Propulsion enhancement of flexible plunging foils: Comparing linear theory predictions with high-fidelity CFD results

Abstract

The fluid–structure interaction of a flexible plunging hydrofoil immersed in a current is solved numerically to analyze its propulsion enhancement due to flexibility at Reynolds number 10 000. After validating with available experimental data, the code is used to assess analytical predictions from a linear theory. We consider large stiffness ratios, with high thrust enhancement by flexibility, and small mass ratios appropriate for underwater propulsion. The maximum thrust enhancement is observed at the first natural frequency, accurately predicted by the linear theory algebraically. The magnitude of the maximum thrust is over-predicted by the theory as the flapping amplitude increases. For large Strouhal numbers the flow becomes aperiodic, which for large enough amplitudes happens at frequencies below the natural frequency. But even at these Strouhal numbers, the linear theory predicts quite well the frequency of maximum thrust enhancement and optimal propulsive efficiency. We conclude that the linear theory constitutes a reliable and useful guide for the design of underwater flexible flapping-foil thrusters, and we provide a practical chart to easily select the optimal flapping frequency as a function of the actuation point, the stiffness and the mass ratios of the hydrofoil.