因橋梁工程技術的進步，橋梁漸趨狹長，受風反應越來越明顯，因此風洞試驗受到重視，但風洞試驗在進行試驗時，消耗時間大，成本也高，相較於以往只能以風洞試驗擷取所需數據，如今數值模擬方法漸趨成熟逐漸成為主流。    
    本研究以數值計算為主風洞斷面試驗為輔，模擬二維幾何斷面橋體在均勻來流下之鄰近紊流流場與結構運動行為。本研究分為三部分，第一部分為利用數值模擬對寬深比B/D=10的矩形斷面進行風力係數及顫振導數分析；第二部分利用前述所選用之參數，對寬深比B/D=5、B/D=20的矩形斷面進行分析；第三部分為利用前述所選用之參數，對高屏溪斜張橋進行風力係數及顫振導數分析。本研究使用計算流體力學的前處理器Pointwise進行模擬風洞試驗的計算域配置、網格繪製以及邊界條件設定，再以ANSYS開發的計算流體力學套裝軟體FLUENT進行分析。
    透過B/D=10進行參數測試，將參數測試結果套用在B/D=5、B/D=20上進行風力係數分析，在小攻角±4區間趨勢預測上都有良好的結果，在大攻角時有些微誤差；於高屏溪斜張橋上進行風力係數分析時，整體趨勢預測良好，在風攻角5°時有些微誤差存在。於B/D=5、B/D=20上進行顫振導數分析，所得結果整體趨勢大致良好；於高屏溪斜張橋上，直接導數的預測上與風洞試驗相較下吻合度良好，但在耦合項誤差稍大。
    根據本文之研究結果，將可提供對橋梁斷面之CFD模式建立及模擬方法，透過快速的數值模擬，以做為風洞試驗前風力係數及顫振導數之評估參考，並為接下來的CFD氣動力及氣彈力模擬做好初期基礎工作。

Duo to the improvement of bridge engineering technology, the bridge span is getting longer and the wind response is more significant. Therefore, the wind tunnel experiments of long-span bridges have become more important. But the time consuming and the high costing are the weak points of wind tunnel experiments. Contrary to wind tunnel experiments, CFD simulations can obtain full-field physical variables with time and be becoming one of the mainstreams in wind engineering.

In this study, the main methodology is 2D CFD simulation associated with the wind tunnel experiments to investigate the aerodynamic behavior of bridge decks. The method of flutter derivatives identification is based on forced vibration. This study is divided into three parts, the first one is to use CFD simulation to analyze the wind force coefficients and the flutter derivatives of a rectangular cross-section with B/D=10. The second part is using the similar configurations of the B/D=10 to analyze the bridge decks with B/D=5 and B/D=20. The third part is adopting the similar parameters to analyze   the Kao-Ping-Hsi cable-stayed bridge. In this study, we use the preprocessing software Pointwise to arrange the calculating domains and then generate the meshes and set up the boundary conditions. Then we use the Ansys Fluent to simulate flow fields around the bridge decks.

Through the tests of the parameters in the case of B/D=10, the optima parameters are identified which are then used to analyze the force coefficients in B/D=5 and B/D=20. There are good agreements in angles of wind attack between 4 and -4 degrees, but with some error in the larger attack angles. The force coefficients of Kao-Ping-Hsi cable-stayed bridge have similar trends with the results of wind tunnel experiments. However the larger errors occur when the wind attack angles are more than 5°. The results of the flutter derivatives in the case of B/D=5 and B/D=20 show that the overall trends are fairly well. Compared to the experiments the flutter derivatives of the Kao-Ping-His Bridge have good agreements with the wind tunnel experiments in the direct flutter derivatives but have some discrepancies in the cross flutter derivatives.

According to the above comparative results, this study provides a reliable CFD approach for 2D simulations of bridge decks. A rapid 2D CFD simulation can be as the preliminary assessment of aerodynamic coefficients and flutter derivatives before the wind tunnel experiments are performed.

