Thèses sur le sujet « High Prandtl »

2007/2008
In this thesis we present the results of an extensive campaign of direct numerical simulations of Rayleigh-B\'enard convection at high Prandtl numbers ($10^{-1}\leq Pr \leq 10^4$) and moderate Rayleigh numbers ($10^{5}\leq Pr \leq 10^9$). The computational domain is a cylindrical cell of aspect-ratio (diameter over cell height) $\Gamma=1/2$, with the no-slip condition imposed to the boundaries. By scaling the results, we find a $1/\sqrt{Pr}$ correction to apply to the free-fall velocity, obtaining a more appropriate representation of the large scale velocity at high $Pr$. We investigate the Nusselt and the Reynolds number dependence on $Ra$ and $Pr$, comparing the results to previous numerical and experimental work. At high $Pr$ the scaling behavior of the Nusselt number with respect to $Ra$ is generally consistent with the power-law exponent $0.309$. The Nusselt number is independent of $Pr$, even at the highest $Ra$ simulated. The Reynolds number scales as $Re\sim \sqrt{Ra}/Pr$, neglecting logarithmic corrections. We analyze the global and local features of viscous and thermal boundary layers and their scaling behavior with respect to Rayleigh and Prandtl numbers, and with respect to Reynolds and Peclet numbers. We find that the flow approaches a saturation regime when Reynolds number decreases below the critical value $Re_s\simeq 40$. The thermal boundary layer thickness turns out to increase slightly even when the Peclet number increases. We explain this behavior as a combined effect of the Peclet number and the viscous boundary layer influences. The range of $Ra$ and $Pr$ simulated contains steady, periodic and turbulent solutions. A rough estimate of the transition from steady to unsteady flow is obtained by monitoring the time-evolution of the system until it reaches stationary solutions ($Ra_U\simeq 7.5 \times 10^6$ at $Pr=10^3$). We find multiple solutions as long-term phenomena at $Ra=10^8$ and $Pr=10^3$ which, however, do not result in significantly different Nusselt number. One of these multiple solutions, even if stable for a long time interval, shows a break in the mid-plane symmetry of the temperature profile. The result is similar to that of some non-Boussinesq effects. We analyze the flow structures through the transitional phases by direct visualizations of the temperature and velocity fields. We also describe how the behavior of the flow structures changes for increasing $Pr$. A wide variety of large-scale circulations and plumes structures are found. The single-roll circulation is characteristic only of the steady and periodic solutions. For other solutions, at lower $Pr$, the mean flow generally consists of two opposite toroidal structures; at higher $Pr$, the flow is organized in multi-cell structures extending mostly in the vertical direction. At high $Pr$, plumes detach from sheet-like structures. The different large-scale-structure signatures are generally reflected in the data trends with respect to $Ra$, but not in those with respect to $Pr$. In particular, the Nusselt number is independent of $Pr$, even when the flow structures appear strongly different varying $Pr$. In order to assess the reliability of the data-set we perform a systematic analysis of the error affecting the data. Refinement grid analysis is extensively applied.
---------------------------------------------------------------------------------------- In questa tesi presentiamo i risultati di un'estensiva campagna di simulazioni numeriche dirette della convezione di Rayleigh-B\'enard ad alti numeri di Prandtl ($10^{-1}\leq Pr \leq 10^4$) e moderati numeri di Rayleigh ($10^{5}\leq Pr \leq 10^9$). Il dominio computazionale \`e una cella cilindrica di allungamento (diametro su altezza cella) $\Gamma=1/2$, con condizioni di non-slittamento ai contorni. Scalando i risultati, troviamo una correzione di $1/\sqrt{Pr}$ da applicare alla velocit\`a di caduta libera, ottenendo una rappresentazione pi\`u appropriata della velocit\`a di larga scala ad elevati $Pr$. Investighiamo la dipendenza del numero di Nusselt e del numero di Reynolds da $Ra$ e $Pr$, comparando i risultati con precedenti lavori numerici e sperimentali. Ad elevati $Pr$ il comportamento di scala del numero di Nusselt rispetto a $Ra$ \`e generalmente compatibile con l'esponente di legge di potenza $0.309$. Il numero di Nusselt \`e indipendente da $Pr$, anche per il pi\`u alto $Ra$ simulato. Il numero di Reynolds scala come $Re\sim \sqrt{Ra}/Pr$, a meno di correzioni logaritmiche. Analizziamo le caratteristiche locali e globali degli strati limite viscosi e termici, ed il loro comportamento di scala rispetto ai numeri Rayleigh e Prandtl, e rispetto ai numeri Reynolds e Peclet. Troviamo che il flusso approccia un regime di saturazione quando il numero di Reynolds scende sotto il valore critico $Re_s\simeq 40$. Lo spessore dello strato limite termico comincia a crescere leggermente anche quando in numero di Peclet aumenta. Spieghiamo questo comportamento come un effetto combinato delle influenze del numero di Peclet e dello strato limite viscoso. L'intervallo di $Ra$ e $Pr$ simulato contiene soluzioni stazionarie, periodiche e turbolente. Una stima approssimata della transizione da flusso stazionario a non stazionario \`e ottenuta monitorando l'evoluzione temporale del sistema fino al raggiungimento di soluzioni stazionarie o statisticamente stazionarie ($Ra_U\simeq 7.5 \times 10^6$ a $Pr=10^3$). Troviamo soluzioni multiple come fenomeni di lungo termine a $Ra=10^8$ e $Pr=10^3$ che, comunque, non comportano differenze significative nel numero di Nusselt. Una di queste soluzioni multiple, anche se stabile per un lungo intervallo di tempo, mostra una rottura della simmetria del profilo di temperatura rispetto al piano mediano. Il risultato \`e simile a quello di alcuni effetti di non-Boussinesq. Analizziamo le strutture del flusso nelle fasi di transizione tramite visualizzazioni dirette dei campi di velocit\`a e temperatura. Descriviamo inoltre come il comportamento delle strutture del flusso cambia al crescere di $Pr$. Un'ampia variet\`a di circolazioni di larga scala e strutture a pennacchio vengono trovate. La circolazione a singolo anello \`e caratteristica solo delle soluzioni stazionarie e periodiche. Per le altre soluzioni, a $Pr$ pi\`u bassi, il flusso medio \`e generalmente composto da due strutture toroidali opposte; a $Pr$ pi\`u alti, il flusso \`e organizzato in strutture multi-cellulari che si estendono maggiormente in direzione verticale. Ad alti $Pr$, pennacchi si staccano da strutture simili a fogli. Le impronte delle differenti strutture di larga scala si riflettono generalmente nell'andamento dei dati rispetto a $Ra$, ma non rispetto a $Pr$. In particolare, il numero di Nusselt \`e indipendente da $Pr$, anche quando le strutture del flusso appaiono molto differenti al variare di $Pr$. Per stabilire l'affidabilit\`a dell'insieme dei dati, effettuiamo un'analisi sistematica degli errori a cui i dati sono soggetti. L'analisi di raffinamento della griglia \`e largamente applicata.
XXI Ciclo
1976

