背向階梯流場構造簡單，局部特性明顯，運用範圍廣泛，因此對於不同外在條件改變流場的研究是值得探討的。本論文針對改變階梯形狀，利用數值方法模擬其流場狀況，並觀察其再接觸點長度的變化。當再接觸長度增加，迴流區跟著增加，若是應用在燃燒室內，駐焰效果也會跟著增加。
本論文數值方法為採用控制體積法來離散統御方程式，配合k-ε 紊流模式來閉合統御方程式，靠近壁面之計算域使用牆函數來計算，並採用六面體網格，經過網格獨立測試後採用45 萬網格數，使用商業軟體fluent 作為求解器。計算邊界條件：進口條件為流速3.8m/s 之均勻流，出口條件為環境壓力一大氣壓。針對五種不同的階梯形狀做計算，發現再接觸點長度會因為階梯形狀改變而改變。
將計算結果和實驗結果比對會發現差異甚鉅，主因為進口速度過小，雷諾數位於過渡區內，而計算時是假設為紊流，造成了誤差的出現。另外對於使用不同的紊流模式，計算出來的結果是否相同，本論文也加以探討，發現背向階梯流場適用k-ε 紊流模式。將來可進一步針對改變階梯形狀對於熱效應之影響，或是加入冷卻噴流對冷卻系統的影響加以研究。

Backward-facing step flow is a simple configuration with distinctlocal characters. It is quite useful in many fields. Five different shapeswere simulated numerically. We compared the change of the length of the reattachment point in each shape and find that the recirculation zone increases with the length of the reattachment point. This will enhance the flame holding effect in a combustion chamber.
The flow field was calculated by a finite volume method, and a k-ε turbulence model was used to simulate the turbulent flow. A near wall function was used to compute the near wall area. The commercial software package, FLUENT, was used to simulate the flow field. Four hundred and fifty thousands hexahedron cells were used in the numerical simulations according to the grid independence study. The lengths of the reattachment points of five different shapes were compared with the experimental data.
The agreement is not good. This is because the Reynolds numbers are in the transition zone, and we used a turbulence model to compute them. We also discussed the effects of different turbulence models on the solutions. We found that the k-ε turbulent model is most suitable for thebackward-facing step flows.

目錄
第一章 前言...............................................1
第二章文獻回顧............................................3
2-1 基本背向階梯流場研究..................................3
2-2 具壁面噴流背向階梯流場研究............................6
2-3 暫態的背向階梯流場研究................................7
第三章 理論分析..........................................10
3-1 統御方程式...........................................10
3-2 紊流模...............................................12
3-2-1 k-ε雙方程式模式...................................13
3-2-2 牆函數.............................................15
3-3 邊界條件.............................................16
第四章 數值方法與結果討論................................18
4-1 數值方法.............................................18
4-1-1 網格獨立測試.......................................18
4-1-2 邊界條件...........................................19
4-1-3 壓力修正方程式.....................................20
4-1-4 鬆弛係數...........................................20
4-1-5 收斂條件...........................................21
4-1-6 計算程序...........................................21
4-1-7 計算結果處理.......................................23
4-2 結果討論.............................................23
4-2-1 幾何外型...........................................23
4-2-2 計算結果...........................................23
4-2-3 結果討論...........................................27
第五章 結論..............................................31
參考文獻.................................................33