章節目錄	I
表目錄	IV
圖目錄	V
第一章 緒論	1
1-1 研究動機	1
1-2 研究方法	2
1-3 論文架構	2
第二章 文獻回顧	5
2-1大跨度橋發展歷史	5
2-2 風力係數、顫振導數及相關研究	5
2-2-1 風力係數	6
2-2-2顫振導數（Flutter Derivatives）	8
2-2-3數值模擬相關研究	9
第三章 理論背景	13
3-1 橋梁氣動力效應	13
3-1-1 顫振效應(Flutter)	13
3-1-2抖振效應（Buffeting）	15
3-1-3渦流顫振（Vortex Shedding）	16
3-1-4 扭轉不穩定現象（Torsion Instability）	16
3-1-5 風馳效應（Galloping）	17
3-2橋樑受風力現象之理論	18
3-2-1自身擾動力(Self-Excited Force)	18
3-2-2抖振力(Buffeting Force)	19
第四章 計算流體力學	21
4-1計算流體力學之介紹	21
4-2計算流體力學之方程式的建立	22
4-3數值方法	23
4-3-1速度及壓力耦合求解疊代方法	23
4-3-2對流與擴散之離散方法	25
4-4風效應概述	27
4-4-1風效應	27
4-4-2 均勻紊流場特性	28
4-5紊流模式	30
4-6數值模擬之顫振導數識別方法	34
4-6-1強制垂直振動之垂直向風力	34
4-6-2強制扭轉振動之垂直向風力	35
4-6-3強制扭轉振動之扭轉向風力	36
4-6-4強制垂直振動之扭轉向風力	37
第五章 實驗與斷面模擬設置	39
5-1風洞實驗室與儀器介紹	39
5-1-1 風洞實驗室特性	39
5-1-2皮托管	39
5-1-3壓力轉換器	40
5-1-4雷射位移計	40
5-2 橋樑斷面模型製作	41
5-2-1斷面模型（Deck Section Model）簡介	41
5-2-2斷面模型製作原理	41
5-2-3 斷面模型之縮尺	43
5-2-4 斷面模型之製作	43
5-3實驗架設	44
5-3-1 風力係數	44
5-3-2 顫振導數	44
5-4  CFD數值模擬	45
5-4-1 計算域	46
5-4-2邊界條件	47
5-4-3 網格設計	47
第六章：結果與討論	49
6-1前言	49
6-2紊流模式比較	50
6-2-1模擬結果與比較	50
6-2-1.1風力係數比較	50
6-2-1.2顫振導數比較	51
6-2-2小結	52
6-3收斂殘差值比較	53
6-3-1模擬結果與比較	53
6-3-1.1顫振導數比較	53
6-3-2小結	54
6-4網格配置方式	55
6-4-1模擬結果與比較	55
6-4-1.1風力係數比較	55
6-4-2小結	56
6-5網格加密比較	56
6-5-1模擬結果與比較	57
6-5-2小結	57
6-6二次改變收斂殘差值大小	57
6-6-1模擬結果與比較	57
6-6-2小結	58
6-7 矩形斷面模擬與比較	58
6-7-1 矩形模擬斷面風壓流線圖比較	59
6-8 高屏溪斜張橋斷面模擬與比較	59
6-8-1小結	60
第七章 結論與建議	61
7-1結論	61
7-2建議	62
參考文獻	65
表附錄	71
圖附錄	75

表目錄
表2-1 各項顫振導數所代表之物理意義	71
表6-1 網格比較	72
表6-2 殘差值比較表	72
表6-3 網格配置比較表	73
表6-4 網格加密結果比較表	73
表6-5 殘差值比較表	74
表6-6 再接觸位置表	74