NUMERICAL AND EXPERIMENTAL STUDY OF TRANSIENT LAMINAR NATURAL CONVECTION OF HIGH PRANDTL NUMBER FLUIDS IN A CUBICAL CAVITY
Obai Younis Taha Elamin

La convección natural en espacios cerrados, se encuentra ampliamente en sistemas naturales e industriales. El objetivo general de este trabajo es desarrollar y validar una herramienta de simulación capaz de predecir las tasas de enfriamiento de aceite en un tanque. Esta herramienta ha de tener en cuenta la variación de la viscosidad del aceite para dar información detallada de las tasas de enfriamiento del aceite bajo diferentes condiciones de contorno térmicas realisticas.
En primer lugar, la influencia de diferentes condiciones de contorno térmicas en las paredes, la variación de la viscosidad y la conductividad de la pared en la convección natural del flujo laminar transitorio en una cavidad cúbica con seis paredes térmicamente activo están analizadas.
Para analizar el efecto individual de las paredes laterales de la cavidad en el proceso de enfriamiento, la segunda parte de este estudio considera que, tanto numéricamente como experimentalmente, la transición de la convección natural laminar en una cavidad cúbica con dos paredes opuestas frías y verticales.
Nuevas relaciones de escala que tengan en cuenta la variación de la viscosidad con la temperatura, no publicadas anteriormente en la literatura, se derivan de las velocidades de la capa límite, por el tiempo necesario para la capa límite para alcanzar el estado estacionario y para la velocidad y el espesor de las intrusiones horizontales.
NUMERICAL AND EXPERIMENTAL STUDY OF TRANSIENT LAMINAR NATURAL CONVECTION OF HIGH PRANDTL NUMBER FLUIDS IN A CUBICAL CAVITY
Obai Younis Taha Elamin

