臺灣博碩士論文加值系統

本文之研究乃是利用泛用型計算流體力學軟體STAR-CD作可壓縮管流的模擬，將其結果與一維假設下(Quasi-One-Dimensional Assumption)的可壓縮流理論做比較，藉此希望能對其物理真實現象做深入的了解，並提供日後在應用可壓縮流理論時，作為參考的依據。分析模型共分為低長寬比約13的直流道、L型、U型流道，並且探討截面漸縮效應，及高長寬比為1000的微直流道、U型微流道。模擬結果顯示，在低長寬比的漸縮流道中，摩擦效應可以忽略，且與理論不同的是，在真實流場中摩擦是會造成流體平均流速減少，而熱傳效應僅能使近壁面的流體加熱，截面均溫性甚差；L型及U型流道部分，由模擬結果顯示，在彎道入口時，流體會在外側形成最大壓力區，內側速度高於外側；反之當流體通過彎道後，外側的流速高於內側，溫度也較內側為低。此外，模擬結果亦可發現彎道會造成流體加速，於進出口前後壓差較漸縮流道為小的情況下，管道出口的馬赫數可以達到超音速流的狀態。在高長寬比微流道的模擬中可以發現真實流場與理論預測十分吻合，相同長度的彎管流場現象，溫度部分與直微流道近似，其餘結果也與理論相符合。藉此本研究可知，當流道為高長寬比的微流道時，可以使用理論來計算與預測流場現象，進而節省數值模擬所花費的時間。

The purposes of this study are to simulate compressible channel flows by a CFD commercial software (STAR-CD) and to compare the numerical results with those predicted by the conventional theory based on a quasi-one-dimensional assumption. We expect to obtain the real physical phenomena of channel flows encountered in practical applications. The physical models in the present study include the low-aspect-ratio channels (L/W=13), L-type and U-type channels with a converging effect on the cross sectional area, the high-aspect-ratio microchannels (L/W=1000) and U-type microchannels. Unlike the theory which shows a reduction in the average flow velocity by wall friction, the results reveal that the friction effect for low-aspect-ratio channels is negligible, the fluid is heated only near the wall and the temperature distribution is quite non-uniform across the cross section of channels. For the L-type and U-type channels, a high pressure region is formed at the entry in the outer region of the curved section and the flow velocity in the inner region is higher than that in the outer one. The behavior of flow after the curved section is reversed and the fluid temperature at the outer region is lower than the inner one. In addition, the simulation results also reveal that the fluid is accelerated in the curved section. The Mach number at the channel exit can reach a supersonic state if the pressure difference between the inlet and outlet is lower than that in a converging channel. It is also found that for high-aspect-ratio microchannels the numerical results are in good agreement with those according to the theoretical prediction. With an identical channel length, both the straight and the U-type microchannels have similar velocity and temperature fields. This fact indicates that, for high-aspect-ratio microchannels, one can simply utilize the theory based on a quasi-one-dimensional assumption to predict the phenomena of channel flows.

目錄
摘要......................................................I
Abstract ................................................II
誌謝....................................................III
目錄.....................................................IV
圖目錄...................................................VI
表目錄....................................................X
第一章 緒論...............................................1
1.1 前言..................................................1
1.2 文獻回顧..............................................2
1.3 研究動機..............................................7
第二章 理論分析...........................................9
2.1 可壓縮流..............................................9
2.1.1 可壓縮流場的定義....................................9
2.2 統御方程式...........................................10
2.2.1 流體面積變化效應...................................13
2.2.2 具有摩擦的絕熱管流.................................15
2.2.3 具有熱傳的管流.....................................19
2.2.4 具有熱傳及摩擦的漸縮管流...........................22
2.3 STAR-CD統御方程式....................................22
2.3.1 紊流模式...........................................24
第三章 數值方法..........................................27
3.1 Generalized Quasi-One-Dimensional Method.............27
3.2 STAR-CD數值方法......................................27
3.2.1 SIMPLE法...........................................28
3.2.2 邊界條件與初始條件.................................31
第四章 結果與討論........................................33
4.1 Generalized Quasi-One-Dimensional Flow理論結果.......33
4.2 STAR-CD數值結果......................................37
4.2.1 漸縮管流...........................................37
4.2.2 L型管流............................................39
4.2.3 U型管流............................................40
4.2.4 長型微流道.........................................42
第五章 結論..............................................44
參考文獻.................................................46

