臺灣博碩士論文加值系統

為瞭解渠道中植生之存在對於水流流速的影響，本研究以水力學的觀點出發，將水流流經植生渠道之流場分為均質水層、植生層以及可透水土層等三個區域進行流場速度之有限元素分析。除了將植物體下方之土壤視為具滲透性之多孔介質之外，亦將植物體本身視為一多孔介質，而將植生層與土層內的水流視為孔隙介質流。

本研究以簡化之雷諾方程式 (Reynolds average Navier-Stokes equation) 搭配修正之Biot多孔彈性介質理論所建立之多孔介質紊流模式作為控制方程式。待控制方程式與邊界條件確定之後，便以Galerkin Method產生待解之有限元素矩陣式，最後將三層之有限元素矩陣結合為全域之有限元素矩陣式後配合邊界條件求解得到流速之分佈情形。

在求得流速分佈後，於相同的流況與參數下與楊（2007）的室內渠槽實驗進行檢核，驗證結果十分吻合，顯示本研究所採用的有限元素分析結果可適當描述水流流經植生渠道的流速分佈情形。分析比較各參數之後，發現紊流強度以及植生所佔之渠道斷面積對於流速之影響較為明顯。

In order to know how vegetation influences streamwise velocity of water flow passing vegetative channel, we divide the flow field into three regions: homogenous water layer (the flow over vegetation), vegetation layer (the flow inside vegetation) and permeable soil layer (the flow inside the soil), then solve the streamwise velocity by finite element analysis. The soil and vegetation are both regarded as porous media and the flow inside the two layers is porous media flow.

The velocity in water layer is solved by Reynold average Navier- Stokes equation and the porous media layer is solved by turbulent model based on Biot’s poroelastic theory. After determination the governing equations, boundary conditions and initialization of the finite element matrix in each layer by Galerkin method, we can solve the streamwise velocity distribution of each layer by coupled global finite element matrix.

After solving velocity distribution, we compare the profiles of velocity with the experimental solution of Yan (2007). As expected, we find it fit well and this reveals that the present finite element solution of velocity distribution can describe the flow passing vegetative channel appropriately. After comparing other factors, we find the turbulence strength factor and the area occupied by vegetation influence stream velocity distinctly.

目 錄

中文摘要...................................................I
ABSTRACT..................................................II
目錄.....................................................III
圖目錄.....................................................V
符號說明..................................................VI
第一章 緒論.........................................................1
1-1 研究之背景、動機與目的.................................1
1-2 文獻回顧...............................................2
1-3 各章節內容介紹.........................................6
第二章 控制方程式與邊界條件................................7
2-1明渠流（水層）之控制方程式..............................7
2-2孔隙介質流（草層、土層）之控制方程式....................9
2-3 邊界條件..............................................12
2-4 紊流模式..............................................14
第三章 有限元素分析.......................................18
3-1 Galerkin method ......................................18
3-2形狀函數 (shape function) .............................23
3-3 數值積分..............................................27
第四章 結果與討論.........................................30
4-1 有限元素分析模式之驗證................................30
4-2 流速影響因子之討論....................................31
第五章 結論與建議.........................................34
5-1 結論..................................................34
5-2 建議..................................................35
參考文獻..................................................36


圖 目 錄

圖2-1. 研究區域示意圖.........................................................................40
圖3-1. 研究區域之網格劃分方式示意圖.............................................40
圖3-2. 主控區域正方形元素及四邊形元素.........................................40
圖4-1. 實驗水槽俯視平面圖.................................................................40
圖4-2. 實驗佈置示意圖.........................................................................41
圖4-3. 依植生渠槽實驗參數進行有限元素分析之流速分佈圖.........41
圖4-4. 之百喜草草溝流速分佈圖.............................................42
圖4-5. 之百喜草草溝流速分佈圖..............................................42
圖4-6. 不同 值之渠道中央流速剖面圖..............................................42
圖4-7. 不同 值之渠道中央流速剖面圖..............................................43
圖4-8. 不同疏密程度草種之渠道中央流速剖面圖.............................43
圖4-9. 不同土壤密度下之渠道中央流速剖面圖.................................43
圖4-10. 其他參數不變之下 之流速分佈圖..........................44
圖4-11. 其他參數不變之下 之流速分佈圖..........................44
圖4-12. 其他參數不變之下 之流速分佈圖..........................44
圖4-13. 不同草高下之渠道中央流速剖面圖.......................................45
圖4-14. 不同土層厚度下之渠道中央流速剖面圖...............................45

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