本研究結合流固雙向動態耦合模式、牛頓力學和顆粒碰撞模式描述球體在黏性流體中的運動，球體周遭流場採用大渦模式計算，共探討了三種不同狀況下球體顆粒與流體之間的互制現象，模擬結果並與實驗進行驗證及分析。結果顯示：(1)比流體密度較小之浮球顆粒墜入水中再浮起的過程中、附加質量係數CA = 0.50與雷諾數Re或球體密度無關；(2)在雙球自由墜落的過程中，當雙球的初始間隙小於0.75D時，因為側向力不對稱的緣故，雙球落下的軌跡會呈現S字型方式落下；(3)球體沿斜坡滑落入水中，碰撞水中另一顆球體，兩球之間的碰撞力採用Chen (2014)之線性碰撞模式，滾動的摩擦係數CR = 0.25，模擬結果十分接近實驗結果，亦即本研究所發展之流固雙向動態耦合模式可模擬球體在水中的墜落、滾動及碰撞。

This study integrates a large eddy simulation (LES) model and a moving-solid algorithm to simulate the falling process of spheres in the water. The simulation results are verified by the results of laboratory experiments and the analytic solution. The numerical model then is utilized to investigate three different flow conditions: one buoyant sphere falling into water; the interaction of two free-falling spheres; the collision of two spheres in the water. The results revealed that the added mass coefficient CA = 0.50 is independent of the Reynolds number and the density ratio of the sphere to the fluid. The interaction of two free-falling spheres is influenced by the initial gap between two spheres. The falling trajectories of the spheres is like a S shape when the initial gap is smaller than 0.75D, due to asymmetric pressure on the sphere surface. In the collision case, the collision forces between two moving spheres is simulated by the linearized collision model of Chen (2014). The good agreement between the experimental observation and numerical simulation demonstrates that the present numerical model can be used to simulate the falling, rolling and collision of spheres in viscous fluid.

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