本研究使用數值計算軟體模擬有限長圓柱具有兩個不同圓頂蓋的周邊壓力場與速度場, 分別觀察與比較圓柱頂端設置1D與2D圓蓋, 雷諾數 ($Re_{D}$) 為250, 560, 1080的結果。
本研究設置圓頂蓋圓心的位置為座標原點, 討論流場在橫截面 (Y-Z 平面) 與垂直剖面 (X-Y平面) 的結果。
圓柱壁面的壓力分布結果顯示, 圓柱前端 (X/D = -0.03) 受到顯著的三維流動影響, 正壓與負壓的最大絕對值都小於圓柱中段 (X/D = -1, -2, -6, -10) 的模擬結果; 圓柱底部 (X/D= -24) 則是明顯地受到壁面邊界層的影響, 正壓與負壓的最大絕對值比圓柱前端的結果更小。
在圓柱前端與中段, 圓柱周邊的局部摩擦係數皆隨著雷諾數增加而變小; 在圓柱前端, 具 2D 圓頂蓋圓柱的周邊局部摩擦係數對應入流角度比具 1D 圓頂蓋圓柱的數值結果有更顯著的波動表現。
壓力計算結果顯示, 圓柱底部的壓力阻力係數小於圓柱前端與中段的數值。
剪應力的積分結果顯示, 圓柱底部接近壁面的部位與具 2D 圓頂蓋圓柱前端的摩擦阻力係數都小於具 1D 圓頂蓋圓柱前端的數值。
總阻力係數成份包括摩擦阻力係數與壓力阻力係數, 具 2D 圓頂蓋圓柱前端的總阻力係數明顯地小於 1D 圓頂蓋圓柱前端的數值。
圓柱中段的總阻力係數模擬結果印證過去學者的實驗結果(ReD = 250, CD≈1.29; ReD= 560, CD≈1.15; ReD = 1080,CD≈1)。
模擬在圓頂蓋面上的速度結果顯示, 隨著雷諾數增加, 邊界層的厚度相對地變小, 且在雷諾數為 1080 時有迴流泡的產生。
比較過去 PIV 實驗量測結果與本研究的數值模擬結果顯示, 在垂直觀測剖面 (Z/D = 0) 上, 隨著圓頂蓋尺寸增大, 來自圓頂蓋的下洗流逐漸遠離圓柱; 在橫截觀測面 (X/D = -1.5, -5.5, -10.5) 上, 尾流區域形成一對反向旋轉且對稱的渦流。

In the study, the Computational Fluid Dynamics (CFD) numerical software is used to simulate the pressure and velocity fields around a finite cylinder having a circular cover cap of two different sizes.
The top of the cylinder has a 1D or 2D cap, and Reynolds numbers ($Re_{D}$) are 250, 560 and 1080, respectively.
In the study, the center of the cap is set as the origin of the coordinates, and the results on the cross section (Y-Z plane) and the vertical cut section (X-Y plane) are discussed respectively.
The pressure distribution results on the cylinder wall surface show that the section near the free end of the cylinder (X/D = -0.03) is affected by the three-dimensional flow, and the absolute values of both the maximum positive pressure coefficient and negative pressure coefficient are smaller than the results at the middle sections of the cylinder (X/D = -1, -2, -6, - 10).
The section near the base of the cylinder is significantly affected by the wall boundary layer, and the absolute values of the maximum positive pressure coefficient and negative pressure coefficient are even smaller than the results of the section near the free end of the cylinder.
The local friction coefficient around the cylinder surface becomes smaller when the Reynolds number increases in the section near the free end and the middle section;
in the section near the free end of the cylinder, the local friction coefficient against the incident flow angle of the cylinder with a 2D cap fluctuates more significantly than that of the cylinder with a 1D cap.
The pressure drag coefficient near the base section is smaller than those of the free end and middle sections.
The integrated shear stress results show that the friction drag coefficient near the free end section of the cylinder with a 2D cap is smaller than that of the cylinder with the 1D cap.
The total drag coefficient is comprised of the friction drag coefficient and the pressure drag coefficient, and the total drag coefficient near the free end section of the cylinder with the 2D cap is significantly smaller than that of the cylinder with 1D cap.
The simulated total drag coefficient at the middle section of the cylinder confirms the experimental results of the previous studies (ReD = 250, CD≈1.29; ReD= 560, CD≈1.15; ReD = 1080, CD≈1).
The simulated results of the velocity fields around the circular cover cap show that when the Reynolds number increases, the boundary layer thickness on the cap decreases, and the recirculation bubble appears when the Reynolds number reaches 1080.
Comparisons between the numerical simulation results and the previous PIV results show that when the cap size increases, the downwash flow from the free end becomes away from the cylinder on the observed X-Y plane (Z/D = 0), and a pair of symmetrical and counter-rotating vortexes form in the wake region on the observed Y-Z plane (X/D = -1.5, -5.5, -10.5).

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