The effect of airfoil elasticity on quasistatic aerodynamics and divergence

Abstract

Shape-morphing airfoils are of interest due to their benefits for aerodynamic efficiency and commonly involve chordwise elasticity of the airfoil. We aim to examine the influence of chordwise elasticity on the aerodynamic properties and stability in the quasistatic limit. We model a shape-morphing airfoil as two, rear and front, Euler–Bernoulli beams connected to a rigid support at an arbitrary location along its chord. This setup is mounted on a torsion spring and is exposed to a uniform flow. We model aerodynamic forces acting on the wing via thin airfoil theory and obtain the solution of the elastic deflection via regular asymptotic expansions. Then, we substitute this result into the moment balance equation to find the rotation angle. This procedure allows us to examine the influence of chord-wise elasticity on the lift, aerodynamic center, twist angle, and the onset of divergence. We examine these results in terms of the elastic axis location and the dimensionless ratio between aerodynamic moment to bending stiffness. The lift curve slope is smaller than 2π up to the hinge location of about 0.53 chord and is greater than 2π elsewhere. The chord-wise elasticity moves the aerodynamic center forwards and increases the twist angle. In addition, chord-wise elasticity is found to increase the onset of divergence relative to the rigid case. Moreover, unlike the rigid case, divergence also exists for hinges in the front quarter chord. Finally, we present several possible cases of an actuated airfoil validated by numerical simulations.