Zhao, Xiaozheng = 滑移邊界條件下湍流熱對流的實驗研究 / 趙晓争. / "September 2010." / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 52-57). / Abstracts in English and Chinese. / Zhao, Xiaozheng = Hua yi bian jie tiao jian xia tuan liu re dui liu de shi yan yan jiu / Zhao Xiaozheng. / Abstract --- p.i / 摘要 --- p.ii / Acknowledgement --- p.iv / Contains --- p.iv / List of Figures --- p.vii / List of Tables --- p.xi / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Turbulence --- p.1 / Chapter 1.2 --- Turbulent Rayleigh-Benard Convection --- p.2 / Chapter 1.2.1 --- Physical Picture --- p.2 / Chapter 1.2.2 --- Governing Equations and Characteristic Parameters --- p.5 / Chapter 1.2.3 --- Nu Scaling --- p.7 / Chapter 1.2.4 --- Boundary Layer --- p.8 / Chapter 1.3 --- Motivations of the Present Work --- p.10 / Chapter 2 --- Experimental Setup --- p.13 / Chapter 2.1 --- The Convection Cell --- p.13 / Chapter 2.2 --- Temperature Probe and Translation Stage --- p.15 / Chapter 2.3 --- Calibration of the Thermistors --- p.17 / Chapter 2.4 --- Data Acquisition Units --- p.18 / Chapter 2.5 --- The Working Fluids --- p.19 / Chapter 2.6 --- Heat Leakage Prevention --- p.21 / Chapter 3 --- Heat Transfer and Thermal Boundary Layer Measurement --- p.23 / Chapter 3.1 --- The Setup and Experimental Procedure --- p.23 / Chapter 3.2 --- The Mean Temperature and Temperature Fluctuation Profiles across the Interfaces --- p.24 / Chapter 3.2.1 --- Profiles across the Water-FC77 Interface --- p.24 / Chapter 3.2.2 --- Profiles across the FC77-Mercury Interface --- p.27 / Chapter 3.3 --- Nu Results --- p.29 / Chapter 3.3.1 --- Results Obtained with Assumption of Pure Conduction --- p.30 / Chapter 3.3.2 --- Results from Mean Temperature Profile --- p.32 / Chapter 3.3.3 --- Comparison of the Two Methods --- p.33 / Chapter 3.4 --- Boundary Layer Thickness --- p.37 / Chapter 3.5 --- Summary --- p.39 / Chapter 4 --- Influence of Flow in the Water (Mercury) Layer on the FC77 Layer --- p.41 / Chapter 4.1 --- Experimental Setup --- p.41 / Chapter 4.2 --- Main Results --- p.42 / Chapter 4.3 --- Probability Density Function and Temperature Oscillation --- p.44 / Chapter 4.4 --- Summary --- p.50 / Chapter 5 --- Conclusions and Perspective --- p.51 / Chapter 5.1 --- Conclusions --- p.51 / Chapter 5.2 --- Perspective for Future Work --- p.52

Cai, Debin = 高普朗特數湍流對流中速度場和溫度場能量級串傳遞的實驗研究 / 蔡德斌. / "September 2010." / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (p. 84-88). / Abstracts in English and Chinese. / Cai, Debin = Gao pu lang te shu tuan liu dui liu zhong su du chang he wen du chang neng liang ji chuan chuan di de shi yan yan jiu / Cai Debin. / Abstract (in English) --- p.i / Abstract (in Chinese) --- p.ii / Acknowledgements --- p.iii / Contents --- p.iv / List of Figures --- p.vi / List of Tables --- p.xv / Chapters / Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Turbulence --- p.1 / Chapter 1.2 --- Turbulent Rayleigh-Benard Convection --- p.2 / Chapter 1.3 --- Small-Scale Properties of Turbulent Convection --- p.6 / Chapter 1.4 --- Motivations and structure of this thesis --- p.9 / Chapter 1.4.1 --- Motivations --- p.9 / Chapter 1.4.2 --- Organization of this thesis --- p.15 / Chapter 2. --- Experimental apparatus and techniques --- p.16 / Chapter 2.1 --- Turbulent Rayleigh-Benard convection cell --- p.16 / Chapter 2.2 --- The working fluid 1-Pentanol --- p.20 / Chapter 2.3 --- Technique and instruments in temperature structure function measurement --- p.21 / Chapter 2.3.1 --- Temperature detecting probe --- p.22 / Chapter 2.3.2 --- Electronic instruments for temperature measurement --- p.25 / Chapter 2.4 --- Technique and instruments in velocity structure function