ampoule or applied magnetic fields. / Graduate / 0346 / 0794 / 0548 / jordan.roszmann@gmail.com

Nous développons dans ce travail de thèse un outil de simulation numérique pour les matériaux à changement de phase (MCP), en tenant compte du phénomène de convection naturelle dans la phase liquide, pour des configurations en deux et trois dimensions. Les équations de Navier-Stokes incompressible avec le modèle de Boussinesq pour la prise en compte des forces de flottabilité liées aux effets thermiques, couplées avec une formulation de l’équation d’énergie suivant la méthode d’enthalpie, sont résolues par une méthode d’éléments finis adaptatifs. Une approche mono-domaine, consistant à résoudre les mêmes systèmes d’équations dans les phases solide et liquide, est utilisée. La vitesse est ramenée à zéro dans la phase solide, en introduisant un terme de pénalisation dans l’équation de quantité de mouvement, suivant le modèle de Carman-Kozeny, consistant à freiner la vitesse à travers un milieu poreux. Une discrétisation spatiale des équations utilisant des éléments finis de Taylor-Hood, éléments finis P2 pour la vitesse et éléments finis P1 pour la pression, est appliquée, avec un schéma d’intégration en temps implicite d’ordre deux (GEAR). Le système d’équations non-linéaires est résolu par un algorithme de Newton. Les méthodes numériques sont implémentées avec le logiciel libre FreeFem++ (www.freefem.org), disponible pour tout système d’exploitation. Les programmes sont distribués sous forme de logiciel libre, sous la forme d’une forme de toolbox simple d’utilisation, permettant à l’utilisateur de rajouter d’autres configurations numériques pour des problèmes avecchangement de phase. Nous présentons dans ce manuscrit des cas de validation du code de calcul, en simulant des cas tests bien connus, présentés par ordre de difficulté croissant : convection naturelle de l’air, fusion d’un MCP, le cycle complet fusion-solidification, chauffage par le bas d’un MCP, et enfin, la solidification de l’eau. / In this thesis we develop a numerical simulation tool for computing two and three-dimensional liquid-solid phase-change systems involving natural convection. It consists of solving the incompressible Navier-Stokes equations with Boussinesq approximation for thermal effects combined with an enthalpy-porosity method for the phase-change modeling, using a finite elements method with mesh adaptivity. A single-domain approach is applied by solving the same set of equations over the whole domain. A Carman-Kozeny-type penalty term is added to the momentum equation to bring to zero the velocity in the solid phase through an artificial mushy region. Model equations are discretized using Galerkin triangular finite elements. Piecewise quadratic (P2) finite-elements are used for the velocity and piecewise linear (P1) for the pressure. The coupled system of equations is integrated in time using a second-order Gear scheme. Non-linearities are treated implicitly and the resulting discrete equations are solved using a Newton algorithm. The numerical method is implemented with the finite elements software FreeFem++ (www.freefem.org), available for all existing operating systems. The programs are written and distributed as an easy-to-use open-source toolbox, allowing the user to code new numerical algorithms for similar problems with phase-change. We present several validations, by simulating classical benchmark cases of increasing difficulty: natural convection of air, melting of a phase-change material, a melting-solidification cycle, a basal melting of a phase-change material, and finally, a water freezing case.