臺灣博碩士論文加值系統

本文使用計算流體力學的方式探討具障礙物管流：渦輪機葉片內冷卻流場與顱內動脈瘤內流場。在渦輪機葉片內冷卻流場的研究，旨在希望藉由內冷卻流道設計提高燃氣渦輪機葉片的熱傳增益，進而提高燃燒室出口溫度，以增加渦輪引擎單位重量之推力與提升燃氣渦輪機的熱效率。本論文此部分探討平滑與具45度攻角障礙物之靜止方形截面雙通管道流場，以及具90度攻角障礙物之靜止與旋轉方形管道之發展流與全展流，最後探討文獻中甚少報導之高旋轉速（相對於先前文獻高旋轉速意指Ro＞0.5）下具45度攻角多重障礙物流場與熱傳模擬。由於真實渦輪葉片內冷卻流道流場最大雷諾數Re=100000，最大旋轉速Ro=2，且流道內溫度不均勻造成流場有較大的密度變化，因此採用求解可壓縮Navier-Stokes方程式是較佳的選擇，而本文為了與低Re之實驗結果比較驗證並且期望將來可以利用相同的程式求解真實渦輪機在高Re和高Ro下之內冷卻流場，因此數值方法主要採用有限體積法搭配預調法(Preconditioning Method)求解可壓縮Navier-Stokes方程式以模擬低雷諾數(Re=10000)之流場，式中時間項採用顯式三點向後差分法來進行離散，而對流項的處理則使用AUSMDV，並應用Van Leer 所提出的Kappa法求解網格介面左右兩側流體流動性質，此外為了防止數值震盪之發生，則搭配minmod限制子來監控變數的變化與提高空間精度為二階，而擴散項的求解則採用中央差分法。計算結果以主流與二次流速度分佈、再附著長度、壓力與無因次熱傳比值等探討相關物理現象，並與前人實驗結果進行比較。本文所探討之各算例計算結果大多與實驗量測值吻合。而結果亦包含發展流與全展流流場之模擬，可供週期全展假設與真實情形差異之參考。本文主要結論為高旋轉速(Ro=1.5和2)下主流方向在第四對肋條後每一節距內皆呈現一對對轉展向渦旋結構，此結構未見於靜止或低轉速(Ro≦0.2)下管道流場，而此渦旋結構為促進高轉速下有較高無因次熱傳比值的重要流場機制。在迎風面熱傳與旋轉數的關係存在三個臨界旋轉速(Roc1=0.1，Roc2=0.5，Roc3=1)，其中Ro<Roc1時無因次熱傳比值會隨著Ro增大而下降，Ro>Roc1則會快速上升，當Ro> Roc2其上升的變化會較為平緩，在Ro> Roc3以後無因次熱傳比值會較靜止管道佳；對於背風面而言，無因次熱傳比值則會隨著Ro的增加逐漸增高，此結果與前人熱傳實驗趨勢一致。
另一種具障礙物管流應用即為顱內動脈瘤的治療，在顱內動脈瘤流場數值模擬方面，由於側向動脈瘤之流場實驗量測文獻甚少，且鮮少有文獻探討動脈瘤與彎曲型母管角度（γ）的關係，此外在動脈瘤入口處加裝人工支架的治療方法逐漸成為主流，對於加裝人工支架的動脈瘤流場，是否達到治療效果的預測變為非常重要。因此，本文在此部分探討是否存在一比較危險的γ角，使得顱內側向動脈瘤內的血液動力特性危及瘤壁等等，以及探討安裝不同孔隙率（Cα）之人工支架在直型母管與彎型母管(僅討論較危險γ角的案例)的動脈瘤入口，對瘤內流場特性之影響。數值模擬方法以有限體積離散方法模擬計算探討脈動狀態下內頸動脈側向動脈瘤模型之脈動流場特性，其中時間精度為二階之Crank-Nicolson法，空間精度採用二階上風法（對流項）與中央差分法（擴散項），並且搭配SIMPLEC演算法解決壓力與速度的耦合問題。結果討論血流動力因素之相關物理量包含瘤內渦漩結構、瘤內速度向量場與二次流、流入瘤體之流量、瘤璧剪應力以及壓力分佈。結果顯示各算例之計算結果皆與實驗量測值相吻合。從各種血流動力因子綜合探討發現γ為45度時較為危險，針對最危險夾角之案例安裝不同孔隙率的人工支架，並將不同孔隙率之人工支架模型類比為治療時所需商用人工支架的層數，發現安裝雙層人工支架比單層人工支架有更大的改善，但安裝三層人工支架則與兩層差異不大。在直型母管側向動脈瘤研究中發現動脈瘤內之相關血流動力因子其量值皆遠低於彎形母管側向動脈瘤，在安裝不同孔隙率之人工支架模型後發現安裝雙層人工支架較單層佳，安裝三層則與兩層差異不大，此結果與彎管相似。此外，因動脈瘤內之血栓形成可以減低其破裂之機率，故經檢視瘤內環境是否適合血栓形成之低剪應力區(壁面剪應力<0.5Pa)，發現對於彎形母管加裝單層人工支架而言，在動脈瘤開口處會有局部位置大於低剪應力區，甚至會大於高剪應力區(壁面剪應力>1.5Pa)，然而安裝雙層人工支架後瘤內大部分的區域皆小於低剪應力區。而在檢視直形母管時發現，無論加裝單層或雙層人工支架瘤內區域皆小於低剪應力區。由上述得知彎形母管較直形母管側向動脈瘤危險，但在加裝雙層人工支架後都能將瘤內的剪應力降到適合產生血栓的環境。而上述結論可以作為人工支架廠商設計人工支架與醫生臨床治療之參考。

