Academic literature on the topic 'Convection de Rayleigh- Bénard et Bénard-Marangoni'

Natural convection is omnipresent on Earth. A basic and well-studied model for it is Rayleigh–Bénard convection, the fluid flow in a layer heated from below and cooled from above. Most explorations of Rayleigh–Bénard convection focus on spatially uniform, perfectly conducting thermal boundary conditions, but many important geophysical phenomena are characterized by boundary conditions which are a mixture of conducting and adiabatic materials. For example, the differences in thermal conductivity between continental and oceanic lithospheres are believed to play an important role in plate tectonics. To study this, Wang et al. (J. Fluid Mech., vol. 817, 2017, R1), measure the effect of mixed adiabatic–conducting boundary conditions on turbulent Rayleigh–Bénard convection, finding experimental proof that even if the total heat transfer is primarily affected by the adiabatic fraction, the arrangement of adiabatic and conducting plates is crucial in determining the large-scale flow dynamics.

We present the results from numerical and theoretical investigations of rotating Rayleigh–Bénard convection for relatively large dimensionless rotation rates, 170 < Ω < 274, and a Prandtl number of 6.4. Unexpected square patterns were found experimentally by Bajaj et al. (Phys. Rev. Lett., vol. 81, 1998, p. 806) in this parameter regime and near threshold for instability in the bulk. These square patterns have not yet been understood theoretically. Sánchez-Álvarez et al. (Phys. Rev. E, vol. 72, 2005, p. 036307) have found square patterns in numerical simulations for similar parameters when only the Coriolis force is included. We performed detailed numerical studies of rotating Rayleigh–Bénard convection for the same parameters as the experiments and simulations. To better understand these patterns, we compared the effects of the Coriolis force as well as the centrifugal force. We also computed the coefficients of the amplitude equation describing one-, two- and three-mode bulk solutions to rotating Rayleigh–Bénard convection. We find that squares are unstable, but we do find stable limit cycles consisting of three coupled oscillating amplitudes, which can superficially resemble squares, since one of the three amplitudes is rather small.

We conduct direct numerical simulations for turbulent Rayleigh–Bénard (RB) convection, driven simultaneously by two scalar components (say, temperature and concentration) with different molecular diffusivities, and measure the respective fluxes and the Reynolds number. To account for the results, we generalize the Grossmann–Lohse theory for traditional RB convection (Grossmann & Lohse, J. Fluid Mech., vol. 407, 2000, pp. 27–56; Phys. Rev. Lett., vol. 86 (15), 2001, pp. 3316–3319; Stevens et al., J. Fluid Mech., vol. 730, 2013, pp. 295–308) to this two-scalar turbulent convection. Our numerical results suggest that the generalized theory can successfully capture the overall trends for the fluxes of two scalars and the Reynolds number without introducing any new free parameters. In fact, for most of the parameter space explored here, the theory can even predict the absolute values of the fluxes and the Reynolds number with good accuracy. The current study extends the generality of the Grossmann–Lohse theory in the area of buoyancy-driven convection flows.

We report an investigation of temperature profiles in turbulent Rayleigh–Bénard convection of water based on direct numerical simulations (DNS) for a cylindrical cell with unit aspect ratio for the same Prandtl number Pr and similar Rayleigh numbers Ra as used in recent high-precision measurements by Funfschilling et al. (J. Fluid Mech., vol. 536, 2005, p. 145). The Nusselt numbers Nu computed for Pr = 4.38 and Ra = 108, 3 × 108, 5 × 108, 8 × 108 and 109 are found to be in excellent agreement with the experimental data corrected for finite thermal conductivity of the walls. Based on this successful validation of the numerical approach, the DNS data are used to extract vertical profiles of the mean temperature. We find that near the heating and cooling plates the non-dimensional temperature profiles Θ(y) (where y is the non-dimensional vertical coordinate), obey neither a logarithmic nor a power law. Moreover, we demonstrate that the Prandtl–Blasius boundary layer theory cannot predict the shape of the temperature profile with an error less than 7.9% within the thermal boundary layers (TBLs). We further show that the profiles can be approximated by a universal stretched exponential of the form Θ(y) ≈ 1 − exp(−y − 0.5y2) with an absolute error less than 1.1% within the TBLs and 5.5% in the whole Rayleigh cell. Finally, we provide more accurate analytical approximations of the profiles involving higher order polynomials in the approximation.

