本文主要利用數值方法探討圓柱於剪切流中流體-彈性不穩定之運動行為，理論模型則係基於暫態之連續與動量守恆方程式並利用SIMPLEC 數值方法以求出流場特性，同時解析圓柱之結構應力，流體-結構交互作用分析上則採用超限插值法(TFI)以模擬圓柱運動行為，分析結果與文獻數據比對後，可驗證理論模型正確性。研究結果顯示圓柱表面受剪切流橫向力之影響而產生側向升力，力方向是從高流速一方往低流速一方作用，作用力大小隨剪切參數的增加而變大，圓柱後方渦流溢放之史卓荷數同樣隨剪切參數呈些微地遞增，且當入口流型態由均勻流轉換成剪切流時，前端停滯點位置會往高流速方向偏移，偏移角度的大小與剪切參數呈線性增加，而後探討剪切流內圓柱流體-彈性振動之阻力振幅、升力振幅與運動軌跡，並解析不同彈性係數、阻尼係數等結構參數之影響，本文亦針對不同剪切參數、質量比等效應對流體-彈性振動之臨界速度影響作進一步的探討。

The present study aims to explore dynamical behavior of the fluid-elastic instability of a circular cylinder in shear flow by numerical simulations. The theoretical model comprises two groups of transient conservation equations of mass and momentum and the governing equations are solved numerically with an iterative SIMPLEC(Semi-Implicit Method for Pressure-Linked Equations Consistent) algorithm to determine the flow property and to analysis structure stress simultaneously. Additionally, the TFI (Transfinite interpolation) computation procedure is applied to characterize the behavior of fluid-structure interaction. The predictions are in reasonable agreement with literature showing the validity of the present theoretical model. The numerical results indicate that there is a transverse force acting from high velocity side toward the low velocity side in shear flow. The magnitude of this transverse force increases with the shear parameter. The Strouhal number slightly increases as the shear parameter increases for all Reynolds number. As the pattern of the approach flow changes from the uniform to shear flow, the front stagnation point shifts to high velocity side, and the base pressure increase. The magnitude of the shift of front stagnation point is linear with the shear parameter. Furthermore, this study appraises the amplitude and orbit of fluid elastic vibration of a circular cylinder in shear flow, and shows the effects of the spring constant and damping factor on fluid elastic vibration of the cylinder. In addition, various effects including shear parameter and mass ratio on the critical velocity of the fluid elastic vibration also has been examined detail.

目錄

中文摘要-----------------------------------------------------------------------I
英文摘要----------------------------------------------------------------------II
目錄---------------------------------------------------------------------------IV
圖目錄-----------------------------------------------------------------------VI
表目錄----------------------------------------------------------------------VIII
符號說明---------------------------------------------------------------------IX

第一章 緒論------------------------------------------------------------------1
1.1 研究動機-------------------------------------------------------1
1.2 文獻回顧-------------------------------------------------------2
1.3 研究目的-------------------------------------------------------5
第二章 理論分析------------------------------------------------------------7
2.1 理論分析-------------------------------------------------------7
2.1.1 流體統御方程式-----------------------------------------8
2.1.2 圓柱運動方程式---------------------------------------8
2.2 超限插值法(TFI)--------------------------------------------12
2.3 數值方法------------------------------------------------------16
2.3.1 SIMPLEC演算法-------------------------------------17
第三章 結果與討論----------------------------------------------------19
3.1 網格與時間解析---------------------------------------------20
3.2 理論驗證--------------------------------------------------------21
3.3 圓柱於剪切流內流場行為探討---------------------------22
3.3.1 史卓荷數變化------------------------------------------22
3.3.2 壓力分佈變化------------------------------------------23
3.3.3 停滯點位置變化---------------------------------------24
3.3.4 阻力係數與升力係數變化---------------------------24
3.3.5 圓柱背壓值變化---------------------------------------25
3.4 圓柱於剪切流中流體-彈性振動之探討----------------25
3.4.1 圓柱擺動振幅與運動軌跡--------------------------26
3.4.1.1 彈性係數效應之影響------------------------27
3.4.1.2 阻尼係數效應之影響------------------------28
3.4.2 剪切參數對流體-彈性振動臨界速度之影響---29
3.4.3質量比對流體-彈性振動臨界速度之影響-------29
第四章 結論----------------------------------------------------------------31
參考文獻---------------------------------------------------------------------33

