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中文論文名稱 基於SST k-ω模型之二維橋樑斷面氣彈力模型特性模擬
英文論文名稱 Simulation on the aeroelastic characteristics of 2D bridge deck cross sections based on SST k-ω model
校院名稱 淡江大學
系所名稱(中) 土木工程學系碩士班
系所名稱(英) Department of Civil Engineering
學年度 108
學期 2
出版年 109
研究生中文姓名 陳政謙
研究生英文姓名 Cheng-Chien Chen 陳政謙
學號 607380218
學位類別 碩士
語文別 中文
口試日期 2020-07-28
論文頁數 108頁
口試委員 指導教授-林堉溢
委員-鄭啟明
委員-黎益肇
中文關鍵字 計算流體力學、自由振動、流固耦合、長跨度橋樑 
英文關鍵字 Computational fluid dynamics, Free vibration, Fluid-structure interaction, Long span bridge 
學科別分類 學科別應用科學土木工程及建築
中文摘要 論文提要內容:
因橋樑工程技術進步快速,使得橋樑跨徑及斷面趨於狹長,使得橋樑受風後之流場與結構之間產生互制現象-氣彈力效應所引發之氣動力不穩定現象機率大為增加。因此,橋樑在設計階段需考慮橋樑顫振效應的臨界風速。本研究以數值計算為主,風洞斷面試驗為輔,著重於矩形斷面之橋樑顫振臨界風速之探討,透過CFD二維數值模擬方法預測橋樑受風之位移反應進而找出顫振臨界風速。
二維橋樑斷面試驗模擬常以強制振動(forced vibration)以及自由振動(free vibration)方法來模擬橋體氣彈力效應。強制振動方法為透過給予橋體週期性之強制振動,以調整振動頻率來求取不同約化風速下之顫振導數。自由振動方法為輸入橋體之已知條件,計算結構受風下之網格運動位移及速度,並透過改變約化風速模擬出橋體在受風作用下,模擬流場與結構之互制現象。
本研究利用CFD方法,於均勻流場下,採自由振動方法來模擬寬深比B/D=5及B/D=13之矩形斷面之受風運動行為。透過輸入橋板結構特性,並以更改風速的方式來模擬橋樑受不同風速下之氣彈力行為,並將橋板受風後之位移歷時進行輸出,計算位移歷時反應之均方根值,進而推估橋板之顫振臨界風速。將模擬結果與橋樑風洞試驗進行比對,結果發現B/D=5斷面之氣彈力行為預測與實驗相當吻合。垂直向渦致振動現象位於風速1 m/s-2.63 m/s之間,扭轉向渦致振動現象位於風速1.7 m/s-3 m/s之間。數值模擬對於顫振臨界風速預測結果為6.7 m/s,風洞試驗結果為7.6 m/s,其誤差約為11%,顯示數值模擬結果相對於風洞試驗結果較為保守。對於B/D=13斷面之顫振臨界風速預測誤差偏高,數值模擬之顫振臨界風速為10.2 m/s,其洞試驗結果為14.3 m/s,誤差約為28.7%,原因為由於B/D=13斷面為耦合顫振斷面,在氣彈力行為上有垂直向頻率及扭轉向頻率會相互影響,從位移頻率結果中,發現數值模擬在高風速下之垂直位移頻率有上升太快之現象,使得垂直向及扭轉向頻率位於9.3 m/s時已耦合於一特定頻率,因此,影響了數值模擬預測B/D=13斷面之顫振臨界風速之精度。然而,B/D=5斷面為單自由度顫振斷面,顫振行為主要由扭轉向阻尼控制,從位移頻率結果中,發現扭轉向頻率與實驗相當吻合,因此,數值模擬應用於預測B/D=5斷面之氣彈力行為具有一定精度。
研究結果顯示,採用SST k-ω紊流模型應用於預測二維橋樑斷面氣彈力之模擬方法,可合理推估二維橋樑斷面受風反應,未來應可做為風洞試驗前顫振臨界風速之初步評估參考。
英文摘要 Abstract:
Due to the improvement of bridge engineering technologies, bridge span lengths are getting longer and deck cross sections are more slender. That enhances the probability of the aeroelastic instability, which caused by the flow-structure interaction of the bridge deck under wind excitations. Therefore, the critical flutter wind speed has to be considered in the bridge designed stage. In this study, the main methodology is 2D CFD simulations associated with the wind tunnel experiments to investigate the critical flutter wind speeds of the bridge decks by using the displacement responses at different wind speeds.

