The propulsive performance of dual flapping foils in a tunnel and their vortex motions have been studied through numerical simulations. The dual flapping foils can be high efficient. They can be used for the propulsor of surface vessels or underwater vehicles. Computational fluid dynamics (CFD) techniques has been adopted to simulate the dual flapping foils in a tunnel; the thrust, propulsive efficiency at various flapping frequency have been investigated. The mean thrust of the dual foils has not changed significantly, while the efficiency decreases slightly, due to the tunnel block effects. Given pitch motion amplitude (θ0), the thrust coefficient of flapping foil increases as the increase of Strouhal number St. The thrust coefficient decreases as the increase of θ0, and the maximum propulsion efficiency is achieved at higher St.


The propulsion of flapping foil origins from biomimetics. The flapping foil is of efficiency, which could help the reduction of greenhouse gas emission. The noisy can be reduced significantly as the cavitation can be generally avoided. This environment friendly propulsion technology is promising. However, a single-flapping-foil propulsor will generate periodical lateral force as it swings. The lateral force will cause yaw motion of a vehicle. When two foils are arranged with symmetry, and they perform counter flapping motion, the lateral forces of these two foils will cancel each other. Several researches (Jones,2000; Alben,2005; Lin,2015) indicated that the dual flapping foil may improve the propulsion performance due to the counter motion.

The propulsion performance of the flapping foil depends on the Reynolds numbers, flapping frequency, heave and pitch motion amplitudes, phase difference between the heave and pitch motions. The hydrodynamic problem can be solved through inviscid method or the computational fluid dynamic method. Anderson et al (1998) investigated the high propulsive efficiency of flapping foils; the dominant parameters for high efficiency and the vortex structure induced by the flapping foil have been revealed. Ashraf et al (2011) investigated the effects of Reynolds number through numerical simulation; they found that the thicker foil can reduce the leading edge vortex shedding. Ellington et al (1996) performed experiments on a flapping plate; the leading edge of vortex can be reduced or eliminated when the Strouhal number increases. For flapping foil without leading edge vortex shedding, Xu and Wu (2013) proposed an unsteady vortex method based on boundary element; the effects of the motion parameters on the thrust and propulsive efficiency have been investigated.

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