圖目錄
圖1- 1 背向階梯流場示意圖................................38
圖4- 1 CASE 1 計算幾何外型...............................39
圖4- 2 CASE 1 Z=0.1m 處X-Y 剖面速度向量圖 黃興閎[23].....40
圖4- 3 CASE 1 Z=0.1m 處X-Y 剖面速度向量圖................40
圖4- 4 CASE 1 Z=0.05m 處X-Y 剖面速度向量圖...............41
圖4- 5 CASE 1 Z=0.15m 處X-Y 剖面速度向量圖...............42
圖4- 6 CASE 1 分離點後方0.5h 處Y-Z 剖面速度向量圖........43
圖4- 7 CASE 1 分離點後方1h 處Y-Z 剖面速度向量圖..........44
圖4- 8 CASE 1 分離點後方1.5h 處Y-Z 剖面速度向量圖........45
圖4- 9 CASE 2 計算幾何外型...............................46
圖4- 10 CASE 2 Z=0.1m 處X-Y 剖面速度向量圖 黃興閎[23]....47
圖4- 11 CASE 2 Z=0.1m 處X-Y 剖面速度向量圖...............47
圖4- 12 CASE 2 Z=0.05m 處X-Y 剖面速度向量圖..............48
圖4- 13 CASE 2 Z=0.15m 處X-Y 剖面速度向量圖..............49
圖4- 14 CASE 2 分離點後方0.5h 處Y-Z 剖面速度向量圖.......50
圖4- 15 CASE 2 分離點後方1h 處Y-Z 剖面速度向量圖.........51
圖4- 16 CASE 2 分離點後方1.5h 處Y-Z 剖面速度向量圖.......52
圖4- 17 CASE 3 計算幾何外型..............................53
圖4- 18 CASE 3 Z=0.1m 處X-Y 剖面速度向量圖 黃興閎[23]....54
圖4- 19 CASE 3 Z=0.1m 處X-Y 剖面速度向量圖...............54
圖4- 20 CASE 3 Z=0.05m 處X-Y 剖面速度向量圖..............55
圖4- 21 CASE 3 Z=0.15m 處X-Y 剖面速度向量圖..............56
圖4- 22 CASE 3 分離點後方0.5h 處Y-Z 剖面速度向量圖.......57
圖4- 23 CASE 3 分離點後方1h 處Y-Z 剖面速度向量圖.........58
圖4- 24 CASE 3 分離點後方1.5h 處Y-Z 剖面速度向量圖.......59
圖4- 25 CASE 4 計算幾何外型..............................60
圖4- 26 CASE 4 Z=0.1m 處X-Y 剖面速度向量圖 黃興閎[23]....61
圖4- 27 CASE 4 Z=0.1m 處X-Y 剖面速度向量圖...............61
圖4- 28 CASE 4 Z=0.05m 處X-Y 剖面速度向量圖..............62
圖4- 29 CASE 4 Z=0.15m 處X-Y 剖面速度向量圖..............63
圖4- 30 CASE 4 分離點後方0.5h 處Y-Z 剖面速度向量圖.......64
圖4- 31 CASE 4 分離點後方1h 處Y-Z 剖面速度向量圖.........65
圖4- 32 CASE 4 分離點後方1.5h 處Y-Z 剖面速度向量圖.......66
圖4- 33 CASE 5 計算幾何外型..............................67
圖4- 34 CASE 5 Z=0.1m 處X-Y 剖面速度向量圖 黃興閎[23]....68
圖4- 35 CASE 5 Z=0.1m 處X-Y 剖面速度向量圖...............68
圖4- 36 CASE 5 Z=0.05m 處X-Y 剖面速度向量圖..............69
圖4- 37 CASE 5 Z=0.15m 處X-Y 剖面速度向量圖..............70
圖4- 38 CASE 5 分離點後方0.5h 處Y-Z 剖面速度向量圖.......71
圖4- 39 CASE 5 分離點後方1h 處Y-Z 剖面速度向量圖.........72
圖4- 40 CASE 5 分離點後方1.5h 處Y-Z 剖面速度向量圖.......73
圖4- 41 Spalart-Allmaras 紊流模式........................74
圖4- 42 k-ω紊流模式.....................................75
圖4- 43 Reynolds stress 紊流模式.........................76

表目錄
表3- 1 紊流模式常數表....................................14
表4- 1 網格獨立測試......................................19
表4- 2 空氣性質..........................................20
表4- 3 鬆弛係數..........................................21
表4- 4 背向階梯幾何外型..................................23
表4- 5 再接觸點位置......................................27
表4- 6 紊流模式誤差表....................................29

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