二維顆粒流中之運動模擬分析

Abstract

顆粒流在日常生活或是在工業上都是非常常見的，顆粒流的形式有時候像液體，例如沙漏中的沙子，有時候像固體，例如工業大量製造藥品，很多藥丸都是顆粒型式。微觀的來說，顆粒都是簡單遵守牛頓運動法則的，但是巨觀看到現象卻複雜許多。 在本論文中，將建構一個簡單的模型，這個簡單的模型是用來在顆粒流當中運動的，由兩個球形組成，這兩個球形可以週期性的收縮膨脹在一個長方形的箱子裡，箱子裡裝滿了小沙粒顆粒，沙粒和運動的模型碰撞設定為完全彈性碰撞，箱子的縱軸方向邊界條件是固定的，沙粒碰到上下的邊界會以完全彈性碰撞的方式反彈，箱子的橫軸方向邊界條件是周期性的，從右邊離開的沙粒會從左邊回來，沙粒之間的碰撞為非彈性碰撞，顆粒流的一個重要特性就是沙粒之間的彼此碰撞會散失能量，而散失能量的多寡將會影響顆粒留的行為，利用事件導向的模擬，動畫將呈現模型如何和沙粒互動，模型運動的週期存在某個特定值使得整個運動最快速或是最有效率，在本論文中將討論固定恢復係數時最有效率的運動周期，以及固定運動周期時最有效率的恢復係數。

The flow of granular materials is common in natural and industrial environment, which displays either liquid, such as sand flow in hourglass, or solid , such as pharmaceutical pills, behavior. The evolution of particles follows Newton's equations. It seems very simple to describe, however its behavior is tremendously complex. In this study, a simple model of swimmer in granular material is constructed. The swimmer is made of two spheres that contract and extend periodically in a rectangular box filled with small particles. The spheres are elastic that impose noslip boundary conditions. The boundary condition of the box is periodic in horizontal direction, and bounded in vertical direction. A distinguishing feature of granular flows is that the interaction of particles leads to energy dissipation which plays an important role in granular flow. Using event-driven simulation, the animation shows how such swimmer interacts with surrounding particles. The frequency of the swimming motion has an optimal value for certain restitution coefficient. By adjusting the restitution coefficient, we can see how energy dissipation affects the formation of surrounding particles and swimming efficiency.