Convection in a Boussinesq fluid confined by a annular channel fast rotating about a vertical axis and uniformly heated from below, is one of our concerns in this thesis. An assumption that the channel has a sufficiently large radius in comparison with its gap-width is employed, so that the curvature effect can be neglected. The aspect ratio of the channel has great influence on the convective flow in it. Guided by the result of the linear stability analysis, we perform three-dimensional numerical simulations to investigate the convective flows under three different types of aspect ratios, which are namely the moderate or large aspect ratios, the very small aspect ratios and the moderately small aspect ratios. Also, we numerically study how convection in the channel is affected by inhomogeneous heat fluxes on sidewalls, which is a simple simulation of the thermal interaction between the Earth's core and mantle. Convection and dynamo action in a rapidly rotating, self-gravitating, Boussinesq fluid sphere is the other concern. We develop a finite element model for the dynamo problem in a whole sphere. This model is constructed by incorporating dynamo equations with globally implemented magnetic boundary conditions to a whole sphere convection model, which is also presented here. The coordinate singularity at the center usually encountered when applying the spectral method is no longer an obstacle and no nonphysical assumptions (i.e. hyper-diffusivities) are used in our model. A large effort has been made to efficiently parallelize the model. Consequently, it can take the full advantage of modern massively parallel computers. Based on this dynamo model, we investigate the dynamo process in a sphere and find that self-sustaining dynamos are more difficult to obtain in a sphere than in a spherical shell. They are activated at relatively high Rayleigh numbers. Moreover, the magnetic fields generated are not dipole-dominant, different from those generated in most dynamo simulations.

Laminar natural convection heat transfer from the vertical surface of a cylinder is a classical subject, which has been studied extensively. Furthermore, this subject has generated some recent interest in the literature. In the present investigation, numerical experiments were performed to determine average Nusselt numbers for isothermal vertical cylinders (103 < RaL < 109, 0.5 < L/D <10, and Pr = 0.7) with and without an adiabatic top in a quiescent ambient environment which will allow for plume growth. Results were compared with commonly used correlations and new average Nusselt number correlations are presented. Furthermore, the limit for which the heat transfer results for a vertical flat plate may be used as an approximation for the heat transfer from a vertical cylinder was investigated.

L'objectif de cette thèse est de contribuer à la simulation numérique des transferts de chaleur par conduction dans les parois, par rayonnement et par convection thermosolutale dans des cavités fermées ou dans des conduites. Dans la plupart des cas pratiques, les trois modes de transfert de chaleur sont fortement couplés lorsque le fluide en mouvement est un mélange de gaz. Le transfert de chaleur par convection naturelle associé à la condensation surfacique dans une cavité à deux dimensions, remplie d'air humide a été étudié numériquement. Les parois verticales, d'épaisseur finie, sont en contact avec une ambiance extérieure froide. La modélisation faiblement compressible permet à la fois de tenir compte de la diminution de la masse du mélange et de la pression thermodynamique. Egalement, une étude de la convection mixte associée à l'évaporation d'un film liquide ruisselant sur les deux parois d'un canal vertical a été menée. Les effets des forces d'Archimède thermique et solutale sur le développement de l'écoulement ont été montrés. Les résultats ont été obtenus en considérant que les propriétés du mélange sont constantes ou basées sur la règle d'un tiers. Deux mélanges binaires de gaz parfaits air-vapeur et air-hexane ont été considérés en vertu de diverses conditions aux limites / The purpose of this thesis is the contribution to the numerical simulation of heat transfer by conduction, radiation and thermosolutal convection in a closed cavity or in a vertical channel. In most practical cases, the three modes of heat transfer are strongly coupled when the fluid in motion is a mixture of gases. Heat transfer by natural convection and surface condensation in two-dimensional enclosures in contact with a cold external ambient through a wall of finite thickness was studied numerically. Special attention was given on the modeling of the flow of a binary mixture consisting of humid air. Low-Mach number assumption was introduced in order to account for decreases in mixture mass and average pressure within the enclosure between the initial and steady states. Also, a numerical investigation was conducted to study mixed convection in a vertical channel with evaporation of thin liquid films on wetted walls. The effects of the thermal and solutal buoyancy forces on the flow field, heat and mass transfer are illustrated. Results were obtained both for variable and for constant properties using the one-third rule. Air-water vapor and air-hexane vapor mixtures, assumed as ideal gases, are considered under various boundary conditions

