Uncovering the Fluid–Structure Interactions of Wave‑Assisted Propulsion via Cyber‑Physical Fluid Dynamics

Wave-Assisted Propulsion (WAP) uses a flapping underwater foil to absorb the kinetic energy of surface vessel motions imposed by waves and convert it into forward thrust, assisting the ship's propulsion system. Moreover, it can dampen the oscillations of the vessel and improve its stability. However, designing and tuning WAP is challenging due to the nonlinear behavior of fluid–structure interactions, irregular sea states, and the large structural parameter space (stiffness, damping, inertia). It is also difficult to build hardware that precisely matches the desired properties (e.g., a spring with a target stiffness, prescribed damping, or variable physical inertia), while high-fidelity simulations can be expensive and time-consuming. Thus, we address this challenge with a cyber‑physical fluid dynamics (CPFD) platform that enables pitch and heave motion. In this system, virtual structural parameters—mass, damping, stiffness, and inertia—are implemented in real time through software, replacing physical components. The platform features a 3D-printed hydrofoil actuated in pitch and heave by a servomotor, with feedback from high-resolution encoders and a 6-axis force/torque sensor. At each control step, it solves a one-degree-of-freedom equation of motion and applies the corresponding torque, enabling real-time parameter adjustments. This approach has been validated through ring-down free decay tests. With these developments, we aim to identify regions of optimal thrust and surface vessel stability within the parameter space and to study the underlying hydrodynamic behavior. The results offer insights into practical sizing and tuning guidelines for WAP systems, with quantified propulsion gains applicable to a range of marine vehicles.