雖然現有固定翼飛行器已能滿足人們飛行的需求，但建立多功能之多元化飛行器一直是人類之目標。振翅翼提供一高效率之推進方式，且如同鳥類一般振翅飛行也一直是人們所嚮往。為完成振翅機，必需對振翅翼流進行研究。本文利用數值計算來探討振翅翼流之流場現象空氣動力及聲音行為。首先在流場區域建立動態非結構四面體網格以模擬振翅翼拍撲運動，然後採用二步Runge-Kutta時間積分與上風體積法求解固定座標系統下非穩態三維尤拉方程式。 爲評估本數值求解步驟之準確性，首先進行自由流測試。接著在一週期内不同時間提出之氣動力係數、速度向量圖及等聲壓值圖以了解兩種拍動角度下NACA0012翼剖面振翅翼流之氣動力、聲音行為及流場現象。

Creating the versatile flight vehicle with multifunctional capabilities is always the goal of mankind. Flapping-wings provide a highly efficient way of propulsion, so that besides the existing fixed-wing aircraft, the flight like birds is attracting the people’s interest. To accomplish the ornithopter, it is necessary to study the flapping-wing flows. In this thesis, the numerical computations are performed to study the phenomena of flapping-wing flows and related aerodynamic and noise behaviors. First, the dynamic unstructured tetrahedral meshes are created in the whole flow domain to simulate the flapping motion. Then the two-stage Runge-Kutta time integration scheme and a finite volume upwind method are adopted to solve the unsteady three-dimensional Euler equations in a stationary coordinate system. To evaluate the present solution procedure, the freestream test is performed first. Then the aerodynamic coefficients, velocity vectors and contours of the sound pressure level at different time during the period are presented to understand the aerodynamic and noise behaviors and the flow phenomena for the flapping wing with cross section of NACA0012 airfoil.

【1】 McMichael, J. M., and Francis, M. S., “Micro Air Vehicles –Toward a New Dimension in Flight,” Report to TTO, DARPA, Department of Defense, USA, 1997.
【2】 DeLaurier, J. D., “The Development and Testing of a Full-Scale Ornithopter,” Canadian Aeronautics and Space Journal, Vol. 45, No. 2, June 1999, pp. 72-82
【3】 Http://www.ornithopter.net/index_e.html.
【4】 Stanford, S., Kornbluh, R., Low, T., Delaurier, J., Loewen, D., and Zdunich, P., “Flapping Wing Flight Using Artificial Muscles,” NASA/DoD Second Biomorphic Explorers Workshop Bioinspired Engineering of Exploration Systems 2000, December 4-6, 2000.
【5】 Archer, R. D., Sapuppo, J., and Betteridge, D. S., “Propulsion Characteristics of Flapping Wings,” Aeronautical Journal, September 1979, pp. 355-371.
【6】 DeLaurier, J. D., “The Development of an Efficient Ornithopter Wing,” Aeronautical Journal, May 1993, pp. 153-162.
【7】 DeLaurier, J. D., “An Aerodynamic Model For Flapping-Wing Flight,” Aeronautical Journal, April 1993, pp. 125-130.
【8】 DeLaurier, J. D., “A Study of Mechanical Flapping-Wing Flight,” Aeronautical Journal, Oct 1993, pp. 125-130.
【9】 Ramamurti, R., and Sandberg, W. C., “Simulation of Flow About Flapping Airfoil Using Finite Element Imcompressible Flow Solver,” AIAA Journal,Vol. 39,No. 2,pp253-260,February, 2001.
【10】 Ramamurti, R., and Sandberg, W. C., “Computational Study of 3-D Flapping Foil Flows,” AIAA Paper 2001-0605, 2001.
【11】 Tuncer, H. I., and Platzer, F. M., “Thrust Generation due to Airfoil Flapping,” AIAA Journal, Vol. 34, No. 2, February 1996, pp. 324-331.
【12】 Lomtev, I., Kirby, R. M., and Karniadakis, G. E., “A Discontinuous Galerkin ALE Method for Compressible Viscous Flows in Moving Domains,” Journal of Computational Physics, Vol. 155, 1999, pp. 128-159.
【13】 Togashi, F., Ito, Y., Murayama, M., Nakahashi, K., and Kato, T., “ Flow Simulation of Flapping Wings of An Insect Using Overset Unstructured Grid,” AIAA Paper 2001-2619, 2001.
【14】 Neff, M. F., and Hummel, D., “Euler Solutions for A Finite-Span Flapping Wing, ”Conference on Fixed, Flapping and Rotary Wing Vehicles at very low Reynolds Numbers,5th-7th, 2000.
