A Novel Unsteady Vortex Ring Method for Aerodynamic Calculations of a Flapping Wing Rotor

A new bio-inspired flapping wing rotor (FWR) configuration combining the high lift of a flapping wing (FW) with the vertical take-off and landing characteristics of a rotor has proved its concept feasibility in the last decade and can be used for reconnaissance and aerial photography missions in complex and confined environments. During high-frequency flapping motion, the leading and trailing edge vortices of the flapping wing rotor alternately shed and form vortex sheets in the wake, resulting in periodic lift and a highly unsteady flow field. In the past, unsteady potential flow aerodynamic methods were derived based on a two-dimensional (2D) airfoil and extended to three dimensions by the blade element theory, neglecting the spanwise evolution effect of the vortices. In this paper, an unsteady vortex ring method (UVRM) model was developed based on two-dimensional (3D) potential flow theory for the aerodynamic calculation of a flapping wing rotor, which takes into account the spanwise evolution of shedding vortices at the leading and trailing edges of the flapping wing. The calculation results of the UVRM for several typical cases were compared with those of the computational fluid dynamics (CFD) method to verify the reliability of the UVRM. Then, fluid-structure interaction analysis for the flapping wing rotor was conducted based on the UVRM model, and the phase difference between twist deformation and flapping angle was found to be approximately 90 degrees. In addition, the effects of wing chordwise and spanwise deformation on the aerodynamic performance of the flapping rotor were investigated based on the UVRM. The results show that the wing chordwise deformation has a positive effect on the mean lift coefficient of the flapping rotor. The wing spanwise deformation has a negative effect on the mean lift coefficient of the flapping rotor. The unsteady vortex ring method model proposed in this paper provides a solution to obtain the aerodynamic force of the flapping wing rotor in an efficient and accurate way.