A CFD-informed quasi-steady model of flapping wing aerodynamics.

Aerodynamic performance and agility during flapping flight are determined by the combination of wing shape and kinematics. The degree of morphological and kinematic optimisation is unknown and depends upon a large parameter space. Aimed at providing an accurate and computationally inexpensive modelling tool for flapping-wing aerodynamics, we propose a novel CFD (computational fluid dynamics)-informed quasi-steady model (CIQSM), which assumes that the aerodynamic forces on a flapping wing can be decomposed into the quasi-steady forces and parameterised based on CFD results. Using least-squares fitting, we determine a set of proportional coefficients for the quasi-steady model relating wing kinematics to instantaneous aerodynamic force and torque; we calculate power with the product of quasi-steady torques and angular velocity. With the quasi-steady model fully and independently parameterised on the basis of high-fidelity CFD modelling, it is capable of predicting flapping-wing aerodynamic forces and power more accurately than the conventional blade element model (BEM) does. The improvement can be attributed to, for instance, taking into account the effects of the induced downwash and the wing tip vortex on the force generation and power consumption. Our model is validated by comparing the aerodynamics of a CFD model and the present quasi-steady model using the example case of a hovering hawkmoth. It demonstrates that the CIQSM outperforms the conventional BEM while remaining computationally cheap, and hence can be an effective tool for revealing the mechanisms of optimization and control of kinematics and morphology in flapping-wing flight for both bio-flyers and unmanned air systems.