Hydrodynamic performance of a penguin wing: Effect of feathering and flapping

The penguin is the fastest underwater swimmer among the wing-propelled diving birds. To figure out the mechanism for its excellent swimming, the hydrodynamic performance of a penguin wing is numerically investigated using an immersed boundary method with the incompressible flow solver. This study examines the effects of feathering, flapping, and Strouhal number (St) under preset motion. Results indicate that feathering is the primary contributor to thrust generation. The change in angle of attack (AoA) can qualitatively reflect the change in lift but not thrust. Therefore, a new variable, angle of thrust (AoT, a(T)), is introduced to effectively reflect the change of thrust across different kinematic parameters. Optimal feathering amplitude balances the decrease in AoA and the increase in feathering angle to achieve the highest AoT and thrust. Excessive feathering amplitude degrades the leading-edge vortex to shear layers, transforms the pressure side to the suction side, and ultimately causes negative thrust (drag). Spatial analysis of the thrust shows that the outer three-fifths of the wing are the primary source of thrust, contributing 85.4% of thrust generation at optimal feathering amplitude. Flapping amplitude has little impact on the optimal feathering amplitude. The optimal feathering amplitude increases linearly with the St number in the scope of examination, leading to larger thrust but lower swimming efficiency. Thus, a dimensionless number, St(m), is introduced to describe the optimal wing motion. This work provides new insights into the propulsion mechanism of aquatic swimmers with flapping-feathering wings and helps design novel bio-inspired aquatic vehicles.