measurement --- p.28 / Chapter 3. --- Cascades of Temperature Fluctuations in High Prandtl Number Turbulent Convection --- p.31 / Chapter 3.1 --- Selection of the experimental parameters --- p.31 / Chapter 3.2 --- Temperature structure function at the cell centre --- p.33 / Chapter 3.2.1 --- Experiment arrangements --- p.34 / Chapter 3.2.2 --- Experiment results of temperature structure function at the cell centre --- p.37 / Chapter 3.3 --- Temperature structure function near the cell sidewall --- p.43 / Chapter 3.4 --- Intermittency in the high Pr number system --- p.49 / Chapter 3.5 --- Summary --- p.51 / Chapter 4. --- Cascades of Velocity Fluctuations in High Prandtl Number Turbulent Convection --- p.52 / Chapter 4.1 --- Experiment technique --- p.52 / Chapter 4.2 --- Velocity structure function at the cell centre --- p.54 / Chapter 4.2.1 --- Analysis with time average method only --- p.55 / Chapter 4.2.2 --- Homogeneity and isotropy at the cell centre --- p.61 / Chapter 4.2.3 --- Analysis with spatial average method --- p.65 / Chapter 4.3 --- Velocity structure function near the sidewall --- p.70 / Chapter 4.4 --- Summary --- p.75 / Chapter 5. --- Comparison between Different Experiments --- p.77 / Chapter 5.1 --- Comparison between High and Low Pr Number Cases --- p.77 / Chapter 5.2 --- Comparison between the Temperature and Velocity Structure Function Measurements in High Pr number System --- p.80 / Chapter 6. --- Conclusion --- p.82 / References --- p.84

Chan, Tak Shing = 粗糙表面的熱湍流對流的Nusselt數和雷諾數的測量 / 陳德城. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (p. 63-67). / Abstracts in English and Chinese. / Chan, Tak Shing = Cu cao biao mian de re tuan liu dui liu de Nusselt shu he Leinuo shu de ce liang / Chen Decheng. / Table of Contents --- p.v / List of Figures --- p.xi / List of Tables --- p.xii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- What is turbulence ? --- p.1 / Chapter 1.2 --- Rayleigh Benard convection system --- p.3 / Chapter 1.2.1 --- Oberbeck-Boussinesq approximation and equations of Rayleigh- Benard system --- p.5 / Chapter 1.2.2 --- Some coherent structures of Rayleigh-Benard convection system --- p.7 / Chapter 1.3 --- Motivation --- p.8 / Chapter 2 --- Experimental methods and setups --- p.12 / Chapter 2.1 --- Convection cell --- p.12 / Chapter 2.2 --- Temperature measurement --- p.15 / Chapter 2.3 --- Experimental techniques --- p.16 / Chapter 2.3.1 --- Heat leakage prevention --- p.16 / Chapter 2.3.2 --- Water absorption of Dipropylene Glycol --- p.21 / Chapter 2.3.3 --- Particle Image Velocimetry --- p.22 / Chapter 3 --- Heat flux measurement --- p.25 / Chapter 3.1 --- Water Results --- p.26 / Chapter 3.1.1 --- Experimental procedures --- p.26 / Chapter 3.1.2 --- Heat leakage/ heat absorption estimation --- p.27 / Chapter 3.1.3 --- Results and discussions --- p.29 / Chapter 3.2 --- Dipropylene Glycol Results --- p.32 / Chapter 3.2.1 --- Experimental procedures --- p.32 / Chapter 3.2.2 --- Heat leakage/ heat absorption estimation --- p.33 / Chapter 3.2.3 --- Result and discussions --- p.34 / Chapter 3.3 --- More discussion --- p.41 / Chapter 4 --- Large scale circulation and Reynolds number measurement --- p.44 / Chapter 4.1 --- Flow pattern of turbulent Rayleigh-Benard convection over rough plates --- p.46 / Chapter 4.2 --- Reynolds number measurement --- p.48 / Chapter 4.2.1 --- Reynolds number determined from oscillation of temper- ature signals --- p.48 / Chapter 4.2.2 --- Reynolds number determined from velocity measurement near sidewall --- p.55 / Chapter 5 --- Conclusion --- p.61 / Chapter 5.1 --- Conclusion --- p.61 / Bibliography --- p.63