圖目錄
圖2-1 橋梁斷面受風力示意圖	75
圖2-2各型橋梁斷面的風力係數與顫振導數之（一）	76
圖2-3各型橋梁斷面的風力係數與顫振導數之（二）	77
圖3-1橋面版節點與單位長度受風力之示意圖	78
圖4 1 Fluent網格元素類型	78
圖4-2  流體流經鈍體之分離現象（Simiu, E、R.H. Scanlan）	79
圖4-3 流體與鈍體之再接觸現象（Simiu, E、R.H. Scanlan）	79
圖5-1風力係數與顫振導數之實驗儀器配置流程圖	80
圖5-2力感應器作用於模型上之幾何示意圖	81
圖5-3風力係數實驗架構圖	82
圖5-4順風向顫振導數實驗架構圖	83
圖5-5耦合顫振導數實驗架構圖	84
圖5-6 CFD數值模擬流程圖	85
圖5-7 CFD數值模擬計算域	85
圖5-8 邊界條件	86
圖5-9網格設計	86
圖6-1紊流模式比較之風力係數	87
圖6-2(a) 紊流模式比較之顫振導數	88
圖6-2(b)紊流模式比較之顫振導數	89
圖6-3(a) 殘差值比較之顫振導數	90
圖6-3(b) 殘差值比較之顫振導數	91
圖6-4原始網格設置方式	92
圖6-5改變網格配置方式	92
圖6-6 網格配置方法之風力係數比較	93
圖6-7 網格配置尾跡比較圖	94
圖6-8網格加密處示意圖	95
圖6-9 殘差值之風力係數比較	96
圖6-10  B/D=5風力係數	97
圖6-11  B/D=20風力係數	98
圖6-12(a)  B/D=5之顫振導數比較	99
圖6-12(b)  B/D=5之顫振導數比較	100
圖6-13(a)  B/D=20之顫振導數比較	101
圖6-13(b)  B/D=20之顫振導數比較	102
圖6-14(a)風壓流線圖	103
圖6-14(b)風壓流線圖	103
圖6-14(c)風壓流線圖	104
圖6-14(d)風壓流線圖	104
圖6-14(e)風壓流線圖	105
圖6-14(f)風壓流線圖	105
圖6-14(g)風壓流線圖	106
圖6-14(h)風壓流線圖	106
圖6-14(i)風壓流線圖	107
圖6-15(a)風壓流線圖	108
圖6-15(b)風壓流線圖	108
圖6-15(c)風壓流線圖	109
圖6-15(d)風壓流線圖	109
圖6-15(e)風壓流線圖	110
圖6-15(f)風壓流線圖	110
圖6-15(g)風壓流線圖	111
圖6-15(h)風壓流線圖	111
圖6-15(i)風壓流線圖	112
圖6-16(a)風壓流線圖	113
圖6-16(b)風壓流線圖	113
圖6-16(c)風壓流線圖	114
圖6-16(d)風壓流線圖	114
圖6-16(e)風壓流線圖	115
圖6-16(f)風壓流線圖	115
圖6-16(g)風壓流線圖	116
圖6-16(h)風壓流線圖	116
圖6-16(i)風壓流線圖	117
圖6-17模擬斷面	118
圖6-18 高屏溪斜張橋之風力係數比較	119
圖6-19(a) 高屏溪斜張橋之顫振導數比較	120
圖6-19(b) 高屏溪斜張橋之顫振導數比較	121

1.	Bratt, J. B. and Scruton, C., “Measurement of Pitching Moment             Derivatives for an Aerofoil Oscillating about the HalfChord Axis,” British  Aerodynautical Research Council, R. & M., No. 1921 (1938).
2.	Bratt, J. B. and Wight, K. D., “The Effect of Mean Incidence, Amplitude of Oscillation, Profile, and Aspect Ratio on Pitching Moment Derivatives, ” British Aerodynatutical Research Council, R. & M., No. 2064 (1946).
3.	Gu, M., Xiang, H. and Lin, Z., “Flutter- and Buffeting-Based for Long-Span Bridges,” Journal of Wind Eng. and Industrial Aerodynamics, Vol 80, pp. 373-382 (1999). 
4.	Halfman, R. L., “Experimental Aerodynamic Derivatives of a Sinusoidally Oscillating Airfoil in Two-Dimensional Flow,” NACA Technical Report, 1108 (1952).
5.	Hikami, Y., Shiraishi, N., “Rain-Wind Induced Vibrations of Cable Stayed Bridges,”Journal of Wind Engineering and Industrial Aerodynamics, Vol. 29, pp.409-418(1988).
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, 
7.	Huang,M. H., ”Flutter and Buffeting analysis of Bridges Subjected to Skew Wind,”Jornal of Applied Science and Engineering, Vol.15, No.4, pp.401-413 (2012)
8.	Kazama, K., Yamada, H. and Miyata, T., “Wind Resistant Design for Long Span Suspension Bridges,” Journal of Wind Engineering and Industrial Aerodynamics, No. 54/55, pp.65-74 (1995)
9.	Larsen, A., “Advances in Areoelastic Analyses of Suspension and Cable-Stayed Bridges,” Journal of Wind Eng. and Industrial Aerodynamics, Vol 74-76, pp. 73-90 (1998).
10.	Larsen, G. L. and Livesey, F. M., “Performance of Streamlined Bridge Decks in Relation to The aerodynamic of a Flat Plate,” Journal of Wind Eng. and Industrial Aerodynamics, Vol 69-71, pp. 851-860 (1997).
11.	Matsumoto,M.,”Aerodynamic damping of prisms,” Journal of Wind Engineering and Industrial Aerodynamics,”Vol.59,pp.159-175 (1996)
12.	Nagao, F., Utsunomiya, H., Oryu, T. and Manabe, S., “Aerodynamic Efficiency of Triangular Fairing on Box Girder Bridge,” Journal of Wind Eng. and Industrial Aerodynamics, Vol 49, pp. 565-574 (1993).
13.	Patruno,L., “Accuracy of numerically evaluated flutter derivatives of bridge deck sections using Rans:Effects on the flutter onset velocity,” Journal of Wind Engineering and Industrial Aerodynamics,”Vol.89,pp.49-65(2015)
14.	Scanlan, R. H. and Tomko, J. J., “Airfoil and Bridge Deck Flutter 
Derivatives,” Journal of Eng. Mech. Div., ASCE, Vol. 97, pp.1717-1737 (1971).
15.	Saito, T., Shiraishi, N. and Ishizaki, H., “On Aerodynamic stability of double-decked / trussed girder for cable-stayed “Higashi-Kobe Bridge” ,”Journal of Wind Engineering and Industrial Aerodynamics, Vol 33, pp. 323-332 (1990).
16.	Santo, H. P., Branco, F. B., “Wind forces on bridges – numerical vs. experimental methods,” Journal of Wind Eng. and Industrial Aerodynamics, Vol 32, pp. 145-159 (1989).
17.	Scanlan, R. H. and Gade, R. H., “Motion of Suspended Bridge Spans under Gusty Wind, ”Journal of the Structural Division, ASCE, pp.1867-1883 (1977).
18.	Scanlan, R. H. and Sabzevari, A., “Suspension Bridge Flutter   Revisited,” ASCE Structural Engineering Conference (1967).
19.	19Scanlan, R. H., “Interpreting Aeroelastic Models of Cable-Stayed Bridges, ” Journal of Engineering Mechanics, ASCE, Vol. 113(4), pp. 555-576 (1987).
20.	
Singh, L., Jones, N. P., Scanlan, R. H. and Lorendeaux, O., “Identification of Lateral Flutter Derivatives of Bridge Decks, ” Journal of Wind Eng. and Industrial Aerodynamics, Vol 60, pp. 81-89 (1996).
21.	Simiu, E., Scanlan, R. H., “Wind Effects on Structures ,” John Wiley & Sons. 1986.

