臺灣博碩士論文加值系統

本研究係以實驗與數值模擬方式，針對單相流體於仿生式楔型微流道具不同階層數與深寬比之幾何參數，於固定散熱面積為前提進行探討。內容包括對流場與溫度場之模擬分析、設計實驗與建立設備，驗證結果並整理出經驗關係式，最後依性能效益進行評估。數值分析使用ESI-CFD-ACE+計算流體力學軟體進行模擬，其誤差範圍為0.2%~32.2%，平均誤差為9.7%。實驗試片之矽晶圓採用半導體製程進行製作，且工作介質為去離子水，其雷諾數範圍介於92到1835之間。結果顯示壓降與熱傳值於不同參數下與雷諾數皆有合理的趨勢與對應關係，而楔形結構將產生二次流行為且進入過渡流區，並使溫度均勻性提升，帶來更好的熱傳性能。
對於楔型結構而言，其楔型階層數越高、深寬比越小(短邊除以長邊)其熱傳性能越高，且圓弧轉角相對於直角能夠降低壓降值並提升效能。整體而言在階層2之圓角楔型性能曲線最高，相對於直管於深寬比為1且在雷諾數為1477時效能可提升至179.7%、深寬比為0.5且在雷諾數為737時效能可提升至174.9%、深寬比為0.333且在雷諾數為727時效能可提升至161.7%，而相同階層數下亦得到於深寬比越小則性能值越高之結果。
此外，對微型樹狀類結構提出線段積分法，深入考慮分支結構對於流體所產生之變化與入口效應長度之不可忽略性，其摩擦因子與紐賽數應不再只透過出入口溫度與壓力值進行古典理論計算。研究顯示此法能考慮整體內部流場變化，其發展流之文獻值和實驗值較為吻合，平均誤差僅在14.6%，優於古典理論於微尺度下產生較大之誤差達60.7% 之多，並佐證此類微型結構於理論上需被提出探討與修正。

In this study, the single phase flow fluid characteristics in the bionics wedge-shaped microchannel with different aspect ratios and branching levels were investigated under constant heat transfer surface. The distributions of velocity and temperature fields inside the microchannel were simulated and analyzed. Then an experiment was designed and set up to verify the simulation. The experimental results were compared with the simulated results and the empirical correlations were determined to acquire the coefficient of performance (COP). The software of ESI-CFD-ACE+ was used for numerical simulations. The errors between the results obtained from the experiments and those obtained from the simulations were in the range of 0.2%-32.2% with an average error of 9.7%. The silicon wafers used in the experiments were fabricated by semiconductor manufacturing process, and the working fluid was de-ionized water flowing at the Reynolds number ranging from 92 to 1835. The experimental results showed that the curves of corresponding trends of pressure drop and heat transfer versus the Reynolds number were reasonable. The wedge-shaped structure helped to generate secondary flows and make the fluid flowing into the developing regime. The resulting temperature distributions were more uniform within the microchannel and the performance of heat transfer for wedged-shaped microchannel was enhanced.
For wedge-shaped structure, the effect of aspect ratios on the performance of heat transfer is more than that of the branching level. The higher the branching level and the smaller the aspect ratio, the better the performance of the heat transfer. Moreover, compared with the rectangular bend, the rounded bend can decrease the pressure drop, which also helps to improve the performance. Through the integrated crossover comparison, it was found that for the rounded bend wedge-shaped microchannels, when the branching level was 2, the COP curve was the best among all configurations studied. Compared with the straight microchannels, the COP could increase to 179.7% at Reynolds number of 1447 with the channel respect ratio of 1. And at Reynolds number of 737 with the channel respect ratio of 0.5, the COP could increase to 174.9%. While for the channel respect ratio of 0.33, the COP could increase to 161.7% at Reynolds number of 727. For the same branching level, the compared results show that the COP curve was better for the microchannel structural configurations with small aspect ratios.
The sectional integral method was used in this study to account for the specific structures of wedge-shaped microchannels. Since such kind of microchannel structures induced the flow to change its situation along the branching part of the channel, the effects brought about by the entrance length in the developing flow could not be ignored under such a situation. Therefore, the friction factor and Nusselt number should not be calculated by the classical theory involved only the entrance and exit parameters of pressure and temperature. The research done in this study showed that the results, verified by the experimental data, obtained from this improved method helped incorporate the variation of flow field along the length of the channel. The average error for the COP curve was 14.6%, better than that of 60.7% obtained from the classical theory in micro-scale, which demonstrated that accounting for the entrance effect resulting from the developing flow by using the sectional integral method was essential to describe the behavior of flow and heat transfer for bionics wedge-shaped microchannels.

