臺灣博碩士論文加值系統

流體在通過柱狀結構物時，在結構物下游表面常產生交替射出之渦流，使作用於結構物之升力與阻力作週期性之變化，從而引起結構物之橫向振動與流向振動。而結構物之振動同樣也會影響交替射出渦流之強度與頻率，改變升力與阻力之變化。此種相互影響之作用稱為互制。當渦流之射出頻率與結構物自然振動頻率相近時，二者產生共振，而結構物之安全則受到威脅，甚至遭到破壞。史上遭到此種渦流引發振動破壞的吊橋不下50座，而核電廠輪機輪葉受到此種效應破壞的案例也非罕見。流場與彈性柱互制系統之研究始於1960年代，係以實驗與簡化之理論方法進行。由於電腦容量及運算速度之限制，直至1990年代後期才發展出以數值進行研究之方法。這是一個新的力學計算領域，也具有重要的工程應用價值。
　　本研究以數值方法模擬流場與彈性圓柱互制之系統。流場部份係在以圓心為原點之非慣性座標直接求解流速與壓力。彈性圓柱振動部分則在慣性座標求解圓柱之位移、速度與加速度。每一時階，先解流場，並計算作用於圓柱之力；再由此力計算圓柱之振動。而圓柱之振動又將影響下一時階流場之制御方程式及邊界條件，從而達到互制之目的。數值模式將前人已有之「自由下落圓柱與流場之相互運動」模式加以修正來建立。
　　本研究將系統化地研究四個無因次參數對流場特性及圓柱振動特性之影響。四個參數即圓柱振動之自然頻率、雷諾數、質量比及阻尼比。流場特性包括渦流射出頻率，阻力，升力，圓柱表面壓應力、剪應力、渦度分布，停滯點及分離點位置，流場等壓力線、等渦度線及流線等。圓柱振動特性包括圓柱之位移、速度及加速度，振動頻率，共振區間，最大振幅，及各種作用力與位移間之相位差等。上述各項特性對時間之演化也將是重要的研究課題。對此種振動分析而言，波譜分析方法將是個必要的分析工具。在研究中，尚可利用數值模擬廣搜尋之能力，找出控制此非線性系統之槓桿點，以小而有效的改變消減共振效應。

Due to the vortex alternatively shedding form the downstream surface of the structure for a flow past an elastic cylindrical structure, the drag and lift forces on the structure show a periodic variation with time. The structure is then vibrated periodically both in in-line and transverse directions. Respectively, the shedding intensity and frequency of the vortex are also affected by the vibration of the structure. This is the so-called flow-structure interaction. Synchronization occurs when the natural frequency of the structure is close to the vortex shedding frequency. It can cause structure fatigue, and may lead to drastic failure of the structure. The lab experimental and simplified theoretical studies of the flow-structure interaction system started after 1960. The numerical study of this system has not been developed until the late of 1990’s. This new frontier of computational mechanics has its importance in the field of engineering application.
A numerical model will be set up to simulate the interaction of a flow and an elastic circular cylinder. A 2-D non-inertial coordinate, which is fixed at the center of the cylinder, will be implemented to solve directly for the velocities and the pressure of the flow field, and an inertial coordinate will be adopted to solve for the motion of the cylinder. The interaction is reached as follows. At each time step, the flow field is solved first, and then the motion of the cylinder is calculated using the force produced by the flow field computation. At the next time step, the motion of the cylinder changes the conditions of the flow. An existing successful numerical code ”the interaction of a flow and a freely falling circular cylinder” will be modified to meet the need of this project.
The characteristics of the flow field and the cylinder vibration will be studied systematically according to four non-dimensional parameters, i.e. the natural frequency of the cylinder, the Reynolds number, the mass ratio, and the damping ratio. The characteristics of the flow field include vortex shedding frequency, drag and lift forces, the pressure, shear force, and vorticity distributions on the cylinder, stagnation and separation points, the pressure, stream-function, and vorticity contours, and so on, while those of the cylinder vibration consist of the displacement, velocity and acceleration of the cylinder, vibrating frequency, zone of vibration, maximum amplitude, phase angle, and so forth. The evolution of the characteristics mentioned will be discussed also. It has not been forgotten that energy spectrum analysis plays an important role for the study of such system. Due to the broadly searching ability of numerical model, it is also possible to find the leverage point so that a simple and effective way may be set up to diminish the amplitude of the synchronization.