Free convection in enclosed spaces is found widely in natural and industrial systems. The general objective of this work is to develop and validate a simulation tool able to predict the cooling rates of oil in a tank. This tool has to take into account the variation of the oil viscosity to give detailed information of the cooling rates of the oil under different realistic thermal boundary conditions.
First, the influence of different thermal wall boundary conditions, the variation of the viscosity and the wall conductivity on the transient laminar natural convection flow in a cubical cavity with the six walls thermally active is studied numerically.
To analyze the individual effect of the side walls of the cavity on the cooling process, the second part of this study considers, numerically and experimentally, the transient laminar natural convection in a cubical cavity with two cold opposite vertical walls. The shadowgraph technique is employed to visualize the development of the transient convective flow. New scaling relations that take into account the viscosity variation with temperature, not reported previously in the literature, are derived for the boundary layer velocities, for the time needed for the boundary layer to reach the steady state and for the velocity and thickness of the horizontal intrusions.

Sirtuins (SIRT) regulate the transcription of various genes involved in the development of diet-induced obesity and chronic disease; however, it is unknown how they change acutely following a high-fat meal. The purpose of this study was to determine the effect of a high-fat meal (65% kcals/d; 85% fat recommendation), on SIRT1-7 mRNA expression in blood leukocytes at 1, 3, and 5-h post-prandial. Men and women (N=24) reported to the lab following an overnight fast (>12H). Total RNA was isolated and reverse transcribed prior to using a Taqman qPCR technique with 18S rRNA as a normalizer to determine SIRT1-7 mRNA expression. An additional aliquot of serum was used to measure triglycerides. Data was analyzed using a RM ANOVA with P<0.05. Triglycerides (P<0.001; 124%) peaked at 3-h. SIRT 1 (P=0.004; 70%), and SIRT 6 (P=0.017; 53%) decreased expression at 3-h. SIRT4 (P=0.024) peaked at 5H relative to baseline (70%) and 3-h (68%). To our knowledge, this is the first study to report that consumption of a high-fat meal transiently alters SIRT mRNA expression consistent in a pattern that mirrors changes in serum triglycerides. Decrease in expression of SIRT1 and SIRT6 combined with an increased SIRT4 would be consistent with an increase in metabolic disease risk if maintained on a chronic basis.

