abstract: The central purpose of this work is to investigate the large-scale, coherent structures that exist in turbulent Rayleigh-Bénard convection (RBC) when the domain is large enough for the classical ”wind of turbulence” to break down. The study exclusively focuses on the structures that from when the RBC geometry is a cylinder. A series of visualization studies, Fourier analysis and proper orthogonal decomposition are employed to qualitatively and quantitatively inspect the large-scale structures’ length and time scales, spatial organization, and dynamic properties. The data in this study is generated by direct numerical simulation to resolve all the scales of turbulence in a 6.3 aspect-ratio cylinder at a Rayleigh number of 9.6 × 107 and Prandtl number of 6.7. Single and double point statistics are compared against experiments and several resolution criteria are examined to verify that the simulation has enough spatial and temporal resolution to adequately represent the physical system. Large-scale structures are found to organize as roll-cells aligned along the cell’s side walls, with rays of vorticity pointing toward the core of the cell. Two different large- scale organizations are observed and these patterns are well described spatially and energetically by azimuthal Fourier modes with frequencies of 2 and 3. These Fourier modes are shown to be dominant throughout the entire domain, and are found to be the primary source for radial inhomogeneity by inspection of the energy spectra. The precision with which the azimuthal Fourier modes describe these large-scale structures shows that these structures influence a large range of length scales. Conversely, the smaller scale structures are found to be more sensitive to radial position within the Fourier modes showing a strong dependence on physical length scales. Dynamics in the large-scale structures are observed including a transition in the global pattern followed by a net rotation about the central axis. The transition takes place over 10 eddy-turnover times and the subsequent rotation occurs at a rate of approximately 1.1 degrees per eddy-turnover. These time-scales are of the same order of magnitude as those seen in lower aspect-ratio RBC for similar events and suggests a similarity in dynamic events across different aspect-ratios. / Dissertation/Thesis / Doctoral Dissertation Mechanical Engineering 2017

De nombreux corps du système solaire possèdent des enveloppes liquides internes, comme par exemple les noyaux métalliques des planètes telluriques et les océans profonds des satellites de glace de Jupiter et Saturne, dans lesquelles se produisent des courants de convection. La modélisation de la dynamique de ces enveloppes est cruciale pour comprendre la génération des champs magnétiques planétaires (pour les noyaux) et pour mieux déterminer l’habitabilité potentielle des satellites joviens. La convection dans ces enveloppes est généralement produite par la combinaison d’au moins deux sources de flottabilité : une source thermique et une source solutale. Une telle situation est plus complexe qu’un régime de convection purement thermique ou purement solutale, d’une part en raison de l’existence d’un couplage thermochimique lorsqu’un processus de fusion ou de cristallisation se produit à l’une des frontières de l’enveloppe, et d’autre part à cause de la forte différence de diffusivité moléculaire entre les champs thermique et compositionnel qui permet potentiellement le développement d’instabilités double-diffusives. Classiquement, ces complexités ont été ignorées dans les simulations numériques de la dynamo terrestre ; les champs thermique et compositionnel ayant été combinés en une seule variable nommée « codensité ». Cette approche est sans doute simpliste mais permet d’esquiver une difficulté technique liée à la description du champ compositionnel dont la très faible diffusivité nécessite de recourir à des méthodes numériques adaptées. Cette thèse présente d’abord l’implémentation d’une méthode semi-Lagrangienne du type « particle-in-cell » dans un code de dynamo pré-existant, permettant ainsi de traiter de manière plus réaliste le champ de composition dans les enveloppes liquides internes des planètes. Les optimisations réalisées sont détaillées ainsi que les résultats de tests sur des cas de benchmark qui valident cet outil. Une comparaison avec des méthodes Eulériennes est également présentée. Une première exploration de la physique de la convection compositionnelle et thermochimique en rotation dans la limite d’un nombre de Prandtl compositionnel infini est ensuite conduite dans le contexte du noyau liquide terrestre. Il est montré que la dynamique convective est très différente de celle de la convection thermique pure. Notamment, les matériaux légers injectés à la frontière graine/noyau liquide sont capables d’atteindre la frontière noyau/manteau et de s’y accumuler pour former une couche