臺灣博碩士論文加值系統

高爾夫球在所有的球類運動當中速度算是最快的一個，因此不僅是球體材質會影響飛行距離的長短，球體外形所產生的氣動力學現象更是另一個重要的關鍵；很多文獻只討論球體的材料及結構，且大部份廠家也都是改變外皮層數或材料，很少談到運用不同表面凹洞所造成氣動力的影響，而且在球體的製程上，總是只能等到成品完工後才有辦法測試飛行的好壞，因此藉由計算流體力學的方法研究高爾夫球流場及氣動力現象，實是有系統且節省成本的方式。
　　本論文以結構和非結構網格計算高爾夫球流場並比較其適當性，並使用FLUENT 6.2.16軟體進行數值運算，計算出各種球體之氣動力參數及噪音，最後將飛行距離可視化呈現。結果顯示結構式網格對於氣動力參數有較準確的計算；在球體外形設計上，增加小凹洞有助於升力的提升，且在低發射角度時，凹洞較深球體之升力影響效果大於阻力，會讓球飛得更遠(臨界深度為0.25 mm)；至於噪音方面，凹洞深之球體會產生較低的噪音值。在球桿與飛行距離方面的探討，飛行距離隨著木桿的號數增加而遞減，每種木桿號數之間的飛行距離大約相差13.5m；鐵桿與木桿有類似的趨勢，在鐵桿各桿號之間飛行距離差介於6~11m。特殊用桿方面，飛行距離與發射角度呈反比。

The speed of golf balls can be regarded as the fastest in all ball games. The flying distance of a golf ball is influenced not only by its material, but also by the aerodynamics of the dimple on its surface. A lot of documents have only discussed the material and structure of golf balls, and most manufacturers have only changed the coating or the material of golf balls, but have seldom mentioned the influences the concave surfaces on the overall aerodynamics of golf balls. In the cycle of the golf ball design and manufacture, the flying behavior of golf balls can only be tested after the golf balls are completely made. By using Computational Fluid Dynamics method, the flow field and aerodynamics characteristics of golf balls can be studied and evaluated before the golf balls are actually manufactured. By the way, the manufacturing cost can be greatly reduced.
Using FLUENT as solver, this thesis used structured and non-structured grids to come out with the most appropriate grid systems for the simulations of golf balls. Then, numerical simulations were carried out to estimate the aerodynamics parameters and noise levels for various kinds of golf balls having different dimple configurations. With the obtained aerodynamics parameters, the flying distance and trajectory for a golf ball were determined and visualized. The results showed that structured grids produced more accurate results. In terms of dimple layout, it was found that the lift coefficient of the golf ball increased if small dimples were added between the original dimples. When launched at small angles, golf balls with deep dimples were found to have greater lift effects than drag effects. Therefore, the golf balls would fly further until critical depth on 0.25 mm. As far as noise generation was concerned, deep dimples produced lower noise levels. When different club types were considered, it was found that the flying distance decreased with the no. of wooden clubs. For every increment in the no. of wooden club, the flying distance differed by about 13.5 m. A similar trend was observed for iron clubs but the distance differed about 6 m to 11 m. If a special-purpose club was used, the flying distance was found inversely proportional to the launch angle.

摘要................................................................................................................I
Abstract.........................................................................................................II
誌謝.............................................................................................................IV
目錄..............................................................................................................V
表目錄.........................................................................................................IX
圖目錄..........................................................................................................X
符號索引...................................................................................................XV
1. 緒論..........................................................................................................1
1.1 研究動機與背景......................................................................……..1
1.1.1 高爾夫球的歷史演進.................................................................1
1.1.2 球體結構.....................................................................................3
1.1.3 高爾夫球飛行要素.....................................................................3
1.1.4 氣動力性能.................................................................................5
1.2 文獻回顧..................................................................................……..7
1.2.1 氣動力相關文獻.........................................................................7
1.2.2 噪音相關文獻...........................................................................10
1.2.3 風洞實驗相關文獻...................................................................11
1.2.4 飛行軌跡探討相關文獻...........................................................12
1.3 研究方法..................................................................................……13
2. 數值分析................................................................................................15
2.1 統御方程式..................................................................................…15
2.1.1 連續(continuity)方程式............................................................15
2.1.2 動量(momentum)方程式..........................................................15
2.2 紊流模式..........................................................................................16
2.2.1 Standard κ-ε紊流模式...............................................................16
2.2.2 RNG κ-ε紊流模式.....................................................................17
2.2.3 Realizable κ-ε紊流模式.............................................................18
2.3 遠場噪音模式..................................................................................18
2.3.1 Lighthill’s聲學近似模式...........................................................19
2.3.2 Ffowcs-Williams and Hawkins方程式......................................20
2.4 數值方法..........................................................................................21
2.4.1 擴散項(Diffusion Terms) .........................................................21
2.4.2 對流項(Advection Terms) ........................................................22
2.4.3 矩陣方程式求解.......................................................................22
2.4.4 速度與壓力間之耦合算法(velocity-pressure coupling
algorithm) .................................................................................23
2.4.5平行運算....................................................................................24
3. 研究構型、格點與流場特徵描述........................................................26
3.1 幾何模型與網格系統......................................................................26
3.2 邊界條件..........................................................................................29
3.3 案例說明.........................................................................................32
3.4 噪音探測點位置.............................................................................36
4. 模擬驗證................................................................................................37
4.1 三維高爾夫球定性驗證.................................................................37
4.2 三維圓球定性驗證.........................................................................38
4.3 三維圓球定性、定量驗證...............................................................38
4.4 風洞實驗與模擬之驗證.................................................................39
4.5 二維圓柱紊流噪音參數之驗證.....................................................42
5. 研究結果分析與討論............................................................................44
5.1 二維模擬.........................................................................................44
5.2 三維模擬.........................................................................................51
5.3 球體噪音分析.................................................................................76
5.4 球桿對於飛行軌跡之影響.............................................................79
6. 結論........................................................................................................83
6.1 結論.................................................................................................83
6.2 未來展望.........................................................................................84
參考文獻.....................................................................................................86
作者簡介.....................................................................................................91

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