The three-dimensional deformable wing kinematics was described as an input condition in the commercial CFD solver (Fluent 16

## 3.3putational method

2 package) to estimate the force generation and flow structure around the wings during the flapping motion. The wing motion was defined by using a user-defined function at a flapping frequency of 20 Hz to obtain a Reynolds number of approximately 15 000. Young & Lai used a dynamic mesh feature for a turbulent model, which was found to have no difference with the laminar model in terms of the force generation of a flapping wing at Reynolds numbers ranging from 100 to 50 000. Therefore, in this study, an incompressible laminar model was chosen to simulate the airflow around the wing. Similar CFD with laminar model was explored in previous studies [49,56,57].

Only one wing was simulated with a symmetric condition, as the flapping mechanism was designed to flap the wings symmetrically in a symmetric plane as shown in figure 4. The computational domain included a half cylinder with a diameter (D) and a length (L) of 12R (840 mm), as show in figure 4a. The wing was placed behind the inlet at a distance of 6R (420 mm), and the wing surface was considered as a membrane without any roughness. In the hovering condition, there was no inflow velocity at the inlet. Six flapping cycles were simulated at a time step of 1/1000 of a cycle. The motion of a wing was a combination of flapping around the flapping axis (z-axis) and rotation around the feather axis (?-axis), which was attached to the leading edge of the wing, as shown in figure 4b. The flapping angle, denoted by ?, was defined as the angle between the x-axis and the feather axis. The rotation angle, denoted by ?r, was determined by the angle between the ?-axis and the wing chord. The distance from the flapping axis to the symmetric plane was 8 mm (d/2 = 8 mm), which is equal to half the distance between the flapping axes of the two wings. (más…)