Results from direct numerical simulation (DNS) for three-dimensional Rayleigh–Bénard convection in a cylindrical cell of aspect ratio 1/2 and Prandtl number Pr=0.7 are presented. They span five decades of Rayleigh number Ra from 2 × 106 to 2 × 1011. The results are in good agreement with the experimental data of Niemela et al. (Nature, vol. 404, 2000, p. 837). Previous DNS results from Amati et al. (Phys. Fluids, vol. 17, 2005, paper no. 121701) showed a heat transfer that was up to 30% higher than the experimental values. The simulations presented in this paper are performed with a much higher resolution to properly resolve the plume dynamics. We find that in under-resolved simulations the hot (cold) plumes travel further from the bottom (top) plate than in the better-resolved ones, because of insufficient thermal dissipation mainly close to the sidewall (where the grid cells are largest), and therefore the Nusselt number in under-resolved simulations is overestimated. Furthermore, we compare the best resolved thermal boundary layer profile with the Prandtl–Blasius profile. We find that the boundary layer profile is closer to the Prandtl–Blasius profile at the cylinder axis than close to the sidewall, because of rising plumes close to the sidewall.

An experimental study of Rayleigh–Bénard convection in the strongly turbulent regime is presented. We report results obtained at low Prandtl number (in mercury, Pr = 0.025), covering a range of Rayleigh numbers 5 × 106 < Ra < 5 × 109, and compare them with results at Pr∼1. The convective chamber consists of a cylindrical cell of aspect ratio 1.Heat flux measurements indicate a regime with Nusselt number increasing as Ra0.26, close to the 2/7 power observed at Pr∼1, but with a smaller prefactor, which contradicts recent theoretical predictions. A transition to a new turbulent regime is suggested for Ra ≃ 2 × 109, with significant increase of the Nusselt number. The formation of a large convective cell in the bulk is revealed by its thermal signature on the bottom and top plates. One frequency of the temperature oscillation is related to the velocity of this convective cell. We then obtain the typical temperature and velocity in the bulk versus the Rayleigh number, and compare them with similar results known for Pr∼1.We review two recent theoretical models, namely the mixing zone model of Castaing et al. (1989), and a model of the turbulent boundary layer by Shraiman & Siggia (1990). We discuss how these models fail at low Prandtl number, and propose modifications for this case. Specific scaling laws for fluids at low Prandtl number are then obtained, providing an interpretation of our experimental results in mercury, as well as extrapolations for other liquid metals.

AbstractTurbulent rotating convection is usually studied in a cylindrical geometry, as this is its most convenient experimental realization. In our previous work (Kunnen et al., J. Fluid Mech., vol. 688, 2011, pp. 422–442) we studied turbulent rotating convection in a cylinder with the emphasis on the boundary layers. A secondary circulation with a convoluted spatial structure has been observed in mean velocity plots. Here we present a linear boundary-layer analysis of this flow, which leads to a model of the circulation. The model consists of two independent parts: an internal recirculation within the sidewall boundary layer, and a bulk-driven domain-filling circulation. Both contributions exhibit the typical structure of the Stewartson boundary layer near the sidewall: a sandwich structure of two boundary layers of typical thicknesses ${E}^{1/ 4} $ and ${E}^{1/ 3} $, where $E$ is the Ekman number. Although the structure of the bulk-driven circulation may change considerably depending on the Ekman number, the boundary-layer recirculation is present at all Ekman numbers in the range $0. 72\times 1{0}^{- 5} \leq E\leq 5. 76\times 1{0}^{- 5} $ considered here.

