臺灣博碩士論文加值系統

本論文將以力元理論探討低雷諾數流場中，有限平板模擬魚類尾鰭在不同史卓荷數(Strouhal Number, St)下進行上下(Heave)擺動之BCF泳動模式的受力機制。透過力元理論分析撓性平板之推力機制，發現推力產生來自於平板加速變形運動所產生的C_Da、流場中渦流而產生的C_Dv以及存在於物體表面的C_Df。其中與流場渦流(Vorticity)有關的C_Dv 與C_Df所提供之推力貢獻，將隨著史卓荷數St和變形量a_0增加時所導致流場中渦流強度增強，而明顯提升。
透過力元理論分析可以清楚了解環繞於平板周圍的渦流結構對於其所造成之受力變化，同時進行定量描述。仔細觀察剛性與撓性平板拍動時，三維流場中流場與C_Dv之分布，發現前緣渦皆對平板產生阻力貢獻；而除了剛性板外，平板周圍的渦流結構皆對於整體撓性平板產生極大之推力貢獻。造成剛性板做上下擺動仰角不變之運動幾乎沒有推力產生之主要因素為輔助勢流，由於輔助勢流包含幾何外型之影響，因此若將剛性板進行些微的撓曲變形，即會造成推力的遽增。
本文最後進行推進效率分析，在撓曲變形平板下以St=0.4的推進效率最佳，不過其所產生之推力值並非最大，因此不管是追求高游動速率還是高續航力，都必須在游動策略上有所取捨。

In this study, we investigate three-dimensional thrust mechanisms of finite rigid and deformable flapping plates simulated as a caudal fin of the BCF (body and/or caudal fin) swimming fish at low Reynold numbers Re=500 from the perspective of force element theory. Three values in Strouhal Number (St=0.2, 0.4 and 0.6) ranged in the nature regime and four stiffness (a_0=0, 0.1, 0.15, and 0.2) of the plate are considered. It is shown that the thrust generation of the flapping plate is mainly dominated by the acceleration of the body C_Da as well as vorticity in the flow field and on the body surface C_Dv and C_Df; moreover, C_Dv and C_Df will dramatically increase accompanied by the increasing in St and a_0 due to the generation of stronger vortices, including two sides of the tip vortices and the trailing-edge vortices.
Further, we could precisely quantify the force contribution of each vortex strucuture in the flow field. Carefully examining, it is shown that the leading-edge vortex generated in a stroke of flapping motion provodes resistance contribution. However, the vortices around two sides and the trailing edge of plate enhanced by the deformation have contribution to the thrust except the cases of rigid plate. The main reason that results in nearly zero thrust contribution for the heaving rigid plates is due to geometric effects of the auxiliary potential. Therefore, given by a slight deflection, the flapping plate could sufficiently gain thrust forces to move forward.
In a final, the propulsive efficiency η of flapping plates is computed for different St, and show that η attains to the optimum at St=0.4, whilst the thrust force is the greatest at St=0.6. Therefore, no matter how fish pursue high swimming velocities or high cruising endurance, it must be trade-off under a swimming strategy.

目錄
口試委員會審定書 #
誌謝 i
中文摘要 ii
ABSTRACT iii
目錄 iv
圖目錄 vi
表目錄 ix
第1章 緒論 1
1.1. 前言 1
1.2. 研究背景 3
1.3. 文獻回顧 3
1.3.1. 魚類游動模式文獻回顧 3
1.3.2. 理論分析模式 8
1.3.3. 魚類BCF泳動推進與尾流關係 9
1.3.4. 力元理論文獻回顧 11
1.4. 研究目的 12
1.5. 全文概述 12
第2章 力元理論 13
2.1. 前言 13
2.2. 輔助勢流 14
2.3. 力元理論推導 15
第3章 數值方法及控制方程式 22
3.1. 簡介 22
3.2. 網格產生 22
3.2.1. 網格產生時間 23
3.2.2. 數值擴散 24
3.2.3. 網格品質 24
3.3. 控制方程式 25
3.3.1. 質量守恆方程式 26
3.3.2. 動量守恆方程式 26
3.4. 數值求解方法 26
3.4.1. 分離求解器 27
3.4.2. 空間離散 28
3.4.3. 時間離散 33
3.4.4. 壓力-速度耦合關係的處理 35
第4章 結果與討論 42
4.1. 流場參數設定 43
4.2. 運動參數設定 44
4.3. 輔助勢流場數值計算結果 46
4.4. 數值結果驗證 46
4.5. 以力元理論觀點分析AR=1之平板在不同St、a_0流場下之推力 47
4.5.1. 平板阻力隨時間的變化 47
4.5.2. 環境渦流對於平板推力之影響 52
4.6. 以力元理論觀點分析三維流場特性 58
4.6.1. 平板區環境渦流對於平板的影響 62
4.6.2. 平板周圍環境渦流對於平板的影響 69
4.7. 推進效率(η)之探討 74
第5章 結論與未來展望 76
5.1. 結論 76
5.2. 未來展望 77
參考文獻 78

[1]Anderson, J. M., Streitlien, K., Barrett, D. S. & Triantafyllou, M. S. 1998 Oscillating foils of high propulsive efficiency. J. Fluid Mech. 360, 41–72.
