臺灣博碩士論文加值系統

摘要
本研究利用最小平方有限元素法(LSFEM)模擬血管中因為非對稱腫瘤，造成流場中流況及質傳的影響。本文中建立了3種非對稱的腫瘤大小(53.18%、65.75%、77.65%)模式，來探討其對流場、剪應力、壓力降的變化及對迴流區域的影響。同時利用質傳來探討血液中氧濃度受腫瘤及其後迴流區影響的變化情形。
本文中模擬流場介於雷諾數100-1000之間，其流場及壓力趨勢皆與前人的研究相符合，在3種不同腫瘤模式中，在腫瘤前端入口前剪應力為最大值，而在腫瘤末端會有迴流區域產生，也就是低剪應力產生，而在腫瘤壁(53.18%)上最大剪應力值與正常管壁同斷面的最大剪應力值的比值大約為2.06：1，隨著腫瘤增大此比值會變小，此結果與雷諾數的大小並無明顯相關。
在質傳方面，腫瘤前端的氧濃度質傳量為最大，此位置也就是與剪應力發生最大的地方相近似，而在流過腫瘤末端氧濃度分佈會分為2部分，正常濃度部分是沿著正常的管壁，而另一部分低氧濃度則是在腫瘤末端迴流區域與管壁附近，由氧濃度質傳分佈說明血管腫瘤迴流區與內膜增生的相關。 基於此數值模擬方式，本研究可以有效的利用數值模擬來模擬整個複雜的流場與質傳分佈。

ABSTRACT

In this research, the least-squares finite element method (LSFEM) is employed to study the influence of asymmetric stenosis on the flow fields and mass transfer in the blood vessel. There are three kinds of asymmetric arterial stenosis (53.18% , 65.75% , 77.65%) established in the article. The changes of flow fields, shear stress, pressure drop, reversed flow regions and the variation of blood density on mass transfer in the reversed flow regions distal to the arterial stenosis are carefully examined.
In this article, the Reynolds number is between 100-1000 in the flow fields. Both the flow field and pressure drop are in according with the results of early researcher’s studies. In three kinds of different arterial stenosis models, the maximum shear stress occurs in the throat of the arterial stenosis. The low shear stresses exist in the reversed flow regions distal to the arterial stenosis. At the same cross-section of the arterial, the ratio between the peak shear stress at the wall of arterial stenosis(53.81%) and that in the normal wall is 2.06: 1; and this result is irrelevant with different Reynolds numbers. As the increase of the arterial stenosis, the peak shear stress ratio between the normal and abnormal walls is decreased.
In the mass transfer, the maximum oxygen mass transfer occurs proximal to the stenosis; and it is the same place that the peak wall shear stress exists. Concentration distribution distal to the arterial stenosis will form into two streams, the normal oxygen concentration stream is along the normal artery wall, and the low oxygen concentration is formed in the reverse region distal to the arterial stenosis. It is clear that the mass transfer of oxygen can be used to see the changes and distributions in arterial stenosis of the blood vessel.
Based on the numerical simulation, this research can be concluded that this numerical model can simulate the whole complicate flow domain in good agreement with the available simulation results and the observed experiments.

目 錄
第一章 序論
1-1 研究動機.........................................01
1-2 研究方法和目的...................................02
1-3 文獻回顧.........................................04
第二章 理論分析
2-1 歷史回顧.........................................07
2-2 理論推導.........................................08
2-3控制方程式........................................10
第三章 模型建立與邊界條件給定
3-1 模型建立與格網建立...............................19
3-2 邊界條件給定.....................................21
第四章 結果分析與討論
4-1不同大小腫瘤相同雷諾數(Re=105.33)的速度分佈………..23
4-2 同一腫瘤不同雷諾數的速度分佈......................23
4-3壓力降比較.........................................24
4-4迴流區域的探討.....................................24
4-5管壁上剪應力值的比較...............................25
4-6質傳在腫瘤的探討.................................26
第五章 結論與建議
5-1 結論............................................29
5-2 建議............................................30
附錄一、共軛梯度法介紹(Conjugate Gradient Method).......50
元素-元素技巧（Element-by-Element Technique）...50
附錄二.共軛梯度法(conjugate Gradient Method)簡介........54
附錄三、使用共軛梯度法..................................56

圖 目 錄
圖一、2-D的腫瘤模型及側面圖...........................35
圖二、橢圓上點的表示...................................35
圖三、非對稱腫瘤的均勻網格.............................36
圖四、53.18%的腫瘤網格圖...............................36
圖五、65.75%的腫瘤網格圖...............................37
圖六、77.65%的腫瘤網格圖...............................37
圖七、53.18%腫瘤的速度分佈(Re=105.33) .................38
圖八、65.75%腫瘤的速度分佈(Re=105.33) .................38
圖九、77.65%腫瘤的速度分佈(Re=105.33) .................39
圖十、65.75%腫瘤的速度分佈(Re=210.67) .................39
圖十一、65.75%腫瘤的速度分佈(Re=316) ..................40
圖十二、65.75%腫瘤的速度分佈(Re=438.6) ................40
圖十三、壓力降比較.....................................41
圖十四、53.18%腫瘤前後二端迴流區向量圖.................41
圖十五、65.75%腫瘤迴流區探討(Re=438.6) ................42
圖十六、65.75%腫瘤迴流區向量圖(Re=438.6) ..............42
圖十七~二十、53.18%剪應力圖............................43
圖二十一~二十四、 為(Ang and Mazumdar)53.18%剪應力圖...45
圖二十五、最大剪應力在不同雷諾數及腫瘤的比值............46
圖二十六、取壁上剪應力斷面..............................47
圖二十七、質傳氧濃度在迴流區探討........................47
圖二十八、Sh計算值.....................................48
圖二十九、Kaazempur-Mofrad等人(2005)Sh計算��...........48
圖三十、速度向量圖......................................49

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