本研究使用沉浸邊界法模擬兩球體在不可以縮液體方腔中的交互運動，探討drafting, kissing 跟 tumbling (DKT)現象，研究兩球在沉降過程中，不同的初始間距、直徑比例之下，流場與兩球體之運動變化。本研究之數值方法與單球沉降之實驗結果比較做驗證。對於兩球體之沉降運動，三種不同的幾何擺放方式將在此探討，分別為Setup-A:大球放置於標準球上方；Setup-B:兩相等之標準球垂直擺放；Setup-C:大球放置於標準球下方。
研究結果顯示，kissing的時間點會隨著初始間距增加而延後，對於Setup-A，kissing的時間長度隨著直徑比增加而縮短，反之，對於Setup-C，kissing的時間長度隨著直徑比的增加而增長，當初始間距與直徑比例到達某特定值時，則不會發生DKT現象。對於Setup-A與Setup-C兩球間距在球到達終端速度時會增加，而Setup-B之間距則維持一個定值，最後，初始間距與直徑比例對於影響DKT現象的出現將被探討，藉由改變這兩個參數，DKT現象的變動過程顯而易見。

In present study, the drafting, kissing and tumbling (DKT) phenomenon of two spheres sedimenting in a long container filled with an incompressible fluid is numerically investigated by using the immersed-boundary technique. The main emphasis of this study is to investigate the effect of the initial gap sizes and diameter ratio between two spheres on the flow pattern during sedimentation. The method is first validated with flows induced by a sphere settling under gravity in a small container for which experimental data are available. For sedimentation of two spheres with different sizes, three initial configurations are considered: in Setup-A, the larger sphere is initially located above the regular one; in Setup-B, there are two identical regular spheres; in Setup-C, the regular sphere is initially located above the larger one.

The results show that, for all three initial configurations, the kissing time delays as the initial gap size increases. For Setup-A, the duration of kissing decreases with the increase of diameter ratio. Instead, for Setup-C, the duration of kissing increases with the increase of diameter ratio and there is no DKT phenomenon beyond threshold initial gap size and diameter ratio. For both Setup-A and Setup-C, the gaps between two spheres at terminal velocity increase, whereas for Setup-B that remain constant because of the same terminal velocity of two spheres. Finally, the effects of initial gap size and diameter ratio on the occurrence of DKT process are investigated. By changing these two parameters, the results reveal the transitions between the DKT phenomena.

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