摘 要..............................................................................................................................................I
Abstract.........................................................................................................................................II
致 謝............................................................................................................................................IV
目 錄.............................................................................................................................................V
圖目錄.........................................................................................................................................IX
表目錄.......................................................................................................................................XIV
符號說明....................................................................................................................................XV

第一章 緒論...................................................................................................................................1
1.1 研究動機與目的......................................................................................................................1
1.2 文獻回顧..................................................................................................................................3
第二章 實驗系統與設計...............................................................................................................7
2.1 微流道製程介紹......................................................................................................................7
2.2 實驗儀器與流程介紹..............................................................................................................9
2.3 幾何結構與其理論分析........................................................................................................11
2.4 實驗不準確度分析 (experimental uncertainties)......................................................................16
第三章 理論分析.........................................................................................................................19
3.1 統御方程式............................................................................................................................19
3.1.1 質量守恆方程式.................................................................................................................19
3.1.2 動量守恆方程式.................................................................................................................20
3.1.3 能量守恆方程式.................................................................................................................21
3.2基本假設.................................................................................................................................22
3.3數值模擬.................................................................................................................................23
3.3.1 軟體介紹.............................................................................................................................23
3.3.2 數值方法.............................................................................................................................23
3.3.2.1 有限體積法......................................................................................................................23
3.3.2.2 內差法..............................................................................................................................25
3.3.2.3 SIMPLEC 演算法.............................................................................................................25
3.3.3 邊界條件 (boundary condition).............................................................................................25
3.3.4 容積條件 (volume condition)................................................................................................26
3.3.5 初始條件 (initial condition)...................................................................................................26
3.3.6 求解設定 (solver condition)..................................................................................................27
3.3.7 網格形式.............................................................................................................................29
3.3.8 網格獨立性分析.................................................................................................................29
3.4 經驗關係式............................................................................................................................31
3.4.1 雷諾數 (Reynolds number)...................................................................................................31
3.4.2 普朗數 (Prandtl number).......................................................................................................31
3.4.3 布林克曼數 (Brinkman number)...........................................................................................31
