# 臺灣博碩士論文加值系統

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 本文主要在探討二維晶格波茲曼法結合大渦模型應用到三種不同的紊流場並提出了有系統與廣泛的研究評估。此三種數值模擬的範例分別為頂蓋驅動流場、背向階梯流場以及紊流噴流衝擊冷卻。紊流統御方程式使用流函數-渦度法配合大渦模型表示之，並使用晶格波茲曼法將統御方程式做離散，採用D2Q5的晶格波茲曼模型模擬速度場及溫度場。首先在前兩個範例，頂蓋驅動流與背向階梯流場的驗證中，與基準的實驗結果相比較之下，發現使用晶格波茲曼法結合大渦模擬，模擬結果是相當可靠與準確的。最後，將晶格波茲曼法結合大渦模擬實際應用到噴流衝擊流場進行數值模擬與討論。首先對具有兩種熱邊界的紊流衝擊噴流作驗證，等溫邊界(Re=10200,H/W=2.6)與等熱通量邊界(Re=10000,H/W=2)，對於紊流噴流衝擊流場與熱傳的數值預測值與文獻的數據作驗證。另外，對於暫態噴流衝擊亦進行分析，其研究範圍為300〈=Re〈=1500，2〈=H/W〈=4，0.5〈=q〈=1.5，工作流體為空氣(Pr=0.71)。數值結果顯示紐賽數隨著雷諾數的增加而增加，而改變了衝擊高度(H/W)會使得流場提早轉變為紊流，並且對紐賽數的分布有顯著的影響。在整個模擬的結果可以發現，晶格波茲曼法結合大渦模擬，模擬暫態之紊流流場具有相當的準確性，在未來紊流場的模擬應用上是很有前途的。
 In this study, systematic and comprehensive research has been proposed to evaluate a two-dimensional Lattice Boltzmann Method (LBM) coupled with a Large Eddy Simulation (LES) model and has been applied to three different turbulent flow type. Three numerical examples, lid driven cavity, backward facing step flow and turbulent jet impingement cooling are employed. Turbulent governing equations using the stream function-vorticity method combined the Large-Eddy Simulation model is solved and discreted with Lattice Boltzmann model. A numerical scheme to solve the flow and the temperature fields using the D2Q5 is presented. In the first two examples, the LBM coupled with LES for predicting the lid driven cavity, and the backward facing step flow have been evaluated by comparing the numerical results with benchmark experimental data. The good agreement indicates the LBM coupled with LES is reliable and accurate. Finally, a practical application of LBM coupled with LES for jet impingement is simulated and discussed. The validation of the turbulent impinging jet with two thermal boundary, constant temperature boundary (Re=10200,H/W=2.6) and constant flux (Re=10000,H/W=2) are studied first. The numerical predictions of turbulent jet impingement flow and heat transfer have been evaluated by comparing with the available data in the literature. In addition, the analysis of transient jet impingement is carried out for 300〈=Re〈=1500,2〈=H/W〈=4,0.5〈=q〈=1.5 . The fluid considered here is air (Pr=0.71). The results show that Nu increases with increasing jet Reynolds number, while the increase in parameters H/W to advance the time of flow field from the transition to turbulence and has a significant influence on the Nusselt number distribution. The results demonstrate that the present numerical model is a promising tool to investigate the solution of fluid flow and heat transfer for turbulent flow.
