由於近幾十年壓電材料的普遍性有明顯增加，竟而延伸出許多新壓電獵能器的概念。所謂的壓電獵能器，是利用壓電效應，將動能轉換成電能。舉例來說，可以利用環境中的振動能，透過壓電效應將機械動能轉換成電能。本論文基於此概念，研析流致振動系統，透過流固耦合的理論與實驗參數分析，提出結構振動所產生之應變能最佳化的設計。此流致振動系統包含一端固定於方柱之懸臂式撓性樑以及流速可變之流場系統。該方柱的尾流由於雷諾數的變化，將會發生渦漩洩離。這個現象導致撓性樑兩側行進波性的壓力差，使撓性樑產生振動。也就是說，撓性樑在方柱的尾流中，會因為動壓的不穩定性因振動而產生應變能。另一方面，撓性樑的變形也會反饋到尾流而改變動壓場。也就是說，此撓性樑變形狀，將類似鰻魚或水蛇的鰻行式擺尾方式。此撓性樑的動態反應和應變能因上流速度、集合參數和彎曲剛度來控制。面對這類高強度、多物理量的流固耦合問題，本論文提出兩個分析方法：水洞實驗分析以及數值模擬計算。水洞實驗的部分包括動態反應分析與質點影像測速(PIV) ；模擬計算部分結合計算流體力學與計算固體力學來求取結構振動與流場變化之間的作動響應。從本研究所得到之實驗與計算的結果，經驗證後可將撓性樑的擺動方式可分為分隔板式振動以及行進波式振動。因樑剛度、動壓場、渦流脫落頻率等參數的變化也會引起擺動方式極大改變。雖然波動式變形所造成的應變能可轉換成較高的電能，然而本研究發現，由於擺動頻率相當低且曲率變化可能造成正負電荷互相抵消，故轉換率較低。透過參數分析與實驗驗證，本研究提出撓性樑最大的應變能量，將發生在撓性樑與尾流呈現最佳耦合時。

Owing to the increased availability of piezoelectric materials, there has been a growing interest towards piezoelectric energy harvesters in the last decades as they can use ambient vibrations for powering low-consumption electronic devices. Periodic vortex shedding occurs in the wake of square cylinders placed in fluid flow. This results in a travelling pressure wave in the wake which can cause structural vibrations. When placing a flexible polymeric plate in the wake of a square cylinder, the oscillatory dynamic pressure impinging on the plate will trigger its vibrations. The plate response simultaneously modifies the wake structures and thus the dynamic pressure. If the plate is flexible enough, it starts to undulate in a manner similar to anguilliform swimming motion. Optimum anguilliform swimming motion is almost two-dimensional and therefore, the plate response can be considered as a cantilever beam response. Electricity can be generated from the strain energy resulting from acute bending by using piezoelectric cells attached at the plate surface. The geometric parameters of the bluff body and the beam, the stiffness and the incoming fluid velocity: determine its response and strain energy output. Such a strongly coupled fluid-structure interaction problem was investigated by carrying out experiments in water tunnel involving shape capture and particle image velocimetry studies as well as fluid-structure interaction modelling where computational structural mechanics and computational fluid dynamics solvers are coupled. Results showed that the beam can jump into radically different flapping patterns. From splitter plate oscillations to travelling waves; depending on: the dynamic pressure distribution, the vortex shedding frequency and the beam stiffness. The undulating pattern showing optimum plate-wake interaction leads to greater power output. Piezoelectric energy harvesting from the undulating plate is more challenging as there is a greater risk of charge cancellations resulting from the frequent curvature changes. Moreover, the low flapping frequency also limits the power output.

Publications
Binyet, E.; Huang, C. Y.; Chang, J. Y. Polymeric flexible plate in the wake of a bluff body for energy harvesting, Procedia Engineering, 2017, 199, 1296-1301
Binyet, E.; Huang, C. Y.; Chang, J. Y. Characterization of a vortex-induced vibrating thin plate energy harvester with particle image velocimetry. Microsystem Technologies, 2018, 24, 4569-4576.
Binyet, E.; Huang, C. Y.; Chang, J. Y. Water tunnel study of a cantilever flexible plate in the wake of a square cylinder. Microsystem Technologies, in press.
