Numerical Simulation of Boundary Effects on the Groyne flow

本研究是以有限元素法模擬求解二維、穩定、不可壓縮的黏性紊流流場。首先將水深平均連續方程式與動量方程式轉換成有限元素模式，進行數值模擬的運算。由於元素大小不同及格點位置分布未能符合局部精度的需求，導致演算的誤差，利用均方根誤差範數的定義，估算出每一個元素在求解過程中所產生的誤差，並根據此誤差量進行網格調整。網格調整的方式採用r型網格調整，即在不增加元素數目與不提高元素形狀函數的自由度之條件下，重新分配元素大小及格點的位置，期望能調整至最佳的網格配置。 本研究以上述數值方法探討丁壩流場，邊界設定分別採用可滑移(free slip)邊界與無滑移(no slip)邊界進行演算，並討論均勻網格及網格自動化調整作運算之效益。為提高計算精度及效率，採用二次分區加密方式，提昇丁壩區之流場描述。數值模擬結果與前人研究的結果相比較，其無滑移邊界模式的模擬結果較趨近真實流況，並進一步應用此模式模擬探討在不同福祿數、雷諾數、曼寧係數，其對於丁壩後方迴流區域的影響。Using the finite element method, this research simulates and solves the two-dimensional, steady, incompressible, and viscous turbulence flow. First, it changes the depth-averaged governing equation into the finite element model so as to proceed the operation of numerical simulation. In the process of the operation, arithmetic errors are made because of the side differences among elements and also because of the unfitness between the positions and distributions of nodes and the need of local accuracy. Therefore, the research uses the definition of the root-mean-square norm to estimate the errors, produced in the process of operation, of each element, and also to do the mesh relocation. In other words, to R-refinement the size and the location of each element without adding the number of elements and raising the degree of freedom of the shape function, so as to get the best mesh relocation. Centered on the groyne flow, this research uses boundary condition with free slip boundary and no slip boundary to do the operation separately, and further to discuss the results of uniform mesh and the automatic adaptive refinement. In order to raise the accuracy and the efficiency of the operation as well as the description of groyne flow field , the study uses two stages to push the mesh more densely .Then, compare the results of no slip boundary model according to the studies made before to get the identical tendency. The final step is to discuss the influences made by the Froude number, the Reynolds number, and the manning coefficient in the recirculation region of groyne.中文摘要..............................................Ⅰ 英文摘要..............................................Ⅱ 目錄..................................................Ⅲ 表目錄................................................Ⅵ 圖目錄................................................Ⅶ 符號說明..............................................Ⅹ 第一章 緒論...........................................1 1-1 研究動機.........................................1 1-2 研究目的.........................................2 1-3 研究方法.........................................2 1-4 研究流程.........................................5 第二章 文獻回顧.......................................6 2-1 數值方法的相關研究...............................6 2-2 丁壩流場的相關研究...............................8 第三章 理論基礎與方法.................................11 3-1 數值模式概述.....................................11 3-2 水理計算.........................................11 3-2-1 控制方程式....................................11 3-2-2 邊界條件......................................13 3-3 建立有限元素模式.................................14 3-4 座標轉換.........................................18 3-5 數值積分.........................................19 3-6 疊代過程.........................................20 3-7 誤差範數.........................................21 3-8 一階誤差導數定義.................................22 3-9 調整程序.........................................24 3-10 網格調整的限制..................................26 第四章 模式驗證與應用.................................28 4-1 丁壩流場.........................................28 4-1-1 前人實驗與數值模式設計概述....................28 4-1-2 數值模擬實驗設計..............................29 4-1-3 邊界條件及計算區域............................30 4-1-4 初始網格......................................31 4-1-5 網格調整方式..................................31 4-2 結果與討論.......................................32 4-2-1 流場中流速及水深的分布與前人實驗和模式的比較..32 4-2-2 邊界效應對再接觸點的影響......................36 4-3 有限元素無滑移邊界模式的應用.....................37 4-3-1 福祿數的改變對迴流區域的影響..................37 4-3-2 雷諾數的改變對迴流區域的影響..................39 4-3-3 曼寧係數的改變對迴流區域的影響................40 第五章 結論與建議.....................................41 5-1 結論.............................................41 5-2 建議.............................................42 參考文獻..............................................43 附錄..................................................6