本論文主要探討三維空間暫態內具有旋轉效應之方形體內自然對流現象,針對科氏力及旋轉浮力的效應下所產生的旋轉與側邊溫差熱驅動自然對流,問題著重於溫度產生之浮力與科氏力所引起的流動機制與變化形態,並探討其熱傳變化情形。

本文採用廣義緊緻格式與保有頻散關係格式(Dispersion relation preserving，簡稱DRP)離散方法離散空間項,及採用具有TVD(Total Variation Dimimishing)保持性質的Runge-Kutta型的時間離散格式。針對不同的瑞立數(Rayleigh Number)、泰勒數(Taylor Number)以及旋轉瑞立數(Rotating Rayleigh number)進行分析,比較內部流場的變化與影響，分析其各項物理性質,如熱傳、渦度及流場結構。

研究結果顯示,當離心力與科氏力增大,足夠影響整個流場與熱場的變化。轉速增快時,熱壁與冷壁的邊界層厚度具有明顯改變,總體來說具有較佳的對流效應,提高Nusselt數。由旋轉浮力效應所驅動熱流場,會在上壁與下壁面產生往腔體流進的螺旋點,形成渦軸往對立的壁面移動,且成對的發生,由結果觀察知,當轉速高時,旋轉浮力效應會使熱浮力所帶動的流場在方形體內部遭到旋轉浮力的影響,而總體的熱傳效應由於科氏力的增加而增加,說明轉速越快熱傳效應隨之愈高,但越容易發生不穩定的現象。

關鍵字：保有頻散有限差分法、科氏力、離心力

目錄
中文摘要
英文摘要
誌謝
目錄
圖目錄
符號說明
第一章 緒論
1.1 前言
1.2 研究動機與目的
1.3 文獻回顧
1.4 論文內容與架構
第二章 物理與數學模型
2.1 基本物理假設
2.2 統御方程組
2.3 邊界條件
2.4 格點配置
2.5 同位網格壓力與速度藕合關係
第三章 數值方法
3.1 對流與擴散問題
3.2 空間離散格式
3.3 時間離散格式
3.4 演算法的疊代程序
3.5 誤差設定標準
3.6 問題說明與程式驗證
第四章 結果與討論
4.1 Topology 理論分析
4.2 旋轉浮力與熱浮力所控制的流場
4.3 旋轉浮力對於熱浮力所控制流場的影響
4.4 旋轉浮力與Nusselt數關係及影響
4.5 科氏力對於熱浮力所控制流場的影響
4.6 科氏力與Nusselt數關係及影響
4.7 科氏力對於旋轉浮力所控制流場的影響
4.8 流場結構分析
4.8.1 渦度等位面
4.8.2 極限流線圖
第五章 結論與未來展望
5.1 結論
5.2 未來展望
參考文獻
Appendix：無因次化推導

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