title: An analytical model and scaling of chordwise flexible flapping wings in forward flight.
abstract: Aerodynamic performance of biological flight characterized by the fluid structure interaction of a flapping wing and the surrounding fluid is affected by the wing flexibility. One of the main challenges to predict aerodynamic forces is that the wing shape and motion are a priori unknown. In this study, we derive an analytical fluid-structure interaction model for a chordwise flexible flapping two-dimensional airfoil in forward flight. A plunge motion is imposed on the rigid leading-edge (LE) of teardrop shape and the flexible tail dynamically deforms. The resulting unsteady aeroelasticity is modeled with the Euler-Bernoulli-Theodorsen equation under a small deformation assumption. The two-way coupling is realized by considering the trailing-edge deformation relative to the LE as passive pitch, affecting the unsteady aerodynamics. The resulting wing deformation and the aerodynamic performance including lift and thrust agree well with high-fidelity numerical results. Under the dynamic balance, the aeroelastic stiffness decreases, whereas the aeroelastic stiffness increases with the reduced frequency. A novel aeroelastic frequency ratio is derived, which scales with the wing deformation, lift, and thrust. Finally, the dynamic similarity between flapping in water and air is established.
authors.affiliation: Department of Mechanical and Aerospace Engineering, University of Alabama in Huntsville, Huntsville, AL 35899, USA.
authors.forename: Deepa
authors.initials: D
authors.lastname: Kodali
authors.forename: Chang-Kwon
authors.initials: CK
authors.lastname: Kang
mesh_terms: D000388:Air; D000392:Air Movements; D000465:Algorithms; D000818:Animals; D001696:Biomechanical Phenomena; D005426:Flight, Animal / Q000502:physiology*; D008954:Models, Biological; D009038:Motion; D018583:Pliability; D016059:Range of Motion, Articular; D013623:Tail / Q000502:physiology; D014867:Water; D014921:Wings, Animal / Q000502:physiology*
chemical_list: D014867:Water