本研究在探討有限長度圓柱繞流的Magnus效應，運用長寬比 (AR)為2到10、轉速比(α)為0到7，在各雷諾數(Re)從10到1000之間，分析圓柱所受到的升力、阻力以及流線分布，整理出之間的趨勢關聯性，並以物理現象去描述解釋。 本研究使用一般商業軟體Ansys Fluent CFD，模擬設想是以甘油為低Re工作流體，圓柱採用雙邊自由端(兩側皆無固定端)。 選擇在雷諾數10到1000的層流，其中低雷諾數在三維流場中，流經圓柱的流體分離可以分為橫向流場分離(transverse flow separation, TFS)與縱向流場分離(longitudinal flow separation, LFS)，前此研究，發現圓柱在靜止不旋轉時: (a)在雷諾數介於50到120之間之定常流在圓柱中間橫截面的流線會有一類源點(source-like point)，是因為不同AR會造成兩側流場的分歧匯集能力變動、TFS和LFS相互抗衡，原本封閉渦旋被拉扯而改變路線，形成流線從源點散開的景象；且升力係數會隨著Re增加而單調上升，而阻力係數亦然。 (b)低雷諾數下當圓柱轉速增加時，流體因受環流渦度而改變流線，先前的類源點逐漸消失，取而代之的是渦旋，並有數個鞍點的出現。(i)阻力係數CD在低轉速比時是低AR的短圓柱較大，接著會出現交錯反轉情形。(ii)而升力係數CL在圓柱低速旋轉時，所有長寬比AR的圓柱有接近的值，並隨轉速線性上升。然而隨AR遞增依序會到達一穩定值後停止上升。從升力阻力比(CL/CD)的結果可以發現在高轉速長圓柱有最佳值，且必須在轉速比介於1到2之間，可以說產生升力的效果最好。超過該轉速區間後升阻比即開始下降。

This research has been focusing on flow over a rotational cylinder. The drag and lift force and the streamline distribution on the cylinder has been calculated in the condition of aspect ratio (AR) from 2 to 10, Reynolds number (Re) from 10 to 1000 and the spinning ratio (α) from 0 to 7. The data above has been generalized and plot to study the relationship between them on order to explain their physical meaning. This research is accomplished by the software of Ansys Fluent to solve the governing equations by finite element theory. A large scale of water tunnel has been designed for adequate space for a higher AR cylinder without effect of boundary layers. Glycerin is applied as the working fluid in low Re flow. Also the cylinder used is a two-free-end cylinder which indicates that there is no attachment on both sides of the cylinder. The calculation has been set up in the range of Re between 10 and 1000. Due to the convergence of flow over the cylinder in three dimensional space, the separation of flow passing the cylinder can be divided into transverse flow separation (TFS) and longitudinal flow separation (LFS). (a) Before this study it has been found out at a static cylinder without spinning during the range of Re=50-120 where vortex shedding does not occur yet, a source-like pattern downstream of the cylinder can be observed. This phenomenon is because the competition of the intensity of TFS and LFS. A pair of circulating eddies will be influenced by the TFS and changes its direction making the streamlines spreading from the source-like point. (b) As for the conditions of rotational cylinders, streamline changes rapidly because of the vorticity of circulation. The source-like point mentioned above slightly shifts then vanish eventually. Several saddle points may occur and their locations depends on AR. (i) Drag coefficient of a higher AR has a higher C¬D at a stationary cylinder. However at α over 1, the C¬D intersects with the lower AR, and then been overtaken eventually. (ii) Lift coefficient C¬L increases rapidly with an increasing α in the same slope when the cylinder starts to rotate. Then C¬L will stop at a steady value from AR low to high. (iii) Also from the ratio of lift and drag coefficient CL/CD, we can find that best lift efficiency occurs at the circumstances of long (slender) spinning cylinder and has to be at the spinning ratio between 1 and 2. CL/CD will start to decrease out of this range.

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