目錄
目次 頁次

中文摘要 ………………...………….…………………… I

英 文 摘要 ………………...………….…………………… III

目 錄 …………………...……….…………………… V
表 目 錄 …………………...……….…………………… VIII
圖 目 錄 …………………...……….…………………… IX
符號說明表 …………………...……….…………………… XI

第一章 概論………………………………………………. 1
1.1 概述……………………………………………….……… 1
1.2 前人研究……………………………………….………… 2
1.2.1 圓柱為固定之狀況………………………………... 2
1.2.2 圓柱為強制運動之狀況…………………………... 4
1.2.3 圓柱與流場互制之狀況：物理實驗部分………… 5
1.2.4 圓柱與流場互制之狀況：數值部分……………… 6
1.3 研究目的……………….………………………………… 7
1.4 章節介紹…………………………………………………. 8

第二章 理論分析…………………………………………. 10
2.1 流場部份......…………………………………………....... 10
2.1.1 控制方程式……………………………………….. 10
2.1.2 起始條件………………………………………….. 12
2.1.3 邊界條件………………………………………….. 13
2.1.3.1 內邊界條件………………………………. 13
2.1.3.2 外邊界條件………………………………. 13
2.1.4 作用力…………………………………………….. 14
2.2 圓柱振動部分……………….………………………….... 15
2.3 互制部分…………………………………………………. 19

第三章 數值方法…………………………………………. 20
3.1 求解流場…...……………………………………..…….... 20
3.1.1 流場計算…………………………………………. 20
3.1.2 起始條件…………………………………………. 22
3.1.3 邊界條件…………………………………………. 23
3.1.3.1 內邊界條件………………………………. 23
3.1.3.2 外邊界條件………………………………. 23
3.1.4 座標轉換…….…………………………………… 24
3.1.5 網格系統…….………………………………. 27
3.1.6 求解昇力與阻力係數………………………... 29
3.1.7 求解流線函數 ……………………………...
31
3.1.8 求解渦度 …………………………………..
32
3.1.9 時階 的限制………………………………..
33
3.2 彈性圓柱振動…………………………………..……....... 35
3.3 互制…………………………………………………..…... 35
3.4 波譜分析理論……………………………………………. 37
3.5 其他說明………………………………………………….. 39
3.5.1 二階段計算………………………………….. 39
3.5.2 慣性座標之流線…………………………………. 40

第四章 結果與討論………………………………………. 41
4.1 彈性圓柱運動與流場隨時間之變化……………………. 42
4.2 自然頻率之影響………………………………………….. 43
4.3 雷諾數的影響……………………………………… 49
4.3.1 對共振區間的影響………………………….. 49
4.3.2 對CLrms與CDavg的影響………………………… 50
4.3.3 對波譜能量（ES）的影響………………………. 51
4.3.4 CLrms、CDavg與共振區間之關係………..……….. 51
4.4 彈性圓柱之質量的影響……………………………... 52
4.4.1 對共振區間的影響………………………….. 52
4.4.2 對CLrms與CDavg的影響………………………… 53
4.4.3 對波譜能量（ES）的影響………………………. 54
4.4.4 CLrms、CDavg與共振區間之關係…………………. 55
4.5 阻尼比的影響…………………………………………….. 55
4.5.1 對共振區間的影響………………………….. 56
4.5.2 對CLrms與CDavg的影響………………………… 57
4.5.3 對波譜能量（ES）的影響………………………. 57
4.5.4 CLrms、CDavg與共振區間之關係……………..….. 58
第五章 結論與建議………………………………………. 59
5.1 結論…………………………………..…………………... 59
5.2 建議………………………………………………………. 65
參考文獻…………………………………………………….. 66

表……………………………………………………………... 71

圖……………………………………………………………... 76

謝誌…………………………………………………………... 96

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