圓柱粒子在卡羅流體中運動之邊界效應

Abstract

本文由理論角度探討邊界對一粒子在卡羅流體（Carreau fluid）中運動的影響，並改變卡羅流體的性質以比較邊界對粒子速度及流場影響的程度。關於粒子在各種流體中運動之現象，諸如流場以及終端速度之變化，已受到廣泛的研究，而卡羅流體亦漸漸受到矚目。本研究的焦點為大小不同之圓柱粒子在不同邊界以及不同性質之卡羅流體中運動的現象，主要分為拖曳係數以及終端速度兩部分，藉由模擬之結果進行定性及定量分析，考慮的變因包含卡羅流體鬆弛時間，卡羅流體指數，圓柱粒子長度，圓管管壁直徑，粒子終端速度，並根據所得之拖曳力及終端速度作迴歸分析以預估粒子在無邊界流場中之終端速度。結果顯示，改變邊界大小對流場對稱性的影響比改變流體性質與粒子大小來的明顯，因此，邊界對拖曳係數的影響較流體性質及粒子大小明顯許多，而在卡羅流體中，終端速度與邊界之非線性關係亦得到證實。

The wall effect of a particle moving in a Carreau fluid is investigated theoretically by considering a cylindrical particle in a cylindrical tube. In particular, the influences of the key parameters of the system under consideration on the drag coefficient and the corresponding flow field at various conditions are discussed. These include the relaxation time constant and the index characterizing a Carreau fluid, the length of a particle, and the diameter of a circular tube. The problem of a particle in an unbounded fluid can be recovered as a limiting case of the present problem. According to the result, changing the boundary size affects the symmetry of flow field more obviously than that particle’s size or property of fluid. So, the boundary size affects the drag coefficient more obviously than that of particle or property of fluid. The non-linear relationship between terminal velocity and boundary size has been verified, also.