數值模擬均勻流通過球體的阻力係數及旋轉球體的運動特性

Numerical calculation on the drag coefficient of a sphere in a uniform flow field and the motion of a rotational sphere

謝爾庭(Erh-Ting Hsieh)

指導教授 ： 張憲國

國立交通大學/工學院/土木工程系所/碩士(2016年)

摘要

台灣部份海岸面臨飛砂及沙丘消失問題，目前多以編籬定沙的方式來克服。瞭解飛砂的運動行為是決定編籬定沙的方式及解決海岸飛砂問題的根本。本文以理論分析，考慮空氣通過球體的重力、阻力及Magnus力，探討球體的軌跡及運動特性。
本文以流體計算力學的Fluent軟體，模擬均勻流通過圓球下的流場，及計算出作用於球體的阻力。比較本文數值計算的阻力係數與Morrison(2013)公式，結果頗為吻合，證實Morrison (2013)公式及本文計算結果是可靠的。當流體流速大，均勻流通過圓球後會產生週期性的尾流，此尾流會影響阻力係數大約7%。
應用本文發展的二維圓球運動的數值計算來探討桌球的運動軌跡及運動特性。由一般選手打擊的起始條件，計算結果發現桌球旋轉方向、旋轉角速度主要影響球體運動的軌跡，而球的大小及尾流影響運動軌跡的並不明顯。本研究結果可做為解決飛砂工程及桌球選手訓練的參考。

關鍵字

數值模擬 ； 阻力係數 ； 旋轉球體

並列摘要

Some parts of the coastal areas in Taiwan have been suffering from the problem of blown sands and dune erosion. Sand-settle fences are commonly taken to solve the problem of blown sands. However, understanding the dynamics and motion of blown sands is a key to fix suitable spaces and heights of the fences. Under the research motive this thesis investigates the trajectory and kinematic properties of a sphere considering gravitational, frictional and Magnus forces on it. The Fluent software is utilized to simulate the flow field of a uniform current passing through a sphere and calculate its drag force. The accuracy of all computations is confirmed by small differences of the drag coefficient between the present results and Morrison’s (2013). Periodic wakes behind the sphere are simulated for large Reynolds number. The wakes make a periodically varying drag coefficient of which the maximum is larger than the mean by approximately 7%.
A numerical model is developed to compute the two-dimensional trajectory and kinematic properties of a top/under-spinning table-tennis ball, of which the motion is like for the sphere, with a common initial condition of regular players. The initial angular speed and direction of a rotational ball are the key factors in determining the motion. However, the change in the diameter of current balls and generated wakes are minor factors in affecting the motion. The results of this study can be applied for the wind-blown sand engineering and skill knowledge of table tennis players.

並列關鍵字

Numerical calculation ； drag coefficient ； rotational sphere

參考文獻

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5. Chester, W., Breach, D., & Proudman, I., On the flow past a sphere at low Reynolds number, Journal of Fluid Mechanics, 37 (4), 751-760, 1969.

6. Goldstein, S., Concerning some solutions of the boundary layer equations in hydrodynamics, Paper presented at the Mathematical Proceedings of the Cambridge Philosophical Society,1930.