摘要 I
誌謝 V
目錄 VI
圖錄 XI
符號說明 XXXI

第一章 緒論 1
1-1 研究動機 1
1-2 渦輪葉片內冷卻流道流場 2
1-2-1文獻回顧 3
1-2-2 文獻總結 8
1-2-3 研究目的 9
1-3 顱內動脈與側向動脈瘤流場 10
1-3-1 文獻回顧 11
1-3-2 文獻總結 13
1-3-3 研究目的 15

第二章 統御方程式、數值方法與實驗系統 21
2-1 統御方程式 21
2-1-1不可壓縮 Navier-Stokes 方程式 21
2-1-2可壓縮 Navier-Stokes 方程式 22
2-2 預調法 23
2-2-1 預調矩陣 23
2-2-2 雙時間步階預調法 26
2-3 數值方法 29
2-4大渦數值模擬 30
2-5 實驗設備 32

第三章 具障礙物流場應用於渦輪葉片冷卻流道 36
3-1具180度銳轉U型平滑管道 38
3-1-1 問題描述、數值方法與邊界條件 38
3-1-2 結果與討論 40
3-1-3 結論 42
3-2 具45度交錯排列肋條U型銳轉管道 44
3-2-1 問題描述、數值方法與邊界條件 46
3-2-2 結果與討論 46
3-2-3 結論 51
3-3 具90度並列多重肋條靜止與旋轉方形管道 52
3-3-1 問題描述、數值方法與邊界條件 52
3-3-2 結果與討論 54
3-3-3 結論 57
3-4 具90度並列肋條靜止與旋轉全展管流流場 59
3-4-1 問題描述、數值方法與邊界條件 59
3-4-2 結果與討論 61
3-4-3 結論 65
3-5高轉速下具45度交錯式多重肋條方形管道(AR=2)流場與熱傳 67
3-5-1 問題描述、數值方法與邊界條件 67
3-5-2 結果與討論 68
3-5-3 結論 71

第四章 具障礙物流場應用於動脈瘤治療 106
4-1 具180度銳轉U型母管之不同角度動脈瘤 107
4-1-1 問題描述、數值方法與邊界條件 107
4-1-2 結果與討論 110
4-1-3 結論 116
4-2具環型理想人工支架於45度動脈瘤之彎曲母管 117
4-2-1 問題描述、數值方法與邊界條件 117
4-2-2 結果與討論 118
4-2-3 結論 121
4-3具不同孔隙率人工支架於具45度動脈瘤之彎曲母管 122
4-3-1 問題描述、數值方法與邊界條件 122
4-3-2 結果與討論 123
4-3-3 結論 128
4-4具不同孔隙率人工支架於直型母管之側向動脈瘤 130
4-4-1 問題描述、數值方法與邊界條件 130
4-4-2 結果與討論 131
4-4-3 結論 138

第五章 結論與未來建議 205
5-1渦輪葉片冷卻流道流場模擬之結論 205
5-2動脈瘤流場數值模擬之結論 209
5-3 本文主要貢獻 212
5-4未來建議 214

附錄 A 幾何與激擾效應對於固態燃料衝壓引擎燃燒室流場駐焰特性之影響 217
附錄 B 全速度下流場之二維時間精確解數值 236
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