臺灣博碩士論文加值系統

本文以數值方法分析均勻流流過一排等間距配置方柱的流場分岐過程。數值方法採用等間距交錯配置之格網系統；控制方程式中空間項的離散，對流項採七階精準之上風差分法，擴散項採六階精準之中央差分法，壓力場採用MAC（Marker—And—Cell Method）法解答。數值計算結果發現，固定間距比流場隨著雷諾數漸次增加產生相當有趣的轉變過程。當雷諾數很小時，流過柱體間隙的射流為獨立平行流，不受鄰近射流影響；但是，當雷諾數加大時，出現第一次叉形分岐，原本平行獨立的兩兩射流便開始相互影響，結合成雙射流之合流型態；當雷諾數持續增加，流場保持第一次叉形分歧後的雙射流之合流型態，直到第二次叉形分歧出現，成對的射流又開始相互影響結合成四射流之合流型態；當雷諾數再次增加時，流場由原本隨時間不再變化的穩定尾流流場開始變得不穩定；當超出臨界雷諾數時，轉變為渦漩溢出流場。
本研究探討流過一列方柱流場隨著雷諾數增加所產生的流動型態轉變過程。轉變過程採用非線性理論與流場分歧圖分析之。我們發現，流過方柱的流場，隨著雷諾數增加時，流場沿垂直空間方向呈現叉形分歧過程，最終伴隨著或普分歧（Hopf Bifurcation）轉變為週期性震盪之渦漩逸出流場（Vortex Shedding Flow）。

We present a direct numerical simulation of transition of flow past an array of square cylinders with pitch to side ratio equals to 1.7 . The numerical experiments are conducted by solving the 2D incompressible Navier - Stokes equations with increasing Reynolds numbers（Re）. The spatial discretization consists a seventh — order accurate upwind - biased method for the convective terms and a sixth — order central difference method for the diffusive terms . It is already known that the wakes behind the square cylinders forming by two symmetry re — circulated bubbles are independent of each other when Re is small . Above a critical Reynolds number Rec2=25.08 , the confluence of two wakes occurs due to a first pitchfork bifurcation . After Mizushima and Kawaguchi , we call the twin — wakes as the 2σ flow . As Re is increased to Rec4=28.204 , the 2σ flow transits to 4σ flow after a successive spatially supercritical bifurcation . Furthermore , as Re is increased to Recrt=32 , the periodic vortex shedding flow region is reached after the first Hopf bifurcation . The spatial and temporal transition processes of the flow past an array of square cylinders are illustrated by using bifurcation diagrams of velocity of the flow with increasing Re .

目錄
誌謝 Ⅰ
中文摘要 Ⅱ
英文摘要 Ⅲ
目錄 Ⅳ
圖目錄 Ⅶ
表目錄 Ⅸ
符號索引 Ⅹ
第一章 緒論
1.1 前言……...………………...…………………….…………1
1.2 研究目的……..….………………………………………...2
1.3 文獻回顧………....……………………..…………………3
1.4 本文大綱………….…………………………………….…7
第二章 數學模式
2.1 計算範圍流場之定義………....……...………..….....…8
2.2 基本假設………………………..…….…………..….…...9
2.3 控制方程式……………..………………...………..……10
2.4 初始條件………..………….…………………...…….…12
2.5 邊界條件……….….……….………...…...…..…………13
第三章 數值方法
3.1 動量方程式之離散過程………….…………...………18
3.1.1 時間項之離散…….……...………………...…………18
3.1.2 對流項與擴散項之離散.…...……………………...19
3.2 壓力修正方程式………..……....….………….….…21
3.3 MAC數值演算法………….…………...……..………25
3.4 數值運算的求解步驟…………..…….......…...……26
3.5 數值方法的精確度………....…….…………………27
3.5.1 時間間隔……………………………..….……………27
3.5.2 鬆弛係數……….……………………..………………28
3.5.3 連續方程式吻合度…..……………..………………28
3.5.4 計算網格…..…………………….……………………28
3.5.5 計算時間……………………………..….……………29
第四章 結果分析與討論
4.1 多樣流場型態……………...………….……………..30
4.1.1 1σ流場型態……………...…………….……………31
4.1.2 2σ流場型態…………………………………………31
4.1.3 3σ流場型態…………………………………………32
4.1.4 4σ流場型態………………….…...…………………33
4.1.5 週期性震盪之渦漩逸出流場…………….……….33
4.1.6 流場穩定性探討.…………………...…….…………34
4.2 流場分歧過程…………………….………….....……38
4.2.1 臨界雷諾數…………………….…………..…………38
4.2.2 流場分歧圖………………………………...…………39
第五章 結論與建議
5.1 結論………….…………………………………………41
5.2 建議………….…………………………………………42
參考文獻 …….………………………………………………………….………44

參考文獻
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