【15】 Jones, K. D., and Platzer, M. F., “Numerical Computation of Flapping-Wing Propulsion and Power Extraction,” AIAA Paper 97-0826, 1997.
【16】 Jones, K. D., Dohring, C. M., and Platzer, M. F., “Experimental and Computational Investigation of the Knoller-Betz Effect,” AIAA Journal, Vol. 36, No. 7, July 1998, pp. 1240-1246.
【17】 Jones, K. D., Duggan, S. J., and Platzer, M. F., “Flapping-Wing
Propulsion For A Micro Air Vehicle,” AIAA Paper 2001-0126,
2001.
【18】 Liu, H., and Kawachi, K., “A Numerical Study of Insect Flight,” Journal of Computational Physics, Vol. 146, 1998, pp. 124-156.
【19】 Lighthill,Sir,J.,”The Inaugural Goldstein Memorial Lecture-Some Challenging New Application for Basic Mathematical Methods of Fluids that were Originally Pursued with Aeronautical Aims, ”AeronauticalJournal, pp.41-52, February, 1990.
【20】 Lehmann F. O., “Aerial Locomotion in Flies and Robots: Kinematic Control and Aerodynamics of Oscillating Wings,” Arthropod Structure and Development, Vol. 33, 2004, pp. 331-345.
【21】 Gebert, G., Gallmeier, P., and Evers, J.,“ Equations of Motion for Flapping Flight, ” AIAA Paper 2002-4872, 2002.
【22】 Mittal, R., Utturkar, Y., and Udaykumar,H. S., “Computational Modeling and Analysis of Biomimetic Flight Mechanisms,” AIAA Paper 2002-0865, 2002.
【23】 Harada, M., “Calculation Method for Optimal Circulation Distribution on A Finite Span Flapping Wing,” AIAA Paper 2002-3414, 2002.
【24】 Lasek, M., Pietrucha, J., and Sibilski, K., “Micro Air Vehicle Maneuvers As a Control Problem,” AIAA Paper 2002-0526, 2002.
【25】 Jones, K. D., Castro, B. M., Mahmoud, O., Pollard, S. J., Platzer, M. F., Neff, M. F., Gonet, K., and Hummel, D., “A Collaborative Numerical and Experimental Investigation of Flapping-Wing Propulsion,” AIAA Paper 2002-0706, 2002.
【26】 Lian, Y., Shyy, W., Viieru, D., and Zhang, B., “ Membrane Wing Aerodynamics for Micro Air Vehicles,” Progress in Aerospace Sciences, Vol. 39, 2003, pp. 425-465.
【27】 Zeng, R., and Ang, H., “Aerodynamics Computation of Flapping-Wing Simulating Bird Wings,” Journal of Nanjing University of Aeronautics and Astronautics, Vol. 35, No. 1, Jan-Feb, 2003, pp. 6-12.
【28】 Kirill, V. R., and Vladimir, A. R., “Aerodynamics of Flapping-Wing Propulsors,” Progress in Aerospace Sciences, Vol. 39, 2003, pp. 585-633.
【29】 Ho, S., Nassef, H., Pornsinsirirak, N., Tai, Y. C., and Ho, C. M., “Unsteady Aerodynamics and Flow Control for Flapping Wing Flyers,” Progress in Aerospace Sciences, Vol. 39, 2003, pp. 635-681.
【30】 Hover, F. S., Haugsdal, Q., and Triantafyllou M. S., “Effect of Angle of Attack Profiles in Flapping Foil Propulsion,” Journal of Fluids and Structures, Vol. 19, 2004, pp. 37-47.
【31】 Lasek, M., Pietrucha, J., Zlocka, M., and Sibilski, K., “Analogies Between Rotary and Flapping Wings From Control Theory Point of View,” AIAA Paper 2001-4002, 2001.
【32】 胡舉軍， “旋翼與振翅翼之數值研究” 成功大學航太所博士論文，2002年12月
【33】 Liu, C. Y. and Hwang, C. J., “ New Strategy for Unstructured Mesh Generation,” AIAA Journal, Vol. 39, No. 6, June 2001, pp. 1078-1085.
