The hydrodynamics of a three-dimensional self-propelled flexible plate in a quiescent flow were simulated using the immersed boundary method. 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. Several types of trapezoidal plates were simulated by changing the shape ratio (S = Wt/Wl), where Wt is the trailing edge width and Wl is the leading edge width. The aspect ratio was fixed at AS = (Wl + Wt)/2L = 0.4, where L is the length of the plate. To explore the hydrodynamics of a rectangular plate (S = 1.0), the average cruising speed (UC), the input power (P), and the swimming efficiency (η) were determined as a function of the flapping frequency (f). The kinematics of the plate, the maximum angle of attack (φmax), and the mean effective length (Leff) were examined to characterize the hydrodynamics, including the peak-to-peak amplitude (At/A) and the Strouhal number (St=fAt/Uc). Next, the effect of S on the hydrodynamics was explored for 0.1 ≤ S ≤ 3.0. The swimming efficiency was found to be the highest at S = 0.5. The maximum thrust (Ft,max) of S = 0.5 decreased by 15% compared to that of S = 1.0, and the maximum lateral force (Fl,max) decreased by more than 50%. The velocity field behind the plate and the vortical structures around the plate were visualized. The influence of the tip vortex on the swimming efficiency was examined.
Bibliographical noteFunding Information:
This work was supported by a grant from the National Research Foundation of Korea (NRF) (No. 2018001483 and 2018M3C1B7071955) and by the KUSTAR-KAIST Institute.