Schooling benefits from a system of active and passive hydrofoils

Fishes school to swim more efficiently while not much of fish schooling is understood from the perspective of fluid–structure interactions. To understand the benefits of fish schooling, we investigate thrust, efficiency, and wake structure of a two-hydrofoil system where the upstream hydrofoil is forced pitching (active) and the downstream hydrofoil is free pitching (passive). The streamwise and lateral separations between the two hydrofoils are 0.109c and 1.0D, respectively, where c is the chord length and D is the diameter of the leading edge. The active hydrofoil pitches with normalized amplitudes A^∗=0.55 – 0.80 and normalized frequencies St_D=0.23–0.33. It is found that the upstream active hydrofoil undergoes up to 38% thrust enhancement in the presence of the downstream passive hydrofoil while the downstream passive hydrofoil achieves the same thrust as the upstream active hydrofoil under certain conditions. The maximum combined thrust and efficiency achieved for the two-hydrofoil system are 95% and 180% higher than those for a single isolated hydrofoil. These are some reasons for fish swimming in school. Three distinct flow structures (vortex impingement flow, vortex trapping flow, and vortex splitting flow) are identified in the A^∗– St_D domain, where the vortex trapping flow provides the greatest thrust and efficiency enhancement.