臺灣博碩士論文加值系統

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
1 INTRODUCTION 1
1.1 Motivation and background .......................... 1
1.2 Literature review ................................ 1
1.3 Problem description............................... 4
2 MATHEMATICAL MODEL AND NUMERICAL METHODS 6
2.1 Flow chart of fluid and flexible cylinder interaction . . . . . . . . . . . . . 6
2.2 Governing equations of fluid flow ....................... 7
2.3 Equation of motion of flexible cylinder .................... 8
2.4 Pseudospectral methods ............................ 9
2.4.1 Pseudospectral matrix element method . . . . . . . . . . . . . . . . 9
2.4.2 Fourier pseudospectral matrix method . . . . . . . . . . . . . . . . 11
2.5 Direct-forcing immerse dboundary method .................. 12
2.6 Domain decomposition ............................. 13
2.7 Courant-Friedrichs-Lewy condition ...................... 17
2.8 Adaptive Adams-Bashforth equation ..................... 18
2.9 Numerical procedure .............................. 19
2.10 Computational environments.......................... 21
3 RESULTS AND DISCUSSION 23
3.1 Grid independence and validation....................... 23
3.2 Cross-flow past a flexible circular cylinder at Re = 200 . . . . . . . . . . . 26 3.3 Transitional flow ................................ 33
4 CONCLUSIONS AND FUTURE WORK 37
4.1 Conclusions ................................... 37
4.2 Future work................................... 38
BIBLIOGRAPHY .................................. 39

[1] Griffin, O. M., 1985 Vortex induced vibrations of marine cables and structures. Naval Research Laboratory Memorandum Report number 5600, Washington, D.C., USA.
[2] Vandiver,J.K.,1991 Dimensionless parameters important to the prediction of vortex- induced vibrations of long flexible cylinders in ocean currents. Journal of Fluids and Structures 7, 423-455.
[3] Newman, D., Karniadakis, G. E., 1996 Simulation of the flow over the flexible cable: a comparison of forced and flow-induced vibration. Journal of Computational Physics 10, 439-453.
[4] Newman, D., Karniadakis, G. E., 1997 A direct numerical simulation study of flow past a freely vibrating cable. Journal of Fluid Mechanics 344, 95-136.
[5] Olinger, D. 1996 A low-order model for vortex shedding patterns behind vibrating flexible cables. Physics of Fluids 10, 1953–1961.
[6] Evangelinos, C., Karniadakis, G. E., 1999 Dynamics and flow structures in the turbu- lent wake of rigid and flexible cylinders subject to vortex-induced vibrations. Journal of Fluid Mechanics 400, 91-124.
[7] Evangelinos, C., Lucor, D., Karniadakis, G. E., 2000 DNS-derived force distribu- tion on flexible cylinders subject to vortex-induced vibration. Journal of Fluids and Structures 14, 429-440.
[8] Ku, H. C., Hatziavramidis, D., 1985 Solutions of the two-dimensional Navier-Stokes equations by Chebyshev expansion methods. Computers & Fluids 13, 99-113.
[9] Ku, H. C., Rosenberg, A. P., 1989 A pseudospectral matrix element method for solution of three-dimensional incompressible flows and its parallel implementation. Journal of Computational Physics 83, 260-291.
[10] Chern, M. J., Borthwick, A. G. L., and Eatock Taylor, R., 1999 A pseudospectral σ-transformation model of 2D nonlinear waves. Journal of Fluids and Structures 13, 607-630.
[11] Chern, M. J., Borthwick, A. G. L., and Eatock Taylor, R., 2005 Pseudospectral ele- ment model for free surface viscous flows. International Journal of Numerical Methods for Heat and Fluid Flow 15, 517-554.
· 39 ·
[12] Lin, J. M. 2020 Pseudospectral matrix element method coupled with direct-forcing immersed boundary method for a long flexible cylinder. Master thesis, National Tai- wan University of Science and Technology, Taipei, Taiwan.
[13] Marciniak, A., Jankowska, M. A., 2020 Interval methods of Adams-Bashforth type with variable step sizes. Numerical Algorithms 84, 651–678.
[14] R. Courant, K. Friedrichs, H. Lewy, 1928 U ̈ber die partiellen Differenzengleichungen der mathematischen Physik. Mathematische Annalen 100, 32-74.
[15] Chorin, A. J., 1968 Numerical solution of the Navier-Stokes equations. Mathematics of Computation 22, 745-762.
[16] Rajani, B.N., Kandasamy, A., Majumdar, S., 2009 Numerical simulation of laminar flow past a circular cylinder. Applied Mathematical Modelling 33, 1228-1247.
[17] Ding, H., Shu, C., Yeo, K.S., Xu, D., 2007 Numerical simulation of flows around two circular cylinders by mesh-free least square-based finite difference methods. Interna- tional Journal for Numerical Methods in Fluids 53, 305-332.
[18] Liu C., Zheng, X., Sung, C.H., 1998 Preconditioned multigrid methods for unsteady incompressible flows. Journal of Computational Physics 139, 35-57.
[19] Evangelinos, C., Karniadakis, G. E., 1996 Transition in the wake of flexible beams and cables. Proceedings of the Seventh International Offshore and Polar Engineering Conference 41, 1714, Honolulu, Hawaii, USA.