Introdução - Evidências mostram que a ingestão de uma refeição hipercalórica, rica em lipídios e açúcares, provoca elevação da concentração plasmática de glicose e de triacilgliceróis (TG), bem como de lipopolissacarídeos (LPS) no período pós-prandial. Sugere-se que essa condição esteja envolvida na gênese da inflamação subclínica, caracterizada pelo aumento da concentração de biomarcadores pró-inflamatórios na circulação sanguínea, como o fator de necrose tumoral (TNF)-α, interleucina (IL)-1β, IL- 6 e as moléculas de adesão intracelular solúvel (sICAM)-1 e vascular solúvel (sVCAM)- 1, o que contribui para o aumento do risco para doenças cardiovasculares. Estudos recentes sugerem que os microRNA (miRNA) atuam como biomarcadores inflamatórios e a análise da sua expressão no período pós-prandial pode contribuir para a redução do risco de doenças cardiovasculares. Objetivo - Investigar o efeito de uma refeição hiperlipídica, rica em ácidos graxos saturados, sobre a expressão de microRNA e a concentração de LPS no plasma no período pós-prandial em mulheres saudáveis. Métodos - Realizou-se um estudo de intervenção no qual foi oferecido uma refeição matinal com alto teor de lipídios, principalmente, de ácidos graxos saturados, mais 500 mL de água, realizando-se coletas de sangue no período basal e 1, 3 e 5 horas após a ingestão da refeição hiperlipídica. A população do estudo foi composta por mulheres saudáveis (n = 11), com idade entre 20 e 40 anos, e IMC de 18,5 a 25 kg/m². Foram avaliadas as concentrações plasmáticas de glicose, insulina, perfil lipídico e de ácidos graxos, citocinas, moléculas de adesão, MCP-1 e LPS. Analisou-se pelo ensaio de PCR em tempo real, um perfil de expressão de 752 miRNA plasmáticos humanos. Essas análises foram realizadas em todos os tempos da coleta de sangue. Resultados - Houve aumento significativo das concentrações plasmáticas de LPS e TG nos tempos 1, 3 e 5 horas em relação ao período basal. As concentrações plasmáticas de insulina elevaram-se de forma significativa após 1 e 3 horas em comparação ao período basal, e reduziu após 5 h se comparado ao tempo 1 h. Os ácidos graxos saturados plasmáticos mirístico e palmítico aumentaram após o consumo da refeição. Houve aumento das concentrações plasmáticas de TNF-α após 5h se comparado ao basal e ao tempo 1 h. E houve aumento da concentração de sVCAM-1 após 5 h vs o basal. Em relação aos miRNA, 45 miRNA tiveram suas concentrações alteradas se comparadas entre todos os tempos, destes 33 miRNA vs o basal. Conclusões - O aumento de TG e insulina após a refeição hiperlipídica pode contribuir para explicar a participação da dieta no desenvolvimento de um quadro inflamatório, promovido, também, por um quadro de endotoxemia pós-prandial. Junto a isso, os miRNA podem exercer papel importante na regulação deste quadro. Uma refeição hiperlipídica, com elevado teor de ácidos graxos saturados, ocasiona um quadro de endotoxemia metabólica e altera a expressão de microRNA plasmáticos envolvidos na regulação do processo inflamatório no período pós-prandial.
Introduction Evidence shows that a high caloric meal, rich in lipids and carbohydrates, increase glucose and triacyclglycerols (TG) concentrations, furthermore in lipopolysaccharides (LPS) in the postprandial period. This condition is involved with subclinic inflammation genesis, characterized by increased concentration of inflammatory biomarkers in blood circulation, like tumor necrose fator (TNF)-α, interleukin (IL)-1β, IL-6 and soluble intracellular adhesion molecule (sICAM)-1 and soluble vascular (sVCAM)-1, what contributes to rise cardiovascular disease risk. Recent studies indicate that microRNAs (miRNA) act as inflammatory biomarkers and analysis of their expression in the postprandial state could contribute to reduction of cardiovascular disease risk. Objective This study investigates the high-fat high-saturated meal effect above miRNA expression and LPS concentration at the postprandial period in healthy women. Methods An interventional study was carried out in which a breakfast with a high lipid content, mainly of saturated fatty acids, plus 500 mL of water was offered. Blood samples were collected at baseline and 1, 3 and 5 hours after ingestion of the high-fat meal. The study population consisted of healthy women (n = 11), aged between 20 and 40 years, and BMI of 18.5 to 25 kg / m². Plasma concentrations of glucose, insulin, lipid profile and fatty acids, cytokines, adhesion molecules, MCP-1 and LPS were evaluated. An expression profile of 752 human plasma miRNA was analyzed by the real-time PCR assay. These analyzes were performed at all times of blood collection. Results - There was a significant increase in the plasma concentrations of LPS and TG at times 1, 3, 5 hours in relation to the baseline. Plasma insulin concentrations increased significantly after 1 and 3 hours compared to baseline, and decreased after 5 h compared to 1 h. Myristic and palmitic saturated fatty acids increased after consumption of the meal. There was an increase in plasma concentrations of TNF-α after 5 hours compared to the baseline and at 1 h. And there was an increase in sVCAM-1 concentration after 5 hours vs baseline. Regarding the miRNA, 45 miRNA had their concentrations altered when compared among all the times, of these 33 miRNA vs the baseline. Conclusions - The increase of TG and insulin after the high-fat meal may contribute to explain diet participation in the development of an inflammatory condition, also promoted by postprandial endotoxemia. In addition, microRNAs may play a key role in the regulation of this condition. High-fat high-saturated meal generates a metabolic endotoxemia state and changes plasma microRNAs expression which are involved in regulation to inflammatory process in the postprandial period.

