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研究生: 盧艾偉
Lu, Ai-wei
論文名稱: 應用等位函數法模擬潰壩時自由液面及流場的演變
Simulation of The Free Surface and Flow Fields Induced by Dam Breaking Using Level Set Method
指導教授: 黃清哲
Huang, Ching-Jer
學位類別: 碩士
Master
系所名稱: 工學院 - 水利及海洋工程學系
Department of Hydraulic & Ocean Engineering
論文出版年: 2008
畢業學年度: 96
語文別: 中文
論文頁數: 87
中文關鍵詞: 等位函數法碎波邊界層潰壩渦流
外文關鍵詞: level set method, moving wall problem, wave breaking, vortex, boundary layer
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  • 本文旨發展二維數值黏性造波水槽,用以模擬平板移動過程與水體的相對關係。為模擬真實流體的運動情形,本模式擬求解非穩態Reynolds Averaged Navier-Stokes (RANS) 方程與紊流模式(k-e model),並採用質點等位函數法追蹤波浪碎波時複雜自由液面的變化情形。本文經數值實驗測試(Zalesak’s problem、Moving wall problem),得到不錯的結果,證明本數值模式的準確性。在確認模式的準確性後,為了解碎波流場的運動特性,本文藉由平板移動問題,探討碎波區域自由液面變化、流場特性以及邊界層內水平與垂直速度運動特性與剪應力變化關係。本文數值結果顯示,當平板移動速度增加時,在碎波區域會因為受到碎波水體拍擊自由液面影響,產生一順時針方向渦流。從邊界層垂直流速剖面可發現,波浪發生碎波時,邊界層內的流體會有向上運動的趨勢,而平板移動的過程中,對底床邊界層流場所造成的影響範圍,隨著平板加速度的增加而減少。

    In this study numerical model was developed to solve the unsteady two-dimensional Reynolds Averaged Navier-Stokes (RANS) equation and the turbulent k-e equations for simulating the evolution of breaking water surface generated by a moving plate. A hybrid particle level set method was adopted to capture the complex free surface evolution, beginning from the steepening of the wave profile to the wave breaking. Accuracy of the numerical model was confirmed by solving the Zalesak problem and moving wall problem. After having verified the accuracy of the present numerical scheme, evolution of the overturning waves generated by a moving plate and the associated flow fields and velocity profiles within the bottom boundary layer have been revealed to details. Our numerical simulation shows that as the speed of the plate increases, due to the reattachment of the splash-up, a clockwise vortex is formed in the flow. Furthermore, when wave breaking occurs, the fluid particles within the bottom boundary layer show a tendency to move upward.

    中文摘要 I ABSTRACT II 誌謝 III 目錄 IV 表目錄 VI 圖目錄 VII 符號說明 XIV 第一章 緒論 1 1-1 研究動機 1 1-2 前人研究 1 1-3 本文架構 4 第二章 理論分析 5 2-1 控制方程式 5 2-2 無因次化處理 9 2-3 等位函數法(LEVEL SET METHOD) 11 2-4 質點等位函數法(PARTICLE LEVEL SET METHOD) 12 2-5 初始條件和邊界條件 13 第三章 數值方法 19 3-1 計算網格配置 19 3-2 控制方程式之離散化 19 3-3 SIMPLER演算法 25 3-4 自由液面邊界條件的處理 28 3-4-2 等位函數重佈過程 30 3-4-3 自由液面上的連續條件 31 3-5 計算流程 33 第四章 結果與討論 35 4-1 數值模式驗證 35 4-1-1 等位函數法之驗證 35 4-1-2 孤立波之驗證 42 4-1-3 平板移動(Moving Wall)之驗證 46 4-2 平板往流體方向運動的自由液面變化 48 4-3 碎波區域流場變化 49 4-4 邊界層內水平、垂直流速與剪應力變化關係 50 4-5 紊流動能 78 第五章 結論與建議 81 5-1 結論 81 5-2 建議 82 參考文獻 83

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