In the field of metal casting, solute composition inhomogeneities at the macroscale are called macrosegregation, and the transition from the elongated grains in the outer portions of a casting to the more rounded grains in the center is termed Columnar to Equiaxed Transition (CET). Simultaneous prediction of macrosegregation and CET is still an important challenge in the field. One of the open questions is the role of melt convection on the CET and the effect of the CET on macrosegregation. A three-phase macroscale model for macrosegregation and CET was developed. The model accounts for numerous phenomena such as columnar dendrite tip undercooling, undercooling behind the columnar tips, and nucleation of equiaxed grains. This three-phase model was used to develop a less complex model that consists of two phases only and disregards undercooling behind the columnar tips and nucleation of equiaxed grains. An in-house parallel computing code on the OpenFOAM platform was developed to solve the equations of these models. The models were used to perform columnar solidification simulations of a numerical benchmark problem. It was found that the predictions of these models are nearly identical. It was also found that the dendrite tip selection parameter, which appears in the constitutive relation for the dendrite tip velocity, plays a key role in these models. With a realistic value for this parameter these models account for columnar dendrite tip undercooling, but as its value is increased in the simulations, predictions of these models converge to predictions of a model that neglects undercooling. Next, the three-phase model was used to perform CET simulations in the numerical solidification benchmark problem in the presence of melt convection. It was found that accounting for stationary equiaxed grains does not change the overall macrosegregation pattern nor the form of channel segregates. Finally, for the first time in the field of solidification, we developed accurate constitutive relations for macroscale solidification models that are based on a formal mesoscale analysis on the scale of a representative elementary volume that is used in developing volume-averaged macroscale models. This upscaling enabled us to present relations that incorporate changes in the shape of grains and solute diffusion conditions around them during growth. The models and constitutive relations we developed can now be used to predict critical phenomena such as macrosegregation, channel segregates, and CET in castings.

A computational fluid dynamics (CFD) validation experiment is conducted for convection flow from a heated plate in buoyancy aided and opposed orientations. The design of the experiment to meet CFD validation completeness standards is described. Previous experiments and simulations have been completed, but none measure or present to necessary boundary conditions to define the simulation boundary conditions. Experimental measurements of forced and mixed convection are presented, along with measured boundary conditions sufficient to compute simulations for validations purposes. Some simulation results are described, but a complete validation study is not included. Simulations are conducted to ensure all necessary boundary conditions are being measured. This document and the corresponding website will provide sufficient explanation and data to repeat the experiment and sped the setup of future validation experiments. The data and boundary conditions are available for download on a website dedicated to validation data dissemination. Along with the validation data, the response quantities provide some insight into the flow characteristics of the boundary layer for convective flow from a vertical flat plate.