【34】 賴建文， “動態四面體/稜鏡型網格之建立” 成功大學航太所碩士論文，2004年6月
【35】 “CATIA Documentation,” DASSUALT SYSTEM, 2002
【36】 Hwang, C. J. and Yang, S. Y., “Locally Implicit Total Variation Diminishing Schemes on Mixed Quadrilateral-Triangular Meshes,” AIAA Journal, Vol. 31, No. 11, November 1993, pp. 2008-2015
【37】 Hwang, C. J. and Yang, S. Y., “Inviscid Analysis of Transonic Oscillating Cascade Flows Using a Dynamic Mesh Algorithm,” Journal of Propulsion and Power, Vol. 11, No. 3, May-June 1995, pp. 433-440
【38】 Farhat, C., Degand, C., Koobus, B., and Lesoinne, M., “An Improved Method of Spring Analogy For Dynamic Unstructured Fluid Meshes,” AIAA Paper 98-2070, 1998
【39】 Murayama, M., Nakahashi, K., and Matsushima, K., “Unstructured Dynamic Mesh for Large Movement and Deformation,” AIAA Paper 2002-0122, 2002
【40】 Spekreijse,S.P.,Prananta,B.B., and Kok J.C., “A Simple,Robust and Fast Algorithm to Compute Deformations of Multi-block Structured Grids,” NLR-TP-2002-105
【41】 楊世英， “在動態網格上以區域隱式法探討穿音速振動葉片流場” 成功大學航太所博士論文，1993年6月
【42】 Frink, N.T., Parikh, P., and Pirzadeh, S., “A Fast Upwind Solver for the Euler Equations on Three-Dimensional Unstructured Meshes,” AIAA Paper 91-0102, 1991.
【43】 Barth, T.J., “A 3-D Upwind Euler Solver for Unstructured Meshes,” AIAA Paper 91-1548-cp,1991.
【44】 Vijayan, P., and Kallinderis, Y., “A 3D Finite-Volume Scheme for the Euler Equations on Adaptive Tetrahedral Grids,” Journal of Computational Physics, Vol. 113, 1994, pp. 249-267.
【45】 Walters, R.W., and Thomas, J.L., “Advances in Upwind Relaxation Methods,” State-of-the-Art Surveys on Computational Mechanics, New York, American Society of Mechanical Engineers, 1989, pp. 145-183.
【46】 Frink, N.T., “Upwind Scheme for Solving the Euler Equations on Unstructured Tetrahedral Meshes,” AIAA Journal, Vol. 30, No. 1, 1992, pp.70-77.
【47】 Okong’o, N., and Knight, D., “Accurate Three-Dimensional Unsteady Flow Simulation Using Unstructured Grids,” AIAA Paper 98-078, 1998.
【48】 Shu,C. W., “Total-Variation-Diminishing Time Discretizations,” SIAM Journal on Scientific and Statistical Computing, Vol. 9, No. 6, 1988, pp. 1073-1084.
【49】 Pirzadeh, S., “Structured Background Grids for Generation of Unstructured Grids by Advancing-Front Method,” AIAA Journal, Vol. 31, No. 2, 1993, pp. 257-265.
【50】 Nakahashi, K. and Togashi F., “Intergrid-Boundary Definition Method for Overset Unstructured Grid Approach,” AIAA Journal, Vol. 38, No. 11, November 2000
【51】 Togashi, F., Nakahashi, K, Ito, Y., Shimbo, Y, and Iwamiya, T., “Flow Simulation of NAL Experimental Supersonic Airplane/Booster Separation Using Overset Unstructured Grids,” AIAA Paper 2000-1007, 2000.
【52】 Togashi, F., Ito, Y., Nakahashi, K., and Obayashi, S., “Extensions of Overset Unstructured Grids to Multiple Bodies in Contact,” AIAA Paper 2002-2809, 2002.
【53】 Batina, J. T.,”Unsteady Euler Airfoil Solutions Using Unstructured Dynamic Meshes,”AIAA Paper 89-0115,1989.
【54】 Batina, J. T.,”Unsteady Euler Algorithm with Unstructured Dynamic Meshes for Complex-Aircraft Aerodynamic Analysis,”AIAA Journal ,Vol.29,No.3,pp.327-333,1991.
【55】 Thomas, P. D., and Lombard, C. K., “Geometric Conservation Law and Its Application to Flow Computations on Moving Grids,” AIAA Journal, Vol. 17, No.10, 1979, pp. 1030-1037.
【56】 Vinokur, M., “An Analysis of Finite-Difference and Finite-Volume Formulations of Conservation Laws,” Journal of Computational Physics, Vol. 81, No. 1, 1989, pp. 1-52.
【57】 郭仲裕， “自調有限體積上風法之建立及其於葉片噪音計算之應用” 成功大學航太所博士論文，1997年6月。
【58】 環保署網站http://ivy2.epa.gov.tw/out_web/f/noise/