臺灣博碩士論文加值系統

流體、熱傳與電磁領域不僅影響廣泛而且多變，為了有效地探討，必須提出科學且有條理的研究方法。本文展示以系統化的數值模擬方法，應用於各類工業上的複雜問題，以及自然對流問題，探討其動力行為。主要討論的主題有二 :

(1)自然對流 (Free Convection) (2)強制對流(Force Convection) 等。

文中第一部份透過求解 Boussinesq 近似之 Rayleigh-Benard 三維方程，以研究于封閉空穴內之自然對流現象，當 Ra 數提高時，將出現解分岔與多重解的現象。本文由極限環 (limiting cycles) 的穩定與否的觀察切入，探討由穩態解過渡至混沌狀態之動力現象，分析所得之時間序列解，將紀錄成一張完整的分岔圖表，以了解于空穴內多重解、叉狀分岔、頻率倍分岔之現象。
文中第二部份，研究高溫射頻手術 (Radio Frequency Ablation)，
利用通有交流電的電極棒，由電位差所產生電子熱傳，探討在手術過程內能有效的把癌細胞消滅，達到不用開刀就能完成手術的目的。此外，亦考慮血液的灌流 (perfusion) 效應，觀察它對手術所造成的影響。文中第三部份模擬實際的室內空調，考慮冷氣噴出後、對整個室內的溫度分佈及舒適度 (PMV) 分析 ，探討在不同地點及時間時，對吾人所處位置之影響。

本論文中使用已套裝化之CFDRC，它提供一有限體積之數值方法，求解三維質量、動量與能量之對流-擴散傳輸方程式。為求得精確的結果，吾人皆採用二階以上的上風方法來近似對流項及擴散項；對於暫態問題方面，時間項以 Crank-Nicolson方法來加以離散。離散後的代數式系統則採用代數多重網格方法(AMG)和共軛梯度方形方法(CGS)來加速求解。

本論文主要的目的不只在於建構數值模型以提供設計與評估之醫學和工業應用，同時也採用各類先進的科學視算技術 (如三維之速度場及壓力場分析、粒子軌跡線 (Particle trace lines) 及漩渦中心線 (Vortex core lines) 的展示等，對各種複雜的物理機制進行深入的探討，這已充分展現數值模擬方法應用的廣度及深度。

Fluid, heat transferring and electromagnetic field are not only broadly influential but also changeable. In order to discuss these three efficiently, scientific and reasonable approach must be presented. My thesis demonstrates and applies industrial complicated problems and natural convection problem with the systematized numerical simulation, in which we probe into diverse motive force activities. Two topics:

(1) Free Convection (2) Force Convection will be discussed in this thesis.

Firstly, We study the three-dimensional natural convection problem inside a cubical cavity by virtue of the Rayleigh-Benard problem with Boussinesq approximation made in the equations of motion. As the Ra number is increased, the bifurcation phenomenon with multiple solutions occurs. This paper employed the theory underlying the limiting cycles to study their stability evolving from steady to chaotic state. The scientifically calculated bifurcation diagram helps to explore in details the multiple solutions, pitchfork bifurcation, Hopf bifurcation and Frequency-doubling phenomenon.

Secondly, I study in Radio Frequency Ablation (RFA)
which utilizes the electron heat transfer produced by electric potential difference in alternating current electrode. I probe into the process of eliminating cancer cells in Radio Frequency Ablation which may reach the goals of surgical operation but without any surgical operation. Perfusion effect in blood is concerned during Radio Frequency Ablation process.

Thirdly, by simulating the air conditioning, the temperature redistribution indoors and the PMV analysis, I investigate its effect to my own position in different location and time.

1. 導論
1.1 前言 ........................................... 1
1.2 研究之動機 ..................................... 2
1.3 論文之架構 ..................................... 2

2. 數值方法
2.1 有限體積方法 ................................... 5
2.2 有限體積之離散方法 ............................. 6
2.3 邊界條件 ....................................... 8
2.4 求解程序 ....................................... 9

PartI 基礎研究

3 自然對流
3.1 簡介 ........................................... 17
3.1.1 文獻回顧 ..................................... 17
3.1.2 Rayleigh-Benard 對流問題 ..................... 18
3.1.3 本章簡述 ..................................... 19
3.2 數學及物理模式 ................................. 19
3.2.1 基本假設 ..................................... 19
3.2.2 統御方程式 ................................... 20
3.2.3 Boussinesq 近似方程 .......................... 21
3.3 題目描述 ....................................... 21
3.3.1 程式之測試及比較 ............................. 22
3.3.2 求解方法和解與網格無關之測試 ................. 22
3.4 多重解 ........................................ 23
3.4.1 分岔理論 ..................................... 23
3.4.2 Pitchfork Bifurcation ........................ 26
3.4.3 Hopf Bifurcation ............................. 26
3.4.4 模式 I 與 II 之流場型態 ...................... 27
3.5 週期解過渡至渾沌解之分析 ....................... 44
3.5.1 混沌理論 ..................................... 44
3.5.2 整體分岔圖 ................................... 47
3.5.3 極限環與漩渦運動之穩定性分析 ................. 47
3.5.4 頻譜與相圖分析 ............................... 49
3.5.5 頻率倍分岔 ................................... 50
3.5.6 過渡至渾沌 ................................... 51

Part II 應用研究

4 考慮血液灌流效應之高溫射頻手術(RFA)
4.1 高溫射頻燒灼手術之簡介 ......................... 69
4.2 高溫射頻燒灼手術之治療 ......................... 69
4.3 熱電(thermoelectric)系統的控制方程式 ........... 70
4.4 數值模型 ....................................... 72
4.5 結果及討論 ..................................... 75
4.5.1 比較兩種電極棒所造成腫瘤燒灼體積大小的差異 ... 75
4.5.2 熱對流係數 h_bl 的假設對手術過程的影響 ....... 76
4.5.3 肝腫瘤表面平均溫度隨手術時間之變化 ........... 77
4.5.4 手術時血管裡之血液流動情形 ................... 77
4.5.5 肝動脈的影響 ................................. 77

5 室內空調模擬之研究
5.1 室內空調之簡介 .................................103
5.2 數值模型 .......................................105
5.2.1 統御方程式 ...................................106
5.2.2 邊界及初始條件之設定 .........................107
5.3 舒適感模式 .....................................107
5.3.1 PMV 舒適感模式 ...............................108
5.4 結果與討論 .....................................109
5.4.1 隨時間變化之室內溫度分佈圖 ...................109
5.4.2 舒適感及流場流動之分析 .......................109
6 結論
6.1 成果與貢獻 .....................................121
6.2 未來之展望 .....................................122
附錄 A 頻譜分析技術及程式驗證 ......................123

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