A self-propelled flexible plate with a Navier slip surface

The hydrodynamics of a three-dimensional self-propelled flexible plate with a Navier slip surface was explored in an effort to assess its role in the hydrodynamics of a slip boundary that mimics the mucus layer. The Navier slip arises when the component of the tangential velocity at a wall is proportional to the strain. The immersed boundary method was employed to simulate the flow. For comparison, simulations were also performed with the no-slip condition. The clamped leading edge of the flexible plate was forced into a prescribed harmonic oscillation in the vertical direction but was free to move in the horizontal direction. For validation of the results obtained with the Navier slip, experiments were performed on a solid surface with a seaweed covering. The average cruising speed (Ū_C), the input power (P ¯ ), and the propulsion efficiency (η) of the plate were determined as a function of the flapping frequency (f) to characterize its kinematics. The drag reduction due to the Navier slip was determined by examining the changes in the powers resulting from its effects on the Lagrangian momentum forces. The reduction in the power in the tangential direction due to the Navier slip condition is greater than that in the normal direction. The effects of the Navier slip on the force (F), power (P), and propulsion performance of the plate were evaluated. The hydrodynamic benefits of the slip condition for a self-propelled flexible body were elucidated in detail.