Natural convection is a phenomenon that occurs in a wide range of applications such as cooling towers, air conditioners, and power plants. Natural convection may be used in decay heat removal systems such as spent fuel casks, where the higher reliability inherent of natural convection is more desirable than forced convection. Passive systems, such as natural convection, may provide better safety, and hence have received much attention recently. Cooling of spent fuel rods is conventionally done using water as the coolant. However, it involves contaminating the water with radiation from the fuel rods. Contamination becomes dangerous and difficult for humans to handle. Further, the recent nuclear tragedy in Fukushima, Japan has taught us the dangers of contamination of water with nuclear radiation. Natural convection can perhaps significantly reduce the risk since it is self-sufficient and does not rely on other secondary system such as a blower as in cases of forced convection. The Utah State University Experimental Fluid Dynamics lab has recently designed an experiment that models natural convection using heated rod bundles enclosed in a rectangular cavity. The data available from this experiment provides and opportunity to study and validate computational fluid dynamics(CFD)models. The validated CFD models can be used to study multiple configurations, boundary conditions, and changes in physics(natural and/or forced convection). The results are to be validated using experimental data such as the velocity field from particle image velocimetry (PIV), pressure drops across various sections of the geometry, and temperature distributions along the vertically heated rods. This research work involves modeling natural convection using two-layer turbulence models such as k - ε and RST (Reynolds stress transport) using both shear driven (Wolfstein) and buoyancy driven (Xu) near-wall formulations. The interpolation scheme employed is second-order upwinding using the general purpose code STAR-CCM+. The pressure velocity coupling is done using the SIMPLE method. It is ascertained that turbulence models with two-layer formulations are well suited for modeling natural convection. Further it is established that k - ε and Reynolds stress turbulence models with the buoyancy driven (Xu)formulation are able to accurately predict the flow rate and temperature distribution.

This study presents the numerical analysis of steady laminar flow heat transfer in a horizontal rectangular duct with differential heating on the vertical walls. Three heating configurations: one uniform wall temperature (CS1) and two linearly varying wall temperature cases (CS2 and CS3) are analysed. The study considers the combined effects of natural convection, forced convection and radiation heat transfer on the overall heat transfer characteristics. Air, which is assumed to be a non-participating medium, is chosen as the working fluid. A computational fluid dynamics solver is used to solve a set of governing equations for a range of parameters.For chosen duct aspect ratios, the numerical model simulates the flow and heat transfer for two main effects: buoyancy and radiation heat transfer. Buoyancy effect is represented by Grashof number, which is varied from 2,000 to 1,000,000. The effect of radiation heat transfer is examined by choosing different wall surface emissivity values. The weak and strong radiation effect is represented by the emissivity values of 0.05 and 0.85 respectively. Three duct aspect ratios are considered - 0.5, 1 and 2. The heat transfer characteristics of all the above heating configurations - CS1, CS2, and CS3 are analysed and compared. The numerical results show that, for all heating configurations and duct aspect ratios, the overall heat transfer rate is enhanced when the buoyancy effect increases. Since buoyancy effect induces natural circulation, this circulation is therefore the main mechanism that enhances heat transfer. Radiation heat transfer is found to significantly influence convection heat transfer in high Grashof numbers.

A parallel numerical method has been implemented for solving the Navier Stokes equations on Cartesian and non-orthogonal meshes. To ensure the accuracy of the code first, second and third order differencing schemes, with and without flux-limiters, have been implemented and tested. The most computationally expensive task in the code is the solution of linear equations, and a number of linear solvers have been tested to determine the most efficient. Krylov space, incomplete factorisation, and other iterative and direct solvers from the literature have been implemented, and have been compared with a novel black-box multigrid linear solver that has been developed both as a solver and as a preconditioner for the Krylov space methods. To further reduce execution time the code was parallelised, after a series of experiments comparing the suitability of different parallelisation techniques and computer architectures for the Navier Stokes solver. The code has been applied to the solution of two classes of problem. Two natural convection flows were studied, with an initial study of two dimensional Rayleigh Benard convection being followed by a study of a transient three dimensional flow, in both cases the results being compared with experiment. The second class of problems modelled were free surface flows. A two dimensional free surface driven cavity, and a two dimensional flume flow were modelled, the latter being compared with analytic theory. Finally a three dimensional ship flow was modelled, with the flow about a Wigley hull being simulated for a range of Reynolds and Froude numbers.