A theoretical treatment of the problem of unsteady turbulent free convection over a vertical flat plate is presented in this dissertation. An exhaustive review of the relevant publications revealed, that at the present time no solution of this problem has been given. The development of a method, by which the abovementioned problem could be tackled, is a substantial part of the dissertation. The equations of conservation of mass, momentum, and energy, written in a general form, were the starting point of the derivation. Various assumptions, simplifying the partial differential equations, were introduced. In the end, boundary layer equations were obtained. Turbulence was simulated by a phenomenological model, consisting of an algebraic law of the wall and a partial differential rate equation. The turbulence model is based on the concept of effective viscosity. Also, a constant turbulent Prandtl number was employed. The problem of an isothermal plate in a stagnant non-stratified fluid was treat; d, and appropriate initial and boundary conditions were formulated„ The system of equations was solved by an explicit finite- difference method. The numerical stability criteria were established. A computer programme, based on the numerical scheme, was developed and employed for calculations. The calculations were carried out for dry air, water, and mercury, representing gases, liquids, and liquid metals, respectively. In this way, a broad range of Prandtl numbers was covered. Temperature velocity, and effective viscosity profiles are presented here together with some other results of the calculations* An important observation is that the overall heat transfer coefficient goes through a temporary minimum before attaining its steady state value. The transient, which is extremely fast, can be divided into throe characteristic stages: the initial conduction regime, an intermediate stage, and the steady state. Our results were verified by comparison with data available from other independent sources. Due to the lack of data covering ■the whole transient, only the first and third stages were considered, The initial conduction regime was compared with an analytical solution and the final steady state results with experimental data of various authors, respectively. The agreement is good and no serious discrepancies were discovered. Although the present method produces reliable results, it cannot be widely employed, because the computing times are almost prohibitive with the present-day computers.

Les modèles d'ascendance convective utilisés actuellement dans les paramétrisations de la convection ne prennent pas en compte explicitement le terme de pression non-hydrostatique, bien que son rôle fondamental soit documenté et expliqué depuis les années 70. Pour palier cette limitation, un modèle anélastique pronostique à deux colonnes d'une ascendance convective,prenant en compte explicitement le terme de pression non-hydrostatique, a été développé avec une géométrie 2D et 3D. Des fonctions de forme sont introduites pour réduire l'impact de la basse résolution horizontale. Trois paramètres doivent être prescrits : la hauteur et le rapport d'aspect de l'ascendance ainsi que la taille totale de la cellule convective. Le modèle est évalué en utilisant des profils de flottabilité idéalisés et constants, puis en s'appuyant sur une simulation LES de développement diurne de la convection profonde. Le comportement du modèle est en accord avec notre connaissance de la pression non hydrostatique à l'intérieur des nuages et de son rôle.L'ascendance simulée atteint rapidement un état stationnaire (5 min) en réponse au champ de flottabilité. Ainsi une version diagnostique a été développée, confirmant les résultats de la version pronostique. Sous le cœur de l'ascendance, un gradient de pression dirigé vers le bas est simulé permettant à l'ascendance de franchir la barrière d'inhibition convective. La future implémentation de ce modèle dans un schéma de convection, pour remplacer les formulations des modèles d'ascendance actuelles, devrait permettre d'augmenter la durée des évènements convectifs.

