Reduced Order Model for Unsteady Aerodynamics of Flapping Wing Micro Air Vehicle in Hover

Abstract

Aerodynamics of a flapping wing Micro Air Vehicle (MAV) in hover is highly unsteady. Wake shed by the airfoil remains close to the airfoil surface. In this case, using low fidelity quasi-steady aerodynamic models does not give good estimate of lift and drag forces. Also, Momentum Disc Theory (MDT) alone cannot be used to model the inflow for such a complicated wake. High fidelity methods such as Computational Fluid Dynamics (CFD) are too computationally expensive for doing optimization and sensitivity studies for flapping MAVs. So, medium fidelity tools such as Unsteady Vortex Lattice Method (UVLM) have been used for modeling inflow of flapping wing mainly for forward flight conditions. However, presently there are no reduced order threedimensional (3D) aerodynamic models which can be used for doing preliminary design studies for flapping wing MAVs in hover. In the present work, a reduced order scheme is proposed which uses MDT and UVLM for modeling inflow of a flapping 2D airfoil. Results indicate that retaining only a fraction of the shed vortices is sufficient to get reasonable accuracy. For example, retaining vortices shed in the recent two out of ten oscillations reduced the error in lift by 88% as compared to quasi-steady calculation, i.e. it captures 88% of the unsteadiness. Addition of inflow calculated using MDT along with retaining two oscillations, helps capture 92% of the unsteadiness. Furthermore, the proposed scheme also helps capture about 90% of the unsteadiness in drag calculations. Since the proposed scheme simplifies computation significantly, it can be extended to create a 3D aerodynamic model for flapping wing MAV in hover.