臺灣博碩士論文加值系統

中文摘要
本文主旨在建立一套數值模式，模擬波浪通過海底地形之波浪變形特性和流場變化，藉以探討海底地形和波浪互制時液面的變化特性及流場特性。數值模式採用有限體積法，求解雷諾平均 Navier-Stokes 方程式 (Reynolds Averaged Navier-Stokes Equations, RANS)，以期能夠呈現波浪場中非線性與黏性效應的影響，同時配合 k-ε 紊流模式來模擬紊流效應。其中時間差分項以顯式法來離散，壓力場則藉著預測—修正方式來建立，配合 MAC (Marker And Cell) 交錯網格系統，採用不等間距網格，自由液面採用流體體積法以建立高效率的數值模式。本模式與傳統方法之最大不同係使用 RANS (Reynolds Averaged Navier-Stokes)，模擬波浪與結構物互制，完整地考慮非線性、黏性和紊流效應。為了研究波浪通過潛堤後非線性效應影響，本文討論波浪變形及主頻至三倍頻波浪振幅的變化，並採用Lin 和 Huang (2002) 之 四支波高計之分析方法，探討不同位置高階自由波和強制波之振幅以及不同間距下之反射率和透射率。


關鍵詞: 雷諾平均 Navier-Stokes 方程式、流體體積法、潛堤、坑洞

Abstract
The purpose of the present study is to develop a numerical model for studying the properties of wave transformations over seabed topography (submerged breakwaters or pit). The significant benefit of the present study over the traditional way of analyzing wave propagation problems is to apply the RANS (Reynolds Averaged Navier-Stokes) by taking account of the entire nonlinear, viscous and turbulent effects on the physical problem. The k-εmodel is employed to simulate the flow kinematics and the turbulence effects in the RANS. The RANS is used to simulate the flow field; and the transport equations are discretized by the finite volume method, based on a staggered grid system with variable width and height. The unsteady term is treated by an explicit method. The pressure field is obtained by a predictor-corrector procedure. In order to update the free surface configuration with every time step, the Volume of Fluid (VOF) method is implemented. To better understand the nonlinear effects following the wave propagation over the seabed topography, we make a detailed investigation concerning the wave deformation process and the change in harmonic wave amplitude. To understand the basic mechanism of wave evolution and decomposition, Lin and Huang (2002) is used to determine the amplitude of high frequency components and the ratio of reflection and transmission.

Keywords: Reynolds Averaged Navier-Stokes Equations, RANS, volume of fluid, submerged breakwater, pit

目錄
中文摘要 I
英文摘要 II
謝誌 III
目錄 IV
圖目錄 VI
表目錄 Ⅷ
符號說明 IX
第一章　緒論 1
1-1　前言 1
1-2　前人研究 2
1-2-1　波浪通過坑洞之研究 3
1-2-2　波浪通過潛堤之研究 4
1-3　研究目的 11
1-4　本文組織 12
第二章　RANS模式 14
2-1　RANS方程式簡介 14
2-2　初始條件和邊界條件條件 16
2-2-1　上游邊界條件 16
2-2-2　下游邊界條件 17
2-2-3　底部邊界條件 18
2-2-4　自由表面邊界條件 18
2-3　數值方法 20
2-3-1　自由表面處理方法 20
2-3-2　複雜地形處理方法 22
2-3-3　壁函數法的處理 25
2-4　計算程序 26
第三章　波浪變形之分析工具 29
3-1　頻譜分析 29
3-2　高頻成份波的分解機制 29
第四章　結果與討論 37
4-1　數值模式驗證 37
4-1-1　數值驗證 –波浪通過單一潛堤驗證 37
4-1-2　數值驗證 –波浪通過雙列潛堤驗證 43
4-2　波浪通過海底底床之波浪變形特性 46
4-2-1　流場變化 48
4-2-2　波浪變形 57
第五章　結論與建議 71
5-1　結論 71
5-2　建議 72
參考文獻 73




圖目錄
圖2-1 波浪和結構物作用的示意圖 14
圖2-2 流體體積法 (VOF)處理自由表面示意圖 21
圖2-3 結構物邊界網格示意圖 24
圖2-4 壁函數法之示意圖 26
圖2-5 RANS波浪流場數值模式計算流程圖 28
圖3-1 波高計空間式意圖 31
圖4-1 波浪通過潛堤之渦漩生成與實驗量測之比較 39
圖4-1 波浪通過潛堤之渦漩生成與實驗量測之比較 (續) 40
圖4-2 造波水槽之實驗配置示意圖 41
圖4-3 實驗量測和數值模擬之液面變化 41
圖4-4 實驗量測和數值模擬之流場圖 42
圖4-5 波浪通過潛堤自由液面振幅之空間變化 43
圖4-6 波浪通過潛堤不同位置之波形變化 44
圖4-7 數值計算與實驗量測之流速時序列結果比較 45
圖4-8 波浪與海底地形作用示意圖 47
圖4-9 波浪通過雙列潛堤之流場變化圖 ( S/L=1/8 ) 50
圖4-10 波浪通過雙列潛堤之流場變化圖 ( S/L=4/8 ) 52
圖4-11 波浪通過雙坑洞之流場變化圖 55
圖4-12 波浪通過單一坑洞之流場變化圖 56
圖4-13 波浪通過潛堤不同位置之波形時序列圖 58
圖4-14 波浪通過單一坑動不同位置之波形時序列圖 59
圖4-15 波浪通過潛堤在不同位相之空間波形變化 60
圖4-16 波浪通過潛堤在不同位相之空間波形變化 ( S/L = 1/8 ) 61
圖4-17 波浪通過雙列潛堤在不同位相之空間波形變化 ( S/L = 4/8) 61

圖4-18 波浪通過雙列潛堤，不同位置波高計資料的頻譜圖 64
圖4-19 波浪通過雙列潛堤時主頻至三倍頻無因次波浪振幅空間變化圖 65
圖4-19 波浪通過雙列潛堤時主頻至三倍頻無因次波浪振幅空間變化圖(續) 66
圖4-19 波浪通過雙列潛堤時主頻至三倍頻無因次波浪振幅空間變化圖(續) 67
圖4-20 波浪通過雙列潛堤不同潛堤間距之反射和透射率之變化圖 68
圖4-21 波浪通過雙列潛堤時，不同位置高階自由波和強制波無因次振幅變化圖 70



表目錄
表1-1 障礙物對入射波影響之前人研究 2
表1-2 前人研究方法及成果 (波浪與坑洞互制作用) 3
表1-3 前人研究方法及成果 (波浪通過潛堤之非線性問題) 6
表1-4 前人研究方法及成果 (主頻波與高階諧和波間能量的轉換) 8
表2-1 RANS 數值方法整理表 27
表3-1 強制波與自由波之比較 31

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