Lam Siu = 高普朗特數湍流對流的實驗硏究 / 林霄.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2000.
Includes bibliographical references (leaves 97-100).
Text in English; abstracts in English and Chinese.
Lam Siu = Gao pu lang te shu tuan liu dui liu de shi yan yan jiu / Lin Xiao.
Abstract (in English) --- p.i
Abstract (in Chinese) --- p.ii
Acknowledgements --- p.iii
Table of Contents --- p.iv
List of Figures --- p.vi
List of Tables --- p.ix
Chapters
Chapter I. --- Introduction --- p.1
Chapter II. --- Turbulent Rayleigh-Benard Convection --- p.5
Chapter 2.1 --- Rayleigh-Benard Convection --- p.5
Chapter 2.2 --- The Convection Equations --- p.6
Chapter 2.3 --- The parameters --- p.7
Chapter 2.4 --- Recent Developments --- p.9
Chapter 2.4.1 --- Heat Transport --- p.9
Chapter 2.4.2 --- Large-scale Circulation and thermal Plumes --- p.11
Chapter 2.4.3 --- Boundary Layers --- p.12
Chapter III. --- Experimental Setup and Methods --- p.15
Chapter 3.1 --- The Apparatus --- p.15
Chapter 3.2 --- The Working Fluids --- p.18
Chapter 3.3 --- Thermal Measurements --- p.23
Chapter 3.4 --- Flow Visualization --- p.26
Chapter IV. --- Heat Transport in Turbulent Convection --- p.29
Chapter 4.1 --- The Non-Boussinesq Effect --- p.30
Chapter 4.2 --- Experimental Results --- p.34
Chapter 4.2.1 --- 1-Pentanol --- p.35
Chapter 4.2.2 --- Triethylene Glycol --- p.36
Chapter 4.2.3 --- Results from Dipropylene Glycol --- p.37
Chapter 4.3 --- Discussion on the Results --- p.38
Chapter 4.4 --- Summary --- p.43
Chapter V. --- Local Temperature Measurements --- p.45
Chapter 5.1 --- Temperature Time Series and Histograms --- p.45
Chapter 5.2 --- Mean Temperature Profiles and Thermal Boundary Layers --- p.55
Chapter 5.3 --- RMS Profiles --- p.58
Chapter 5.4 --- Skewness Profiles --- p.65
Chapter 5.5 --- Summary --- p.68
Chapter VI. --- Measurements on the Viscous Boundary Layers --- p.70
Chapter 6.1 --- Power Spectrum --- p.70
Chapter 6.2 --- Two-Probe Cross-correlation --- p.76
Chapter 6.3 --- Laser Light Scattering --- p.84
Chapter 6.4 --- Summary --- p.90
Chapter VII --- . Conclusions --- p.93
References --- p.97

Chan Ho-Sun = 在粗糙表面的高普朗特數湍流對流實驗 / 陳浩新.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2004.
Includes bibliographical references (leaves 69-72).
Text in English; abstracts in English and Chinese.
Chan Ho-Sun = Zai cu cao biao mian de gao Pulangte shu tuan liu dui liu shi yan / Chen Haoxin.
Abstract (in English) --- p.i
Abstract (in Chinese) --- p.ii
Acknowledgements --- p.iii
Table of Contents --- p.iv
List of Figures --- p.vi
List of Tables --- p.viii
Chapters
Chapter 1. --- Introduction --- p.1
Chapter 2. --- Theories about the Convection --- p.7
Chapter 2.1 --- Rayleigh-Benard convection --- p.7
Chapter 2.2 --- The Convection Equations --- p.8
Chapter 3. --- Setup of the Experimental Environment --- p.15
Chapter 3.1 --- The Convection Cell --- p.15
Chapter 3.2 --- Thermistors --- p.19
Chapter 3.3 --- The Working Fluids --- p.22
Chapter 3.4 --- Thermal Measurements --- p.27
Chapter 3.5 --- Temperature Control Box --- p.28
Chapter 4. --- Heat Transport Measurement --- p.29
Chapter 4.1 --- Correction Procedures --- p.30
Chapter 4.2 --- The Non-Boussinesq Effects --- p.33
Chapter 4.3 --- Experiment Results --- p.41
Chapter 4.3.1 --- Triethylene Glycol --- p.41
Chapter 4.3.2 --- Dipropylene Glycol --- p.45
Chapter 4.4 --- Discussion on the Results of Heat Transport --- p.50
Chapter 4.5 --- Discussion on the Results of RMS Fluctuations --- p.60
Chapter 4.6 --- The data set of pr =1400 --- p.63
Chapter 5. --- Conclusion --- p.65
References --- p.69