In this thesis I address several topics concerning the interaction of convection and density stratification in oceans and lakes. I present experimental and theoretical investigations of the interaction between a localized buoyancy source and a heat flux through a horizontal boundary, and of the interactions between salt fingers and intermittent turbulence or shear. ¶ An extensive series of laboratory experiments were used to quantify the stratification and circulation that result from the combined presence of a localized buoyancy source and a heat flux through a horizontal boundary. Previous studies found that convection in the form of a turbulent buoyant plume tends to produce a stable density stratification, whereas the distributed flux from a horizontal boundary tends to force vigorous overturning and to produce well-mixed layers. A new result of this thesis is that a steady density profile, consisting of a mixed layer and a stratified layer, can exist when the plume buoyancy flux is greater than the distributed flux. When the two fluxes originate from the same boundary, the steady state involves a balance between the rate at which the mixed layer deepens due to entrainment on the one hand and vertical advection of the stratified water far from the plume (due to the volume flux acquired by entrainment) on the other hand. There is a monotonic relationship between the normalized mixed layer depth and flux ratio R (boundary flux/plume flux) for 0 < R > 1, and the whole tank overturns for R > 1. The stable density gradient in the stratified region is primarily due to the buoyancy from the plume and for R > 0 there is a small increase in the gradient due to entrainment of buoyancy from the mixed layer. For the case of fluxes from a plume located at one boundary and a uniform heat flux from the opposite boundary the shape of the density profile is that given by Baines & Turner (1969), with the gradient reduced by a factor (1 + R) due to the heating. Thus, when R < - 1 there is no stratified region and the whole water column overturns. When 0 > R > - 1, the constant depth of the convecting layer is determined by the Monin-Obukhov scale in the outflow from the plume. ¶ One application of these laboratory experiments is to surface cooling in lakes and reservoirs that have shallow sidearms. During prolonged periods of atmospheric cooling, gravity currents can form in these sidearms and as the currents descend into the deeper waters they are analogous to isolated plumes. This can result in stratification at the base of a lake and an upwelling of cold water. Away from the shallow regions, surface cooling leads to a mixed surface layer. The depth of this layer will be steady when the rate of upwelling balances the rate at which the mixed layer deepens by turbulent entrainment. A series of laboratory experiments designed to model the depth distribution of a lake with a shallow sidearm showed that the steady depth of the mixed layer depended on the ratio of the area of the shallow region to the area of the deep region. Significant stratification resulted only when the reservoir had shallow regions that account for more than 50 % of the surface area. The depth of the surface mixed layer also depended on the ratio of the depths of the shallow and deep regions and no significant stratification forms if this ratio is greater than 0.5. These results are in good agreement with observations of circulation and stratification during long periods of winter cooling from Chaffey reservoir, Australia. Theoretical time scales are also developed to predict the minimum duration of atmospheric cooling that can lead the development of stratification. ¶ In the second part of this thesis, I report a series of laboratory experiments which are designed to investigate the fine structure and buoyancy fluxes that result from salt finger convection in the presence of shear and intermittent turbulence. We find that, when salt finger convection in deep linear gradients is superposed with a depth-dependent spatially periodic shear, variations in the density profile develop on the same wavelength as the shear. The laboratory experiments presented in this thesis were carried out in a continuous density gradient with a spatially periodic shear produced by exciting a low-frequency baroclinic mode of vertical wavelength 60 mm. The density gradient consisted of opposing salt and sugar gradients favourable to salt fingers (an analogue to the oceanic heat/salt system). Where the shearing was large the salt finger buoyancy fluxes were small. Changes in salinity gradient due to the resulting flux divergence were self-amplifying until a steady state was reached in which the spatial variations in the ratio of salt and sugar gradients were such that the flux divergence vanished. Thus, along with reducing the mean salt finger buoyancy flux, a spatially varying shear can also lead to the formation of density structure. ¶ In the ocean intermittent turbulence can occur in isolated patches in salt finger-favourable regions. I present new results