Binyet, E.; Chang, J.; Huang, C. Flexible Plate in the Wake of a Square Cylinder for Piezoelectric Energy Harvesting—Parametric Study Using Fluid–Structure Interaction Modeling. Energies, 2020, 13(10), 2645

References
[1] International Energy Agency, World Energy Outlook 2010, IEA PUBLICATIONS, SOREGRAPH, Paris, France, 2010, ISBN: 978 92 64 08624 1
[2] Wang, H. F.; Zhou, Y.; Chan, C. K.; Wong, W. O.; Lam, K. S.; Flow Structure Around A Finite-Length Square Prism, Proc. 15th Australasian Fluid Mechanics Conference, The University of Sydney, 2004
[3] Okajima Atsushi Strouhal numbers of rectangular cylinders, J. Fluid Mech., 1982, vol. 123, pp. 379-398.
[4] Taylor, George W.; Burns, Joseph R.; Kammann, Sean M.; Powers, William B.; Welsh, Thomas R. The Energy Harvesting Eel: A Small Subsurface Ocean/River Power Generator", IEEE Journal of Oceanic Engineering, 2001, Vol. 26, No. 4
[5] Allen, J. J.; Smits, A. J. Energy Harvesting Eel, Journal of Fluids and Structures, 2001, vol. 15, 629-640
[6] Shi, S.; New, T. H.; Liu, Y. Effects of aspect-ratio on the flapping behavior of energy-harvesting membrane, Experimental Thermal and Fluid Science, 2014, 52, 339-346
[7] Romanenko, E. V; Fish and Dolphin Swimming Russian Academic Monographs No.2; Pensoft: Sofia, Bulgaria, 2002, ISBN: 954-642-150-2, Chap. 1.
[8] Shelton, Ryan M.; Thornycroft, Patrick J. M.; Lauder, George V. Undulatory locomotion of flexible foils as biomimetic models for understanding fish propulsion, The Journal of Experimental Biology, 2014, 217, 2110-2120
[9] Lighthill, M. J. Note on the swimming of slender fish, Fluid Mech., 1960, 9, 305-317
[10] Wu, T. Yao-Tsu Hydromechanics of swimming propulsion, part 1 Swimming of a two-dimensional flexible plate at variable forward speeds in an inviscid fluid, J. Fluid Mech, 1971, 46, part 2, 337-355
[11] Giacomello, Alberto; Porfiri, Maurizio Underwater energy harvesting from a heavy flag hosting ionic polymer metal composites, Journal of Applied Physics, 2011, 109
[12] Dowell, E. H. Aeroelasticity of Plates and Shells; Noordhoff International Publishing: Leyden, The Netherlands, 1974.
[13] Sonalla, M. I. Vibrations of Cantilever Beams With Various Initial Conditions, Master’s Thesis, The Ohio State University, Columbus, OH, USA, 1989.
[14] Lighthill, M. J. Large-Amplitude Elongated-Body Theory of Fish Locomotion. Biol. Sci. 1971, 179, 125–138.
[15] Timoshenko, S.; Goodier, J. N. Theory of Elasticity, McGraw-Hill The Maple Press Company, York, USA, 1951, ISBN 10: 0070642702
[16] Wu, T. Yao-Tsu. Swimming of a waving plate, Fluid Mech., 1960, 10, 321-344
[17] Eloy, Christophe; Lagrange, Romain; Souilliez, Claire; Schouveiler, Lionel Aeroelastic instability of cantilevered flexible plates in uniform flow, J. Fluid Mech., 2011, 611, 97-106
[18] Tang, Liaosha; Païdoussis, Michael P.; Jiang, Jin Cantilevered flexible plates in axial flow: Energy transfer and the concept of flutter-mill, Journal of Sound and Vibration, 2009, 326, 263–276
[19] Shi, S.; New, T.H.; Liu, Y. Flapping dynamics of a low aspect-ratio energy-harvesting membrane immersed in a square cylinder wake. Exp. Therm. Fluid Sci. 2013, 46, 151–161.