chimiquement stratifiée, dont l’existence a été évoquée théoriquement mais qui n’a jamais pu être produite dans de précédentes simulations. Enfin, la dynamique double-diffusive des couches stratifiées est également discutée, et de premières simulations de « salt fingers » sont présentées. / Numerous planetary bodies contain internal liquid layers in which convective currents are generated by the combination of buoyancy sources of thermal and compositional origin. The strong difference between the thermal and chemical molecular diffusivities and the possibility of thermo-chemical coupling at melting or freezing boundaries create a convective regime that is much more complex than pure thermal convection, partly due to the potential occurrence of double-diffusive instabilities. Traditionally, numerical simulations have modeled the dynamics of the liquid part of planetary cores in a more simplistic way by neglecting the diffusivity difference and combining both fields into one single variable, an approximation that is convenient but maybe not relevant. However, distinguishing both fields and dealing with a large or infinite diffusivity ratio makes it compulsory to use numerical methods that minimize numerical diffusion as much as possible. In this thesis, I adapted a semi-Lagrangian particle-in-cell method into a pre-existing dynamo code to describe the weakly diffusive compositional field. I optimized the code for massively parallel computing and validated it on two different benchmarks. I compared the particle-in-cell method to Eulerian schemes and showed that its advantages extend beyond its lower numerical dissipation. Using this new tool, I performed first numerical simulations of rotating pure compositional and thermochemical convection in the limit of null chemical diffusivity. I explored the physics of pure compositional convection and addressed questions related to the existence and the dynamics of a stratified layer below the Earth’s core mantle boundary. In particular, I showed that the stratification could potentially be of chemical origin and proposed some mechanisms to explain its formation. In the case of a thermally stratified layer, I performed a scaling analysis of fingering instabilities, wrote the first steps of a linear stability analysis and ran a few simulations of fingering instabilities in the rotating case. The potential effects of the magnetic field and the coupling of thermochemical boundary conditions in planetary cores are finally discussed in this thesis.

Kyoto University (京都大学) / 0048 / 新制・課程博士 / 博士(工学) / 甲第16376号 / 工博第3457号 / 新制||工||1523(附属図書館) / 29007 / 京都大学大学院工学研究科都市社会工学専攻 / (主査)教授 細田 尚, 教授 後藤 仁志, 准教授 米山 望 / 学位規則第4条第1項該当

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L’évaporation d’une solution solvant/soluté est un processus transitoire qui prend fin lorsque le solvant a totalement disparu. Le refroidissement créé par le changement de phase provoque des gradients à la fois thermiques et de concentration en solvant. Ces homogénéités diffusent ensuite dans l’épaisseur de la solution et sont susceptibles d’engendrer un écoulement fluide. L’origine de cette convection peut être liée à des variations de tension de surface ou de densité. Des travaux expérimentaux ont montré que l’épaisseur des dépôts issus de séchages de solutions solvant/soluté semblait pouvoir être corrélée avec les cellules de convection de la zone fluide. Une compréhension approfondie des phénomènes à l’origine de la convection devrait donc participer à un meilleur contrôle de la qualité des dépôts.Sur la base de travaux numériques et expérimentaux publiés, nous avons étudié l’apparition de la convection pour trois types de modèles représentant le processus d’évaporation d’une solution de Polyisobutylène-Toluène : un modèle purement thermique qui s’applique pour les temps courts, un modèle solutal qui est valable sur les temps longs et enfin un modèle couplé thermique/solutal qui représente les transferts sur l’ensemble de la gamme des temps étudiés. Le caractère transitoire de l’évaporation induit une difficulté pour caractériser la naissance de la convection à partir d’un régime de conduction. En effet, cette convection apparaît à partir d’un germe qui est une petite perturbation de la solution diffusive. Si l’amplitude de cette perturbation est trop faible, son amplification à des intensités suffisantes ne pourra pas avoir lieu avant la fin du régime transitoire et l’écoulement ne deviendra donc jamais convectif. Le rôle de la perturbation est donc primordial. Dans des travaux numériques antérieurs, cette perturbation a été imposée à l’état initial, généralement avec une distribution aléatoire du champ thermique ou de vitesse. Lors de cette thèse, nous avons opté pour un modèle plus physique, basé sur l’introduction d’un transfert thermique sur les parois latérales qui joue le rôle de perturbateur de l’écoulement diffusif transitoire.Dans cette