The hydrodynamic benefits of the protruding eyes and mouth (e&m) of a stingray's smooth body are explored using the penalty immersed boundary method. A self-propelled flexible plate was realized in the present study; a 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. The e&m was formulated by the superposition of several rigid plates. Simulations without the e&m were also performed for comparison. The pressure distributions and vortical structures around the flexible plate were visualized to characterize the hydrodynamic roles of the e&m. The streamwise and spanwise vortices generated by the e&m function together enhance the average cruising speed and thrust, where the streamwise vortices enhance the negative pressure at the leading edge of the flexible plate and the spanwise vortices increase the pressure difference between the upper and lower sides of the plate. A parametric study was performed to find an optimal shape of the e&m that maximizes the average cruising speed (U¯c) and propulsion efficiency (η) as a function of the spanwise width. The presence of the e&m increased the U¯c and η by more than 20.5% and 10.6%, respectively.

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