Computational investigation of a doubly hinged flapping-wing model

To understand the effect of the spanning motion of bird wings, a numerical study of a patented model was carried out. A doubly hinged flapping-wing model with the elastic membranes fixed on the upper and lower surfaces is presented. The effect of the membranes is the same as a torsional spring with piecewise stiffness characteristic. The inner wing is driven by harmonic kinematics, while the outer wing responds passively to the aerodynamic and inertial/elastic forces. The ratio of the elastic constant of the lower membrane to the upper one is determined to be a key parameter. Different elastic ratios and hinge-axis positions were considered. It is found that when the elastic ratio is greater than unity, the doubly-hinged model could increase the average lift coefficient compared with the rigid model. On one hand, the average lift coefficient increases with the elastic ratio, but the rate of increase tends to zero. On the other hand, the average drag coefficient first decreases and then increases with the ratio increasing. When the hinge axis moves from wing tip to the root, the average lift coefficient first increases and then decreases, whereas the average drag coefficient behaves in an opposite way.