本文利用晶格波茲曼法結合邊界格點判斷法討論一開放圓型攪拌混合器於流體的擴散問題，其中採用不可壓縮的D2Q9晶格速度模型，並使用被動純量法推得濃度模型求得濃度場。流場的擾動可經由改變葉片運動模式產生不同的混合效益。本文主要包含二種葉片運動模式：(1)等角速度旋轉(2)區間擺動並透過改變入口之間距、流體雷諾數、振幅等情況的速度場及濃度場變化。結果顯示在水平區間擺動的混合效益最差，原因是攪拌棒置放在兩入口之間，而擺動振幅不夠大時反而會把流體推走對混合並無助益反而會使混合效率降低。垂直區間擺動下在振幅 時混合效益最好，主要是因為振幅小的情況下，攪拌棒近乎垂直，可以有效地阻擋流體無法直接流出，並且使流體改變流動方向，增加混合效益。結果亦發現等角速度旋轉的混合效益介於兩者之間。

In this dissertation, the Lattice Boltzmann method is applied to simulate the effect of flow field and convection diffusion of the open stirred tank with an impeller, which moves in difference patterns, i.e., constant angular velocity motion, horizontal oscillating motion and vertical oscillating motion. It reveals that the vertical oscillating motion could lead to a better mixing performance, and the mixing performance of the constant angular speed is between the horizontal oscillating and the vertical oscillating.

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