Generally, two main methods, forced vibration method and free vibration method, are used to simulate the aeroelastic behavior of the bridge decks. The forced vibration method is to determine the flutter derivatives of the bridge deck at various reduced wind speeds by giving the bridge deck a periodical vibration and modifying vibration frequencies. The free vibration method is to calculate the displacements and velocities of the meshes at differernt reduced wind speeds by inputting the known conditions of the bridge deck. Then the phenomenon of fluid-structure interactions can be simulated.
In this study, the free vibration method is used to simulate the phenomenon of fluid-structure interactions of rectangular deck cross sections with B/D=5 and B/D=13 in uniform inflow. By inputting the structural parameters of the bridge decks and changing inlet wind speeds in FLUENT, the vertical and torsional displacements of the deck are then obtained. After the root-mean-square values of the displacements at different wind speeds are calculated, the relationship between the responses and wind speeds can be formed. The critical wind speed of the bridge deck is identified as the corresponding wind speed at which the sharp increase of the torsional response occurs. Finally, the numerical results are compared with those in wind tunnel experiments. The results show that there are good agreements between the experiments and the predictions of the aeroelastic behavior in B/D=5. The vertical vortex-induced vibration phenomenon occurs at 1 m/s to 2.63 m/s, and the torsional vortex-induced vibration phenomenon occurs at 1.7 m/s to 3 m/s. The critical flutter wind speeds are 6.7 m/s and 7.6 m/s in CFD and wind tunnel experiments, respectively. The relative error is about 11%. However, for the B/D=13 cross section, the discrepancies of the results between CFD and experiments are larger. The critical flutter wind speed are 10.2 m/s and 14.3 m/s in CFD and wind tunnel experiments, respectively. The relative error is about 28.7%. The error reason is that the B/D=13 cross section is coupled flutter. The vertical frequencies have an effect on torsional frequencies. In displacement frequency results, it is found that the vertical displacement frequency of numerical simulation is risen so fast that the vertical and torsional frequencies are coupled to a specific frequency at 9.3 m/s. Therefore, it results in the accuracy of critical flutter wind speed in numerical simulation. However, the B/D=5 cross section is single degree of freedom flutter. This flutter behavior is mainly controlled by torsional damping. In the displacement frequency results, it is found that the torsional frequency is quite consistent with the experiment. Therefore, numerical simulation can be precisely used to prediction the aeroelastic behavior of B/D=5 cross section.

The comparisons of the results show that the simulation method based on SST k-ω model can estimate the critical wind speeds of the bridge decks reasonably. It can be used in the preliminary design stage before wind tunnel experiments are conducted.