We report an experimental study of confinement effects in quasi-2-D turbulent Rayleigh–Bénard convection. The experiments were conducted in five rectangular cells with their height $H$ and length $L$ being the same and fixed, while the width $W$ was different for each cell to produce lateral aspect ratios (${\it\Gamma}=W/H$) of 0.6, 0.3, 0.2, 0.15 and 0.1. Direct flow field measurements reveal that the large-scale flow slows down as ${\it\Gamma}$ decreases and there are more plumes travelling through the bulk region. Moreover, the reversal frequency of the large-scale flow is found to increase drastically in smaller ${\it\Gamma}$ cells, by more than 1000-fold for the highest value of Rayleigh number reached in the experiment. The reversal frequency can be well described by a stochastic model developed by Ni et al. (J. Fluid Mech., vol. 778, 2015, R5) and the probability density functions (PDF) of the time interval between successive reversals are found to follow Poisson statistics as in the 3-D system. It is further observed that the bulk temperature fluctuation increases significantly and its PDF changes from exponential to Gaussian as ${\it\Gamma}$ decreases. The influences of geometric confinement on the global heat transport are also investigated. The measured Nu–Ra relationship suggests that, as the lateral aspect ratio decreases, the relative weight of the boundary layer contribution in the global heat transport increases compared to that from the bulk. These results demonstrate that in the quasi-2-D geometry, geometric confinement has strong effects on both the global and local properties in turbulent convective flows, which are very different from the previous findings in 3-D and true 2-D systems.

We critically analyse the different ways to evaluate the dependence of the Nusselt number ($\mathit{Nu}$) on the Rayleigh number ($\mathit{Ra}$) in measurements of the heat transport in turbulent Rayleigh–Bénard convection under general non-Oberbeck–Boussinesq conditions and show the sensitivity of this dependence to the choice of the reference temperature at which the fluid properties are evaluated. For the case when the fluid properties depend significantly on the temperature and any pressure dependence is insignificant we propose a method to estimate the centre temperature. The theoretical predictions show very good agreement with the Göttingen measurements by He et al. (New J. Phys., vol. 14, 2012, 063030). We further show too the values of the normalized heat transport $\mathit{Nu}/\mathit{Ra}^{1/3}$ are independent of whether they are evaluated in the whole convection cell or in the lower or upper part of the cell if the correct reference temperatures are used.

We report experimental results for the power spectra, variance, skewness and kurtosis of temperature fluctuations in turbulent Rayleigh–Bénard convection (RBC) of a fluid with Prandtl number $Pr=12.3$ in cylindrical samples with aspect ratios $\unicode[STIX]{x1D6E4}$ (diameter $D$ over height $L$) of 0.50 and 1.00. The measurements were primarily for the radial positions $\unicode[STIX]{x1D709}=1-r/(D/2)=1.00$ and $\unicode[STIX]{x1D709}=0.063$. In both cases, data were obtained at several vertical locations $z/L$. For all locations, there is a frequency range of about a decade over which the spectra can be described well by the power law $P(f)\sim f^{-\unicode[STIX]{x1D6FC}}$. For all $\unicode[STIX]{x1D709}$ and $\unicode[STIX]{x1D6E4}$, the $\unicode[STIX]{x1D6FC}$ value is less than one near the top and bottom plates and increases as $z/L$ or $1-z/L$ increase from 0.01 to 0.5. This differs from the finding for$Pr=0.8$ (He et al., Phys. Rev. Lett., vol. 112, 2014, 174501) and the expectation for the downstream velocity of turbulent wall-bounded shear flow (Rosenberg, J. Fluid Mech., vol. 731, 2013, pp. 46–63), where $\unicode[STIX]{x1D6FC}=1$ is found or expected in an inner layer ($0.01\lesssim z/L\lesssim 0.1$) near the wall but in the bulk. The variance is described better by a power law $\unicode[STIX]{x1D70E}^{2}\sim (z/L)^{-\unicode[STIX]{x1D701}}$ than by the logarithmic dependence found or expected for $Pr=0.8$ and for turbulent shear flow. For both $\unicode[STIX]{x1D6E4}$, we found that, independent of Rayleigh number, $\unicode[STIX]{x1D701}\simeq 2/3$ near the sidewall ($\unicode[STIX]{x1D709}=0.063$), where plumes primarily rise or fall and the large-scale circulation (LSC) dynamics is most influential. This result agrees with a model due to Priestley (Turbulent Transfer in the Lower Atmosphere, 1959, University of Chicago Press) for convection over a horizontal heated surface. However, we found $\unicode[STIX]{x1D701}\simeq 1$ along the sample centreline ($\unicode[STIX]{x1D709}=1.00$), where there are relatively few plumes moving vertically and the LSC dynamics is expected to be less important; that result is consistent with one of two possible interpretations by Adrian (Intl J. Heat Mass Transfer, vol. 39, 1996, pp. 2303–2310) of a model due to Libchaber et al. (J. Fluid Mech., vol. 204, 1989, pp. 1–30). We discuss the composite nature of fluctuations in turbulent RBC, with contributions from intrinsic background fluctuations, plumes, the stochastic dynamics of the LSC, and the sloshing and torsional mode of the LSC. None of the models advanced so far explicitly consider all of these contributions.