22.	Sarkar, P. P., Jones, N. P. and Scanlan, R. H. (1992), "System identificatioin for estimation of flutter derivatives", Journal of Wind Eng. and Industrial Aerodynamics, 41-44, pp.1243-1254.
23.	Shuji,S.,Toshio,U., “Aerodynamic simulation by CFD on flat box girder of super-long-span suspension bridge” Journal of Wind Engineering and Industrial Aerodynamics,”Vol.91,pp.279-290(2003)
24.	Tanaka,H.,Yamamura,N. and Tatsumi,M. ,”Coupled Mode Flutter Analysis Using Flutter Derivatives,”Journal of Wind Engineering and Industrial Aerodumamics,Vol.41-44,pp1279-1290(1992)
25.	Un,Y.J.,Soon,D.K., “Sequential numerical procedures for predicting flutter velocity of bridge sections,” Journal of Wind Engineering and Industrial Aerodynamics Vol 91,pp.291-305 (2003)
26.	Vickery, B. J., “Fluctuating lift and drag on a long cylinder of square cross-section in a smooth and in a turbulence stream,” Journal of Fluid Mesh.25, pp. 481-494 (1966).
27.	DMI,”WIND-TUNNEL TESTS FOR KAO PING HIS BRIDGE,SECTION MODEL TEST PART 1”

28.	Yoshimura, T., Savage, M. G., Tanaka, H., and Wakasa, T., “A 
device for suppressing wake galloping of stayed-cables for cable-stayed bridges,” Journal of Wind Engineering and Industrial Aerodynamics, Vol.
29.	王福军“计算流体力學分析─CFD軟件原理與應用”(2004)
30.	林世權,“風攻角和紊流場對長跨徑橋梁抖振的影響”,私立淡江大學土木工程研究所碩士論文(2000) 
31.	謝政宏,“氣動力參數對長跨徑橋梁顫振臨界風速的影響 ＂,私立淡江大學土木工程研究所碩士論文(1999).
32.	李鳳娟,”振態耦合對大跨度橋梁自勵振動現象之影響,”私立淡江大學土木工程研究所碩士論文,(1995)'
33.	黎益肇,”簡單幾何截面長跨度橋梁之氣彈力行為探討,”國立中興大學土木工程學系博士學位論文(2005)
34.	莊耘,”以計算流體動力學CFD進行橋梁風致結構反應之分析與驗證,”國立臺北科技大學土木工程系土木與防災碩士班碩士學位論文,(2015)
35.	何錦海,葉祥海,鄭啟明,”風洞實驗技術於土木建築構造物之應用與驗證計畫-橋梁風洞實驗”內政部建築研究所研究報告(2005)