論文目次 目錄
第一章 緒論 1
1-1 研究動機與目的 1
1-2 研究內容 2
1-3 論文架構 3
第二章 文獻回顧 5
2-1 風力係數 5
2-2 氣彈力行為 6
2-3 端板效應(END PLATE EFFECT) 9
第三章 橋樑理論背景 10
3-1 橋樑受風理論 10
3-1-1 扭轉不穩定現象(Torsion Instability) 10
3-1-2 顫振(Flutter) 11
3-1-3 渦致振動(Vortex Induced Vibration) 12
3-1-4 抖振(Buffeting) 13
3-1-5風馳效應(Galloping) 14
3-2橋體外力形式 15
3-2-1 自身擾動力(Self-Excited Force) 15
3-2-2 抖振擾動力(Buffeting Force) 16
第四章 研究方法 17
4-1 概述 17
4-2 流體運動 18
4-3 速度及壓力耦合求解迭代方法 19
4-4 固體運動方程式 22
4-5 流固耦合運算機制流程 24
4-6 壁面函數(WALL FUNCTION) 24
第五章 風洞試驗與模擬斷面設置 27
5-1 前言 27
5-2 風洞實驗室及流場介紹 27
5-2-1 風洞實驗室 27
5-2-2 平滑流場(Smooth Flow) 27
5-3 實驗室儀器 28
5-3-1 皮托管(Pitot Tube) 28
5-3-2壓力電壓轉換器 29
5-3-3 位移量測—雷射位移計 29
5-4 橋樑斷面模型 30
5-4-1 斷面模型製作原理 30
5-4-2斷面模型之製作 32
5-5 實驗架設 32
5-5-1 風力係數 32
5-5-2 橋樑氣彈力模型位移歷時反應 33
5-6 CFD數值模擬 34
5-6-1 格網繪製 34
5-6-2 計算域及邊界條件 34
5-6-3 格網設計 35
5-7 有限元素數值模型之建立 37
第六章 結果與討論 38
6-1前言 38
6-2 氣動力分析 39
6-2-1 格網比較 39
6-2-2 格網y+比較 41
6-3 氣彈力分析 45
6-3-1 顫振臨界風速 45
6-3-2 格網配置及求解設定 45
6-3-3 B/D=5 斷面之氣彈力特性 46
6-3-4 B/D=13 斷面之氣彈力特性 50
6-4 有限元素建模之顫振臨界風速分析 52
第七章 結論與建議 54
7-1 結論 54
7-2 建議 57
參考文獻 58
附表 60
附圖 66

表目錄
表3-1 各項顫振導數所代表之物理意義 60
表5-1 網格歪斜程度【10】 61
表5-2 氣動力模型格網尺寸 61
表5-3 Mesh2格網配置 61
表5-4 氣彈力模型格網尺寸 61
表5-5 動網格區域設定 62
表6-1 Mesh1格網比較 63
表6-2 格網y+比較之格網資訊 63
表6-3 求解風力係數之殘差值設定 64
表6-4 實驗橋樑斷面資訊 64
表6-5 氣彈力模型每時間步數之殘差值收斂情形 65
表6-6 顫振臨界風速結果 65


圖目錄
圖 1-1 數值模擬 66
圖2-1 橋樑受力方向示意圖 67
圖2-2 B/D=5斷面位於平滑流下雷諾數與史特赫數關係 67
圖2-3 利用SDOF及TDOF方法之垂直及扭轉位移反應(Ur=5.5) 68
圖2-4 利用SDOF及TDOF方法之垂直及扭轉位移反應(Ur=14) 68
圖2-5 斷面模型加裝端板 69
圖4-1 SIMPLE求解流程圖 70
圖4-2 PISO求解流程圖 70
圖4-3 CFD之橋板壓力積分方向 71
圖4-4流固耦合運算機制流程圖 72
圖4-5 固體於流場中之邊界層 73
圖4-6 網格之中心點到壁面的距離yp 74
圖4-7 y+與u+關係(雙log座標) 74
圖5-1 實驗儀器配置流程圖 75
圖5-2 力感應器作用於模型上之幾何示意圖 76
圖5-3 風力係數實驗架構圖 77
圖5-4 耦合架構架設圖 78
圖5-5 CFD數值模擬計算域及邊界條件 79
圖5-6 (a) B/D=5 格網整體無因次化尺寸 80
圖5-6 (b) B/D=13 格網整體無因次化尺寸 80
圖5-7 Mesh1結構化格網設計 81
圖5-8 Mesh2混合型格網設計 82
圖5-9 有限元數值模型架構圖 83
圖6-1 Mesh1格網比較之風力係數 84
圖6-2(b) Mesh1格網比較之風攻角2度上表面之風壓係數 85
圖6-2(d) Mesh1格網比較之風攻角4度上表面之風壓係數 86
圖6-2(e) Mesh1格網比較之風攻角4度下表面之風壓係數 87
圖6-3格網y+比較之風力係數 88
圖6-4(a) 格網y+比較之風攻角0度上表面之風壓係數 89
圖6-4(b) 格網y+比較之風攻角2度上表面之風壓係數 89
圖6-4(c) 格網y+比較之風攻角2度下表面之風壓係數 90
圖6-4(d) 格網y+比較之風攻角4度上表面之風壓係數 90
圖6-4(e) 格網y+比較之風攻角4度下表面之風壓係數 91
圖6-5 (a) B/D=5 Vertical RMS Response 92
圖6-5 (b) B/D=5 Torsional RMS Response 92
圖6-6 (a) B/D=5 垂直頻率 93
圖6-6 (b) B/D=5 扭轉頻率 93
圖6-7 B/D=5 位移頻譜 96
圖6-8 B/D=5,U=7 m/s之位移歷時 97
圖6-9 B/D=5,U=7 m/s之橋板風力歷時 97
圖6-10 B/D=5,U=7.0 m/s之風壓流線圖 99