from laboratory experiments in which a partially mixed patch was produced in deep linear concentration gradients favourable to salt finger convection. Salt fingers give rise to an “up gradient” flux of buoyancy which can reduce the density gradient in a partially mixed patch. This can then lead to overturning convection of the partially mixed patch if a) the ratio of T and S gradients, R\rho =aTz/_ /betaSz, is near one, b) if turbulence results in a nearly well-mixed patch and c) the patch thickness is large enough that convective eddies are able to transport T and S faster than salt fingers. Once overturning occurs, subsequent turbulent entrainment can lead to growth of the patch thickness. Experimental results agree well with the theoretical prediction that h= \surd 8h B/N2 t, where h is the patch thickness, t is time, h is the mixing efficiency of turbulent entrainment, B is the buoyancy flux of the salt fingers and N is the buoyancy frequency of the ambient gradient region. This thickening is in contrast to the collapse that a partially mixed patch would experience due to lateral intrusion in a very wide tank. In regions of the ocean that contain salt fingers there is the possibility that, after a period of initial collapse, an intrusion could enter a regime where the rate of collapse in the vertical is balanced by the growth rate due to turbulent entrainment from the salt fingers buoyancy flux, thus tending to maintain the rate of lateral spread. ¶ A further series of laboratory experiments quantified the buoyancy fluxes that result from salt fingers and intermittent turbulence. A continuous density gradient, favourable to salt finger convection, was stirred intermittently by an array of vertical rods that move horizontally back and forth along the tank at a constant velocity. Previous experiments had found that continuous turbulence destroys any salt fingers present because the dissipation of turbulent kinetic energy occurs at scales that are generally smaller than salt fingers widths. However, when turbulence is present only intermittently, the salt fingers may have time to grow between turbulent events and so contribute to the vertical diffusivities of heat and salt. We conclude that the vertical buoyancy flux of salt fingers is strongly dependent upon the intermittency of the turbulence, and equilibrium fluxes are only achieved if the time between turbulent events is much greater than the e-folding time of the salt fingers. When these results are applied to an oceanographic setting, the effect of intermittent turbulence, occurring more 5% of the time, is to reduce the effective eddy diffusivity due to salt fingers below equilibrium salt finger values, so that at R\rho > > 2 the eddy diffusivity is due only to turbulence. The time averaged salt fingers fluxes are not significantly reduced by intermittent turbulence when R\rho > 2 or if the intermittence occurs less than 2% of the time, and so may contribute significant diapycnal fluxes in many parts of the ocean.

Cette thèse s'inscrit dans le contexte général de l'étude des processus dynamiques intervenant dans les étoiles tels que la convection, la rotation ou le champ magnétique et de leurs interactions non-linéaires. Les résultats de simulations numériques obtenus avec le code 2D éléments finis STELEM et le code pseudo-spectral 3D ASH sont présentés. La première partie de cette thèse concerne la modélisation globale de la dynamo solaire, mécanisme de régénération du champ magnétique. Via des simulations numériques 2D utilisant la théorie des champs moyens, j'ai pu étudier l'influence d'une circulation méridienne au profil complexe dans les modèles de Babcock-Leighton. Même si ces modèles sont capables de reproduire une période de 22 ans, de nombreuses caractéristiques du cycle telles que la migration des taches solaires vers l'équateur sont perdues. Nous montrons que des doutes peuvent être formulés sur la capacité de ces modèles à rendre compte du fonctionnement réel de la dynamo solaire. Dans l'objectif de mieux contraindre les effets de la variabilité du cycle solaire sur le climat terrestre, nous présentons ensuite un premier effort d'application en physique solaire de techniques de prédiction sophistiquées utilisées en météorologie. J'ai également pu effectuer les premiers calculs MHD 3D en géométrie sphérique d'une des étapes clés de la dynamo : l'évolution non-linéaire de structures magnétiques de la base de la zone convective vers la surface où elles émergent sous forme de régions actives. Les effets globaux de la force de courbure magnétique et des écoulements moyens sont pris en compte. Des champs faibles sont susceptibles d'être modulés par les mouvements convectifs, favorisant ainsi l'émergence à des longitudes privilégiées. Nous montrons qu'il est nécessaire de prendre en compte l'effet de la convection dans l'angle de tilt et non d'expliquer la loi de Joy uniquement par la rotation et la force de Coriolis induite. L'introduction d'une atmosphère dans ces modèles est une étape vers une vision 3D globale du Soleil.