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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/9446
標題: | 平行壁面對沉浸球體單擺運動及其碰撞的影響之探討 Investigation on the Influences of Parallel Walls on the Immersed Spherical Pendulum Motion and Its Collision |
作者: | Hung Hsing Chen 陳宏昕 |
指導教授: | 楊馥菱 |
關鍵字: | 壁面效應,沉浸單擺運動,霍夫轉換,耦合距離,碰撞,恢復係數,顆粒流,黏性流, wall effect,wall influence,immersed pendulum motion,Hough transform,coupling distance,collision,coefficient of restitution, |
出版年 : | 2011 |
學位: | 碩士 |
摘要: | 本論文以實驗探討平行側牆對沉浸球體單擺運動的影響,並探討此單擺與一同尺寸下游單擺間的交互作用及其所受之壁面效應。各實驗皆由特定角度釋放上游單擺,保持單擺行進在壁面間中分面上,然後將高速攝影機擷取之影像經由霍夫轉換以標定出各時刻球心位置,進而算出各位置的瞬時速度以及由最大速度導出之特徵雷諾數﹝Rem﹞。藉由改變釋放角度﹝11, 15, 20度﹞與調整甘油水溶液黏度﹝385.5cP ~ 34.62cP﹞並搭配不同尺寸的壁面間距﹝間距對直徑比,W/D = 1.2, 1.4, 1.7, 2.0, 2.4, 3.0, 4.0, 5.0﹞, 本論文之特徵雷諾數落於3.45 ~ 295.39的範圍之間。
在單一單擺實驗中,實驗結果顯示於最大的兩個壁面間距﹝W/D = 4.0, 5.0﹞之下,球體運動幾乎不受壁面影響,而隨著壁面間距下降,最大速度降低的程度愈加顯著且發生位置也更加提前。不過,此一趨勢在低黏度流體中變得較不明顯,表示壁面效應的重要性逐漸降低。 由雙單擺實驗中觀察到兩單擺在實際接觸前,下游單擺早已開始運動,本論文根據此時兩單擺間水平相對距離定義出耦合距離,作為此一交互作用的量化指標。結果顯示,耦合距離隨著壁面間距下降而逐步提升但該間距下的耦合距離卻隨著液體黏度下降而縮短。 此外,碰撞的現象出現於所有黏度低於128.4cP﹝20度﹞的實驗中,於是本論文計算相應的恢復係數。結果顯示,恢復係數隨著壁面間距下降而降低,但此一趨勢在低黏度流體中變得較不明顯,儘管於該間距下之恢復係數值隨著液體黏度上升而下降。 This work investigated the influence of parallel lateral walls on the motion of an immersed spherical pendulum midway between them. In addition, a downstream target pendulum of identical size was introduced to study the interaction between the dual pendulums and how their interaction changed with the wall spacing. The pendulum motion was recorded by a high-speed camera and the image sequence was analyzed using the circular Hough transform procedure to locate the sphere. Its position time sequence was then employed to compute the velocity and the maximal particle Reynolds number, Rem. By changing the pendulum release angle, θo (11, 15,and 20 degrees), and the liquid viscosity, μ(from 385.5 to 34.62cP), a wide range of Rem, from 3.45 to 295.39, had been achieved under five to eight wall spacings represented by the spacing-to-diameter ratios W/D =1.2, 1.4, 1.7, 2.0, 2.4, 3.0, 4.0, and 5.0. In the single-pendulum case, it was observed that as W/D was decreased from 5 to 4, the reduction in maximum velocity was negligible. However, as W/D kept decreasing down to 1.2, much greater deduction in the maximum velocity occurred at an even prior location. This phenomenon persisted as the liquid viscosity was lowered but the discrepancy between different W/D cases was also diminished. Hence, the wall effect was less pronounced for the pendulum motions in a liquid of lower viscosity. In the dual-pendulum case, the target sphere was set in motion prior to physical contact with the impact pendulum and this phenomenon was observed for all the examined viscosities specified above. Therefore, a coupling distance, xtic, was defined as the horizontal distance between two vertical planes with one tangent to the impact pendulum frontal face and the other to the target sphere rear surface. The coupling distance was found to increase as W/D decreased but the value at each W/D decreased as liquid viscosity was lowered. On the other hand, collisions between the dual pendulums occurred when the viscosity was low enough (μ<= 128.4cP [θo = 20 degrees]). The resulting coefficient of restitution, e, was calculated as the ratio between the relative pendulum velocity after and before the collisions. A lower e was found when W/D was decreased but the degree of deduction was lessened when in less viscous liquid. And for each W/D, the value of coefficient increased as the liquid viscosity decreased. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/9446 |
全文授權: | 同意授權(全球公開) |
顯示於系所單位: | 機械工程學系 |
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