Unsteady aerodynamic model of flexible flapping wing

Abstract

Bio-inspired flapping wing has potential application to micro air vehicles (MAV). Due to the nature of lightweight and flexibility of micro flapping wing structures, elastic deformation as a result of aeroelastic coupling is inevitable in flapping motion. This effect can be significant and beneficial to the aerodynamic performance as revealed in the present investigation for a flexible flapping wing of variable camber versus a rigid one. Firstly a two dimensional (2D) unsteady aerodynamic model (UAM) based on potential flow theory has been extended from previous study. Both leading and trailing edge discrete vortices are included in the model with unsteady Kutta condition satisfied to fully characterize the unsteady flow around a flapping wing. A wall function is created to modify the induced velocity of the vortices in the UAM to solve the vortices penetration problem. The modified UAM is then validated by comparing with CFD results of a typical insect-like flapping motion from previous research. Secondly the UAM is further extended for a flexible flapping wing of camber variation. Comparing with a rigid wing in a prescribed plunging and pitching motion, the results show lift increase with positive camber in upstroke by mitigating negative lift. The results also agree well with CFD simulation. Thirdly the 2D UAM is extended to calculate the aerodynamic forces of a 3D wing with camber variation, and validated by CFD results. Finally the model is applied to aerodynamic analysis of a 3D flexible flapping wing with aeroelastic coupling effect. Significant increase of lift coefficient can be achieved for a flexible flapping wing of positive camber and twist in upstroke produced by the structure elastic deformation.

Aerodynamic Analysis of a Flapping Wing Aircraft for Short Landing

“…The fitted data matches experimental data very well, and the R-squared values between experimental and fitting values of flapping and pitching angles are 0.9991 and 0.9921, respectively. Such slight fitting deviations are mainly caused by measurement errors of OptiTrack cameras and the fitting model as shown in Equations (20) and (21).…”

“…A 2D airfoil of the rigid wing defined in an inertial coordinate system is illustrated in Figure 2b. The UAM developed in [20] is used to calculate the aerodynamic forces of the airfoil. The inertial coordinate system ( ξ − η) remains fixed with respect to the Earth.…”

“…θ is the angular displacement about the origin of the z-plane. According to the UAM [20], the aerodynamic force dF of a 2D airfoil of unit span can be expressed: According to the UAM [20], the aerodynamic force dF of a 2D airfoil of unit span dx can be expressed:…”

“…Given the flapping wing motion as shown in Figure 9 obtained from the test data and Equations (20) and (21), the aerodynamic lift and drag forces are calculated using the UAM and CFD, and shown in Figures 13 and 14 respectively. Aerodynamic lift and drag forces obtained in experiments refer to the net vertical and horizontal forces, respectively.…”

“…Based on potential flow theory [9,10] and Joukowski transformation [11,12], Ansari et al [13] constructed an unsteady aerodynamic model (UAM) to calculate the aerodynamic force produced by the leading edge vortex [14][15][16] and trailing edge vortex [17][18][19]. Chen et al [20] further developed the UAM to prevent the adverse effect of vortex penetration using a collision avoidance algorithm and enforced a zero-through-flow boundary condition for both two-dimensional (2D) and three-dimensional (3D) wings.…”