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In this paper, we numerically investigate the propulsive performance ofthree-dimensional pitching flexible plates with varying flexibility andtrailing edge shapes. To eliminate the effect of other geometric parameters,only the trailing edge angle is varied from 45{\deg} (concave), 90{\deg}(rectangular) to 135{\deg} (convex) while maintaining the constant area of theflexible plate. We examine the impact of the frequency ratio f* defined as theratio of the natural frequency of the flexible plate to the actuated pitchingfrequency. Through our numerical simulations, we find that the global maximummean thrust occurs near f*=1 corresponding to the resonance condition. However,the optimal propulsive efficiency is achieved around f*=1.54 instead of theresonance condition. While the convex plate with low and high bending stiffnessvalues shows the best performance, the rectangular plate with moderate bendingstiffness is the most efficient propulsion configuration. Through dynamic modedecomposition, we find that the passive deformation can help in redistributingthe pressure gradient thus improving the efficiency and thrust production. Amomentum-based thrust evaluation approach is adopted to link the instantaneousvortical structures with the time-dependent thrust. When the vortices detachfrom the trailing edge, the instantaneous thrust shows the largest values dueto the strong momentum change and convection process. Moderate flexibility andconvex shape help transfer momentum to the fluid, thereby improving thrustgeneration and promoting the transition from drag to thrust. The increase ofthe trailing edge angle can broaden the range of flexibility that producespositive mean thrust.

A high-fidelity numerical study on the propulsive performance of pitching flexible plates