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研究生： Kamau King'ora
Kamau - King'ora
論文名稱： 紊流中流引致振動之直接力量沉浸邊界模擬
Direct-forcing immersed boundary modeling of vortex-induced vibration in turbulent flow
指導教授： 陳明志
Ming-Jyh Chern
口試委員: 林怡均
Yi-Jiun Peter LIN
洪子倫
Tzyy-Leng Horng
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： 2015
畢業學年度： 103
語文別： 英文
論文頁數： 79
中文關鍵詞： 大渦紊流模擬 、直接力量沉浸邊界法 、渦旋引致振動 、鎖向放大 、共振
外文關鍵詞： Large eddy simulation (LES), Direct-forcing immersed boundary (DFIB), Vortex-induced vibration (VIV), Lock-in, Resonance
相關次數： 點閱：319  下載：4 
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    • 本研究應用直接力量沈浸邊界與大渦法對於紊流中一低質量比、低阻尼比的圓柱體的渦引致振動來進行模擬計算。由於圓柱後方的渦漩交替逸出因此造成作用於圓柱的水動力隨時間而有所變化，進一步造成圓柱體隨時間的振動。而當振動頻率接近於圓柱體的自然頻率時，共振現象會產生，此時大振幅的圓柱運動會導致結構的疲勞及破壞。本研究針對此現象，考慮一能在流動的垂直方向運動的圓柱體，其在雷諾數為十萬以上時，衰減速度(reduced velocity)的改變對此種渦引致振動的影響。在結果中，2S與2T渦漩逸出模式分別在小振幅與大振幅的圓柱振動時被觀察到。而在衰減速度與振動振幅的變化關係中也可看到隨衰減速度由低到高，振幅由很小到產生鎖相放大(lock-in)振幅突然增大的共振現象，同時振動的時序圖也可看到因衰減速度變化而有週期性(periodic)與類週期性(quasi-periodic)的行為。同時本研究所提出的DFIB-LES模式其數值預測結果與已發表的實驗結果有良好之一致性，證明模式的正確性。本模式將對此類紊流中渦引致振動模擬分析有所助益。

    A numerical study of the vortex-induced vibration (VIV) of a flexibly supported circular cylinder with low mass ratio and damping is investigated in turbulent flow using the direct-forcing immersed boundary method and large eddy simulation (DFIB-LES). The fluctuating hydrodynamic forces may cause the solid structure in fluid to vibrate due to vortex shedding behind it. At resonance, high peak amplitude vibration may result to fatigue, yielding, buckling or other forms of failure in the structure. The present study considers a dynamically mounted rigid circular cylinder which is allowed to vibrate transversely in a uniform flow at Reynolds number $\mathcal{O}10^5$. The effect of reduced velocity on VIV is discussed. 2S and 2T vortex shedding modes are found corresponding to low amplitude vibration and high amplitude vibration respectively. The amplitude variation at low reduced velocity is gradual as oppose to the traditional jump from the initial to the upper branch. The upper branch is extended at the expense of the lower branch and the range of synchronisation is wider compared to low Reynolds number cases. The lift force increases rapidly in the initial excitation regime and a sharp peak is found at the beginning of the upper branch. In the upper branch region, the lift decreases rapidly and then gradually and remains almost constant in the desynchronization region. The displacement in low reduced velocity is found to be periodic and transits to quasi-periodic in the lock-in range. The maximum peak amplitude recorded in this study is 1.5 times the diameter of the cylinder. Comparison against the published experimental data proves the capability of the present DFIB-LES model. This proposed model can be useful to investigate the VIV phenomena of the solid structures interacting with flowing fluid.

    Chinese Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Nomenclatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii 1 INTRODUCTION 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Synopsis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 MATHEMATICAL FORMULAE AND NUMERICAL MODEL 7 2.1 DFIB-LES model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.1.1 Governing equations for DFIB-LES . . . . . . . . . . . . . . . . . . 9 2.1.2 The virtual force treatment . . . . . . . . . . . . . . . . . . . . . . 10 2.1.3 Smagorinksy-Lilly SGS model . . . . . . . . . . . . . . . . . . . . . 11 2.1.4 Sub-grid turbulence Kinetic Energy . . . . . . . . . . . . . . . . . . 12 2.2 The equation of motion for a vibrating rigid body . . . . . . . . . . . . . . 13 2.3 Numerical solution for Navier-Stokes equations . . . . . . . . . . . . . . . . 14 2.3.1 Spatial and temporal discretizations . . . . . . . . . . . . . . . . . . 14 2.3.2 Prediction-correction for pressure-velocity . . . . . . . . . . . . . . 15 2.4 Procedures for fluid-structure interaction . . . . . . . . . . . . . . . . . . . 15 2.5 Computational details and computing time . . . . . . . . . . . . . . . . . . 16 2.5.1 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3 RESULTS AND DISCUSSION 19 3.1 Validation of the numerical scheme . . . . . . . . . . . . . . . . . . . . . . 19 3.1.1 Power spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.1.2 Flow visualisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.1.3 Recirculation length . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.1.4 Drag coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.1.5 Strouhal number . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.2 VIV of an elastically mounted rigid cylinder . . . . . . . . . . . . . . . . . 23 3.2.1 VIV of an elastically mounted rigid cylinder at Re = 30, 500 . . . . 24 3.2.2 VIV of an elastically mounted rigid cylinder at Re = 100, 000 . . . . 25 4 CONCLUSIONS AND FUTURE WORK 30 4.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 4.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 CURRICULUM VITAE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

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