thèse, nous avons établi par voie numérique les seuils de transition entre une solution diffusive et un écoulement convectif pour les modèles thermique, solutal et couplé, dans le cas d’une approximation bidimensionnelle du film liquide et des simulations pleinement tridimensionnelles. Des diagrammes spatio-temporels et l’étude des cellules à la surface libre par des reconstructions de Voronoï nous ont permis de mieux comprendre la naissance et la propagation des instabilités dans la solution fluide / The evaporation of a solvent/solute solution is a transient phenomenon which ends when the whole solvent has disappeared. Phase change generates a cooling of the liquid-gas interface, and consequently, it creates thermal and solutal gradients. These homogeneities spread in the core solution and produce, eventually, a fluid flow. This convection can be due to the surface tension and/or buoyancy variations. Experimental works have shown that some coating thicknesses stemming from drying processes are correlated to the size of the convection cells in the fluid region. A thorough understanding of the physical phenomena responsible to fluid convection should contribute to improve the control of deposit quality.Based on numerical and experimental works, we have studied the onset of convection for three kinds of models for the drying process of a Polyisobutylene-Toluène solution: A pure thermal model which is valid for short times, a solutal model devoted to the simulation of long times, only, and a thermal/solutal coupled model which takes into account the heat and mass transfer over a long time period of the evaporation process. The transient nature of the evaporation problem raises the issue of how to define the onset of the convective flow from a diffusive solution. Indeed, this flow motion occurs from a seed which is a small perturbation of the transient diffusive solution. If the perturbation is too weak, the necessary time interval for a significant growing of its magnitude will be greater than the time scale of the transient regime: thus the solution will never be considered as convective. Consequently, the influence of the perturbation is fundamental. In previous numerical works, this perturbation was imposed at the initial state, often through a random spatial distribution applied to the velocity or temperature field. In the present contribution, we have adopted a physical model where the adiabatic lateral walls have been replaced by diathermal walls: The local thermal inhomogeneities create a very weak flow acting as a small disturbance for the transient diffusive solution.In this thesis, we have developed a numerical model to evaluate the thresholds between the diffusive solutions and the convective flows, for the thermal, solutal and thermal/solutal coupled models, for two- and three-dimensional approximations of the Polyisobutylene-Toluène liquid film. Space-time diagrams and convective cell reconstructions at the liquid-gas interface by a Voronoï algorithm allowed us to get a better understanding of the way the disturbances propagate from the lateral walls for finally giving rise to a convective flow in the core fluid

Natural convection in liquid metals has been studied by direct observation of the fluid flow, using radioactive tracer techniques. The study is of importance in understanding the solidification of metals since fluid flow strongly influences the heat and mass transfer in the system which in turn strongly influences the structure, homogeneity, and mechanical properties of the solid metal produced. The system examined in this investigation was a rectangular liquid cell of variable thickness, positioned on edge. A small driving force for natural convection was imposed across the liquid cell and when steady state conditions were reached, a small amount of the same material containing a radioactive isotope was added to the top of the cell. The tracer material was picked up by the flow and after a given time interval the liquid was quenched to fix the tracer position. The resultant solid block was autoradiographed to determine the distribution of the added radioactive material. Thermal convection was observed in liquid tin and liquid lead using radioactive Sn¹¹³ and radioactive TI²º⁴ respectively. The results show that the flow rates increase with increasing temperature difference across the liquid cell, increasing average temperature, and increasing liquid cell thickness. Flow rates with Grashof numbers from 10⁶ to 10⁸ were experimentally observed. A finite difference numerical solution for the problem of thermal convection is presented for Prandtl numbers of 10.0, 1.0, 0.1, and 0.0127 with Grashof numbers from 2 x 10³ to 2 x 10⁷. The experimental results for liquid tin (Pr = 0.0127) are found to approach the theoretical analysis for large cell thicknesses and large temperature differences. The flow behavior of various types of fluids is compared with