Dans ce travail nous étudions numériquement le déclenchement d'instabilités thermo-solutales dans le cas du séchage d'une solution polymère. L'évaporation du solvant entraine une baisse de la température et de la concentration du solvant en surface. Ceci peut générer des instabilités thermo-convectives et solutales, induites par les variations de la masse volumique (poussée d'Archimède) et/ou de la tension superficielle (effet Marangoni). L'épaisseur du milieu ainsi que les gradients de température et de concentration évoluent au cours du séchage et il s'agit donc d'un problème transitoire. Deux modèles simplifiés sont mis en place, tenant respectivement compte des effets thermique et solutal. L'étude porte principalement sur trois points : la détermination du rôle respectif de chaque phénomène, le caractère transitoire du problème, et enfin l'influence de l'évolution de la viscosité de la solution avec la concentration au cours du séchage sur les seuils de transition entre les régimes conductif et convectif
This work aims to study numerically how instabilities are activated in the drying of solvent/polymer solution. Solvent evaporation induces both a cooling and a decrease in solvent concentration at the free surface. Consequently, density variations (buoyancy) and/or superficial tension variations (Marangoni effect) can generate convection into the bulk. Besides, since the temperature and concentration gradients but also the thickness of the solution evolve during the drying, we are dealing here with a full transient problem. For this purpose, two simplified models are established for thermal and solutal regimes respectively. This study mainly focuses on: the transient character of the problem, the role of each phenomenon (thermal/solutal), on one hand, and the impact of the evolution of the solvent mass fraction and by the way of the viscosity of the solution, on the other hand, on the instability thresholds and the flow structure

Dans ce travail nous étudions numériquement le déclenchement d'instabilités thermo-solutales dans le cas du séchage d'une solution polymère. L'évaporation du solvant entraine une baisse de la température et de la concentration du solvant en surface. Ceci peut générer des instabilités thermo-convectives et solutales, induites par les variations de la masse volumique (poussée d'Archimède) et/ou de la tension super ficielle (eff et Marangoni). L'épaisseur du milieu ainsi que les gradients de température et de concentration évoluent au cours du séchage et il s'agit donc d'un problème transitoire. Deux modèles simplifiés sont mis en place, tenant respectivement compte des e ffets thermique et solutal. L'étude porte principalement sur trois points : la détermination du rôle respectif de chaque phénomène, le caractère transitoire du problème, et enfi n l'influence de l'évolution de la viscosité de la solution avec la concentration au cours du séchage sur les seuils de transition entre les régimes conductif et convectif.

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

Ce mémoire analyse le phénomène de convection turbulente dans diverses cellules de Rayleigh-Bénard remplies d'hélium gazeux et liquide. Une des spécificités de cette étude est sa mise en oeuvre en environnement cryogénique, afin de bénéficier de conditions expérimentales optimales, tant en terme de contrôle thermique qu'en terme de plage de variation des paramètres de contrôle : les Nombres de Prandtl (Pr) et de Rayleigh. Ce dernier est en particulier exploré sur plus de 11 décades. Trois contributions principales se dégagent de cette étude. Tout d'abord, la mise en évidence d'un effet de conduction déterminant dû à la paroi latérale. Négligé dans les travaux antérieurs, cet effet est étudié expérimentalement puis modélisé. Il permet de lever certaines incohérences apparues dans des publications de références. En outre, le ré-examen de publications antérieures conforte l'idée que le Nombre de Nusselt (Nu) dépend du Nombre de Rayleigh suivant une loi de puissance d'exposant supérieur à 0,3, plutôt que 2/7 par exemple. La deuxième contribution porte sur l'influence du Nombre de Prandtl, analysée sur une décade et demie (0,7