圖目錄
圖2-1 流體性質在可變面積導管中的變化 ....................49
圖2-2 使用控制體積來分析在等截面導管的摩擦流動 ..........49
圖2-3 使用控制體積來分析在可變面積導管的摩擦流動 ........50
圖2-4 使用控制體積來分析具熱傳無摩擦的等截面導管流動.....50
圖2-5 使用控制體積來分析具熱傳及摩擦的等截面導管流動.....51
圖2-6 使用控制體積來分析具熱傳且可變面積導管的流動.......51
圖2-7 使用控制體積來分析在具摩擦及熱傳的可變面積導管流動.52
圖3-1 漸縮流道的基本外型.................................52
圖3-2 主格點控制體積示意圖(z方向為出紙方向)[23]..........53
圖3-3(a) 三維漸縮管流道基本外型..........................53
圖3-3(b) 三維L型管流道基本外型...........................54
圖3-3(c) 三維U型管流道基本外型...........................54
圖4-1(a) 壓力沿著漸縮流道軸向分佈圖......................55
圖4-1(b) 速度沿著漸縮流道軸向分佈圖......................55
圖4-1(c) 溫度沿著漸縮流道軸向分佈圖......................56
圖4-1(d) 馬赫數沿著漸縮流道軸向分佈圖....................56
圖4-1(e) 密度沿著漸縮流道軸向分佈圖......................57
圖4-1(f) 具摩擦的絕熱漸縮流道隨著軸向距離其溫度與熵的關係
圖..............................................57
圖4-2(a) 壓力沿著等截面流道軸向分佈圖....................58
圖4-2(b) 速度沿著等截面流道軸向分佈圖....................58
圖4-2(c) 溫度沿著等截面流道軸向分佈圖....................59
圖4-2(d) 馬赫數沿著等截面流道軸向分佈圖..................59
圖4-2(e) 密度沿著等截面流道軸向分佈圖....................60
圖4-2(f) 具摩擦的等截面流道隨著軸向距離其溫度與熵的關係圖 ............................................... 60
圖4-3(a) 壓力沿著漸縮流道軸向分佈圖......................61
圖4-3(b) 速度沿著漸縮流道軸向分佈圖......................61
圖4-3(c) 溫度沿著漸縮流道軸向分佈圖......................62
圖4-3(d) 停滯溫度沿著漸縮流道軸向分佈圖..................62
圖4-3(e) 馬赫數沿著漸縮流道軸向分佈圖....................63
圖4-3(f) 密度沿著漸縮流道軸向分佈圖......................63
圖4-3(g) 隨著軸向距離其溫度與熵的關係圖..................64
圖4-4 漸縮流道外型圖及其尺寸.............................64
圖4-5(a) 壓力沿著漸縮流道軸向分佈圖......................65
圖4-5(b) 速度沿著漸縮流道軸向分佈圖......................65
圖4-5(c) 溫度沿著漸縮流道軸向分佈圖......................66
圖4-5(d) 馬赫數沿著漸縮流道軸向分佈圖....................66
圖4-5(e) 密度沿著漸縮流道軸向分佈圖......................67
圖4-6(a) 壓力沿著漸縮流道軸向分佈圖......................67
圖4-6(b) 速度沿著漸縮流道軸向分佈圖......................68
圖4-6(c) 溫度沿著漸縮流道軸向分佈圖......................68
圖4-6(d) 馬赫數沿著漸縮流道軸向分佈圖....................69
圖4-6(e) 密度沿著漸縮流道軸向分佈圖......................69
圖4-7 L型流道外型圖及其尺寸..............................70
圖4-8(a) L型流道靜壓力分佈圖.............................71
圖4-8(b) L型流道速度分佈圖...............................72
圖4-8(c) L型流道溫度分佈圖...............................73
圖4-8(d) L型流道馬赫數分佈圖.............................74
圖4-9(a) L型流道與L型加上漸縮流道的壓力分佈..............75
圖4-9(b) L型流道與L型加上漸縮流道的速度分佈..............76
圖4-9(c) L型流道與L型加上漸縮流道的溫度分佈..............77
圖4-9(d) L型流道與L型加上漸縮流道的馬赫數分佈............78
圖4-10 U型流道外型圖及其尺寸.............................79
圖4-11(a) U型流道壓力分佈圖..............................80
圖4-11(b) U型流道速度分佈圖..............................81
圖4-11(c) U型流道溫度分佈圖..............................82
圖4-11(d) U型流道馬赫數分佈圖............................83
圖4-11(a) U型流道與U型加上漸縮流道的壓力分佈.............84
圖4-11(b) U型流道與U型加上漸縮流道的速度分佈.............85
圖4-11(c) U型流道與U型加上漸縮流道的溫度分佈.............86
圖4-11(d) U型流道與U型加上漸縮流道的馬赫數分佈...........87
圖4-12(a) 壓力沿著微流道軸向分佈圖.......................88
圖4-12(b) 溫度沿著微流道軸向分佈圖.......................88
圖4-12(c) 速度沿著微流道軸向分佈圖.......................89
圖4-12(d) 馬赫數沿著微流道軸向分佈圖.....................89

表目錄
表1-1 凡諾流中由於摩擦而造成的流體性質改變之歸納表[2]....90
表1-2 瑞里流中由於熱傳效應而造成的流體性質改變之歸納表[2]91
表2-1 標準κ-ε紊流模式的係數一欄表[22] ...................92

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