liquid metals to show that non-metallic analogies to .metallic flow problems have very limited value. Solute convection is experimentally considered from three different viewpoints; a) independent solute convection, b) the influence of solute convection on thermal convection, and c) the thermal and solute conditions for complete liquid mixing. It was found that there must be a horizontal density inversion across the whole liquid cell for complete mixing to occur throughout the liquid zone. Interdendritic liquid flow resulting from the natural convection in the residual liquid pool was observed in lead-tin alloys. The flow penetrated into the solid-liquid zone to a point of approximately 12 - 22 % solid for primary dendrite spacings of from 700 to 1000 microns. Several experimental models are presented for interdendritic flow. A three-dimensional wire mesh model predicts that the finer the dendrite structure, the greater the flow penetration into the solid-liquid zone. The experimental results for the lead-tin alloys compared favorably with the model. As an extension of the fluid flow considerations, an investigation was carried out to determine macrosegregation in castings which have imposed fluid flow patterns. The macrosegregation present in stationary, rotated, and oscillated castings of Al - 3 wt. % Ag was determined by measuring the distribution of radioactive silver added to the melt. It was found that, no significant macrosegregation was present in the stationary and rotated castings. Extensive macro-segregation was detected in the oscillated casting. For the oscillated case the macrosegregation can be accounted for on the basis of the long range movement of dendrite fragments which break and/or melt off in the solid-liquid interface region. This movement is a direct result of turbulent waves associated with the oscillation. The maximum silver concentration is shown to be related to the columnar-to-equiaxed transition. / Applied Science, Faculty of / Materials Engineering, Department of / Graduate

Heat transfer rates have been measured for forced flow of supercritical carbon dioxide normal to a horizontal heated cylinder. The 0.006 inch diameter cylinder was held at various constant temperatures by a feed-back bridge circuit. Free convection results are also included. The effects of bulk fluid temperature, bulk fluid pressure, and surface temperature were studied for a range of bulk fluid temperature and pressure of from 0.8 to 1.4 times the critical temperature and pressure for several free stream velocities from zero to three feet per second. The temperature difference between the heated cylinder and the bulk fluid was varied from 1 deg F to 320 deg F. Flow fields of all data runs were observed. Still photographs and high speed movies have been taken at operating conditions of interest. In a supercritical fluid the heat transfer rate increases smoothly and monotonically with increasing temperature difference, increasing velocity, and increasing pressure. In fluid with the bulk temperature below the pseudo-critical temperature the heat transfer coefficient shows large peaks when the cylinder temperature is near the pseudocritical temperature. Peaks are largest when the bulk fluid pressure is near the critical pressure. The heat transfer coefficient decreases with increasing temperature difference when the bulk fluid temperature is above the pseudo-critical temperature. The heat transfer rate noteably increases with increasing pressure only when vapour-like fluid is in contact with the heated cylinder. Supercritical forced flow has been compared to forced flow boiling. The supercritical case does not exhibit the characteristic strong maxima in heat transfer rate shown in forced flow nucleate boiling. Heat transfer rates at larger temperature differences are very similar in forced flow film boiling and supercritical forced flow heat transfer. With this horizontal, constant temperature cylinder, no "bubble-like" or "boiling-like" mechanisms of heat transfer were observed in supercritical free or forced convection. The flow field and heat transfer rate in free convection were found to be very unstable and sensitive to small temperature disturbances in the bulk fluid. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

