顆粒於穴室流場內之三維軌跡試驗及分析

Abstract

本研究以試驗方式及一系列之分析描述顆粒於三維穴室流場內之運動軌跡。試驗中共使用兩種大小不同之顆粒及試驗佈置。首先以雷射光頁激發微顆粒及長曝光技術進行流場顯影。再者，利用立體影像技術量測粗顆粒之三維空間位置，並應用卡門濾波平滑顆粒運動軌跡及降低量測誤差。為補足試驗上之不足，本研究中亦分析利用有限差分法求解三維速度-渦度Navier-Stokes方程式之速度場，進而得穴室內之細部流場結構，然相關之分析則代表流體顆粒之運動。經三維顆粒追蹤試驗，結果顯示粗顆粒運動軌跡於縱向呈現螺旋方式，然橫向部分則於邊牆及中心對稱面之間來回移動。研究中進一步透過Eulerian及Lagrangian觀點進行流體顆粒、微顆粒及粗顆粒間運動特性之比較，其中包括運動軌跡及速度。其比較結果可歸納出兩點值得深入探討之現象：1) 雖然粗顆粒之估計速度與流體顆粒速度相近，但粗顆粒於運動過程中總侷限於主渦漩內，反之，流體顆粒與微顆粒皆可連接於主渦漩及次渦漩間。2) 當雷諾數增加時，粗顆粒於主渦漩內之運動軌跡愈趨集中於穴室之邊界。最後，文中提出顆粒與液體之微小密度差異、空間限制、慣性力影響及顆粒旋轉效應等四點造成上述現象之可能原因，並進一步以試驗方式進行檢查，然檢查結果摒除顆粒與液體之微小密度差異之原因。空間限制部分則為顆粒大小所形成之限制，此項原因影響粗顆粒通過流線廊道而進入次渦漩之可能。此外，慣性力影響粗顆粒運動則表現於雷諾數之大小與軌跡分佈之變化關係。若比較顆粒旋轉特性時亦發現粗顆粒之旋轉慣性造成與流體顆粒間極大之差異。

Experiments and analysis are performed to character three-dimensional particle paths in a lid-driven cavity. Two types of particles with various diameters and experimental methods are utilized in this thesis. Illuminated micro-particles and artificial long exposure techniques visualize two-dimensional flow field. Stereo image methods measure three-dimensional macro-particle positions and Kalman filter efficiently attenuates measurement errors. To complement of experiments, analysis of velocity fields from three-dimensional Navier-Stokes equations in velocity-vorticity formulation solved by finite difference method extract details of flow structures and these computations stand for motions of fluid-particles. Stereo tracking experiments delineate macro-particle shuttling to and fro from side wall to centre plane in spiral way in cavity flow. Mutual comparisons of trajectories and velocities for fluid- (passive tracers), micro- and macro-particles are carried out in Lagrangian and Eulerian viewpoints to highlight similarities and discrepancies among them. There are two interesting phenomena: 1) macro-particle paths are only confined in primary eddy region even if trajectories and velocities of macro-particle matches computational fluid-particle results, whereas fluid- and micro-particles migrate to primary and corner vortices; 2) preferential paths of macro-particle approach to boundary walls while Re increasing. We afterward come up with some possible mechanisms to explain observations such as density mismatch, steric effect, inertia effect and particle rotation. After further examinations, density mismatch is excluded. The steric effect due to particle size gives an evident limitation for invasion of corner eddies through streamline corridors. Inertia effects contain the Reynolds number dependence of macro-particle trajectories and significant deviation of macro-particle rotation rate relative to fluid-particle.