 目錄中文摘要……………………………………………………………………………I英文摘要…………………………………………………………………………III誌謝…………………………………………………………………………………V目錄…………………………………………………………………………………VI表目錄………………………………………………………………………………IX圖目錄………………………………………………………………………………X符號說明…………………………………………………………………………XIV第一章 緒論………………………………………………………………………1 1-1 研究背景與動機…………………………………………………1 1-2 晶格波茲曼法(LBM)文獻回顧……………………………………3 1-3 大渦模擬(LES)文獻回顧…………………………………………4 1-4 衝擊噴流文獻回顧………………………………………………6 1-5 本文探討的主題與方法…………………………………………8 1-6 本文架構…………………………………………………………8第二章 理論分析…………………………………………………………………9 2-1 統御方程式解析…………………………………………………9 2-2 晶格波茲曼方法(Lattice Boltzmann Method)……………10 2-3 大渦模擬(Large-Eddy Simulation)………………………11 2-4無因次化系統……………………………………………………16 2-5邊界條件…………………………………………………………19 2-6 Nusselt number計算…………………………………………24第三章 數值方法…………………………………………………………………25 3-1晶格波茲曼方程式之推導………………………………………25 3-1-1渦度晶格波茲曼方程式之推導………………………25 3-1-2流線晶格波茲曼方程式之推導………………………28 3-1-3能量晶格波茲曼方程式之推導………………………31 3-2 收斂標準…………………………………………………………35第四章 結果與討論………………………………………………………………36 4-1頂蓋驅動流場……………………………………………………37 4-2 背向階梯流場……………………………………………………38 4-3 衝擊噴流流場……………………………………………………39 4-3-1 衝擊噴流流動現象……………………………………40 4-3-2 衝擊噴流之固定壁面溫度邊界條件…………………41 4-3-3 衝擊噴流之固定壁面熱通量邊界條件………………44第五章 結論與未來方向…………………………………………………………80 5-1 結論………………………………………………………………80 5-2 未來方向…………………………………………………………81參考文獻……………………………………………………………………………82自述…………………………………………………………………………………87表目錄表4-1 頂蓋驅動流場各漩渦中心點位置.........................47圖目錄圖2-1 晶格波茲曼模型示意圖………………………………………………11圖2-2 頂蓋驅動流場示意圖…………………………………………………20圖2-3 背向階梯流場示意圖…………………………………………………21圖2-4 衝擊噴流流場示意圖…………………………………………………22圖4-1 頂蓋驅動流場之流線驗證圖(Re = 400) ………………………………………………48圖4-2 頂蓋驅動流場之流線驗證圖(Re = 1000)………………………………………………49圖4-3 頂蓋驅動流場之流線驗證圖(Re = 5000)………………………………………………50圖4-4 頂蓋驅動流場之流線驗證圖(Re = 10000)……………………………………………51圖4-5 頂蓋驅動暫態流場之流線圖(Re = 20000)……………………………………………52圖4-6 頂蓋驅動暫態流場之流線圖(Re = 20000,t=100000)……………………53圖4-7 頂蓋驅動暫態流場之流線圖(Re = 20000,t=200000)……………………54圖4-8 頂蓋驅動暫態流場之流線圖(Re = 20000,t=300000)……………………54圖4-9 頂蓋驅動暫態流場之流線圖(Re = 20000,t=400000)……………………54圖4-10 頂蓋驅動暫態流場之流線圖(Re = 20000,t=500000)……………………55圖4-11 頂蓋驅動紊流流場殘值收斂圖 (Re = 20000)……………………………………56圖4-12 背向階梯流場之再接觸點驗證圖……………………………………57圖4-13 背向階梯流場之流線圖(Re = 300)…………………………………………………………58圖4-14 背向階梯流場之流線圖(Re = 800)…………………………………………………………58圖4-15 