3D Influence on Propulsive Flapping at Low Reynolds Number

Many of the 2D approximations used for flapping studies at low Reynolds number are questionable. The objective of this study is to characterize the 3-dimensional behaviour of flapping foils with applications to biomimetic flying and swimming robots. The 3D fluid effects of oscillating foils are studied through the comparison of their thrust force, vorticity and energy. We simulate the unsteady flow on an infinite-span flapping foil with heaving, pitching and coupled motion using the Boundary Data Immersion Methods, which is documented to accurately predict low Re stationary and dynamic foils. A range of Strouhal numbers St = AD*f*D/U (D=foil thickness, f=frequency, U=freestream velocity and AD= trailing-edge amplitude/D) are examined by increasing AD=0.0625-3.75 with constant f*D/U. We find that the flow transitions from turbulent 3D structures into uniform 2D flow at around AD=1 (St=0.3). Suitable range of St for each motion is determined where the flow remains 2D and it provides a window over which 2D simulations can represent the realistic 3D flow. Outside of it, running 3D simulation is critical as the flow field, forces, efficiencies and wake energy are all different than their 2D prediction for the same geometry and kinematics.