本文乃利用數值方法模擬分析振翅翼之流場。數值方法是以有限體積法來求解尤拉方程式(Euler equations)與威爾史托克方程式(Navier-Stokes equations)，方程式中的對流項是以有限體積法採用三階上風外插與限制函數來計算，黏滯項則採用二階的有限體積法。時間的積分則採用DDADI數值法來處理。此外，為了加速數值上的收斂性，此數值算則引入隱式殘值平滑法，此上風數值方法為一MUSCL型式之算則。對於較高雷諾數的流場而言，則採用Boldwin-Lomax代數紊流模式來求解。
　　對於研究振翅翼的空氣動力特性，吾人選定NACA 2412 airfoil，針對二維/三維的振翅運動及黏性/非黏性的流場及不同的振翅頻率、不同的流場攻角、不同的俯仰角(Pitching Angle)、不同的相移位角(Phase Shift)、不同的翅膀形狀來研究與分析。結果得知在振翅頻率K=0.2時效率最好。此外梯形翼的效率比直角翼好，若將梯形翼往前掠將會得到更好的飛行效率。

　　A numerical method is developed to study the flapping wing flowfields. The method uses finite-volume method to solve the Euler/Navier-Stokes equations. It uses a third-order upwind finite-volume scheme for discretizing the convective terms and a second-order central finite-volume scheme for discretizing the viscous terms. A diagonal dominant alternating direction implicit scheme (DDADI) coupling with an implicit residual smoothing is used for the time integration to achieve fast convergence of the proposed scheme. The upwind scheme is a MUSCL-type scheme. The Baldwin-Lomax algebra turbulence model is applied to calculate the turbulent flows at high Reynolds numbers.
　　For aerodynamic performances of the flapping wings. The NACA2412 airfoil is chosen for studing. Quantitative understanding the effects of the two dimension/three dimension, viscous flow/invicid flow, flapping frequency, mean angle of attack, pitching angle, phase shift and wing shape are calculated. There is a better propulsion efficiency at reduce frequency of K=0.2. Trapezoidal wing has a better propulsion efficiency than Rectangular wing. If swept angle of trapezoidal wing is negative, the propulsion efficiency is increasing.

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