[2]Bandyopadhyay, P. 2005 Trends in biorobotic autonomous undersea vehicles, IEEE Journal of Oceanic Engineering 30(1), 109-139.
[3]Beal, D. N., Hover, F. S., Triantafyllou, M. S., Liao, J. C., & Lauder, G. V. 2006 Passive propulsion in vortex wakes, J. Fluid Mech. 549, 385-402.
[4]Biesheuvel, A. & Hagmeijer, R. 2006 On the force on a body moving in fluid. Fluid Dyn. Res. 38, 716–742.
[5]Blondeaux, P. O., Fornarelli, F., Guglielmini, L., Triantafyllou, M. S. & Verzicco, M. 2005 Numerical experiments on flapping foils mimicking fish-like locomotion. Phys. Fluids 17, 113601.
[6]Borazjani, I. & Sotiropoulos, F. 2008 Numerical investigation of the hydrodynamics of carangiform swimming in the transitional and inertial flow regimes. J. Expl Biol. 211, 1541–1558.
[7]Buchholz, J. H. J. & Smits, A. J. 2008 The wake structure and thrust performance of a rigid low-aspect-ratio pitching panel. J. Fluid Mech. 603, 331–365.
[8]Burgers, J. M. 1920 On the resistance of fluids and vortex motion. Proc. Kon. Akad. Westenschappente Amsterdam. 1, 774–782.
[9]Chang, C. C. 1992 Potential flow and forces for incompressible viscous flow. Proc. R. Soc. A-Math. Phys. Eng. Sci. 437, 517–525.
[10]Chang, C. C. ＆ Lei, S. Y. 1996 An analysis of aerodynamic forces on a delta wing. J. Fluid Mech. 316, 173-196.
[11]Chang, C. C. ＆ Lei, S. Y. 1996 On the sources of aerodynamic forces: steady flow around a cylinder or a sphere. Proc. R. Soc. Lond. A 452, 2369-2395.
[12]Chang, C. C., Yang, S. H. & Chu, C. C. 2008 A many-body force decomposition with applications to flow about bluff bodies. J. Fluid Mech. 600, 95–104.
[13]Chu, C. C., Chang, C. C. et al. 1996 Suction effect on an impulsively started circular cylinder: vortex structure and drag reduction. Phys. Fluids. 11, 2995-3007.
[14]Dickinson, M. H., Farley, C. T., Full, R. J., Koehl. M. A. R., Kram, R. & Lehman, S. 2000 How Animals Move: An Integrative View. Science 288, 100.
[15]Dong, H., Mital, R. & Najjar, F. M. 2006 Wake topology and hydrodynamic performance of low-aspect-ratio flapping foils. J. Fluid Mech. 566, 309–343.
[16]Drucker, E. G. & Lauder, G. V. 1999 Locomotor forces on a swimming fish: three-dimensional vortex wake dynamics quantified using particle image velocimetry. J. Fluid Mech. 202, 2392–2412.
[17]von Ellenrieder, K. D., Parker, K. & Soria, J. 2003 Flow structures behind a heaving and pitching finite-span wing. J. Fluid Mech. 490, 129–138.
[18]Gharib, M., Rambod, E. & Shariff, K. 1998 A universal time scale for vortex ring formation. J. Fluid Mech. 360, 121–140.
[19]Glauert, H. 1983 The elements of aerofoil and airscrew theory. Cambridge University Press.
[20]Godoy-Diana, R., Aider, J. L. & Wesfreid, J. E. 2008 Transitions in the wake of a flapping foil. Phys. Rev. E 77, 016308.
[21]Godoy-Diana, R., Aider, J. L. & Wesfreid, J. E. 2009 A model for the symmetry breaking of the reverse B’enard–von K’arm’an vortex street produced by a flapping foil. J. Fluid Mech. 622, 23–32.
[22]Gopalkrishnan, R., Triantafyllou, G. S., Triantafyllou, M. S., & Barredt, D. 1994 Active vorticity control in a shear flow using a flapping foil. J. Fluid Mech., 274, 1-22.
[23]Green, M. A. & Smits, A. J. 2008 Effects of three-dimensionality on thrust production by a pitching panel. J. Fluid Mech. 615, 211–220.
[24]Guglielmini, L. & Blondeaux, P. 2004 Propulsive efficiency of oscillating foils. Euro. J. Fluid Mech. 23, 255–278.
[25]Howe, M. S. 1995 On the force and moment on a body in an incompressible fluid, with application to rigid bodies and bubbles at high and low Reynolds numbers. Quart. J. Mech. Appl. Math. 48, 401–426.
