本研究以離散元素法(DEM)模擬類二維垂直振動床，模擬分為兩部分，第一部分模擬探討不同形狀粗糙度之甜甜圈形顆粒體在振動床中之流動行為，考慮的形狀包含由8個球形元素、9個球形元素、10個球形元素及11個球形元素組成的甜甜圈形顆粒，進而探討顆粒形狀對顆粒體在振動床內傳輸性質的影響，傳輸性質包括速度向量場、擾動速度分佈、粒子溫度、自我擴散係數、動能及無因次質量流率。在固定振動條件(振動頻率25Hz與無因次振動加速度為18)下，四種甜甜圈顆粒體各項傳輸性質除自我擴散係數外，均呈現11球形元素>10球形元素>9球形元素>8球形元素的特性，可知較少球元素顆粒體因幾何形狀粗糙度較大，互鎖效應(inter-locking effect)較強，較易影響顆粒體的運動行為。甜甜圈形顆粒體因幾何外形，轉動運動特別明顯，且互鎖效應對於旋轉運動的影響較大，使得轉動方向擴散係數、轉動方向擾動速度及轉動動能之差異皆比x方向與y方向明顯得多。第二部分模擬探討振動床不同相位角下顆粒體的傳輸性質及內部性質，進而了解振動床的迴流機制與不同相位角下球形顆粒體的流動行為，內部性質包括配位數、應力、接觸力強度、啟動摩擦因子及組構張量。平均配位數的結果顯示，顆粒接觸頻率較高區域均在顆粒堆中央部分，而在自由表面顆粒自由彈跳，顆粒體間的接觸頻率較低。由剪應力分佈圖可證實振動床下降過程，邊壁處產生左正右負之剪力帶，造成左側顆粒體反鐘向迴流，右側顆粒體順鐘向迴流，而在振動床上升過程，則是在容器底部產生左負右正之剪力帶。摩擦啟動因子分佈結果顯示，顆粒體在左右邊壁及底部的摩擦啟動因子較大，但未達到滑動摩擦，而顆粒堆中央部分摩擦啟動因子較小。組構張量分佈結果顯示，振動床底部、中央部分及左右邊壁部份，皆為在振動床上升階段時，顆粒間接觸力較接近y方向，在振動床下降階段時，顆粒間接觸力較接近x方向。綜觀各個內部性質(配位數、應力、摩擦啟動因子及接觸力強度)可發現，在平衡位置至波峰之間多為極值發生處，可知該處附近為振動床上升受力最大。

The purpose of the study is to investigate the convection behaviour of spherical and non-spherical particles in quasi-2D vibrating beds by using discrete element method (DEM). The study includes two parts: one is the effect of particle shape on convection behavior (Part I), and the other is the micro exploration of convection mechanism (Part II). In Part I, four kinds of donut-shaped particles used in the study are respectively composed of 8, 9, 10 and 11 sub-spheres by adopting multi-sphere method, and these donut-shaped particles have the same mass and moment of inertia despite different outlines. The numerical results reveal that the transport properties increase with the increase of sub-sphere number, especially in rotational behaviour. This is attributed to the fact that the surface roughness increases with the decreasing sub-sphere number, leading to stronger inter-locking behaviour between particles. In Part II, the convection behavior of a spherical granular assembly is explored from the micro-scale point of view, and a vibrating cycle, including ascending and descending processes, is divided into 12 phases. The DEM results corroborate that the shear bands occur at the regions near the sidewalls during the descending process, whereas take place at the bottom base during the ascending process. It is the shear bands that drive the granular assembly circulate in the vibrating bed. The central part of the vibrating granular bed shows higher coordination number but smaller contact force than the sidewalls and bottom base. In addition, the mobilized friction factor at the sidewalls and bottom base are larger than that in the central part. The fabric analysis also reveals that the contact orientation approaches the vertical direction during the ascending process, but the horizontal direction during the descending process. The micro-scale analysis further points out that, during an entire cycle, the particles collide the most drastically between the balanced position and the wave crest in upward motion.

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