Scaling the self-propulsive performance of pitching and heaving flexible plates

Abstract

Self-propulsive performances of the flexible plates undergoing pitching and heaving motions are investigated numerically. The effects of multiple key dimensionless parameters are considered, such as bending stiffness, heaving amplitude, pitching amplitude and flapping frequency. Despite so many influence factors, results indicate that the cruising speed $U$ (or the cruising Reynolds number $Re_c$ ), the thrust $T$ and the input power $P$ can be summarized as some simple scaling laws vs the flapping Reynolds number $Re_f$ . In the heaving motion, the scaling laws may be not fully independent of bending stiffness because in the motion the role of bending stiffness is more complicated for the thrust generation. Our scaling laws are well supported by biological data on swimming aquatic animals.