Flapping foil power generator performance enhanced with a spring-connected tail

Abstract

The flexibility effects on the performance of a flapping foil power generator are numerically studied by using the immersed boundary-lattice Boltzmann method at a Reynolds number of 1100. The flapping foil system consists of a rigid NACA0015 foil undergoing harmonic pitch and plunge motions and a passively actuated flat plate pinned to the trailing edge of the rigid foil. The flexibility is modeled by a torsional spring model at the conjuncture of the rigid foil and the tail. Here, a parametric study on mass density and natural frequency is conducted under the optimum kinematic condition of the rigid system identified from the literature and numerical simulations made for reduced frequency f* = 0.04–0.24 and pitch amplitude θ0 = 40°–90°. Four typical cases are discussed in detail by considering time histories of hydrodynamic loads and tail deformations under the optimal and non-optimal kinematic conditions. Results show that under the rigid-system optimal kinematic condition, a tail with appropriate mass density (μ = 0.60) and resonant frequency ( fr*=1.18) can improve the maximum efficiency by 7.24% accompanied by an increase of 6.63% in power compared to those of a rigid foil with a rigid tail. This is because the deflection of the tail reduces the low pressure region on the pressure surface (i.e., the lower surface during the upstroke or the upper surface during the downstroke) caused by the leading edge vortex after the stroke reversal, resulting in a higher efficiency. At high flapping frequencies, a spring-connected tail ( fr*=0.13) eliminates the large spike in the moment observed in high stiffness cases, reducing the power required for the pitch motion, resulting in 117% improvement in efficiency over that with a rigid tail at a reduced frequency of 0.24.