Time-varying flexible airfoil shape effects on flapping airfoil power extraction

Research into the effectiveness of flapping airfoil power extraction systems have typically focused on the kinematic parameters defining the pitching and plunging motion, and have used simple basic rigid airfoil shapes. This paper investigates the effect of airfoil shape on the power extraction efficiency of a flapping airfoil system, focusing on the complex flow interactions and vortex structures that are key to flapping airfoil aerodynamics. Two-dimensional Navier-Stokes solutions using the commercial flow solver Fluent are performed using a deformable mesh to alter the camber of the airfoil during the flapping cycle. This camber deformation is superimposed on both sinusoidal and flow driven non-sinusoidal motions at Re = 1,100. The shape of the airfoil is constructed by deforming the camber line via a sinusoidally varying circular arc with a center at the midspan. The phase angle of this sinusoidal camber variation is the primary independent variable, resulting in a broad range of airfoil interactions with the shed vortex flow fields as the shape varies over the flapping cycle. The results show that the efficiency of the system can be increased by judiciously deforming the airfoil shape to interact with the resulting leading and trailing edge vortex structures. Key factors in the sinusoidal motion cases are the interactions between the shed LEV and the airfoil 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 flow driven cases are also strongly affected by the vortex interactions, and the resulting forces and moments can significantly alter the flapping frequency further increasing their impact. Unfavorable interactions reduce the frequency of the flow driven motion, reducing the amount of power produced considerably. The overall variation in power output over the range of the camber deformation phase angle is much larger in the flow-driven cases, ranging from approximately 25% ≤ r) ≤ 38% in the sinusoidal motion cases and 14% ≤ rj ≤ 47% in the flow driven cases. The optimum deformation increases the overall power extraction efficiency by nearly 16% in the best sinusoidal case, and 13% in the flow driven case.