[26]Hsieh, C. T., Chang, C. C. and Chu, C. C. Revisiting the aerodynamics of hovering flight using simple models, 2009, J. Fluid Mech. 623, 121-148.
[27]Hsieh, C. T., Kung, C. F., Chang, C. C. and Chu, C. C. 2010 Unsteady aerodynamics of dragonfly using a simple wing-wing model from the perspective of a force decomposition. J. Fluid Mech. 663, 233-252.
[28]Hultmark, M., Leftwich, M. & Smits, A. J. 2007 Flowfield measurements in the wake of a robotic lamprey. Exp. Fluids 43, 683–690.
[29]Koochesfahani, M. M. 1989 Vortical patterns in the wake of an oscillating aerofoil. AIAA Journal 27, 1200–1205.
[30]Landau, L. D. & Lifshitz, E. M. 1987 Fluid Mechanics, 2nd edn. Pergamon.
[31]Lentink, D., Muijres, F. T., Donker-Duyvis, F. J. & van Leeuwen, J. L. 2008 Vortex wake interactions of a flapping foil that models animal swimming and flight. J. Expl Biol. 211, 267–273.
[32]Lewin, G. C. & Haj-Hariri, H. 2003 Modelling thrust generation of a two-dimensional heaving aerofoil in a viscous flow. J. Fluid Mech. 492, 339–362.
[33]Li, G. J. & Lu, X. Y. 2012 Force and power of flapping plates in a fluid, J. Fluid Mech. 712, 598-613.
[34]Liao, J. C., Beal, D. V. , Lauder, G. V. & Triantafyllou, M. S., 2003 The Karman gait: novel body kinematics of rainbow trout swimming in a vortex street. J. Expl Biol. 206(6), 1059.
[35]Licht, S., Hover, F. & Triantafyllou, M. 2004 Design of a flapping foil underwater vehicle. 13th International Underwater Technology Symposium.
[36]Lighthill, M. J. 1986 Fundamentals concerning wave loading on offshore structures. J. Fluid Mech. 173, 667–681.
[37]Lighthill, M. J. 1969 Hydromechanics of aquatic animal propulsion, Annual Review of Fluid Mechanics. 1(1), 413-446.
[38]Lighthill, M. J. 1971 Large-amplitude elongated-body theory of fish locomotion. Proceedings of the Royal Society of London, Series B, Biological Sciences, 179(1055), 125-138.
[39]Lindsey, C. C. 1978 Form, function and locomotory habits in fish, Fish Physiology, VII Locomotion, W. S. Hoar and D. J. Randall, Eds.New York: Academic, 1–100.
[40]Milano, M. & Gharib, M. 2005 Uncovering the physics of flapping flat plates with artificial evolution. J. Fluid Mech. 534, 403–409.
[41]Webb, P. W. 1984 Form and function in fish swimming, Sci. Amer. 251, 58–68.
[42]Schnipper, T., Andersen, A. & Bohr, T. 2009 Vortex wakes of a flapping foil. J. Fluid Mech. 633, 411–423.
[43]Schouveilera, L., Hover, F. S. and Triantafyllou, M. S. 2005 Performance of flapping foil propulsion, J. Fluids Struct. 20, 949–959.
[44]Sfakiotakis, M., Lane, D. & Davies, J. 1999 Review of fish swimming modes for aquatic locomotion. IEEE Journal of Oceanic Engineering, 24(2), 237-252.
[45]Taylor, G. K., Nudds, R. L. & Thomas, A. L. R. 2003 Flying and swimming animals cruise at a Strouhal number tuned for high power efficiency. Nature 435, 707–711.
[46]Triantafyllou, G. S., Triantafyllou, M. S. & Grosenbaugh, M. A. 1993 Optimal thrust development in oscillating foils with application to fish propulsion. J. Fluids Struct. 7, 205–224.
[47]Triantafyllou, M. S., Triantafyllou, G. S. & Gopalkrishnan, R. 1991 Wake mechanics for thrust generation in oscillating foils. Phys. Fluids 3 (12), 2835–2837.
[48]Tytell, E. D. & Lauder, G. V. 2004 The hydrodynamics of eel swimming. Part I. Wake structure. J. Expl Biol. 207, 1825–1841.
[49]Williamson, C. H. K. & Roshko, A. 1988 Vortex formation in the wake of an oscillating cylinder. J. Fluids Struct. 2, 355–381.
[50]Wu, T. 1960 Swimming of a waving plate. J. Fluid Mech. 10, 321-344.
[51]Wu, J. C. 1981 Theory for aerodynamic force and moment in viscous flow. AIAA J. 19, 432–441.
[52]蕭穎謙 1993 環繞機翼之二維渦漩流的研究，國立台灣大學應用力學研究所博士論文。
[53]蘇正瑜 1998 三角翼外流場之力源分析，國立台灣大學應用力學研究所博士論文。
[54]丁上杰 2009 魚類操控式游動之流體動力與生物物理學研究，清華大學動力機械工程學系博士論文。