Hydrodynamics of a three-dimensional self-propelled flexible plate

Abstract

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 = W-t/W-l), where W-t is the trailing edge width and W-l is the leading edge width. The aspect ratio was fixed at AS = (W-l + W-t)/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 (U-C), the input power ((P) over bar), and the swimming efficiency (eta) were determined as a function of the flapping frequency (f). The kinematics of the plate, the maximum angle of attack (phi(max)), and the mean effective length ((L) over bar eff) were examined to characterize the hydrodynamics, including the peak-to-peak amplitude (A(t)/A) and the Strouhal number (St = fA(t)/(U) over barc). 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 (F-t,F-max) of S = 0.5 decreased by 15% compared to that of S = 1.0, and the maximum lateral force (F-l,F-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. Published under license by AIP Publishing.