兩剛性球垂直於平板邊界運動之拖曳係數

Abstract

本文主要是以數值模擬的方法來探討一個平板的邊界對二顆球形粒子在牛頓流體(Newtonian fluid)及卡羅流體(Carreau fluid)自由沉降之影響，並改變流體之性質來比較的平板邊界對粒子速度以及流場的影響程度。關於多顆球形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。本研究的焦點為邊界以及不同性質之流體對於兩顆球形粒子運動現象之影響，並觀察拖曳係數的變化趨勢、及粒子間的距離與粒子與平板的距離之臨界距離，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n，粒子間的距離，粒子與平板的距離，以及雷諾數的影響。結果顯示，改變平板邊界與粒子間的距離對流場對稱性的影響比改變流體性質及粒子間的距離來的明顯，因此，邊界對拖曳係數的影響較流體性質及粒子間的距離明顯許多。而拖曳係數隨雷諾數變化的趨勢，在卡羅流體中得到和牛頓流體一樣的結果，不過前者shear-thinning的特性使得拖曳係數較後者中的要小。拖曳係數隨Carreau number Cu變化的趨勢也是呈現反比的趨勢，Cu愈大，愈偏離牛頓流體，所以拖曳係數下降愈多。n值對拖曳係數的影響最小，稍稍地呈現正比的趨勢，比較特別的是當流體的Cu值變大時，n值對拖曳係數的影響比較明顯。

The influence of the presence of a boundary on the drag of rigid entities is investigated by considering the movement of two identical, rigid, coaxial spheres normal to a plane in both a Newtonian and a Carreau fluid. The parameters key to the phenomenon under consideration, including the nature of the fluid, the separation distance between two particles, the distance between particle and the plane, and the Reynolds number, on the drag coefficient are discussed. The results of numerical simulation reveal that the influence of a boundary on the drag coefficient is more important than that of the nature of a fluid and that of the distance between two particles. The variation of the drag coefficient as a function of Reynolds number for a Carreau fluid is similar to that for a Newtonian fluid. Due to the shear-thinning nature of the former fluid the drag coefficient in the former is smaller than that in the latter fluid. The magnitude of the drag coefficient is inversely proportional to the Carreau number. The influence of the index parameter of a Carreau fluid becomes appreciable when the Carreau number is sufficiently large.