Numerical and experimental studies of flexibility in flapping wing aerodynamics

A simple, reduced order model is used to investigate the importance of chordwise flexibility on the fluid dynamics surrounding a flapping wing in hovering flight. The reduced order model consists of two rigid elliptical bodies connected by a hinge. The kinematics of one body are controlled, leaving the other to respond passively to the fluid dynamic and inerial/elastic forces. The stiffness and damping of the hinge are controlled experimentally through a torsional spring and internal damping of the hinge. The numerical study uses the viscous vortex particle method with strongly coupled body dynamics and prescribes both the stiffness and damping using linear torsional spring and damper models. Experiments are carried out in a quiescent water tank using suspended particles for flow visualization. Seven experiments are used to verify and validate the numerical code across a broad kinematic range. Hinge deflection is used as the primary metric for comparison; the agreement between computation and experiment are good in all cases. Computations are used to evaluate the response of the reduced order model to an expanded set of kinematics, changing the stiffness and damping of the hinge. It is found that within a region of kinematics, a small degree of flexibility can increase lift production while decreasing power consumption due to an improved model shape. Outside of this range, a reduction in stiffness generally reduces the power consumed by the wing but does so at the expense of lift generation. The change in power consumption, across the investigated range of kinematics, comes from a reduction in the power needed to rotate the body at the end of the stroke. For larger stroke amplitudes, a further power savings results from a reduction in drag as the deformed body reduces the recirculation region trailing the model. However, a range of kinematics exist that increase power consumption due to the influence of vorticity in the fluid field on the generation of forces on the body. Lift is improved at larger stroke amplitudes, with flexibility allowing the model to increase the peak in lift as the wing undergoes dynamic stall. The degree of lift production per unit power consumed is improved across a broad range of kinematics and stiffnesses due to the minimal overlap of regions of lift improvement and decreased power consumption. However, overlap does exist for a narrow range of kinematics and flexibility. Although a small degree of flexibility can improve flight performance, too much flexibility makes the wing too compliant, reducing the effective lifting area of the model.