3.4.4 水力直徑 (hydraulic diameter)...............................................................................................31
3.4.5 入口效應長度 (entry length).................................................................................................32
3.4.6 壓降 (pressure drop).............................................................................................................32
3.4.7 古典摩擦因子 (friction factor)..............................................................................................33
3.4.8 古典紐賽數 (Nusselt number)..............................................................................................34
3.4.9 性能指標 (performance index).............................................................................................36
3.5 線段積分法 (sectional integral method)...................................................................................36
第四章 結果與討論.....................................................................................................................42
4.1流場分布探討.........................................................................................................................42
4.1.1 楔形微流道內部速度場分布與二次流行為.....................................................................42
4.1.2 楔形微流道內部溫度場分布.............................................................................................43
4.2 等效法與線段積分法趨勢比較............................................................................................45
4.2.1 楔形微流道於發展流之摩擦因子趨勢比較.....................................................................45
4.2.2 楔形微流道於發展流之紐賽數趨勢比較.........................................................................47
4.3 壓降值與流率行為之探討....................................................................................................49
4.3.1不同深寬比之壓降值與雷諾數關係..................................................................................49
4.3.2不同階層數之壓降值與雷諾數關係..................................................................................49
4.4 熱傳值與流率行為之探討....................................................................................................51
4.4.1不同深寬比之熱傳值與雷諾數關係..................................................................................51
4.4.2不同階層數之熱傳值與雷諾數關係..................................................................................51
4.5 摩擦因子與雷諾數之探討....................................................................................................52
4.5.1不同階層數之摩擦因子與雷諾數關係..............................................................................52
4.5.2不同深寬比之摩擦因子與雷諾數關係..............................................................................53
4.6 紐賽數與雷諾數之探討........................................................................................................54
4.6.1不同深寬比之紐賽數與雷諾數關係..................................................................................54
4.6.2不同階層數之紐賽數與雷諾數關係..................................................................................55
4.7 性能效益與雷諾數之關係比較............................................................................................57
4.7.1不同深寬比之性能效益與雷諾數之關係..........................................................................57
4.7.2不同階層數之性能效益與雷諾數關係..............................................................................58
第五章 結論與未來展望...........................................................................................................114
5.1 結論......................................................................................................................................114
5.2 未來展望..............................................................................................................................116
參考文獻....................................................................................................................................117

圖1-1、楔型之幾何結構概念圖...................................................................................................3
圖2-1、微流道製作流程圖...........................................................................................................8
圖2-2、楔型微流道試片模組示意圖...........................................................................................9
圖2-3、實驗系統架構圖.............................................................................................................10
圖2-4、楔型分支定義圖.............................................................................................................12
圖2-5、不同階層與轉角之楔型流道示意圖.............................................................................14
圖2-6、粗糙度量測結果.............................................................................................................15
圖2-7、SEM頗面圖量測結果(1).................................................................................................17
圖2-8、SEM頗面圖量測結果(2).................................................................................................18
圖2-9、SEM頗面圖量測結果(3).................................................................................................18
