Two-Dimensional Mechanism of Hovering Flight by Flapping Wings

날개짓에 의한 공중정지비행의 이차원 메카니즘

Numerical simulations are conducted to investigate the mechanism of hovering flight by single flapping wing, and to examine the effect of the phase difference between the fore- and hindwings in hovering flight by two flapping wings. The numerical method used is based on an immersed boundary method in Cartesian coordinates. The Reynolds number considered is Re=150 based on the maximum translational velocity and chord length of the wing. For single flapping wing, the stroke plane angles are $0^{\circ}$, $30^{\circ}$, $60^{\circ}$, $75^{\circ}$ and $90^{\circ}$ and the downstroke angles of attack are varied for each stroke angle. Results show that for each stroke plane angle, there is an optimal angle of attack to maximize the vertical force. Below the stroke angle of $60^{\circ}$, wake capturing reduces the negative vertical force during the upstroke. For two flapping wings, The phase lags of the hindwing are $0^{\circ}$, $90^{\circ}$, $180^{\circ}$ and $270^{\circ}$. The amplitudes of the stroke are 2.5 and 4.0 times the chord length at each phase lag. The results show that maximum vertical force is generated when the phase lag is zero, and the amplitude of the vertical force is minimum at the phase lag of $180^{\circ}$.