Une étude théorique et expérimentale de la convection de Rayleigh-Bénard pour un fluide non-Newtonien rhéofluidifiant a été effectuée. L’approche théorique consiste en une analyse linéaire et faiblement non linéaire de l’instabilité thermo-convective d’une couche horizontale d’un fluide non-Newtonien, d’étendue supposée infinie dans le plan horizontal, chauffée par le bas et refroidie par le haut. Le comportement rhéofluidifiant est décrit par le modèle de Carreau. Pour ce modèle, les conditions critiques d’instabilité du régime conductif sont les mêmes que pour un fluide Newtonien. L’objectif de l’analyse faiblement non linéaire consiste à déterminer d’une part la valeur critique du degré de rhéofluidification à partir duquel la bifurcation primaire devient sous critique et d’autre part l’influence de rhéofluidification sur la sélection du motif de convection au voisinage des conditions critiques, en tenant compte d’un éventuel glissement à la paroi, d’une conductivité thermique finie de celle-ci et de la thermodépendance de la viscosité. Les conséquences sur le champ de viscosité et l’évolution du nombre de Nusselt sont caractérisées. L’approche expérimentale consiste à visualiser par ombroscopie les motifs de convection qui se développent dans une cellule cylindrique. Deux rapports d’aspect ont été considérés : AR = 3 et AR = 4. Les fluides utilisés sont des solutions aqueuses de Xanthan à différentes concentrations. L’influence du degré de rhéofluidification combiné avec la thermodépendance de la viscosité sur le domaine de stabilité des rouleaux et des hexagones ainsi que sur la zone de transitions rouleaux hexagones est mise en évidence
Theoretical and experimental study of Rayleigh-Bénard convection in a non-Newtonian shear-thinning fluid was performed. The theoretical approach consists in a linear and a weakly nonlinear of thermo-convective instability in a horizontal layer of a non-Newtonian fluid, assumed infinite in extent, heated from below and cooled from above. The rheological behavior of the fluid is described by the Carreau model. For this rheological model, the critical threshold is the same as for a Newtonian fluid. The objective of the weakly non linear analysis is to determine on one hand the critical value of the shear-thinning degree above which the bifurcation becomes subcritical and on the other hand, the influence of shear-thinning effects on the pattern selection near the onset, taking into account the possibility of wall slip, a finite thermal conductivity of the walls as well as the thermo-dependency of the viscosity. The impact on the viscosity field and on the evolution of the Nusselt number are characterized. The experimental approach consists in visualizing the convection patterns using the shadowgraph method in a cylindrical cell. Two aspect ratios were considered : AR = 3 and AR = 4. The fluids used are aqueous solutions of xanthan-gum at different concentrations. The influence of shear-thinning effects combined with the thermo-dependency of the viscosity on the stability domain of rolls and hexagons as well as on the transition between rolls and hexagons is highlighted

Le phénomène de Rayleigh-Bénard correspond à l'état instable dans lequel se trouve une couche horizontale d'un fluide dilatable, soumise à un gradient de température DT. Si ce dernier dépasse une valeur critique DTc, des mouvements convectifs naissent à l'intérieur du fluide. Concernant les fluides à seuil, le phénomène devient plus complexe. Le seuil s'ajoute aux forces stabilisatrices au sein du fluide et modifie de manière fondamentale le transfert de matière et le transfert thermique. Au départ, le fluide est au repos ; le gradient de vitesse est alors nul et la viscosité efficace infinie partout. L'approche de stabilité linéaire est incapable de fournir une solution aux équations d'écoulement car on doit perturber, par les forces d'Archimède, un fluide d'une viscosité infinie. Dans ce travail de thèse, des expériences de Rayleigh-Bénard ont été effectuées sur des solutions à base de Carbopol 940 présentant un seuil de contrainte. Le dispositif expérimental nous a permis d'avoir des résultats quantitatifs et qualitatifs intéressants. Les mouvements thermoconvectifs ont ensuite été filmés par la technique d'ombroscopie. L'effet non-linéaire au début de la convection a été observé.

