Spatiotemporal Cooperative Effect Between the Time-asymmetric Ratio of Oscillating Trailing Edge Flap and Pivot Location on the Aerodynamics of a Pitching Airfoil

The time-asymmetric ratio (δ) of an oscillating trailing edge flap (TEF) significantly affects the aerodynamics of a pitching airfoil at low Reynolds numbers and its associated complex flow features. This study aims to investigate how variations in δ influence the lift and drag coefficients for fixed-pivot configurations. Numerical simulations indicate that increasing δ enhances lift during the upstroke, and accelerates flow development. This occurs because δ fundamentally modifies the growth rates of various vortices, directly affecting the pressure distribution on the airfoil surface. The study also examines the impact of pivot location (xp/c) on aerodynamic performance and vortex structures at δ = 0. Results reveal that moving the pivot location backward delays flow evolution without improving lift. A detailed assessment of δ and xp/c highlights the spatiotemporal cooperative effect, leading to the proposal of new definitions for the effective angle of attack to these interactions. At a dimensionless number Z = 0.008, setting δ to ±0.1 quantitatively replicates the effect of a forward or backward pivot, shift equivalent to 0.25c. These findings offer valuable insights into the simplified control of airfoil kinematics for achieving exceptional maneuverability and serve a reference for the design of the new flapping machines.