圖3-1、控制體積之質量進出示意圖.........................................................................................19
圖3-2、CFD之運算模擬之架構..................................................................................................23
圖3-3、三維計算網格示意圖.....................................................................................................24
圖3-4、二維計算網格示意圖.....................................................................................................24
圖3-5、數值分析求解流程圖.....................................................................................................28
圖3-6、結構與非結構型網格示意圖.........................................................................................29
圖3-7、網格數之誤差分析圖表.................................................................................................30
圖3-8、不同深寬比於發展流下特徵長度與摩擦因子之關係曲線圖.....................................39
圖3-9、不同深寬比於發展流下特徵長度與紐賽數之關係曲線圖.........................................39
圖3-10、fRe值隨楔型流道改變之趨勢示意圖..........................................................................40
圖3-11、紐賽數隨楔型流道改變之趨勢示意圖.......................................................................40
圖3-12、實驗之摩擦因子隨楔型流道改變示意圖...................................................................41
圖3-13、實驗之紐賽數隨楔型流道改變示意圖.......................................................................41
圖4-1、速度場於T型分散與匯集處擷取範圍示意圖...............................................................63
圖4-2、速度場於L型轉角處擷取範圍示意圖...........................................................................63
圖4-3、深寬比1於T型分散處速度場之二次流行為圖(雷諾數=810)......................................64
圖4-4、深寬比1於T型匯集處速度場之二次流行為圖(雷諾數=810)......................................64
圖4-5、深寬比2於T型分散處速度場之二次流行為圖(雷諾數=810)......................................65
圖4-6、深寬比2於T型匯集處速度場之二次流行為圖(雷諾數=810)......................................65
圖4-7、深寬比3於T型分散處速度場之二次流行為圖(雷諾數=810)......................................66
圖4-8、深寬比3於T型匯集處速度場之二次流行為圖(雷諾數=810)......................................66
圖4-9、深寬比2於T型分散處速度場之二次流行為圖(雷諾數=187)......................................67
圖4-10、深寬比2於T型匯集處速度場之二次流行為圖(雷諾數=187)....................................67
圖4-11、深寬比2於T型分散處速度場之二次流行為圖(雷諾數=1560)..................................68
圖4-12、深寬比2於T型匯集處速度場之二次流行為圖(雷諾數=1560)..................................68
圖4-13、深寬比1於L型轉角處速度場之二次流行為圖(雷諾數=810)....................................69
圖4-14、深寬比1於L型轉角處流線與渦流三維圖(雷諾數=810)............................................69
圖4-15、深寬比2於L型轉角處速度場之二次流行為圖(雷諾數=810)....................................70
圖4-16、深寬比2於L型轉角處流線與渦流三維圖(雷諾數=810)............................................70
圖4-17、深寬比3於L型轉角處速度場之二次流行為圖(雷諾數=810)....................................71
圖4-18、深寬比3於L型轉角處流線與渦流三維圖(雷諾數=810)............................................71
圖4-19、深寬比2於L型轉角處速度場之二次流行為圖(雷諾數=187)....................................72
圖4-20、深寬比2於L型轉角處流線與渦流三維圖(雷諾數=187)............................................72
圖4-21、深寬比2於L型轉角處速度場之二次流行為圖(雷諾數=1560)..................................73
圖4-22、深寬比2於L型轉角處流線與渦流三維圖(雷諾數=1560)..........................................73
圖4-23、溫度場於T型分散與匯集處擷取點示意圖.................................................................74
圖4-24、溫度場於L型轉角處擷取點示意圖.............................................................................74
圖4-25、深寬比1於T型分散處溫度場三維圖(雷諾數=810)....................................................75
圖4-26、深寬比1於T型匯集處溫度場三維圖(雷諾數=810)....................................................75
圖4-27、深寬比2於T型分散處溫度場三維圖(雷諾數=810)....................................................76
圖4-28、深寬比2於T型匯集處溫度場三維圖(雷諾數=810)....................................................76
圖4-29、深寬比3於T型分散處溫度場三維圖(雷諾數=810)....................................................77
圖4-30、深寬比3於T型匯集處溫度場三維圖(雷諾數=810)....................................................77
圖4-31、深寬比2於T型分散處溫度場三維圖(雷諾數=187)....................................................78
圖4-32、深寬比2於T型匯集處溫度場三維圖(雷諾數=187)....................................................78
圖4-33、深寬比2於T型分散處溫度場三維圖(雷諾數=1560)..................................................79
圖4-34、深寬比2於T型匯集處溫度場三維圖(雷諾數=1560)..................................................79
圖4-35、深寬比1於L型轉角處溫度場三維圖(雷諾數=810)....................................................80
圖4-36、深寬比1於楔型入口處溫度場平面圖(雷諾數=810)..................................................80
圖4-37、深寬比2於L型轉角處溫度場三維圖(雷諾數=810)....................................................81
圖4-38、深寬比2於楔型入口處溫度場平面圖(雷諾數=810)..................................................81
圖4-39、深寬比3於L型轉角處溫度場三維圖(雷諾數=810)....................................................82
圖4-40、深寬比3於楔型入口處溫度場平面圖(雷諾數=810)..................................................82
圖4-41、深寬比2於L型轉角處溫度場三維圖(雷諾數=187)....................................................83
圖4-42、深寬比2於楔型入口處溫度場平面圖(雷諾數=187)..................................................83
圖4-43、深寬比2於L型轉角處溫度場三維圖(雷諾數=1560)..................................................84
圖4-44、深寬比2於楔型入口處溫度場平面圖(雷諾數=1560)................................................84
圖4-45、深寬比1階層數2之摩擦因子於雷諾數下理論與實驗值趨勢比較...........................85
