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研究生： 李梅花
Elisa - Melati Putri
論文名稱： 可彎曲線與流體交互作用之沉浸邊界法數值模擬
Simulation of interaction between a flexible filament and fluid flow by immersed boundary method
指導教授： 陳明志
Ming-jyh Chern
口試委員: 許朝敏
Chao-min Hsu
林怡均
Yi-jiun Peter Lin
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： 2013
畢業學年度： 101
語文別： 英文
論文頁數： 68
中文關鍵詞： 沉浸邊界流 、流固耦合 、可彎曲線 、Dirac delta function 、持續擺動
外文關鍵詞： Immersed boundary method, solid-fluid interaction, flexible filament, Dirac delta function, self-sustained flapping
相關次數： 點閱：301  下載：6 
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    • 模擬流固耦合之問題可藉由數值沉浸邊界法來達成目的，尤其當問題為可彎曲線在流體

    之中擺動。流場在固定正交網格中，以尤拉(Eulerian)描述法利用那維爾–史托克方程

    式來計算流場中之數值，而動態的線則以拉格朗日(Lagrangian)描述法在可移動網格中

    作計算，並藉由Dirac delta function連結流場中此兩種描述法之變數。此研究考慮

    有重力的情況下，將線呈一角度自由釋放會發生振盪之情形。在均勻流中可彎曲線持續

    擺動下可觀察到後方流場渦漩產生及後續的發展現象。且可彎曲線必須給予足夠的長

    度，才足以在模擬中出現持續擺動之現象。當我們將流場改為震盪流時，可彎曲線亦然

    會發生擺動且與流體震盪方向同步。本數值研究經與他人之數值及實驗結果相比有良好

    的一致性，故本篇研究成功地證實以沉浸邊界法並利用Dirac delta function來計算

    可彎曲線與流體之交互作用的關係是可行的。

    Simulation of solid-fluid interaction has been done by immersed boundary method, especially between a flexible filament and fluid flow. The fluid motion which is described by the Navier-Stokes equations is computed based on Eulerian variables under a fixed Cartesian mesh, while the filament motion is determined on the basis of Lagrangian variables under a freely moving mesh. The Eulerian and Lagrangian variables are connected by a smoothed approximation of the Dirac delta function. A hanging filament without ambient fluid and subjected to the gravitational force is considered. For a flexible filament flapping in a uniform flow, the evolution of vortex generation is observed. A self-sustained flapping develops for all filament simulations due to the use of a sufficiently long of filament. For a flexible filament in oscillating flow, a self-sustained flapping also develops as a result of the oscillation of the flow along the filament. The results from the present study are consistent with numerical and experimental data from the previous study. It shows that the immersed boundary method has successfully handled the interaction between the filament and the fluid flow, using a Dirac delta function.

    Chinese Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . iv Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv Nomenclatures . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . vii List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv List of Figures . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . xiv 1 INTRODUCTION 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Literature Review . . . . . . . . . . . . . . .. . . . . . . . . . . . . . 3 1.3 Synopsis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 MATHEMATICAL FORMULAE AND NUMERICAL MODEL 7 2.1 Governing equations for the fluid flow . . . . . . . . . . . . . . . . . . 8 2.2 Equations of motion of a flexible filament . . . . . . . . .. . . . . . . 10 2.2.1 Dimensionless equations . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.2 Dirac delta function . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2.3 Simulation for a rigid immersed boundary . . . . . . . . . . .... . . . 13 2.3 Solution algorithm for a moving filament . . . . . . . . . . . . .. . . . 17 2.4 Computational details . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.5 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3 RESULTS AND DISCUSSION 27 3.1 A hanging filament without ambient fluid under a gravitational force . . 27 3.2 A flexible filament flapping along a uniform flow direction . . . . . . . 29 3.3 A flexible filament flapping across oscillating flow direction . . . . . 34 4 CONCLUSIONS AND FUTURE WORK 36 4.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 CURRICULUM VITAE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

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