Effects of time-varying camber deformation on flapping foil propulsion and power extraction

Research into the effectiveness of flapping foil propulsion and power extraction systems has typically focused on the kinematic parameters defining the pitching and plunging motion, and used simple basic rigid airfoil shapes. In this paper, the effects of a time-varying deformable foil shape on the power extraction and propulsive efficiency of flapping foil systems are studied. Two-dimensional Navier-Stokes solutions using the commercial flow solver Fluent are performed with a deformable mesh to alter the camber of the foil during the flapping cycle. All simulations are assumed to be fully laminar, with a free stream Reynolds number of Re=1100 for the power extraction cases and Re=20000 for the propulsion cases, chosen to match representative cases in the existing literature. The shape of the foil is constructed by deforming the camber line via a circular arc centered at the mid-span, with the magnitude of the circular arc deformation varying sinusoidally in time. The phase angle of this sinusoidal camber variation is the primary independent variable, resulting in a broad range of foil interactions with the shed vortex flow fields as the shape varies over the flapping cycle. This camber deformation is superimposed on kinematically constrained sinusoidal motions for both the power extraction and propulsion regimes, as well as semi-passive motions for power extraction. The results show that the efficiency of these systems can be increased by judiciously deforming the foil shape to interact with the resulting leading and trailing edge vortex structures. For all cases, the power required to deform the foil surface is included in the overall efficiency calculation, and for several cases is a significant factor in the final efficiency. The performance of the power extraction cases is primarily determined by the interactions between the shed LEV and the foil horizontal surface during the plunging stroke and the interaction of the trailing edge as it passes through the vortex during the pitch reversal portion of the cycle. The semi-passive cases for power extraction are also strongly affected by the vortex interactions, and the resulting forces and moments can significantly alter the flapping frequency, further increasing their impact. The propulsion cases show a high dependence on the interaction of the leading edge vortex with the foil curvature to provide high leading suction and greater propulsive forces. For all three regimes, regions of phase angle where the efficiency is increased by the deformation of the foil are shown.