In this thesis, we attempt to address some of these questions. First, we have devised a scheme to extract information of the plumes from simultaneous velocity and temperature measurements. Our method makes explicit use of the physical intuition that the velocity of the buoyant structures, e.g. plumes, should be related to the temperature fluctuation, in some apriori unknown manner as they are generated by buoyancy. Our scheme involves a decomposition of the local velocity measurement into two parts. The part that is correlated with some function of the temperature fluctuation measured at the same time is taken as the velocity of the plumes. Applying this scheme to measurements taken at the center and near the sidewall of the convection cell where the dominant buoyant structures are plumes, we have found the temperature dependence of the plume velocity at these two locations and understood our results from the equations of motion. Using these results of the temperature dependence of the plume velocity, we (i) conclude that heat is not mainly transported through the central region of the convection cell and (ii) obtain a relation between the scaling behavior of the plume velocity structure functions and the temperature structure functions that is different from what is implied by Bolgiano-Obukhov scaling. Then we have studied the possible effects of the large-scale mean circulation on the velocity and temperature statistics using simplified shell models of turbulent convection. We have introduced a large-scale mean flow into two shell models and found that its presence does not change the scaling behavior of velocity and temperature. / In turbulent thermal convection, velocity and temperature measurements taken at a point display complex fluctuations in time. On the other hand, visualization of the flow reveals recurring coherent structures. One prominent flow structure is a plume, which is generated from the thermal boundary layers by buoyancy. Another flow structure is a large-scale mean circulation that spans the entire convection cell. At least two strategies can be employed to study turbulent thermal convection or turbulent flows in general. One is to analyze and understand the fluctuations of the local measurements. The other is to characterize the coherent structures and study and understand their dynamics. These two approaches are not independent but provide complementary knowledge of the flows. Interesting questions hence include whether and how information about the ordered flow structures can be extracted from the fluctuating local measurements and how the presence of the ordered flow structures might affect the statistics of the fluctuations. / Guo, Hao = 热对流湍流中的统计特性与结构 / 郭昊. / "January 2007." / Source: Dissertation Abstracts International, Volume: 68-09, Section: B, page: 6036. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 62-66). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Title and abstract in English and Chinese. / School code: 1307. / Guo, Hao = Re dui liu tuan liu zhong de tong ji te xing yu jie gou / Guo Hao.

Ni, Rui = 關于Kolmogorov常數以及湍流熱對流中能量耗散率、加速度統計、環流反轉研究 / 倪睿. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 105-119). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Ni, Rui = Guan yu Kolmogorov chang shu yi ji tuan liu re dui liu zhong neng liang hao san lu, jia su du tong ji, huan liu fan zhuan yan jiu / Ni Rui.