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

自然界中存在很多的湍流熱對流現象。他們對於工業，科學與技術有著非常重要的影響。在本論文中我們利用多温度探头的技术研究了湍流熱對流的理想模型-湍流瑞利-伯納德對流中的大尺度環流在高普朗特數下的動力學特性。
實驗中，我们利用水和電子液體FC77 作為工作物質，獲得了普朗特數Pr 從5.3 到19.4. 瑞利數Ra 範圍8.3 × 10⁸ 2.94 × 10¹¹.我們用了一個寬高比Γ 為1 的圓柱形對流槽來研究大尺度環流的動力學特性。我們發現，在高普朗特數的時候，大尺度環流仍然是一個single roll. 這個與我們期望的是一樣的。大尺度環流的強度δ 的概率密度函數是一個高斯分佈。但是左邊的尾巴可以用一個指數函數來描述。我們也觀察到了大尺度環流傾向於呆在一個特定的角向位置。我們還發現，大尺度流動的角向運動具有擴散運動的特性。但是，用FC77 作為工作物質時，這個角向運動的擴散係數比用水作為工作物質時小兩個量級。實驗中測量到的雷諾數Re 和瑞利數Ra 之間的標度率與之前的實驗結果相符合。同時這個標度率也和Grossman-Lohse 模型的預測相符合。
大尺度流動豐富的動力學特性，比如說流動停止，流向反轉，扭轉還有平移振盪以及流動模式轉換，都可以在高普朗特數的時候觀察到。比較有趣的是我們發現流動停止在一個三維系統中既不依賴於Ra, 又不依賴於Pr. 這個結果和二維的瑞利-伯納德對流完全不同。
Turbulent thermal convection is of tremendous importance to many areas of science, technology as well as the environment. In this thesis, the dynamics of the large-scale circulation (LSC) in turbulent Rayleigh-B´enard convection, which is an idealised model to study turbulent thermal convection problem, is investigated using the multi-thermal probe technique in the high Prandtl number Pr regime.
Using two kinds of working fluids, namely water and Fluorinert FC77, we achieved Pr from 5.3 to 19.4 and Rayleigh number Ra from 8.3×10⁸ to 2.94×10¹¹. The dynamics of the LSC is measured in an aspect ratio unity convection cell. It is found that the LSC in the high Pr regime is a single roll structure as expected. The probability distribution of the flow strength δ is a Gaussian distribution function with exponential tail to the left. The preferred orientation is also observed, which is revealed by the PDF of azimuthal orientation θ of the LSC. The azimuthal motion of the LSC is a diffusive process, which is the same as previous studies. However, we found that the diffusivity of the angular speed using FC77 as the working fluid is two orders smaller than using water as working fluid. The scaling of the measured Reynolds number Re number based on the oscillation frequency of the LSC with respect to Ra is in good agreement with previous experimental results and also Grossman-Lohse model prediction.
The abundant dynamical features of the LSC, such as cessations, flow reversals, torsional and sloshing oscillations and flow mode transitions are also observed in the high Pr regime. One surprising finding is that the cessation frequency of the LSC ,based on the statistics of the mid-height level of thermistors, is independent of both Ra and Pr, which is quite different from the (quasi) two-dimensional turbulent Rayleigh-B´enard convection.
Detailed summary in vernacular field only.
Detailed summary in vernacular field only.
Detailed summary in vernacular field only.
Xie, Yichao = 高普朗特數瑞利-伯納德對流中大尺度環流動力學特性研究 / 謝毅超.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2012.
Includes bibliographical references (leaves 53-57).
Abstracts also in Chinese.
Xie, Yichao = Gao pu lang te shu Ruili-Bonade dui liu zhong da chi du huan liu dong li xue te xing yan jiu / Xie Yichao.
Abstract --- p.ii
Acknowledgement --- p.iv
Chapter 1 --- Introduction --- p.1
Chapter 1.1 --- Natural convection and Rayleigh-B´enard convection --- p.1
Chapter 1.2 --- Governing equation and control parameters of RB Convection --- p.2
Chapter 1.3 --- The large-scale circulation in turbulent RB convection --- p.4
Chapter 1.4 --- Motivation and organisation of this thesis --- p.6
Chapter 2 --- Experimental Setup and Measurement Techniques --- p.7
Chapter 2.1 --- The convection cell --- p.7
Chapter 2.1.1 --- The conduction plate and sidewall --- p.7
Chapter 2.1.2 --- Cooling and heating system --- p.7
Chapter 2.1.3 --- Level of the convection system --- p.7
Chapter 2.2 --- The thermistor and it’s calibration --- p.9
Chapter 2.3 --- Multi-thermal-probe technique --- p.10
Chapter 2.4 --- Data analysis method --- p.12
Chapter 2.4.1 --- Sinusoidal fitting method (SF method) --- p.12
Chapter 2.4.2 --- Temperature extrema extraction method (TEE method) --- p.13
Chapter 2.5 --- Physical properties of FC77 --- p.14
Chapter 2.6 --- Other equipment --- p.15
Chapter 3 --- Dynamics of LSC in high Pr turbulent RBC --- p.16
Chapter 3.1 --- Background --- p.16
Chapter 3.2 --- Experimental setup and data analyse method --- p.18
Chapter 3.3 --- Results and discussion --- p.19
Chapter 3.3.1 --- General features of the LSC --- p.19
Chapter 3.3.2 --- Statistics of the angular speed --- p.23
Chapter 3.3.3 --- Reynolds number Re --- p.30
Chapter 3.3.4 --- Cessations, reversals and flow mode transitions --- p.34
Chapter 3.3.5 --- Torsional and sloshing motions of the LSC --- p.42
Chapter 3.4 --- Summary --- p.48
Chapter 4 --- Conclusion and outlook --- p.51
Chapter 4.1 --- Conclusion --- p.51
Chapter 4.2 --- Outlook --- p.51
Bibliography --- p.53