[20] Tang, D.M.; Yamamoto, H.; Dowell, E. H. Flutter and limit cycle oscillations of two-dimensional panels in three-dimensional axial flow, Journal of Fluids and Structures, 2003, 17, 225-242
[21] Erturk, A.; Inman, D.J. Piezoelectric Energy Harvesting; John Wiley & Sons: Chichester, UK, 2011. ISBN: 978-0-470-68254-8
[22] Anjana, Jain; Prashanth, K. J.; Asheesh, Kr. Sharma; Arpit, Jain; Rashmi, P.N. Dielectric and Piezoelectric Properties of PVDF/PZT Composites: A Review, POLYMER ENGINEERING AND SCIENCE, 2015
[23] Song, J.; Zhao, G.; Li, Bo.; Wang, J. Design optimization of PVDF-based piezoelectric energy harvesters Heliyon, 2017,3, e00377
[24] Frisch-Fay, R. Flexible Bars; Butterworths: London, UK, 1962.
[25] Tang, D.M.; Levin, D; Dowell, E.H. Experimental and theoretical correlations for energy harvesting from a large flapping flag response, Journal of Fluids and Structures, 2019, 86, 290-315.
[26] Akaydin, H. D.; Elvin, N.; Andreopoulos, Y. The performance of a self-excited fluidic energy harvester, Smart Mater. Struct. 2012, 21
[27] Erturk, A.; Tarazaga, P. A.; Farmer, J. R.; Inman, D. J. Effect of Strain Nodes and Electrode Configuration on Piezoelectric Energy Harvesting From Cantilevered Beams. Journal of Vibration and Acoustics, 2009, 131
[28] Shafer, M. W.; Garcia, E. The Power and Efficiency Limits of Piezoelectric Energy Harvesting. Journal of Vibration and Acoustics, 2013, 136.
[29] Shu, Y.C; Lien, I.C; Efficiency of energy conversion for a piezoelectric power harvesting system. J. Micromech. Microeng., 2006, 16, 2429–2438
[30] Azizi, S.; Ghodsi, A.; Jafari, H., Ghazavi, M. R. A conceptual study on the dynamics of a piezoelectric MEMS (Micro Electro Mechanical System) energy harvester Energy, 2016, 96, 495-506
[31] Kundu, Pijush K; Cohen, Ira M; Dowling, David R; FLUID MECHANICS, sixth edition; Elsevier: 2016. ISBN: 978-0-12-405935-1
[32] Pope, S. B; Turbulent Flows; Cambridge University Press: Cambridge, 2000.
[33] White, Frank M; Fluid Mechanics, Fifth edition; McGraw- Hill: New York, 2003.
[34] Çengel, Yunus A.; Cimbala, John M. Fluid mechanics: fundamentals and applications, 1st ed; McGraw-Hill series in mechanical engineering: New York, 2006. ISBN 0–07–247236–7
[35] Pope Chen, C.; Riley, J. J.; McMurtry, P. A. A Study of Favre Averaging in Turbulent Flows with Chemical Reaction, Combustion and Flame, 1991, 87, 257-277
[36] ANSYS, Inc. ANSYS Fluent Theory Guide; Canonsburg, PA, USA, 2013.
[37] Versteeg, H.K.; Malalasekera W. An Introduction to Computational Fluid Dynamics The finite volume method, 2nd ed.; Pearson Education Limited, Edinburgh Gate, England, 2007.
[38] Zikanov Oleg; ESSENTIAL COMPUTATIONAL FLUID DYNAMICS; John Wiley & Sons, Inc., Hoboken, New Jersey, 2010. ISBN: 978-0-470-42329-5, p. 91
[39] ANSYS, Inc. ANSYS Mechanical User's Guide; Canonsburg, PA, USA, 2013
[40] Cook, R. D.; Malkus, D. S.; Plesha, M. E.; Witt, R. J. Concepts and applications of finite element analysis, 4th ed.; John Wiley & Sons: USA, 2002
[41] Turek, S.; Hron, J.; Razzaq, M.; Wobker, H.; Schäfer, M. Numerical Benchmarking of Fluid-Structure Interaction: A Comparison of Different Discretization and Solution Approaches. Fluid Structure Interaction II, Lecture Notes in Computational Science and Engineering, 2011, 73, 413-424.
