In the present study, the effect of elliptical motion trajectory on the aerodynamic characteristics and propulsive performance of a flapping airfoil is evaluated. A periodic horizontal motion (forward/backward) is combined with vertical motion (upward/downward) of the airfoil to introduce a new kinematic parameter, and of course, an elliptical motion trajectory for flapping airfoil. Similar kinematics is also observed in the flying of birds and swimming of the penguins or turtles. For this modeling, the Navier–Stokes equations are used to simulate the unsteady flow field over a two dimensional NACA0012 airfoil. The Navier–Stokes equations are discretized based on the finite volume method and are solved with a pressure-based algorithm. The flow is assumed to be laminar and incompressible and transient terms are conducted using a second order Euler implicit scheme. It is shown that the combination of horizontal and vertical motions for the flapping airfoil changes the kinematics, motion trajectory and hence the effective angle of attack profile during the flapping cycle. The elliptical motion trajectory will also influence on the fluid structures and change the vortex shedding pattern and wake zone behind the airfoil. Additionally, the introduced kinematics may influence significantly on the aerodynamics and propulsive performance of either pure plunging or pitching/plunging airfoil.

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