Strouhal number impact on propulsion efficiency in fully-active oscillating foils: Unpacking frequency, amplitude, and velocity relationships

Abstract

Oscillating foils play a crucial role in marine and aerial organisms. Propulsion efficiency is gauged by the Strouhal number, combining frequency, amplitude, and velocity. This creates three parameters: reduced frequency, dimensionless amplitude, and Reynolds number. The hydrodynamics between these parameters and their effect on propulsion efficiency is complex. Using RANS simulations, this study shows that a large amplitude significantly increases propulsion efficiency. Flow analysis shows that increasing dimensionless amplitude enhances heaving velocity without affecting pitching velocity. However, an increase in reduced frequency increases both velocities, so there is greater inflow and horizontal force. Polynomial regression shows the horizontal force coefficient correlates with the square of the Strouhal number, and the power coefficient has a cubic relationship. A rise in reduced frequency increases the gradient of the horizontal force and power coefficient curves more than an increase in amplitude, suggesting decreasing propulsion efficiency. This clarifies why larger amplitude values are more efficient and why the optimal Strouhal number is between 0.3 and 0.6. Vortex analysis shows that lower reduced frequencies produce an undulatory wake pattern, not ideal for thrust. A higher amplitude, or frequency creates a leading-edge vortex pattern, reducing propulsion efficiency. A reverse Kármán vortex pattern represents optimal propulsion efficiency.