三維分岔血管質傳現象之數值模擬

Numerical simulation of flow field and mass transfer in a 3-D artery with branches

謝佑莨(You-Liang Hsien)

指導教授 ： 鄧志浩

中原大學/工學院/土木工程學系/碩士(2006年)

https://doi.org/10.6840/cycu200600565

摘要

本研究運用分散式平行運算系統，以最小平方有限元素法(LSFEM)模擬腹主動脈系統的流場。在本文中建立了兩分岔血管位於動脈的同側以及兩分岔血管之間不同間距的模型。著重點在於三維分岔血管質傳現象和流場分析，觀察其速度向量、流線、濃度分佈。當兩分岔血管之間的距離 時，兩分岔血管交互影響越低，兩分岔血管之間的腹主動脈血管管壁上的迴流區域也越來越小。質傳方面，迴流區域是影響氧濃度的最大關鍵，在第一與第二根分岔血管中的迴流造成了低氧濃度的產生，而且低氧濃度會一直延伸至出口處。在腹主動脈血管管壁上的迴流區域同樣也造成了低濃度區的產生，並且當 時，低濃度區也隨之遞減。其他正常區域則是接近入口氧濃度 。運用平行化所得之結果，使用不同數量的CPU可以提昇100％以上的平行效益，對於複雜的數值計算相當有幫助。基於此數值模擬方式，本研究可以有效的利用數值模擬來處理整個複雜的流場與質傳現象。

關鍵字

分岔血管 ； 最小平方有限元素法 ； 質傳 ； 迴流區

並列摘要

A parallel computation system is applied for the numerical simulation in association with the least-squares finite element method (LSFEM) to study the flow fields and mass transfer in the abdominal aorta with two branches, which are on the same side of the artery with diameter D. The effects on flow field and mass transfer in relation to the distance (S) between two branches are investigated. From the distribution of velocity vector, streamline and concentration, it can be found when the distance between two branches is greater than one time of the diameter of the artery ( ) the interaction of flow field is small. The distribution of mass transfer of oxygen concentration is closely related to the existence of the vortex flow. The distribution of low concentration of oxygen is in the circulation zone near the wall of arteries, besides that the concentration is the same as the one in the inlet section. The area of low concentration could be the place of the intimal hyperplasia. This numerical model can be used to have a better understanding of the whole complicated flow field and mass transfer. Based on the parallel system, the computational CPU time can be improved by 100% for the complicated domain.

並列關鍵字

mass transfer ； least-square finite element method ； circulation zone ； Branches

參考文獻

1. Fry, D.L., 1969, “Certain histological and chemical response of the vascular interface to acutely induced mechanical stress in the aorta of the dog”, Circulation Research, 24, 93-108.

2. Caro, C.G., Fitzgeral, J.M. and Schroter, R.C., 1971, “Atheroma and arterial wall shear: observation, correlation and proposal of a shear dependent mass transfer mechanism of atherogenesis”, Proceedings of the Royal Society, 177, 109-159.

“Shear-dependent thickening of the human arterial intima”,

atherosclerosis, 60, pp. 161-171.

4. Johnston, Peter R. and Kilpatrick, David, 1991, “Mathematical modeling of flow through an irregular arterial stenosis”, Journal of Biomechanics 24, 1069-1077.