臺灣博碩士論文加值系統

自然對流問題在許多科學及工業上的應用相當廣泛，目前有許多種類的數值方法皆拿來模擬分析此類問題。近幾十年，晶格波茲曼方法(Lattice Boltzmann method)及計算流體力學(CFD)等數值方法被廣泛應用在此類問題。本文利用簡化的晶格波茲曼方法(LB Model)來處理採用Boussinesq 模式為浮力項的晶格波茲曼方程式，並針對二維自然對流在封閉空穴幾何下，在不同的參考瑞里數(reference Rayleigh number)、紐森數(Knudsen number)、高寬比(aspect ratio)，以及在固定的普蘭特常數(Pr number)為空氣(Pr=0.71)的條件下，探討流體行為以及其不穩定現象。在本研究中，參考瑞里數範圍設定在巨觀尺度下(macroscopic scale ， )，為 ，以及在介觀尺度下(mesoscopic scale， )的範圍為 。本文針對巨觀跟介觀的流體行為及其不穩定現象做分析及探討。在使用晶格波茲曼方法來模擬自然對流的問題中，對於選擇適當的浮力速度( )是非常重要的。因此，本研究提出由kinetic theory為基礎所推導出來的特徵浮力速度來模擬自然對流的問題，並且利用頻譜分析(spectrum analysis)技術來分析非穩態流場的週期性(periodic)和擬週期性(quasi-periodic)之流體不穩定行為。再利用紐賽數(Nusselt number) 及參考瑞里數(reference Rayleigh number)來判定發生非穩態且不穩定流體行為的產生機制及範圍。從本研究的相關結果中可以得知，流體穩定行為與瑞里數(Rayleigh number)、紐森數(Knudsen number)和高寬比(aspect ratio)等，有很大的關聯。尤其是紐森數(Knudsen number)和高寬比(aspect ratio)，其影響流體發生不穩定現象的效應更是明顯。也證明流體的連續性是由紐森數(Knudsen number)來決定，其對於巨/介觀流體行為的影響效果，不可忽視。

Natural convection inside a closed cavity is one of the interesting investigations in many scientific and industrial applications. Many numerical methods have been applied to analyze this problem, including the lattice Boltzmann method (LBM), which has emerged as one of the most powerful computational fluid dynamics (CFD) methods in recent years. Using a simple LB model with the Boussinesq approximation, this study investigates the 2D natural convection problem inside a rectangular cavity at different reference Rayleigh numbers, Knudsen numbers, and aspect ratios of cavity when the Prandtl number is fixed as within the range of in macroscopic scale ( ) and in mesoscopic scale ( ) respectively. The flow structures with instability phenomena in macroscopic scale and in mesoscopic scale are compared and analyzed. In simulating the natural convection problems, a model for choosing the appropriate value of the velocity scale, i.e. , is significantly important to simulate the natural convection problems by LBM. Current work proposes a model to determine the value of characteristic velocity (V) based on kinetic theory. A spectrum analysis is performed to identify the unsteady periodic or quasi-periodic oscillatory flow structure. The relationship between the Nusselt number and the reference Rayleigh number is also exhibited. The simulation results show that the instable flow is generated dependent on the Rayleigh numbers, Knudsen numbers, and aspect ratios of cavity. Meanwhile, the effect of Knudsen number and aspect ratio play the significant roles to influence the oscillatory flow structures.

摘要 I
Abstract III
誌 謝 V
目錄 VI
圖目錄 VIII
表目錄 XII
符號說明 XIII
第一章 序論 1
1-1 研究背景與動機 1
1-2 文獻回顧 2
1-2.1 有關自然對流的相關文獻 4
1-2.2 有關晶格波茲曼數值方法的相關文獻 7
1-3 研究內容與方向 8
第二章 理論模式 10
2-1 物理模型 10
2-2 晶格波茲曼法(Lattice Boltzmann Method) 11
2-2.1 描述速度場的晶格波茲曼方法 12
2-2.2 描述溫度場的晶格波茲曼方法 16
2-2.3 浮力效應項的處理方法 18
2-3 定義出合適浮力特徵速度以符合晶格波茲曼方法的應用 19
2-4週期性流場的頻率比(Frequency ratio) 21
2-5 初始條件及邊界條件 22
2-5.1 速度場初始條件設定 22
2.5.2 速度場邊界條件設定 23
2-5.3 溫度場初始條件設定 24
2-5.4 溫度場邊界條件設定 24
第三章 數值方法驗證 25
3-1 Rayleigh-Bénard對流問題的驗證 25
3-2 自然對流在正方形空穴的驗證 26
第四章 結果與討論 29
4.1問題描述 29
4-2 巨觀尺度(Macroscopic scale)下的結果與討論 32
4-3 介觀尺度(Mesoscopic scale)下的結果與討論 37
4-4 巨觀尺度與介觀尺度比較結果與討論 41
第五章 結論 43
參考文獻 47
自述 84

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