長與有限圓柱的Magnus效應之近地影響：實驗與計算

Abstract

Magnus 效應在過去已經被許多學者探討過且已有廣泛的應用，無論是在工程 碩球類運動中。然而，近年來近地效應與 Magnus 效應的耦合結果又再次引起研 究學者的注意。不過，過去的討論多半著重於靜態的系統–受測物與地面沒有垂直 方向的相對速度;因此，此研究將針對主動旋轉且動態接近地面中的圓柱與其周 遭流場的變化，並將之與靜態結果比較。在本研究中將比較在二維以及三維流場 中動態以及靜態結果。 在研究中探討轉動圓柱幾個重要的無因次參數，分別為圓柱切線方向速度與 入流速度比值 α、圓柱下降速度與入流速度比值 β 以及地面與移動圓柱間距 SG。 所探討的α範圍為0至±0.2和SG 則介於5D到0.5D，D為2cm以及3cm轉動 圓柱直徑。根據圓柱轉動方向分為三種:一是當圓柱為無轉動(α = 0);另一則 是圓柱為逆時針轉動(α > 0);最後則圓柱以順時針轉動(α < 0)。 研究的結果顯示，根據不同的轉動方向流場有著顯著的差異。第一種，在無 轉動條件下，受地面影響造成其尾流寬度減小，其升、阻力增加。第二種，在正 轉條件下，當 SG 減少，其升、阻力會減少，且其渦旋剝離頻率亦增加。其渦旋 會受到地面影響而削弱，因而渦旋剝離位置受入流以及下降速度影響導致尾流向 圓柱下方較低位置發展。第三，在逆轉條件下，當 SG 減少，其升力與渦旋剝離 頻率減少，阻力則增加。其渦旋會受到地面影響而增強，因而下降時渦旋剝離位 置不同造成接近地面後尾流結構不同。且嘗試以穩定性分析正轉、逆轉以及無轉 動條件下在接近地面時穩定情形。 然而，根據結果不論是靜態或動態，所造成流場的變化是一致的，但是作下 降運動對於受力的改變較定點少。

Though Magnus effect and its application had been widely investigated by many scientist and researchers, its behavior under the influence of the near ground effect has recently acquired much attention. However, most studies considered the ground effect as a static surface without relative velocity towards the subject. Therefore, this research is aimed to numerically and experimentally investigate the flow interaction around a rolling cylinder that shifts towards a flat surface in a uniform flow. Further, the results in the dy- namic case were compared to the static cases under both 2 dimensional and 3 dimensional aspects. Some important normalized parameters of the rolling cylinder being discussed through- out the entire investigation are the rotation ratio α, declining velocity ratio β, and the spac- ing gap between the cylinder and the flat surface SG. The range of interest for α is from 0 to ±0.2, and SG from 5D to 0.5D, where D is the diameter of the rolling cylinder chosen to be 2 cm and 3 cm. Note that three types of classification are distinguished according to the rotation motion of the cylinder: One is when the cylinder has non-rotation (α = 0); another would be the cylinder rotating in counterclockwise direction (α > 0); and the other is the clockwise rotation (α < 0) of the cylinder. The results show that the flow pattern significantly varies in each of the three distin- guished types of rotation motion. In the first case, when the cylinder is non-rotation, the ground effect mitigates eddies behind the subject and leads to a higher lift and drag. In the second case, when the cylinder is counterclockwise-rotation, as SG is decreasing, the lift and drag drops, and the separation frequency increases. The vortex around the cylinder is alleviated by the ground effect, and the separation occurs at a lower portion behind the cylinder due to the effect of the incoming flow and declining motion. In the last case, when the cylinder is clockwise-rotation, As SG decreases, the lift and the separation frequency decreases, and the drag increases. The vortex is strengthened by the ground effect, and the separation occurs at a higher portion with the same reasoning. Further, the stability analysis is applied to the three distinguished motions to check for their stability. As a result, the phenomenon of the flow patterns are consistent in both static and dynamics cases, but the force exerted on the cylinder is smaller for the dynamic case.