Unsteady Lifting-Line Free-Wake Aerodynamic Modeling for Morphing Wings

Abstract

A time-stepping, lifting-line solution algorithm for the prediction of the unsteady aerodynamics of morphing wings is presented. The velocity induced by the wake vorticity is determined through a free-wake vortex-lattice model, whereas the Küssner and Schwarz’s unsteady airfoil theory is used to evaluate the sectional loads, and the generalized aerodynamic loads related to body deformation including camber morphing. The wake vorticity released at the trailing edge derives from the bound circulation and is convected downstream as a vortex ring to form the vortex-lattice wake structure. The local bound circulation is obtained by the application of the Kutta–Joukowski theorem extended to unsteady flows. The accuracy of the loads predicted by the proposed solver is assessed by comparison with the predictions obtained by a three-dimensional boundary-element-method solver for potential flows. The two sets of results agree very well for a wide range of reduced frequencies.

Keywords

• unsteady aerodynamics
• lifting-line theory
• time-stepping methods
• aeroelasticity
• free-wake modeling
• Küssner–Schwarz