Lattice-Boltzmann lattice-spring simulations of flexibility and inertial effects on deformation and cruising reversal of self-propelled flexible swimming bodies

•A flapping in vertical direction drives a migration in horizontal direction.•Forward cruising arrives at a maximum along with changing of rigidity.•Rigidity and inertia have significant contribution to cruising direction reversal.•“Sweeping” and “sucking” effects are explicated to reveal the reversal.•Two tandem swimmers can achieve an equilibrium gap distance.

A lattice-Boltzmann lattice-spring method is employed to simulate cruise dynamic behaviors of self-propelled flexible swimming bodies at finite Reynolds numbers in a three-dimensional space. In simulations, the leading edge of the swimmer plunges in the vertical direction and generates a thrust force, which drives the swimmer to move in the horizontal direction freely. To investigate the effect of rigidity and inertia on cruising speed, power coefficient, propulsive efficiency, and deformation are computed while the rigid and inertia are varied at different levels. It is demonstrated that at a given Reynolds number, the cruising forward speed increases as the rigidity decreases from a high level. The forward speed increases continuously and arrives at a maximum as the rigidity reduces to an intermediate level. However, the forward cruise speed decreases when the rigidity continuously decreases. When the rigidity further reduces to a level lower than a critical value, the cruise reverses its direction and the swimmer moves backward. In this study, it is revealed that a snake-shaped two-curved swimming body due to large deformation induces two vortices and their “sucking” effect is responsible for the backward cruise while the reaction force of sweeping motion of one-curved swimming body causes the forward cruise. It is also found that the forward cruise may become backward as the inertia exceeds a critical level, suggesting that the inertia has a significant impact on the cruising direction reversal. It is revealed that two swimmers in a tandem configuration have one equilibrium separating distance, associated with the reverse Karman vortex street, which is independent of initial distances.