[42] Ramm, Ekkehard; Wall, Wolfgang Fluid-structure interaction based upon a stabilized (ALE) finite element method. 4th World Congress on Computational Mechanics: New Trends and Applications, CIMNE, Barcelona, 1998.
[43] De Nayer, G.; Kalmbach, A.; Breuer, M.; Sicklinger, S.; Wuechner, R. Flow past a cylinder with a flexible splitter plate: A complementary experimental-numerical investigation and a new FSI test case (FSI-PfS-1a). Computers & Fluids, 2014, 99, 18-43.
[44] De Nayer, G.; Breuer, M. Numerical FSI investigation based on LES: Flow past a cylinder with a flexible splitter plate involving large deformations (FSI-PfS-2a). International Journal of Heat and Fluid Flow,2014, 50, 300–315
[45] Raback, Peter; Ruokolainen, Juha; Lyly, Mikko; Jarvinen, Esko Fluid-structure interaction boundary conditions by artificial compressibility. ECCOMAS Computational Fluid Dynamics Conference, 2001
[46] Benra, Friedrich-Karl; Dohmen, Hans Josef; Pei, Ji; Schuster, Sebastian; Wan, Bo A Comparison of One-Way and Two-Way Coupling Methods for Numerical Analysis of Fluid-Structure Interactions. Journal of Applied Mathematics, 2011, Volume 2011
[47] Tian, Fang-Bao; Dai, Hu; Luo, Haoxiang; Doyle, James F.; Rousseau Bernard Fluid–structure interaction involving large deformations: 3D simulations and applications to biological systems. J Comput Phys., 2014 , 258
[48] An, X.; Song B.; Tian W.; Ma C. Design and CFD Simulations of a Vortex-Induced Piezoelectric Energy Converter (VIPEC) for Underwater Environment. Energies 2018, 11, 330.
[49] Thielicke, W.; Stamhuis, E.J. PIVlab – Towards User-friendly, Affordable and Accurate Digital Particle Image Velocimetry in MATLAB. Journal of Open Research Software, 2014, 2(1).
[50] Song, J.; Zhao, G.; Li, Bo.; Wang, J. Design optimization of PVDF-based piezoelectric energy harvesters Heliyon, 2017,3, e00377
[51] Liu, K.; Deng, J.; Mei, M.; Experimental study on the confined flow over a circular cylinder with a splitter plate, Flow Measurement and Instrumentation, 2016, 51, 95–104
[52] Guo, H.; Zhang, Y.; Xue, F.; Cai, Z.; Shang, Y.; Li, J.; Chen, Y.; Wu, Z.; Jiang, S. In-situ synchrotron SAXS and WAXS investigations on deformation and α-β Transformation of uniaxial stretched polyvinylidene fluoride. CrystEngComm, 2013, 15, 1597-1606.
[53] Zhang, Y.; Sun, H.; Chang, K. J. Biomimetic Porifera Skeletal Structure of Lead-Free Piezocomposite Energy Harvesters. ACS Applied Materials & Interfaces, 2018, 10 (41), 35539-35546.
[54] Han, J. H.; Kwak, J.; Joe, D. J.; Hong, S. K.; Wang, H. S.; Park, J. H.; Hur, S.; Lee, K. J. Basilar membrane-inspired self-powered acoustic sensor enabled by highly sensitive multi tunable frequency band. Nano Energy, 2018, 53, 198-205.
[55] Donea, J.; Huerta, A.; Ponthot, J.-Ph.; Rodriguez-Ferran, A. Chapter 14 Arbitrary Lagrangian–Eulerian Methods. Encyclopedia of Computational Mechanics Volume 1: Fundamentals, John Wiley & Sons: USA, 2004.
[56] Comsol application gallery. https://www.comsol.com/model/ vibrating-beam-in-fluid-flow-9408, 2016.
[57] Curatolo, M.; La Rosa, M.; Prestininzi P. Energy harvesting in a fluid flow using piezoelectric material. Excerpt from the Proceedings of the 2018 COMSOL Conference in Lausanne, 2018
[58] Molina-Aiz, F. D.; Fatnassi, H.; Boulard, T.; Roy, J.C.; Valera, D.L. Comparison of finite element and finite volume methods for simulation of natural ventilation in greenhouses. Computers and Electronics in Agriculture, 2010, 72, 69–86.
