臺灣博碩士論文加值系統

隨著電腦記憶容量的持續增加及電腦處理速度的改進，運用數值方法模擬熱流場之計算流體力學技術不斷的發展，使得越來越多的複雜問題均有可能解決。本文以自撰FORTRAN 程式，運用PATANKAR 所提SIMPLER 法則，進行數值模擬，並提供具體的數據以作為設計矩形管內散熱鰭片的參考資料。
本文三維程式首先將矩形管流道截面取為扁平的幾何形狀，藉以模擬二維平板的熱場，另外再將矩形管流道截面取為正方形的幾何形狀，進一步計算這兩種幾何形狀的熱入口區(thermal entry length)與結合熱入口區(combined thermal 　and hydrodynamic entry length)的局部紐塞數值，經由與相關文獻之經驗公式比較，確定本程式分析具有散熱鰭片熱流場之適用性，以確認程式之基本架構與所採用數值方法之正確性。
考慮矩形管內障礙物的高度及厚度對流場及熱場的影響，經數值模擬可以發現增加障礙物高度時，因為管道截面積減少使得流場流速增加，進而提高熱對流效應，雖然障礙物後方會形成迴流區，使熱傳效應降低，但對整體的熱傳效應還是有相當的助益。至於增加障礙物厚度方面的影響並不顯著。
在改變雷諾數方面，發現增加雷諾數以提高流體速度，能夠增加整體的熱傳效應。在設置交錯式的障礙物方面，由於障礙物會加速流體混合且提高流速，所以對整體的熱傳效應也有顯著提升。
本文三維程式提供三維矩形管內層流場及熱場的基本架構，未來可討論各種邊界設定或不同形狀障礙物的影響，此外因為迴流區會有流體流滯，造成熱傳效應降低，未來可將障礙物設計成具有孔隙，如此可利用穿過障礙物的流體去破壞迴流區，使迴流區的影響降低。

目錄
中文摘要………………………………………………………….. Ⅰ
英文摘要………………………………………………………….. Ⅲ
目錄…………………………………………………………….... Ⅴ
符號說明………………………………………………………….. Ⅷ
第一章 緒論
1-1 前言……………………………………………………. 1
1-2 研究動機………………………………………………. 1
1-3 文獻回顧………………………………………………. 2
第二章 理論分析與數值方法
2-1 基本假設………………………………………………. 5
2-2 統御方程式…………………………………………... 6
2-3 SIMPLER之理論模式………………………………... 8
2-3-1 SIMPLER法之簡介……………………………. 8
2-3-2 格點配置……………………………………..... 9
2-4 SIMPLER之數值方法………………………………... 10
2-4-1 動量離散方程式……………………………...... 10
2-4-2 壓力離散方程式……………………………...... 12
2-4-3 能量離散方程式……………………………….. 14
2-4-4 SIMPLER解題步驟……………………………. 15
2-5 加速收斂的方法……………………………………... 16
2-6 邊界條件……………………………………………... 17
2-6-1 無障礙物之邊界處理………………………….. 17
2-6-2 障礙物之邊界處理……………………………. 18
2-7 誤差標準設定………………………………………... 19
2-8 代數方程式求解法…………………………………... 20
第三章 結果與討論
3-1 Bench mark測試……………………………………… 21
3-1-1 模擬二維平板…………………………………. 21
3-1-1-1 入口速度場為完全發展流……………... 21
3-1-1-2 入口速度場為均勻流………………..…. 22
3-1-2 流道截面為正方形………………………….… 23
3-2 最佳化格點測試………………………………….…. 24
3-2-1 矩形管………………………………………… 24
3-2-2 矩形管內設置障礙物………………………… 25
3-3 矩形管內障礙物幾何形狀大小對熱流場的影響…. 25
3-3-1 障礙物高度對矩形管熱流場的影響………. 25
3-3-2 障礙物厚度對矩形管熱流場的影響………. 26
3-4 雷諾數的變化對內含障礙物流場及熱場的影響…. 27
3-4-1 流場方面的影響……………………………… 27
3-4-2 熱場方面的影響……………………………… 27
3-5 矩形管內設置交錯式障礙物對流場及熱場之影響.. 28
3-5-1 流場方面的影響……………………………… 28
3-5-2 熱場方面的影響……………………………… 29
3-6 壁面效應對三維矩形管設置障礙物的流場及熱場之影響………………………………………………………… 29
3-6-1 流場方面的影響…………………………….. 29
3-6-2 熱場方面的影響…………………………….. 30
第四章 結論與展望
4-1 結論…………………………………………………. 31
4-2 展望…………………………………………………. 32
參考文獻……………………………………………………….. 34
附圖…………………………………………………………….. 38
附表…………………………………………………………….. 60
附錄 A 三維動量離散方程式推導………………………….... 62
附錄 B 三維壓力修正值離散方程式推導………………….… 64
附錄 C 三維能量離散方程式推導…………………………… 66
附錄 D 三維壓力虛擬值離散方程式推導…………………… 69
附錄 E TDMA(TriDiagonal-Matrix Algorithm)代數方程式推導71
附錄 F 固定壁溫的局部紐賽數數值解推導……….......... 73
附錄 G 二維平板熱場的局部紐賽數經驗公式………... 75

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