Numerical investigation of wake interaction and bio-inspired propulsive performance of tandem flapping foils for soft-robotic underwater locomotion

This study statistically examines wake–vortex interactions and their impact on the bio-inspired propulsive performance of tandem flapping foils for soft-robotic underwater locomotion. While most existing mathematical studies emphasize tandem foils executing pure heaving, pitching, or combined motions, the present work examines four dissimilar flapping trajectories (FT-I, FT-II, FT-III, and FT-IV), including both simple and elliptical paths in single-foil and tandem configurations. Simulations are performed at a Reynolds number of 1173 to evaluate the effects of phase angle, Strouhal number (St), and flapping trajectory on thrust generation and wake interaction. The experimental findings indicate that the thrust generated by an individual flapping foil is primarily determined by the formation of vortices at the trailing edge. The mechanism works similarly to soft robotic swimmers that generate propulsion. Simple flapping mechanics produce a well-defined reverse Kármán vortex street, which generates more thrust than elliptical trajectories because it imparts more momentum to the wake. In tandem layouts, propulsive efficiency is strongly dependent on the phase difference between the upstream and downstream foils, rather than on the amplitude of flapping. The peak thrust is found at St = 0.4, especially with FT-I motion in conditions of 180-degree counter-phase and FT-III motion in conditions of in-phase operation when constructive wake interactions take place. Upstream foil operation is not very sensitive to the downstream spacing, but the downstream foil is highly sensitive to its aft location. The results provide design choices for controlling wake–vortex interactions in efficient underwater propulsion systems based on biomimetic and soft-robotic designs.