[1]Tritton, D. J.,“Experiments on the flow past a circular cylinder at low Reynolds numbers,”Journal of Fluid Mechanics 6, 1959, pp. 547-567
[2]Grove, A. S., Shair, F. H., Petersen, E. E., Acrivos, A.,“An experimental investigation of the steady separated flow past a circular cylinder,”Journal of Fluid Mechanics 19, 1964, pp. 60-80
[3]Nishioka, M. and Sato, H.,“Measurements of velocity distributions in the wake of circular cylinder at low Reynolds number,”Journal of Fluid Mechanics 65, 1974, 97
[4]Nishioka, M. and Sato, H.,“Mechanism of determination of the shedding frequency of vortices behind a cylinder at low Reynolds numbers,”Journal of Fluid Mechanics, Vol. 89, 1978, pp. 49-60.
[5]Friehe, C. A.,“Vortex Shedding from Cylinder at Low Reynolds Number,”Journal of Fluid Mechanics, Vol. 100, 1980, pp. 237-241.
[6]Braza, M., Chassaing, P., Ha Minh, H.,“Numerical study and physical analysis of the pressure and velocity fields in the near wake of a circular cylinder,”Journal of Fluid Mechanics 165, 1986, pp. 79-130.
[7]Williamson, C. H. K.,“Oblique and Parallel Modes of Vortex Shedding in the wake of a Circular Cylinder at Low Reynolds Numbers,”Journal of Fluid Mechanics, Vol. 26, 1989, pp. 576-626.
[8]Griffin, O. M., and Ramberg, S. E.,“The vortex street wakes of vibrating cylinders,”Journal of Fluid Mechanics 66, 1974, pp. 553-576.
[9]Brika, D., and Laneville, A.,“Vortex-induced vibrations of a long flexible circular cylinder,”Journal of Fluid Mechanics 250, 1993, pp. 481-508.
[10]Bretherton, F. P.,“Slow viscous Motion Round a cylinder in a Simple Shear,”Journal of Fluid Mechanics, Vol. 12, 1961, pp. 591-613.
[11]Bearman, P. W., and Zdravkovich, M. M.,“Flow around a circular cylinder near a plane boundary,”Journal of Fluid Mechanics 89, 1978, pp. 33-47.
[12]Jordan, S. K., and Fromn, J. E.,“Laminar Flow Past a Circle in a shear flow,”The Physics of Fluids, Vol. 15, No. 6, 1972, pp. 972-976.
[13]Kiya, M., Tamura, H., Arie, M., “Vortex shedding from a circular cylinder in moderate-Reynolds number shear flow,”Journal of Fluid Mechanics 101, 1980, pp. 721-735.
[14]Kwon, T. S., Sung, H. J., Hyun, J. M.,“Experimental Investigation of Uniform-Shear Flow Past a Circular Cylinder,”Journal of Fluid Engineering 114, 1992, pp. 457-460
[15]Lei, C., Cheng, L., Kavanagh, K.,“A finite difference solution of the shear flow over a circular cylinder,”Ocean Engineering 27, 2000, pp. 271-290.
[16]Sumner, D., and Akosile, O. O.,“On uniform planar shear flow around a circular cylinder at subcritical Reynolds number,”Journal of Fluids and Structures 18, 2003, pp. 441-454.
[17]Brika, D., and Laneville, A.,“The hysteresis and bifurcation phenomena in the Aeolian vibrations,”Journal of Fluid Meachanics 205, 1993, pp. 481-508
[18]Gordan, W. N., and Hall, C. A.,“Construction of curvilinear coordinate systems and application to mesh generation,”International J. Num. Methods in Eng, Vol. 7, 1973, pp. 461-477.
[19]Eriksson, L. E.,“Three-dimensional spline-generated coordinate transformations for grids around wing-body configurations,”Numerical Grid Generation Techniques, NASA CP 2166, 1980
[20]Eriksson, L. E.,“Generation of boundary conforming grids around wing-body configuration using transfinite interpolation,”AIAA J., Vol. 20, 1982, pp. 1313-1320.
[21]Eriksson, L. E.,“Transfinite Mesh Generation and Computer-Aided Analysis of Mesh Effects,”Ph.D. Dissertation, University of Uppsala, Sweden, 1984
[22]Patankar, S. V.,“Numerical Heat Transfer and Fluid Flow,”Hemisphere Publishing Corporation, New York, 1983
[23]Van Doormaal, J. P., and Raithby, G. D., “Enhancements of The SIMPLE Method for Predicting Incompressible Fluid Flows,”Numerical Heat Transfer, Vol. 7, 1984, pp. 147-163.
[24]Munson, B. R., Young, D. F., Okiishi, T. H.,“Fundamentals of Fluid Mechanics,”Third Edition, John Wiley＆Sons, 1998
[25]White, F. M.,“Viscous Fluid Flow,”Second Edition, 1991