Flapping frequency influence on thrust generation and propulsive efficiency of tandem flapping airfoils in forward flight

This study investigates the influence of the Strouhal number on the thrust and propulsive efficiency of two-dimensional tandem elliptical flapping airfoils through numerical simulations validated by in-house experiments at a Reynolds number of 5000. The front and rear airfoils, identical in shape and size, are aligned with the freestream, with the rear airfoil positioned one chord length behind the front. The Strouhal number was varied from 0.2 to 0.7, while the geometric effective angle of attack amplitudes at the pivot points were set to 10, 15, and 20 degrees. Results show that the rear airfoil has minimal effect on the time-averaged thrust of the front airfoil, but the wake of the front airfoil strongly influences the flow field and thrust of the rear one. The thrust produced by the rear airfoil increases with the Strouhal number up to a critical value of 0.4, then decreases, with larger angles of attack producing higher thrust. The growth of the leading-edge vortex on the rear airfoil is controlled by the residual vortex beneath the front airfoil and the shear layer shed from the upper surface of the front airfoil. The residual vortex enhances the local flow angle and increases thrust, while the shear layer intermittently reduces it. When the shear layer passes over the rear airfoil, the local flow angle rises sharply, leading to rapid vortex growth and greater thrust, particularly at a 15-degree angle of attack. These results demonstrate the aerodynamic advantages of tandem flapping configurations under optimized unsteady flow interactions.