本論文將詳述對湍流熱對流系統改變邊界條件的三組實驗。 / 第一組實驗中，在寬高比等於1 的圓柱形對流槽中，通過平滑板和由金字塔狀規則排列的粗糙表面的板的組合，我們對五個對流槽進行測量。对實驗測量得到Nu 和Ra 的关系式，进行两个指数函数关系式的叠加--分别是由GL 模型提出的主体主导的（1/2）指数和边界层主导的(1/4)指数关系式。两个关系式的系数之比表明，粗糙板可以提高主体的贡献，而且将系统从边界层主导转变到主体主导。而對各個板上的測量顯示，改變平板的條件，比如恒定熱量或者恒定溫度條件，以及同一個對流槽中另外一塊板是否粗糙板，該平板的傳熱沒有發生變化。而對於粗糙版，讓它處於恒定熱量或者恒定溫度條件，得到不同的結果；同一個槽中另外一塊板是平板或者粗糙板，該粗糙板的傳熱也會受影響。 / 第二組實驗中，在平滑板组成的对流槽，和两块粗糙板组成的对流槽中，我们添加高分子聚合物，进一步研究添加的效果。对于平滑板的对流槽，研究观察到热传递效率Nusselt 数在添加聚合物之后降低。而且，添加的聚合物越多，Nu 降低越多，在聚合物浓度大约120ppm 的时候，Nu 降低了接近12%，而且保持不变。而对于粗糙板组成的对流槽，当聚合物浓度大于120ppm 的时候，Nu 提高了大约4%。 / 第三組實驗，在两块平滑板组成的圆柱形对流槽中，我们也对底板边界层内的速度场进行了实验测量。结果表明，在倾斜角度小于1°的时候，速度边界层的厚度δ[subscript v]与雷诺数的指数关系，与理论给的平流边界层的结果接近。当倾斜角度比较大的时候，边界层厚度与雷诺数的指数随着角度减小。 在不同瑞利数下，同一个倾斜角度时，测量得到的水平速度剖面通过标准化后，得到的形状是一致不变的。而对于不同的角度，标准化的形状之间，是有区别的。 / In this thesis three sets of experiments of turbulent Rayleigh-Bénard convection with modified boundary conditions are presented. / The first set of measurements were made in cylindrical cells with aspect ratio one and with various combinations of smooth and rough plates in the form of regularly-arrayed pyramids. The experimental results suggest that the Nu - Ra relationship can be represented by the combination of two power laws, corresponding to the bulk dominant regime (exponent=1/2) and boundary layer dominant one (exponent=1/4) of the Grossmann-Lohse model. The behaviors of the coefficients of the two power laws suggest that the roughness of the plate can enhance the contribution of bulk and push the system to change from the boundary dominant state to bulk dominant state. A further examination of the individual plates reveal that the heat transport properties of smooth plates are insensitive to the surface and boundary conditions of the other plate of the same cell, whether smooth or rough, or whether under constant flux or constant temperature. The heat transport properties of the rough plates, on the other hand, appear to depend on surface and boundary conditions of the other plate of the same cell. / In the second set of experiments we study the effect of polymer additives in two Rayleigh-Bńard convection cells, one with smooth top and bottom plates and the other with rough top and bottom plates. For the cell with smooth plates, a reduction of the measured Nusselt number (Nu) was observed. Furthermore, the amount of Nu reduction increases with increasing polymer concentration (c), reaching ~12% for c = 120 ppm and an apparent level-off thereafter. For the cell with rough plates, however, an enhancement (~4%) of Nu was observed when the polymer concentration is greater than 120 ppm. / The third set of experiments investigates the properties of the velocity boundary layer in turbulent Rayleigh-Bénard convection in a cylindrical cell when it is tilted with respect to gravity. It is found that at small tilt angles (θ ≤ 1°), the measured viscous boundary layer thickness δ[subscript v] scales with the Reynolds number Re with an exponent close to that for a Prandtl-Blasius laminar boundary layer. For larger tilt angles, the scaling exponent of δ[subscript v] with Re decreases with θ. The normalized mean horizontal velocity profiles measured at the same tilt angle but with different Ra are found to have an invariant shape. But for different tilt angles, the shape of the normalized profiles is different. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Wei, Ping = 改變邊界條件下的熱湍流對流系統 : 傳熱性質及邊界層的實驗研究 / 韋萍. / "November 2012." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 148-158). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese. / Wei, Ping = Gai bian bian jie tiao jian xia de re tuan liu dui liu xi tong : chuan re xing zhi ji bian jie ceng de shi yan yan jiu / Wei Ping. / Table of Contents --- p.vii / List of Figures --- p.xxii / List of Tables --- p.xxiv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background of Turbulence --- p.1 / Chapter 1.2 --- Rayleigh-Bénard convection system --- p.4 / Chapter 1.2.1 --- Physical picture --- p.4 / Chapter 1.2.2 --- Structure of Rayleigh-Bénard convection --- p.8 / Chapter 1.2.3 --- Previous investigation about Rayleigh-Bérnard Convection --- p.11 / Chapter 1.3 --- Motivation of the thesis --- p.15 / Chapter 1.4 --- Organization of this thesis --- p.17 / Chapter 2 --- Experimental apparatus and method --- p.18 / Chapter 2.1 --- Experimental apparatus --- p.18 / Chapter 2.1.1 --- The convection cell with smooth conducting plate --- p.18 / Chapter 2.1.2 --- The rough conducting plate --- p.20 / Chapter 2.2 --- Experimental techniques --- p.21 / Chapter 2.2.1 --- Temperature measurements --- p.21 / Chapter 2.2.2 --- Particle Image Velocimetry (PIV) --- p.23 / Chapter 2.3 --- Correction of heat flux measurment --- p.25 / Chapter 3 --- Convective Heat Transfer in Bulk- and Boundary-Dominated Regimes in Turbulent Thermal Convection --- p.28 / Chapter 3.1 --- Introduction --- p.29 / Chapter 3.2 --- Apparatus and experimental method --- p.31 / Chapter 3.3 --- Results and discussion --- p.34 / Chapter 3.3.1 --- Homogenity of temperature measurement over plate --- p.34 / Chapter 3.3.2 --- The heat transport measurement Nu --- p.40 / Chapter 3.3.3 --- Different heat transport behaviors over smooth and rough plates --- p.41 / Chapter 3.3.4 --- Fluctuations of local temperature --- p.47 / Chapter 3.3.5 --- Velocity and Reynolds number measurement --- p.48 / Chapter 3.3.6 --- Comparison with theoretical model and understanding . --- p.50 / Chapter 3.4 --- Summary --- p.52 / Chapter 4 --- Enhanced and Reduced Heat Transport in Turbulent Thermal Convection with Polymer Additives --- p.54 / Chapter 4.1 --- Introduction --- p.55 / Chapter 4.2 --- Experimental setup and methods --- p.58 / Chapter 4.2.1 --- The convection cell and experimental parameters --- p.58 / Chapter 4.2.2 --- Characterization of Polymer --- p.59 / Chapter 4.2.3 --- Measurement of the polymer solution viscosity --- p.62 / Chapter 4.3 --- Results --- p.65 / Chapter 4.3.1 --- The Nusselt number measurement --- p.65 / Chapter 4.3.2 --- Fluctuations of Nu and the local temperature --- p.72 / Chapter 4.3.3 --- Velocity and Reynolds number behavior --- p.83 / Chapter 4.4 --- Discussions --- p.90 / Chapter 4.5 --- Summary --- p.94 / Chapter 5 --- Viscous boundary layer properties in turbulent thermal convection in a cylindrical cell: the effect of cell tilting --- p.97 / Chapter 5.1 --- Introduction --- p.98 / Chapter 5.1.1 --- Boundary layer measurements in turbulent thermal convection --- p.98 / Chapter 5.1.2 --- Organization of the chapter --- p.102 / Chapter 5.2 --- Experimental apparatus --- p.103 / Chapter 5.2.1 --- Convection cell --- p.103 / Chapter 5.2.2 --- PIV measurement --- p.104 / Chapter 5.3 --- Results and discussion --- p.104 / Chapter 5.3.1 --- Temperature profile and fluid properties --- p.106 / Chapter 5.3.2 --- Velocity profiles and the Reynolds number scaling --- p.106 / Chapter 5.3.3 --- The viscous boundary layer and its scaling with Ra and Re --- p.114 / Chapter 5.3.4 --- Fluctuations and statistical properties of the velocity field in the boundary layer --- p.121 / Chapter 5.3.5 --- Properties of shear stresses and near-wall quantities --- p.125 / Chapter 5.3.6 --- Dynamical scaling and the shape of velocity profiles in the boundary layer --- p.130 / Chapter 5.4 --- Summary --- p.138 / Chapter 6 --- Conclusion --- p.141 / Chapter 6.1 --- Conclusion of our work --- p.141 / Chapter 6.1.1 --- Comparison of the thermal convection with modified plates --- p.142 / Chapter 6.1.2 --- The effect of polymer additives in smooth and rough cells --- p.143 / Chapter 6.1.3 --- Velocity field with tilting angles --- p.144 / Chapter 6.2 --- Perspectives for further investigation --- p.146 / Bibliography --- p.148

Thesis (Sc.D.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, 1979. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Vita. / Bibliography: leaves 274-279. / Sc.D.

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