Propulsive performance and vortex streets of tandem in-line and tandem-staggered pitching foils

The propulsive performance of tandem pitching foils strongly depends on the position and the oscillation frequency of the foils. Fluid–foil interactions in paired pitching hydrofoils arranged in tandem in-line and tandem-staggered configurations are studied, inspired by the efficient undulatory motions of fish fins and aquatic animals. Symmetric National Advisory Committee for Aeronautics foils oscillating at varying Strouhal numbers (St) and phase offsets (φ) are analyzed using two-dimensional computational fluid dynamics simulations performed in OpenFOAM with an overset-mesh technique. The results reveal a clear transition from drag-dominated to thrust-dominated regimes. Phase synchronization is identified to be a key control parameter: constructive reverse von Kármán vortex streets and higher net thrust are produced by in-phase pitching, whereas destructive wake interactions and lower net thrust are induced by 180° out-of-phase motion. The aft (downstream) foil in tandem configurations achieves up to 28% propulsive efficiency, approximately four times that of the forward (upstream) foil due to wake recapture. Dynamic mode decomposition shows that the tandem-staggered configuration diverts energy into higher harmonics and exhibits weaker jet coherence. Overall, tandem in-line foils provide higher peak efficiency but are phase-sensitive, whereas staggered foils exhibit more uniform power demand across phase offsets, but lower efficiency. These findings highlight a trade-off between stability and performance in multi-foil systems.