以假頻譜矩陣元素法模擬在不同初始條件下橫流與柔性圓柱之交互作用

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研究生：	吳祐朋 You-Peng Wu
論文名稱：	以假頻譜矩陣元素法模擬在不同初始條件下橫流與柔性圓柱之交互作用 Pseudospectral matrix element modeling for cross-flow past a flexible cylinder with different initial conditions
指導教授：	陳明志 Ming-Jyh Chern
口試委員:	林怡均 Yi-Jiun Lin 王謹誠 Chin-Cheng WANG
學位類別：	碩士 Master
系所名稱：	工程學院 - 機械工程系 Department of Mechanical Engineering
論文出版年：	2021
畢業學年度：	109
語文別：	英文
論文頁數：	40
中文關鍵詞：	假頻譜矩陣元素法、直接施力沉浸邊界法、區域分解法、座標轉換、自適應步長
外文關鍵詞：	flow-induced vibration, adaptive step size
相關次數：	點閱：181 下載：2
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海底電纜因為流動所引起的震動，是在工程上相當重要的問題。本研究利用假頻譜矩陣元素法結合直接施力沉浸邊界法建立出一套含有流固耦合的數值模型，並設置一條柔性圓柱，模擬在不同雷諾數下流體通過柔性圓柱所產生的現象，計算其升力及阻力。為了模擬無限長的柔性圓柱並考量計算的難易度，此研究使用一條長度為4π的柔性圓柱，並將圓柱兩端設定週期性邊界條件。在計算升力及阻力部分，運用座標變換減少固體積分合力時所產生的雜訊。而當雷諾數的提升時，圓柱的升力變化量逐漸變大，透過自適應時間步長，增加計算時的穩定性。
透過給定初始位移的方式，成功模擬出難以透過實驗架設的過渡流，觀察圓柱振盪與流動模式，發現柔性圓柱中的最大位移與實驗結果相似，以及以行進波為基礎的過渡流現象。

Vibration of cables, which is induced by flow in ocean is a very important problem in engineering. Numerical models for fluid-structure interaction were established using the pseudospsectral methods combined with the direct-forcing immersed boundary (DFIB) method in this study. A flexible cylinder was set up to simulate phenomena of cross- flow past the flexible cylinder at a variety of Reynolds numbers. In order to simulate an infinite flexible cylinder and consider the feasibility of calculation, a flexible cylinder with a length of 4π was considered. Periodic boundary conditions were imposed at both ends of the cylinder. Coordinate transformation is used to reduce the noise generated when calculating resultant force by the numerical integral. As the Reynolds number increases, lift change of the cylinder gradually becomes large. The stability of the in-house numerical model is increased using the adaptive time step.
By given the initial displacement, successfully simulated transitional flow which is difficult to set up through experiment. Observing the effects of cylinder vibration on the flow patterns, it was found that the maximum displacement in the flexible cylinder was similar to the experimental results, and also found the transitional flow based on the travelling wave response.

ChineseAbstract ................................... i Abstract........................................ ii
Acknowledgements .................................. iii Contents........................................ iv
Nomenclatures .................................... v
List of Tables..................................... ix
List of Figures..................................... x
INTRODUCTION 1
1 Motivation and background .......................... 1
2 Literature review ................................ 1
3 Problem description............................... 4
MATHEMATICAL MODEL AND NUMERICAL METHODS 6
1 Flow chart of fluid and flexible cylinder interaction . . . . . . . . . . . . . 6
2 Governing equations of fluid flow ....................... 7
3 Equation of motion of flexible cylinder .................... 8
4 Pseudospectral methods ............................ 9
4.1 Pseudospectral matrix element method . . . . . . . . . . . . . . . . 9
4.2 Fourier pseudospectral matrix method . . . . . . . . . . . . . . . . 11
5 Direct-forcing immerse dboundary method .................. 12
6 Domain decomposition ............................. 13
7 Courant-Friedrichs-Lewy condition ...................... 17
8 Adaptive Adams-Bashforth equation ..................... 18
9 Numerical procedure .............................. 19
10 Computational environments.......................... 21
RESULTS AND DISCUSSION 23
1 Grid independence and validation....................... 23
2 Cross-flow past a flexible circular cylinder at Re = 200 . . . . . . . . . . . 26 3.3 Transitional flow ................................ 33
CONCLUSIONS AND FUTURE WORK 37
1 Conclusions ................................... 37
2 Future work................................... 38
BIBLIOGRAPHY .................................. 39
                                

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