碩士
國立中山大學
機械與機電工程學系研究所
99
The molten pool shape and thermocapillary convection during melting or welding of metals or alloys are self-consistently predicted from scale analysis. Determination of the molten pool shape and transport variables is crucial due to its close relationship with the strength and properties of the fusion zone. In this work, surface tension coefficient is considered to be negative, indicating an outward surface flow, whereas high Prandtl number represents a thinner thickness of the thermal boundary layer than that of momentum boundary layer. Since Marangoni number is usually very high, the domain of scaling is divided into the hot, intermediate and cold corner regions, boundary layers on the solid-liquid interface and ahead of the melting front. The results find that the width and depth of the pool, peak and secondary surface velocity, and maximum temperatures in the hot and cold corner regions can be explicitly and separately determined as functions of working variables or Marangoni, Prandtl, Peclet, Stefan, and beam power numbers. The scaled results agree with numerical data, different combinations among scaled equations, and available experimental data.

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

The Full Zone model of the thermocapillary (Marangoni) flow in a liquid bridge with an axial magnetic field, measured by the Hartmann number Ha, is studied using a Chebyshev spectral method for low Prandtl number fluids. By introducing a 2nd order vorticity transport formulation, high resolution Gauss-Lobatto grids can be used to investigate the strong stabilization effects from intermediate magnetic fields, which were impossible with previous formulations. The instability mechanism of the axisymmetric base flow is studied up to Ha=500 for Pr=0.001 and up to Ha=300 for Pr=0.02 using linear stability analyses. Over these parameter spaces, the base flow first transitions to three-dimensional stationary disturbances with different axial symmetries. Solutions from the 2nd order vorticity transport formulation show good agreement with previous studies on weak magnetic fields. This work provides better understanding of the magnetohydrodynamic flow in intermediate field strengths, as well as guidance for optically heated float-zone crystal growth processes.