La convection de Rayleigh-Bénard est étudiée expérimentalement dans une cellule circulaire. Des fluides à seuil modèles (gels aqueux de Carbopol) sont mis en œuvre. Leurs comportements rhéologiques et leurs perméabilités en relation avec leurs microstructures ont été finement caractérisés. Dans toute la thèse, les expériences ont été menées sans glissement à la paroi. L'influence du seuil d'écoulement et de la distance entre plaques chaudes et froides sur les transferts thermiques a été approfondie. Trois mécanismes sont discutés pour expliquer le déclenchement de la convection: i) les propriétés visco-élastiques au-dessous du seuil, ii) le fluage au-dessous du seuil, iii) une approche d'un milieu poreux pour les gels de Carbopol considérés comme une suspension de micro-gels. On montre que le nombre de seuil Y, représentant le rapport entre la contrainte du seuil et la contrainte de la poussée d'Archimède est un paramètre important gouvernant l'apparition de l'instabilité. Les valeurs critiques de Y^(-1) sont déterminées entre 60 et 90. La visualisation à l'aide des cristaux liquides thermo-chromiques a permis une vue globale de la cinématique. Les structures observées dans les différents états thermiques montrent l'évolution de la convection. Une analyse qualitative du champ de température est également présentée. Enfin, la simulation numérique dans une cellule carré avec un modèle d'Herschel-Bulkley régularisé dans la gamme des nombres sans dimension utilisée dans les expérience a permis de mettre en évidence les paramètres critiques et la morphologie des champs thermiques et cinématique. Les ordres de grandeurs du nombre de seuil critique prédit se comparent raisonnablement avec les valeurs expérimentales
In this thesis, three main mechanisms proposed in a recent paper (Darbouli et al., Physics of fluids, 25(2) 2013) have been discussed to explain the onset of Rayleigh Bénard Convection in a yield fluid (Carbopol gels): i) the elasto-visco-plasticity behavior of the material below the yield stress, ii) a viscosity at low values of shear rates by creep measurements below the yield stress, iii) a microscopic viewpoint considering the fluid as a porous two phases system. No-slip conditions have been achieved for all the experiments. The results with different Carbopol gels have proved the importance of Y, the yield number which presents the report of the yield stress and the buoyancy effect, as the governing parameter. The critical value of Y^(-1) with no-slip condition has been found between 60 and 90. A visualization measurement with the utilization of thermochromics liquid crystals presents a global view from above. Different structures have been observed in different states of thermal conditions, which describe the evolution of the convection. For several cases the color of the liquid crystals can indicate the temperature field in the whole experiment cell. Numerical simulations with a Herschel-Bulkley model have also been discussed in this thesis. The dimensionless parameters are defined approaching the values obtained in the experiments, so that we can compare the numerical results with some of experimental ones

La convection thermique dans les objets naturels de grande taille est associée à de fortes variations de la pression, hydrostatique au premier ordre. C’est le cas pour l’atmosphère de la Terre (et d’autres planètes), les planètes gazeuses géantes, les étoiles, mais aussi l’intérieur des planètes telluriques. De part l’importance des effets de compressibilité, l’approximation de Boussinesq n’y est pas vérifiée et d’autres modèles, comportant également des approximations, sont utilisés : les modèles anélastiques. Toutefois, peu d’expériences ont été réalisées pour les vérifier. Cette thèse présente une expérience dont les paramètres ont été optimisés afin d’obtenir des effets de compressibilité importants en laboratoire. Pour ce faire, une gravité apparente forte est obtenue à l’aide d’une centrifugeuse et du xénon gazeux est utilisé, nous permettant d’atteindre un nombre de dissipation significatif. Ces expériences ont permis l’observation en laboratoire d’un gradient adiabatique de 3 K/cm et d’un exposant de 0,3 pour la loi de puissance caractérisant le transfert thermique turbulent entre le nombre de Nusselt et le nombre de Rayleigh superadiabatique.L’étude des fluctuations de pression et de température montrant que l’écoulement est quasi-geostrophique dû à la forte rotation imposée par la centrifugeuse, un modèle anélastique quasi-géostrophique est développé afin de réaliser des simulations numériques bidimensionnelles relatives à l’expérience
In large natural objects, thermal convection is associated with large pressure differences, mainly due to hydrostatic balance. This is true in the atmosphere of the Earth (and other planets), in gas giant planets, in stars, but also in the interior of telluric planets. Boussinesq approximation is not valid owing to large compressibility effects, and other approximate models can be used to model these objects, like the anelastic approximation. However, very few experiments have been performed to assess these models. In the present PhD thesis, an experiment is shown, with parameters designed to maximize compressibility effects in a laboratory. In this perspective, an enhanced apparent gravity is obtained using a centrifuge, and Xenon gas is used, allowing us to reach a significant dissipation parameter. In our experiments, we have observed an adiabatic gradient of 3~K/cm and the power law between the superadiabatic Rayleigh number and the Nusselt number measuring the turbulent heat transfer is characterized by an exponent 0.3.Measurements of temperature and pressure fluctuations show that the flow is quasi-geostrophic as a result of the strong rotation rate of the centrifuge. An anelastic, quasi-geostrophic model has then been developed and solved numerically in the same configuration as the experiments

