Force and flow structures of a wing performing flapping motion at low Reynolds number

Aerodynamic force and flow structures of a wing performing a simplified flapping motion that emulates the wing motion of small insects in normal hovering flight are studied, using the method of numerically solving the Navier-Stokes equations. For a typical case (wing rotation-axis is at 0.25 chord position and wing rotation is symmetrical with respect to stroke reversal), large peaks in C_L and C_D are produced near the end of a stroke by the wing-rotation, but the wing-rotation also generates a vortical structure which induces strong downwash velocity, reducing the lift production in the early part of the following stroke; averaging over one flapping cycle, C_L is 28% larger than the steady-state value and is about that needed to support the weight of a small insect. The timing of the wing-rotation at stroke reversal can change the size of the peaks in C_L and C_D and their averages; e.g. in the case of shifting the wing-rotation forward in time by 7.5% of a stroke period, the average C_L becomes 63% larger than the steady-state value, which is larger than that needed for weight supporting (and might provide extra force for control or maneuvers). When the rotation-axis is moved rearward to the middle-chord position, the lift and drag peaks due to the wing-rotation become smaller, and in this case, the wing-rotation generates a vortical structure that tends to prevent the relative motion between positive and negative vorticities, also reducing the lift production in the early part of the following stroke, resulting in a smaller average C_L.