A physical model and a numerical solution procedure has been developed to predict heat transfer behaviour in supercritical fluids. A major area of concentration was the modelling of the turbulent components of shear stress and heat flux. Traditionally, the turbulent fluxes are modelled by algebraic expressions such as the familiar mixing length methods. However, the use of this technique has not been entirely satisfactory. Newer methods for constant-property flows which model turbulent fluxes by considering the transport of quantities such as turbulent kinetic energy and the dissipation rate of turbulence have been extended to supercritical fluids. This involves the solution of two additional partial differential equations that are solved simultaneously with the equations of continuity, energy, and momentum. The numerical scheme has been developed on a completely two-dimensional basis by extending the Pletcher-DuFort-Frankel finite difference method. Computed results for velocity and temperature profiles as well as wall temperature distributions exhibited reasonable agreement with previous experimental data and therefore indicate the viability of the present method. Computations were carried out for supercritical carbon dioxide flowing through a circular duct in the reduced pressure range 1.0037 to 1.098. A consideration of the influence of buoyancy on the mean momentum balance permitted the calculation of unusual velocity profiles in this investigation. The existance of such velocity profiles had been accepted previously but the nature of their growth along a pipe has probably not been suggested previous to this work. No attempt was made to include buoyancy generated turbulence or additional fluctuating property correlations in this work, but suggestions are made regarding possible avenues of approach. Some of the incidental outcomes of this work were a new continuous universal velocity profile implicit in cross stream distance an a new mixing length distribution for turbulent pipe flows. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

Natural convection as a heat transfer mechanism plays a major role in the functioning of many heat transfer devices, such as heat exchangers, energy storage, thermal management and solar collectors. All of these have a large impact on the generation of solar power. Considering how common these devices are not only in power generation cycles, but in a majority of other thermal uses it is clear that increased performance for natural convection heat transfer will have consequences of a high impact. As such, the purpose of this study is to experimentally study the natural convection heat transfer behaviour of a relatively new class of fluids where nano-sized particles are mixed into a base fluid, also known as a nanofluids. Nanofluids have attracted widespread interest as a new heat transfer fluid due to the fact that the addition of nanoparticles considerably increases the thermophysical properties of the nanofluids when compared to those of the base fluid. Furthermore, if these nanoparticles show magnetic behaviour, huge increases in the thermal conductivity and viscosity of the nanofluid can be obtained if the fluid is exposed to a proper magnetic field. With this in mind, the study aimed to experimentally show the behaviour of these so-called magnetic nanofluids in natural convection heat transfer applications. In this study, the natural convection heat transfer of a magnetic nanofluid in a differentially heated cavity is investigated with and without an applied external magnetic field. The effects of volume concentration and magnetic field configuration are investigated. Spherical nanoparticles with a diameter of 20 nm are used with a volume concentration ranging between 0.05% and 0.3%, tested for the case with no magnetic field, while only a volume concentration of 0.1% was used in the magnetic cases. The experiments were conducted for a range of Rayleigh numbers in . The viscosity of the nanofluid was determined experimentally, while an empirical model from the literature was used to predict the thermal conductivity of the nanofluids. An empirical correlation for the viscosity was determined, and the stability of various nanofluids was investigated. Using heat transfer data obtained from the cavity, the average heat transfer coefficient, as well as the average Nusselt number for the nanofluids, is determined. It was found that a volume concentration of 0.05% showed an increase of 3.75% in heat transfer performance. For the magnetic field study, it was found that the best-performing magnetic field enhanced the heat transfer performance by 1.58% compared to the 0.1% volume concentration of the nanofluid with no magnetic field. / Dissertation (MEng)--University of Pretoria, 2017. / Mechanical and Aeronautical Engineering / MEng / Unrestricted

Titan is a unique moon in the solar system as it is the only one with a thick atmo- sphere, and surface lakes and seas. Observations made by the Cassini/Huygens probe showed the potential of a subsurface ocean hidden below the outer crust made of ice. This thesis analyzes the heat transfer through the crust of Titan to understand the long term evolution of the ocean. We developed a finite element model of the heat transfer through a thickening ice crust and investigated the effect of viscosity, internal heat flux, and ammonia concentration in the ocean. While other explanations cannot be ruled out, it was found high values of viscosity and possible ammonia presence could keep the ocean liquid for long periods. 1