圖6-11 (a) B/D=13 Vertical RMS Response 100
圖6-11 (b) B/D=13 Torsional RMS Response 100
圖6-12 (a) B/D=13 垂直頻率 101
圖6-12 (b) B/D=13 扭轉頻率 101
圖6-13 B/D=13 位移頻譜 103
圖6-14 B/D=13,U=10.5 m/s之位移歷時 104
圖6-15 B/D=13,U=10.5 m/s之橋板風力歷時 104
圖6-16 B/D=13,U=10.5 m/s之風壓流線圖 106
圖6-17 B/D=5 顫振導數 107
圖6-18 B/D=13 顫振導數 108
參考文獻 參考文獻
1. Claudio M., Antonino M. M., Luca P., Gianni B., “The effects of free-stream turbulence and angle of attack on the aerodynamics of a cylinder with rectangular 5:1 cross section,” Journal of Wind Engineering & Industrial Aerodynamics 161 pp. 42–58 (2017).
2. Matsumoto, M. Yoshizumi, F., Yabutani, T., Abe, K. and Nakajima, N., “Flutter Stabilization and Heaving-Branch Flutter,” Journal of Wind Eng. and Industrial Aerodynamics, Vol 83, pp. 289-299 (1999).
3. Šarkić A. , HöfferRüdiger and Brčić S. , “Numerical simulations and experimental validations of force coefficients and flutter derivatives of a bridge deck,” Journal of Wind Eng. and Industrial Aerodynamics,Vol.144,pp.172-182 (2015).
4. Fuyou X. , Zhanbiao Z., “Free vibration numerical simulation technique for extracting flutter derivatives of bridge decks,” Journal of Wind Engineering & Industrial Aerodynamics 170 (2017) 226–237
5. Stefano d. M., Luca Patruno, Francesco Ubertini, Giuseppe Vairo, “On the identification of flutter derivatives of bridge decks via RANS turbulence models: Benchmarking on rectangular prisms ” Journal of Engineering Structures, Vol.76, pp.359-370 (2014).
6. Hao Z.,Tao F. , “Flutter stability studies of Great Belt East Bridge and Tacoma Narrows Bridge by CFD numerical simulation ,” The Seven Interational Colloquium on Bluff Body Aerodynamics and(BBAA7) Shanghai, China, September 2-6 (2012).

7. Tetsuro T., “Reliability on CFD estimation for wind-structure interaction problems,” Journal of Wind Engineering and Industrial Aerodynamics, Vol. 81, pp.117-143(1999).
8. Cowdrey, C. F., “A note on the use of end plates to prevent three-dimensional flow at the ends of bluff cylinders, ” Current Papers ARC C.P. 683, Aeronautical Research Council (ARC). (1963)
9. 曾煒翔, “欄杆型式對人行橋氣動力反應的影響” ,私立淡江大學土木工程學系碩士班碩士論文(2018)
10. Bakker, A., 2013. Lecture 7 – Meshing, Applied Computational Fluid Dynamics
11. 林紘毅, “以CFD模擬二維橋樑斷面之氣動力參數及顫振導數研究” ,私立淡江大學土木工程學系碩士班碩士論文(2018)
12. 项海帆 ,“公路桥梁抗风设计指南” 公路桥梁抗风设计指南编写组(1996)
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