圖4-46、深寬比1階層數2圓角之摩擦因子於雷諾數下理論與實驗值趨勢比較...................85
圖4-47、深寬比1階層數1之摩擦因子於雷諾數下理論與實驗值趨勢比較...........................86
圖4-48、深寬比2階層數2之摩擦因子於雷諾數下理論與實驗值趨勢比較...........................86
圖4-49、深寬比2階層數2圓角之摩擦因子於雷諾數下理論與實驗值趨勢比較...................87
圖4-50、深寬比2階層數1之摩擦因子於雷諾數下理論與實驗值趨勢比較...........................87
圖4-51、深寬比3階層數2之摩擦因子於雷諾數下理論與實驗值趨勢比較...........................88
圖4-52、深寬比3階層數2圓角之摩擦因子於雷諾數下理論與實驗值趨勢比較...................88
圖4-53、深寬比3階層數1之摩擦因子於雷諾數下理論與實驗值趨勢比較...........................89
圖4-54、深寬比1階層數2之紐賽數於雷諾數下理論與實驗值趨勢比較...............................89
圖4-55、深寬比1階層數2圓角之紐賽數於雷諾數下理論與實驗值趨勢比較.......................90
圖4-56、深寬比1階層數1之紐賽數於雷諾數下理論與實驗值趨勢比較...............................90
圖4-57、深寬比2階層數2之紐賽數於雷諾數下理論與實驗值趨勢比較...............................91
圖4-58、深寬比2階層數2圓角之紐賽數於雷諾數下理論與實驗值趨勢比較.......................91
圖4-59、深寬比2階層數1之紐賽數於雷諾數下理論與實驗值趨勢比較...............................92
圖4-60、深寬比3階層數2之紐賽數於雷諾數下理論與實驗值趨勢比較...............................92
圖4-61、深寬比3階層數2圓角之紐賽數於雷諾數下理論與實驗值趨勢比較.......................93
圖4-62、深寬比3階層數1之紐賽數於雷諾數下理論與實驗值趨勢比較...............................93
圖4-63、階層數2於不同深寬比壓降值對雷諾數之實驗與模擬比較圖.................................94
圖4-64、階層數2圓角於不同深寬比壓降值對雷諾數之實驗與模擬比較圖.........................94
圖4-65、階層數1於不同深寬比壓降值對雷諾數之實驗與模擬比較圖.................................95
圖4-66、深寬比1於不同階層數下壓降值對雷諾數之實驗趨勢圖.........................................95
圖4-67、深寬比0.5於不同階層數下壓降值對雷諾數之實驗趨勢圖......................................96
圖4-68、深寬比0.333於不同階層數下壓降值對雷諾數之實驗趨勢圖..................................96
圖4-69、階層數2於不同深寬比熱傳值對雷諾數之實驗與模擬比較圖.................................97
圖4-70、階層數2圓角於不同深寬比熱傳值對雷諾數之實驗與模擬比較圖.........................97
圖4-71、階層數1於不同深寬比熱傳值對雷諾數之實驗與模擬比較圖.................................98
圖4-72、深寬比1於不同階層數下熱傳值對雷諾數之實驗趨勢圖.........................................98
圖4-73、深寬比0.5於不同階層數下熱傳值對雷諾數之實驗趨勢圖......................................99
圖4-74、深寬比0.333於不同階層數下熱傳值對雷諾數之實驗趨勢圖..................................99
圖4-75、深寬比1於不同階層數下摩擦因子對雷諾數之實驗趨勢圖(線性座標).................100
圖4-76、深寬比1於不同階層數下摩擦因子對雷諾數之實驗趨勢圖(對數座標).................100
圖4-77、深寬比0.5於不同階層數下摩擦因子對雷諾數之實驗趨勢圖(線性座標)..............101
圖4-78、深寬比0.5於不同階層數下摩擦因子對雷諾數之實驗趨勢圖(對數座標)..............101
圖4-79、深寬比0.333於不同階層數下摩擦因子對雷諾數之實驗趨勢圖(線性座標)..........102
圖4-80、深寬比0.333於不同階層數下摩擦因子對雷諾數之實驗趨勢圖(對數座標)..........102
圖4-81、階層數2於不同深寬比摩擦因子對雷諾數之實驗與模擬比較圖...........................103
圖4-82、階層數2圓角於不同深寬比摩擦因子對雷諾數之實驗與模擬比較圖...................103
圖4-83、階層數1於不同深寬比摩擦因子對雷諾數之實驗與模擬比較圖...........................104
圖4-84、階層數2於不同深寬比紐賽數對雷諾數之實驗與模擬比較圖...............................104
圖4-85、階層數2圓角於不同深寬比紐賽數對雷諾數之實驗與模擬比較圖.......................105
圖4-86、階層數1於不同深寬比紐賽數對雷諾數之實驗與模擬比較圖...............................105
圖4-87、深寬比1於不同階層數下紐賽數對雷諾數之實驗趨勢圖.......................................106
圖4-88、深寬比0.5於不同階層數下紐賽數對雷諾數之實驗趨勢圖....................................106
圖4-89、深寬比0.333於不同階層數下紐賽數對雷諾數之實驗趨勢圖................................107
圖4-90、階層數2於不同深寬比性能效益對雷諾數之關係圖...............................................108
圖4-91、階層數2於不同深寬比性能係數對雷諾數之關係圖...............................................108
圖4-92、階層數2圓角於不同深寬比性能效益對雷諾數之關係圖.......................................109
圖4-93、階層數2圓角於不同深寬比性能係數對雷諾數之關係圖.......................................109
圖4-94、階層數1於不同深寬比性能效益對雷諾數之關係圖...............................................110
圖4-95、階層數1於不同深寬比性能係數對雷諾數之關係圖...............................................110
圖4-96、深寬比1於不同階層數下性能效益對雷諾數之關係圖...........................................111
圖4-97、深寬比1於不同階層數下性能係數對雷諾數之關係圖...........................................111
圖4-98、深寬比0.5於不同階層數下性能效益對雷諾數之關係圖........................................112
圖4-99、深寬比0.5於不同階層數下性能係數對雷諾數之關係圖........................................112
圖4-100、深寬比0.333於不同階層數下性能效益對雷諾數之關係圖..................................113
圖4-101、深寬比0.333於不同階層數下性能係數對雷諾數之關係圖..................................113

表2-1、實驗設備規格.................................................................................................................10
表2-2、管道尺度定義分類表.....................................................................................................13
表2-3、楔型微流道規格尺寸表.................................................................................................14
表2-4、楔型微流道規格尺寸與試片名稱對照表.....................................................................14
表3-1、去離子水及矽晶材性質與溫度之函數表.....................................................................26
表3-2、網格測試結果.................................................................................................................30
表3-3、各深寬比於完全發展流之紐賽數對照表.....................................................................38
表4-1、線段積分法之摩擦因子實驗與理論誤差表.................................................................61
表4-2、線段積分法之紐賽數實驗與理論誤差表.....................................................................61
表4-3、摩擦因子經驗公式係數表.............................................................................................62
表4-4、紐賽數經驗公式係數表.................................................................................................62

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