A predictive framework for energy harvesting based on four canonical modes of vortex–foil interaction

This work presents a predictive framework for energy harvesting of two tandem and staggered flapping foils based on four canonical modes of vortex–foil interaction. The role of the incoming vortex generated by the leading foil in modulating the hydrodynamic load of the trailing foil is systematically analysed. Four canonical interaction modes are classified by the vortex rotation and its interaction position relative to the leading-edge vortex (LEV). The most effective configuration occurs when the foil encounters a counter-rotating vortex on the pressure side, which strengthens the LEV and consequently enhances the lift magnitude, with maximum efficiency achieved when vortex merging occurs near stroke reversal. A second constructive mode occurs when a co-rotating vortex on the suction side promotes LEV roll-up through favourable induced velocities. Force decomposition reveals that in both constructive modes, the incoming vortices improve the efficiency of the trailing foil by enhancing the unsteady lift through altering the local velocity to strengthen the LEV or promote its roll-up, while their low-pressure cores contribute marginally to the unsteady force. Two destructive modes are also observed: direct interaction of a counter-rotating vortex on the suction side leads to only a transient lift increase; a co-rotating vortex on the pressure side reduces the effective angle of attack and leads to the poorest performance. Building on these insights, a mechanism-based predictive framework is established to rapidly identify high-performance configurations without exhaustive parametric exploration. The framework applies broadly to different wake conditions and trailing-foil kinematics and guides the design of multi-foil energy-harvesting systems.