臺灣博碩士論文加值系統

本研究應用具有虛擬力的直接施力沈浸邊界法(Direct Forcing Immersed Boundary Method, DFIB)來模擬均勻流場中的圓球在一定雷諾數範圍內受渦漩引致振動(Vortex Induced Vibration, VIV)的現象。因渦漩引致振動所產生的水動力,在流場中對固體結 構物所造成的擾動力量可能會造成結構損害,但從另一方面來看,也可能成為再生流 動能源轉換的一個方式。本研究主要分析一可在均勻流的橫向方向運動的圓球前有一個固定的小圓球的振動行為。在模擬結果中,小球的直徑及兩球間的間距為本文對水 動力係數、渦漩振動以及能源效率為主要的研究因素。除此之外,此研究也將描述如 何預測小圓球的影響。本研究中發現,固定小圓球會提高的球下游處的升力係數及振幅比且阻力係數會逐漸減弱。在過程中所建立的數值模式以靜止下的球在雷諾數50的流場以及雷諾數300下球的振動現象的已發表的期刊文章進行比較與驗證。這個研究也顯示了直接施力沈浸邊界法對於此圓球在流場中的振動行為有良好的分析預測能力

A direct-forcing immersed boundary (DFIB) method with virtual force is used to investigate the vortex-induced vibration (VIV) of an elastically mounted sphere in uniform flow at a moderate Reynolds number. Fluctuating hydrodynamic forces may cause damage when a solid structure interacts with fluid flow. Conversely, such forces may be exploited as a renewable energy resource. In this study, a smaller fixed sphere placed in front of an elastically mounted sphere to investigate the effect that is given. Variation in the diameters of the small sphere and the gap between both spheres set as a parameter of the smaller fixed sphere. The effects of the small fixed sphere on the hydrodynamic force coefficients, sphere responses, vortex shedding modes and energy efficiency are discussed. In addition, an explanation of how to estimate the effects of the small sphere is also described in this study. The existence of smaller fixed spheres in front of the mounted sphere increases value of lift coefficient and amplitude ratio of the downstream sphere. However, the value of drag coefficient in downstream sphere becomes smaller. The method is validated by comparisons with previously published results for flow past a sphere at Re = 50 for stationary sphere and Re = 300 for VIV phenomena. This study proves the capability of the DFIB model for investigation of VIV on a structure and offers an analysis of the effects of a smaller upstream sphere on VIV phenomena of an elastically mounted sphere.

Chinese Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
Nomenclatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
List of Figures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv

INTRODUCTION
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Literature Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.1 Vortex-induced vibration . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.2 Direct forcing immersed boundary method. . . . . . . . . . . . . . . . . 5
1.2.3 Present study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

MATHEMATICAL AND NUMERICAL MODEL
2.1 Governing Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Direct-forcing immersed boundary method . . . . . . . . . . . . . . . . . . 10
2.3 Equations of motion for rigid body. . . . . . . . . . . . . . . . . . . . . 13
2.4 Numerical procedures. . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.5 Validation and numerical sensitivity studies. . . . . . . . . . . . . . . . 16

RESULTS AND DISCUSSION
3.1 Transverse vibration of a sphere. . . . . . . . . . . . . . . . . . . . . . 24
3.1.1 Sphere responses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.1.2 Vortex shedding modes . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.1.3 Force analyses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2 Transverse vibration behind a smaller fixed sphere . . . . . . . . . . . . 29
3.2.1 Sphere responses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2.2 Vortex shedding modes . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2.3 Force analyses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.3 Energy efficiency of VIV phenomena. . . . . . . . . . . . . . . . . . . . . 40
3.4 Estimate the effect of adding a small fixed sphere. . . . . . . . . . . . . 42

4 CONCLUSIONS AND FUTURE WORK
4.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
BIBLIOGRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
CURRICULUM VITAE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

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