以實驗與深度積分理論探討乾顆粒流潰壩沖刷動床在可變角度渠道之行為

Abstract

本論文以實驗及數值計算模擬乾顆粒瞬間潰壩對於下游沖刷動床之情況。實驗渠道為長270公分，寬4.2公分的實驗。對於初始條件，渠道設計具有可變角度及拆換式邊界的功能，可提供多種的傾斜角及邊界去進行不同類型實驗以進行探討。實驗採用直徑約2.5mm之細磨石顆粒做為模擬潰壩的堆積及底床材料，分析方法則使用粒子影像分析計算顆粒之路徑及流場，再以每一斷面之累積流量百分比定義顆粒流表面與流動層與底床交界線，提供實驗資料與數值理論作驗證。理論採用質量、動量、動能方程式作為基礎，再以深度積分法簡化方程式作為本研究之控制方程式。數值計算採用HLL之有限體積數值方法求解，並將數值計算結果與實驗之影像分析結果進行比較，以檢視現象差異，最終從比較結果中得到了相當好的效果。

In this thesis, a set of experiments of instantly dry dam-break granular flows to downstream erosion of the erodible deposits, and numerical simulation, are presented. In the experiments, the channel is 270 cm long, 4.2 cm wide. For the initial conditions, channel is designed to be variable-angle and features of removable type boundaries, and it can provide the variety of inclination angles and different types of boundaries to discuss the experiments. We use the glossy mill stones of 2.5mm to simulate the dam-break granular flow, and use particle tracking velocimetry (PTV) method to calculate the velocity field and the path of granular flows. Moreover, we calculate the accumulative flow rate of each section to define the lines of surface and bed-load. Furthermore, it can be compared with the results of numerical solutions. In theory, we take mass, momentum and kinetic energy equations as a basis, and use depth-integrated equation to derive the governing equations in depth-averaged modeling. Next, we use HLL scheme and finite volume numerical method to solve the equations. Finally, we take the result of numerical solutions to compare with the image analysis of experiments to observe the phenomenon of differences.