Non-Parametric Kinematic Optimization of Flapping Foil Propulsion Using a Discrete Adjoint Method

Area of Science:

• Fluid dynamics
• Robotics
• Biomimetics

Background:

• Optimizing flapping-foil propulsion is complex due to fluid-structure interactions and limited design spaces with parameterized motions.
• Existing methods struggle with the nonlinear dynamics and temporal coupling inherent in flapping-foil systems.

Purpose of the Study:

• To develop a non-parametric optimization framework for flapping-foil kinematics.
• To enable direct optimization of time-resolved motions without predefined functional forms.
• To enhance underwater propulsion performance and design flexibility.

Main Methods:

• Developed a non-parametric kinematic optimization framework using the discrete adjoint method.
• Employed a Morison-based low-order hydrodynamic model calibrated with Computational Fluid Dynamics (CFD).
• Validated the model for efficient evaluation within its operational regime.

Main Results:

• Optimized non-sinusoidal motions significantly improved propulsion performance compared to sinusoidal motions.
• Achieved a 50.29% increase in mean thrust by optimizing heave and pitch timing and amplitudes.
• Demonstrated a 'generator-like' regime in power-minimization cases, indicating net energy transfer reversal.

Conclusions:

• Non-parametric optimization offers superior design flexibility for flapping-foil kinematics.
• The framework enables substantial improvements in underwater propulsion efficiency.
• Provides a practical approach for designing efficient biomimetic underwater vehicles.