[59] Tabata, Masahisa; Fujima, Shoichi. Finite-element analysis of high Reynolds number flows past a circular cylinder. Journal of Computational and Applied Mathematics, 1991, 38, 411-424
[60] Berrone, S.; Garbero, V.; Marro M. Numerical simulation of low-Reynolds number flows past rectangular cylinders based on adaptive finite element and finite volume methods. Computers & Fluids, 2011, 40, 92–112
[61] Giannelis, N.F.; Vio, G. A. Computational Benchmark of Commercial Fluid-Structure Interaction Software for Aeroelastic Applications. In Proceedings of the 16th International Forum on Aeroelasticity and Structural Dynamics, St. Petersburg, Russia, 2015.
[62] Techet, Alexandra H.; Allen James J.; Smits, Alexander J. Piezoelectric Eels for Energy Harvesting in the Ocean. Proceedings of The Twelfth International Offshore and Polar Engineering Conference, 2002.
[63] http://www.eel-energy.fr/
[64] Akaydın, H. D.; Elvin, N.; Andreopoulos, Y. Wake of a cylinder: a paradigm for energy harvesting with piezoelectric materials. Exp Fluids, 2010, 49, 291–304
[65] Perez, M.; Boisseau, S.; Geisler, M.; Gasnier, P.; Willemin, J.; Despesse, G.; Reboud, J. L. Aeroelastic flutter energy harvesters self-polarized by triboelectric effects, Smart Mater. Struct., 2018, 27
[66] Pobering, Sebastian; Schwesinger, Norbert; A novel hydropower harvesting device. Proceedings of the 2004 International Conference on MEMS, NANO and Smart Systems (ICMENS’04), 2004.
[67] Alben, Silas Flag flutter in inviscid channel flow. physics.flu-dyn, 2014.
[68] Michelin, Sébastien; Doaré, Olivier Energy harvesting efficiency of piezoelectric flags in axial flows. J. Fluid Mech., 2013, vol. 714, 489–504.
[69] Pedley, T. J.; Hill, S. J. Large-amplitude undulatory fish swimming: Fluid mechanics coupled to internal mechanics. The Journal of Experimental Biology, 1999, 202, 3431–3438
[70] Yuelong Yu, Yingzheng Liu, Xavier Amandolese A Review on Fluid-Induced Flag Vibrations. Applied Mechanics Reviews,2019, 71
[71] Wang, X., Alben, S., Li, C., and Young, Y. L. Stability and Scalability of Piezoelectric Flag. Phys. Fluids, 2016, 28(2)
[72] Zienkiewicz, Olek C.; Taylor, Robert L.; Zhu, J. Z. The Finite Element Method: Its Basis and Fundamentals; Elsevier Butterworth-Heinemann: Oxford, 2013.
[73] Eslami M. Reza Finite Elements Methods in Mechanics Solid Mechanics and Its Applications, Volume 216; Springer, 2014.
[74] Raffel, Markus; Willert, Christian E.; Wereley, Steve T.; Kompenhans, Jürgen Particle Image Velocimetry A Practical Guide, 2nd ed.; Springer, 1998. ISBN 978-3-540-72307-3
[75] Thielicke, W. The flapping flight of birds: Analysis and application, 2014.
[76] Tennekes, H.; Lumley, J. L. A First Course in Turbulence; The MIT Press: Massachusetts, 1972.
[77] Colleen, D. Scott-Pomerantz, The K-Epsilon Model in the Theory of Turbulence, PhD Thesis, University of Pittsburgh, Pittsburgh, PA, USA, 2004.
[78] Chorin, A. J. A Numerical Method for Solving Incompressible Viscous Flow Problems, J. Comput. Phys., 1967, vol. 2, 12-26.
[79] Kwak, D.; Kiris, C.; Dacles-Mariani, J.; Rogers, S.; Yoon, S. Incompressible Navier-Stokes Solvers Using Primitive Variables, Computational Fluid Dynamics Review 1998, 1998, 573-596.