Effect of trailing-edge shape on the self-propulsive performance of heaving flexible plates

The effect of trailing-edge shape on the self-propulsive performance of three-dimensional flexible plates is studied numerically. In our study, the trailing edges of the plates are symmetric chevron shapes, and the trailing-edge angle phi varies from 30 degrees (concave plate) to 150 degrees (convex plate). Under different bending stiffnesses K, three regimes of the propulsive performance in terms of propulsive velocity U and efficiency eta as a function of phi are identified. When K is small, moderate and large, the square, convex and concave plate achieves the best performance, respectively. Analyses of vortical structures and velocity fields show that usually the jet behind the plate with the best performance is longest. Besides, the inclination angle of the jet may be small. The different propulsive performances at small and moderate K are mainly attributed to the phase lag of the trailing edge. The force acting on the plate is analysed and it is found that the thrust force is mainly contributed by the normal force. If U, eta and K are rescaled by the normal force and the area moment of the plate, the curves for different phi almost collapse into a single curve when the bending stiffness coefficient is small or moderate. The scaling confirms that the normal force should be the characteristic fluid force at small or moderate K and the phi effect is governed by the area moment. The findings may shed some light on the propulsive performance of aquatic animals.