Cette thèse est dédiée à l’étude analytique et numérique des instabilités d’origine thermique et thermodiffusive de fluides visco-élastiques. L’objectif recherché est de contribuer à la compréhension de la dynamique qui résulte de la compétition entre plusieurs moteurs d’instabilités. En plus du caractère visco-élastique du fluide et de la présence d’un gradient de température vertical déstabilisant, d’autres sources d’instabilités viennent s’y ajouter : Le couplage "convection/écoulement de Poiseuille" d’une part, et le couplage "convection/effet Soret" inhérent aux mélanges binaires d’autre part. Deux configurations physiques sont alors considérées. La première partie de cette thèse est consacrée aux écoulements de convection mixte de type Rayleigh-Bénard-Poiseuille de fluides visco-élastiques, alors que la deuxième partie concerne l’effet de la thermodiffusion sur les instabilités de ces fluides saturant un milieu poreux. Le choix d’un milieu poreux est essentiellement motivé par la suggestion d’un protocole industriel de séparation possible des constituants d’une solution de polymères
This thesis is dedicated to analytical and numerical study of thermal and thermodiffusive instabilities of viscoelastic fluids. The objective is to contribute to the understanding of the dynamics that results from the competition between different origins of instabilities. In addition to the viscoelastic nature of the fluid and the presence of a destabilizing vertical temperature gradient, other sources of instabilities have to be added: the coupling "convection/Poiseuille flow" on the one hand, and the coupling "convection/Soret effect" inherent to binary mixtures on the other hand. Two physical configurations are then considered. The first part of this thesis will be devoted to the Rayleigh-Bénard-Poiseuille mixed viscoelastic fluid convection, while the second part aims to identify the effect of thermodiffusion and viscoelasticity on convective instabilities in a porous medium. The choice of a porous medium in the second part is primarily motivated by the suggestion of an industrial protocol for separating the constituents of a polymer solution

A linear stability analysis of buoyancy and surface tension driven convection in temperature and magnetic field sensitive Newtonian ferromagnetic liquid is studied. The importance of this problem lies in the interesting possibility of regulating convection using a heat source (sink). The problem discussed in this paper leads to a situation that the basic temperature gradient here is non-uniform. The governing equations thereby are of variable coefficients. The principle of exchange of stabilities is shown to be valid. The critical values are obtained using higher order Galerkin technique. The influence of various magnetic and nonmagnetic parameters on the onset of convection has been analyzed. It is found that there is tight coupling between Rayleigh and Marangoni numbers, with an increase in one resulting in a decrease in the other. Variable viscosity parameter and heat source destabilize the system. The effect of heat sink is to stabilize the system. Buoyancy magnetization parameter destabilizes the system both in presence/absence of heat source/sink.

Rayleigh-Bénard and Marangoni convection in a layer of a homogeneous fluid with a free surface in the absence of phase change is a classic (and extensively studied) problem of fluid mechanics. Phase change has a major effect on the convection problem. Most notably, significant latent heat generated at the free surface as a result of phase change can dramatically alter the interfacial temperature, and hence, the thermocapillary stresses. Furthermore, differential evaporation in binary fluids can lead to considerable variation in the concentration field, producing solutocapillarity stresses, which can compete with thermocapillarity and buoyancy. This talk describes numerical studies of convection in alcohol and alcohol-water mixtures due to a horizontal temperature gradient in the presence of phase change. We illustrate how the composition of the liquid and the presence of non-condensable gases (e.g., air) can be used to alter the balance of the dominant forces. In particular, by adding or removing air from the test cell, the direction of the flow can be reversed by emphasizing either the thermocapillary or the solutocapillary stresses.