背向階梯流場之流線圖(Re = 1500)………………………………………………………58圖4-16 背向階梯紊流流場殘值收斂圖(Re = 2400)…………………………………………59圖4-17 背向階梯暫態流場之流線圖(Re = 2400)………………………………………………60圖4-18 衝擊噴流流場之流線圖(Re = 300)…………………………………………………………61圖4-19 衝擊噴流流場之流線圖(Re = 800)…………………………………………………………62圖4-20 衝擊噴流流場之流線圖(Re = 1500)………………………………………………………63圖4-21 衝擊噴流紊流流場殘值收斂圖 (Re = 10200)……………………………………64圖4-22 衝擊噴流紊流溫度場殘值收斂圖 (Re = 10200)………………………………64圖4-23 衝擊噴流等溫壁面條件之網格獨立測試圖 (H/W = 2.6, Re = 10200)………………………………………………………………………65圖4-24 衝擊噴流流場等溫壁面條件之溫度分布圖(Re = 300)……………………66圖4-25 衝擊噴流流場等溫壁面條件之溫度分布圖(Re = 800)……………………67圖4-26 衝擊噴流流場等溫壁面條件之溫度分布圖(Re = 1500)…………………68圖4-27 衝擊噴流流場等溫壁面條件之紐賽數分布圖(Re = 300)………………69圖4-28 衝擊噴流流場等溫壁面條件之紐賽數分布圖(Re = 800)………………69圖4-29 衝擊噴流流場等溫壁面條件之紐賽數分布圖(Re = 1500)……………70圖4-30 紊流衝擊噴流流線圖及等溫壁面條件之溫度分布圖 (H/W = 2，Re = 10000)……………………………………………………………………………71圖4-31 衝擊噴流等熱通量壁面條件之紐賽數驗證圖 (H/W = 2，Re = 10000)……………………………………………………………………………72圖4-32 衝擊噴流流場等熱通量壁面條件之溫度分布圖 (Re=300,q=1.0 )……………………………………………………………………………………………73圖4-33 衝擊噴流流場等熱通量壁面條件之溫度分布圖 (Re=800,q=1.0)………………………………………………………………………………………………74圖4-34 衝擊噴流流場等熱通量壁面條件之溫度分布圖 (Re=1500,q=1.0)……………………………………………………………………………………………75圖4-35 衝擊噴流流場等熱通量壁面條件之溫度分布圖 (H/W=3,Re=800,q=0.5)………………………………………………………………………………76圖4-36 衝擊噴流流場等熱通量壁面條件之溫度分布圖 (H/W=3,Re=800,q=1.0)………………………………………………………………………………76圖4-37 衝擊噴流流場等熱通量壁面條件之溫度分布圖 (H/W=3,Re=800,q=1.5)………………………………………………………………………………76圖4-38 衝擊噴流流場等熱通量壁面條件之紐賽數分布圖 (Re=300，q=1.0)……………………………………………………………………………………………77圖4-39 衝擊噴流流場等熱通量壁面條件之紐賽數分布圖 (Re=800，q=1.0 )…………………………………………………………………………………………77圖4-40 衝擊噴流流場等熱通量壁面條件之紐賽數分布圖 (Re=1500，q=1.0 )………………………………………………………………………………………78圖4-41 紊流衝擊噴流流線圖及等熱通量壁面條件之溫度分布圖 (H/W=2,Re=10000,q=1.0)………………………………………………………………………79
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 1 相變化材料於可攜式電子零件冷卻之數值模擬 2 應用晶格波茲曼法結合大渦法模擬紊流強制對流熱傳問題 3 應用熵增最小化於對齊式與交錯式柱狀形散熱器之電子冷卻數值最佳化 4 應用同倫分析法於非線性熱傳遞問題之研究 5 改良式柱狀鰭片與渦流產生器對散熱器熱性能增強的研究 6 應用晶格波茲曼法與場協同理論於不同阻礙物之背向階梯管道熱流分析 7 波形渠道連接多孔性區域的熱交換增強:燃料電池優化設計 8 雙衝擊噴流混合機制之實驗研究 9 具超疏水表面之矩形截面流道減阻研究 10 促進彎曲流道中之流體混合的微結構設計 11 應用晶格波茲曼法模擬奈米流體熱對流問題 12 應用晶格波茲曼法模擬三維複雜幾何形狀管道之流動問題 13 提升無線分散系統傳輸效能之IEEE 802.11n存取點最大獨立集合演算法 14 具發泡銅材填充之鰭柱散熱座於侷限式矩形衝擊噴流下之熱傳特性實驗研究 15 利用三維晶格波茲曼方法模擬兩相流之流場

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